Theoretical Investigation of Energy Alignment at
Metal/Semiconductor Interfaces for Solar Photovoltaic
Applications
MASSACHUSETTS INSTITUTE
OF rECHNOLOLGY
by
Michelle Ruth Tomasik
JUN 3 0 2015
BA in Chemical Physics, Swarthmore College (2007)
LIBRARIES
Submitted to the Department of Physics
in partial fulfillment of the requirements for the degree of
DOCTOR OF PHILOSOPHY
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2015
Massachusetts Institute of Technology 2015. All rights reserved.
Author
Signature redacted
Department of Physics
May 22nd, 2015
Certified by
Certified by_
Signature redacted
y ITI/
Jeffrey C. Grossman
Professor of Materials Science and Engineering
Thesis Supervisor
Signature redacted
Senthil Todadri
Professor of Physics
Thesis Supervisor
Accepted by
Signature redacted
Professor Nergis Mavalvala
Associate Department Head of Physics
Theoretical Investigation of Energy Alignment at Metal/Semiconductor
Interfaces for Solar Photovoltaic Applications
by
Michelle Ruth Tomasik
Submitted to the Department of Physics
on May 22, 2015, in partial fulfillment of the
requirements for the degree of
DOCTOR OF PHILOSOPHY
Abstract
Our work was inspired by the need to improve the efficiency of new types of solar cells.
We mainly focus on metal-semiconductor interfaces. In the CdSe study, we find that not
all surface states serve to pin the Fermi energy. In our organic-metal work, we explore the
complexity and challenges of modeling these systems. For example, we confirm that aromatic
compounds indeed have stronger interactions with metal surfaces, but this may lead to the
geometry changing as a result of the interaction. We also find that molecules that are not
rigid are strongly affected by their neighboring molecules. Surface roughness will have an
effect on molecules that more strongly bind to metal surfaces. This study of interfaces
relates to one part of the picture of efficiency, but we also look at trying to go beyond the
Shockley-Quiesser limit. We explore the idea of combining a direct and indirect bandgap
in a single material but find that, in quasi-equilibrium, this does no better than just the
direct gap material. This thesis hopes to extend our understanding of metal-semiconductor
interface behavior and lead to improvements in photovoltaic efficiency in the future.
Thesis Supervisor: Jeffrey Grossman
Title: Professor of Materials Science and Engineering
Thesis Supervisor: Senthil Todadri
Title: Professor of Physics
3
Contents
.
. . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 10
1.1.2
Shockley-Quiesser Efficiency Calculation .
. . . . . . . . . . . . . . . 22
1.1.3
Materials for Photovoltaics
. . . . . . . .
. . . . . . . . . . . . . . . 24
1.1.4
How to Improve Efficiency . . . . . . . . .
. . . . . . . . . . . . . . . 28
Interface Energy Alignment . . . . . . . . . . . .
. . . . . . . . . . . . . . . 30
1.2.1
Metal-Semiconductor Interfaces . . . . . .
. . . . . . . . . . . . . . . 30
1.2.2
Interface Effects
. . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 31
1.2.3
Metal-Organic Interface Experimental Data . . . . . . . . . . . . . . . 33
1.2.4
Schottky-Mott model . . . . . . . . . . . .
. . . . . . . . . . . . . . . 34
1.2.5
Fermi level pinning . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 35
1.2.6
IDIS model for both inorganic and organic semiconductor-metal in-
.
.
.
.
.
.
.
Basic Operation of Photovoltaics . . . . .
. . . . . . . . . . . . . . . . . . .
36
1.2.7
ICT model for organic-metal interfaces . .
39
1.2.8
Unified Defect Model for inorganic semiconductor-metal interfaces
40
1.2.9
Challenges for Predicting Interface Energy Alignment
. . . . . .
40
M otivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
.
.
.
43
Methods
44
DFT packages. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
47
Quasiparticle Gap and Optical Gap. . . . . . . . . . . . . . . . . . . . .
48
Optical Gap Calculation . . . . . . . . . . . . . . . . . . . . . . .
48
2.2
.
2.1.1
.
.
Introduction to DFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1
.
2.1
8
1.1.1
terfaces
1.3
. . . . . . . . . . .
.
1.2
Introduction to Solar Energy
.
1.1
2
7
Introduction
.
1
5
. . . . . . 50
. . . . . . . . . . . . . .
. . . . . . 51
Metal Workfunction versus thickness .
. . . . . . 51
2.4
CdSe-metal study . . . . . . . . . . . . . . . .
. . . . . . 53
2.5
Metal-organic study
. . . . . . . . . . . . . .
. . . . . . 55
2.5.1
Choice of Functional . . . . . . . . . .
. . . . . . 60
2.5.2
Binding Energy . . . . . . . . . . . . .
. . . . . . 61
2.5.3
"Isolated" molecules
. . . . . . . . . .
. . . . . . 61
2.5.4
Interface Dipole . . . . . . . . . . . . .
. . . . . . 62
2.5.5
Bader Charge . . . . . . . . . . . . . .
. . . . . . 63
2.5.6
Image Charge . . . . . . . . . . . . . .
. . . . . . 64
3
.
.
.
.
.
.
.
2.3.1
.
Metal Workfunction
.
2.3
.
Ionization Energy and Electron Affinity
2.2.2
Results and Discussion
69
3.1
CdSe-metal interfaces
3.2
Metal-Organic Interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.3
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.2.1
Alq 3 and anthracene . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.2.2
Single molecules on the metal surface . . . . . . . . . . . . . . . . . . . 78
3.2.3
Further distinguishing dipoles at the interface . . . . . . . . . . . . . . 82
3.2.4
Projected Density of States . . . . . . . . . . . . . . . . . . . . . . . . 82
3.2.5
Smooth versus Rough metal surfaces . . . . . . . . . . . . . . . . . . . 86
3.2.6
Difference between 1 and 2 full layers and single molecules . . . . . . . 89
3.2.7
Correction for Band Alignment . . . . . . . . . . . . . . . . . . . . . . 90
3.2.8
Bending of anthracene on Mg . . . . . . . . . . . . . . . . . . . . . . . 92
3.2.9
Modeling Metal-Organic Interfaces . . . . . . . . . . . . . . . . . . . . 97
Photovoltaic Efficiency in Indirect Bandgap Materials
. . . . . . . . . . . . . 102
3.3.1
Hot Carriers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
3.3.2
Direct and Indirect Bandgap Material
. . . . . . . . . . . . . . . . . . 103
4
Conclusion and Outlook
109
5
Acknowledgements
113
6
Chapter 1
Introduction
In this chapter, we first explain why photovoltaics are an important challenge. We then
examine the basic operation of a solar cell and outline the Shockley-Quiesser calculation of
the limiting efficiency.
Next we examine one component of the challenge: metal contact-
semiconductor interfaces.
There is a long history of trying to predict behavior at these
interfaces; we outline the history and the continuing challenges and end with a brief summary
of the problem.
7
Introduction to Solar Energy
1.1
The global energy demands are continuing to grow (see the left side of Figure 1-1) along with
concerns of pollution and global climate change produced by traditional fuels. Renewable
energy is therefore of growing interest, but its implementation is still in its infancy (see the
right side of Figure 1-1).
Annual Energy Demand by Region
World
s00
400
World energy consumption
20
-o
3W0
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-SOM
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100 4Europm
5Eurasia
.'
LU0
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1960
1985 199
199
2000 2005
1970
2010
1980
1990
Year
2000
2010
Figure 1-1: Left: Total energy demand for the world between 1980 and 2010 broken down
by region. The demand has been steadily increasing in this time period, especially in Asia.
Right: Energy consumption in the world between 1965 and 2013 broken down by energy
source. Coal, oil and natural gas dominate the energy sources, but renewable resources are
on the rise. Image from http: //en.wikipedia. org/wiki/World- energy- consumption.
There are many potential sources of energy shown in Figure 1-2. The grey circle in the
middle represents the current world energy consumption, around 16 TWyears in one year.
On the right are estimates of the non-renewable resources: coal, oil, natural gas, and uranium
for nuclear energy. It is clear by comparing the sizes of these estimates to our current usage
that, even if these estimates are off by an order of magnitude, we only have a finite amount
of energy that we can extract from these resources. On the left are representations of all the
renewable sources of energy available in one year. Hydro power has been used in the form
of watermills for centuries, and more recently large dams are harnessing much of the energy
from falling water. Wind power in the form of large wind turbines both out at sea and on
8
land is currently the leading alternative energy producer of electricity. Solar water heating
rivals this energy capture, but is used to heat water for use in the household or for interior
heating. Looking at Figure 1-2, it seems clear that solar energy is underutilized especially
in the area of electricity production. The field of photovoltaics is still struggling to be price
competitive with non-renewable resources, but there is great potential.
Figure 1-2: Potential sources of energy in comparison to the total world energy usage shown
in the middle in grey. On the left are renewable resources; on the right are estimates of the
total non-renewable resources available. Image from [781.
The history of solar cell research goes back over a century and the last 40 years of development is well documented by the National Renewable Energy Laboratory (NREL) in charts
such as Figure 1-3. This table lists efficiencies of solar cells made in the lab and tracks the
maximum as a function of time. They define broad categories of cells shown with different
colors and symbols. The basics of photovoltaic operation will be discussed below in Section
1.1.1, and we will discuss the different branches of this figure in further detail in Section
1.1.3.
9
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points correspond to measurements in a certified National Renewable Energy Laboratory
facility. The color schemes represent different categories of solar cells.
1.1.1
Basic Operation of Photovoltaics
Now that we understand why photovoltaics are an important challenge to tackle, we move
on to discuss the physics behind their operation. In this subsection, we first describe the
basic physical processes where energy is lost. We then describe the operation of the solar
cell in the dark, where it behaves as a diode, in the light, where we can produce useful
electricity, and the challenges of recombination and charge separation. This is followed by
an outline of the famous Shockley-Quiesser efficiency calculation in Section 1.1.2.
We are interested in the electrons in materials because they are the particles that will interact
with light and carry useful energy out of the device. Electrons in a material can be in a range
of states, each with an associated energy. Based on quantum mechanics, some energies are
allowed and others are forbidden. Sets of allowed states are called bands, and the distance
between these allowed bands are called band gaps.
No two electrons can be in the same
state, so at zero temperature, they will fill up the different states, starting with the lowest
energy. If a material has a band gap between the highest occupied and lowest unoccupied
10
state, it is called a semiconductor or insulator. If there is no band gap between those states,
the material is a metal or semimetal. The materials we are interested in are semiconductors,
both organic (small molecules and polymers containing carbon) and inorganic (crystals).
The highest occupied state is call the highest occupied molecular orbital (HOMO) for an
organic molecule, or a valence band maximum (VBM) for an inorganic semiconductor. The
first allowed energy state with higher energy than this HOMO or VBM is called the lowest
unoccupied molecular orbital (LUMO) for an organic molecule, or the conduction band
minimum (CBM) for an inorganic semiconductor.
*
Photo-excitation
Extraction
Relaxation
Transport
-
CBM
/>
-- + p_
Ef,
right
Lcombl
Efleft Extraction
ecombination
Transport
-@----9
---
OVBM
External Load
_
Figure 1-4: Basic operation of a solar cell. Light (orange) excites an electron hole pair
across the band gap (yellow), which then relax down to the band edges (black) and are then
separated (light blue arrows) and used to drive an external load. While the charges are
being extracted, there is a chance for them to recombine (red), and the interface with the
metal contacts (purple) may lead to further energy loss. Figure taken from 1441.
Solar cells take energy from photons and convert it into electricity in the process described
by Figure 1-4. Because we use a material with a band gap, the excited electron and hole
do not immediately relax back down to the ground state. When light reaches this material,
photons (particles of light, shown in orange in Figure 1-4) with energy greater than the band
gap of the material can be absorbed (the yellow arrow) to produce a hole in the valence band
as well as an electron in the conduction band. These holes and electrons are transported
to opposite ends of the solar cell (see the light blue arrows in Figure 1-4), where they are
extracted from the cell through a metal contact as a current to power an external device.
11
To facilitate this charge separation, solar cells have some form of a p-n junction or carrierselective materials. The amount of electrical energy we extract from a solar cell depends
on the number of these carriers (electrons and holes) as well as the excess energy of each
individual carrier.
Source of Energy Loss
Energy is lost at many steps along this process. First of all, any photon with energy less
than the band gap of the material will not be absorbed. The material itself has only a finite
absorptivity, and so some of the available photons will also not be captured. The photons
with energy higher than the band gap will produce electrons and holes that will quickly
relax down to the band edges, thus giving the excess energy off as heat. These processes are
represented in Figure 1-5.
heat
Excess energy above E.
Conduction
band
Eg
=max. Voc
Valence
band
Figure 1-5: Photons with energy above the band gap energy Eg can be absorbed (blue),
although any excess energy will then be released as heat as the excited hole and electron
relax down to the band edge. Photons whose energy is less than that of the band gap will fail
to be absorbed and so will not produce excited holes and electrons (green). Figure courtesy
of Marc Baldo.
Once the electrons and holes are produced, they have some finite chance of recombining,
meaning one hole in the valence band finds one electron in the conduction band and they
combine to return to the ground state.
can not contribute to the current.
Once they recombine, these electrons and holes
Recombination has different forms; it can occur by
12
radiative recombination throughout the device, Auger recombination in areas with high
concentrations, and recombination via impurities and at the metal contacts. These processes
are represented in Figure 1-8 and will be discussed further below.
If the separation of
electrons and holes is not ideal, the cell will produce a lower voltage than the theoretical
maximum. Finally, if there are barriers anywhere to the movement of electrons or holes in
the direction we pull them out, this will reduce the current that we can extract.
Basic Model
(b)
(a)
ECBM
ECBM
Ef, right
R
-6f, left
-
EVBM
EVBM
0
Figure 1-6: (a) Simple solar cell in the dark. On the left in dark blue is the energy of holes
in the hole selective layer, and on the right in green is the electron selective layer's energy
level for electrons. We assume valence and conduction bands and a flat Fermi level in the
middle. (b) The same cell under illumination. The Fermi levels split into quasi-Fermi levels
that represent the populations in valence and conduction bands separately. G is generation
and R is recombination. All of these are discussed later in the text.
We are interested in a more quantitative understanding in order to enhance solar cell design.
To quantify these processes, we first need to talk about the populations of electrons and holes
in the various states since these are the charge carriers that will produce electricity. In this
discussion, we will simplify the picture to the one shown in Figure 1-6, where the valence
and conduction bands in the semiconductor are assumed to be the at the same energy across
the device. We also assume we have perfect electron- and hole-selective layers and no barrier
at the interfaces, meaning we can pull out electrons and holes without loss of energy.
13
In the Dark
Before we can understand how sunlight will produce electricity in a photovoltaic device, we
first need to examine the behavior in the dark. Figure 1-6(a) represents the device, and we
are interested in the population of charge carriers, holes in the valence band and electrons
in the conduction band. At finite temperature, these populations will be non-zero and are
given by:
n
=
Nf(fCBM, Ef, T),
p = Pf (EVBM, Ef, T),
(1.1)
where f is the Fermi-function, Ef is the Fermi level, T is the temperature, ECBM and EVBM
are the energy levels of the conduction and valence bands, N and P are called the effective
conduction and valence band density of states, which are related to how many electrons and
holes the conduction and valence bands can hold. The Fermi level, Ef is also known as the
electrochemical potential and represents the amount of energy it would require on average
to add one more electron to the system. The effective density of states is given by:
27rh2
2
N
2~
=
'
k
= 2P
2(1.2)
27rh2
(
(m*kT
(12
where m* and m* are known as the effective masses of the conduction and valence bands, relating to their curvature, k is the Boltzmann constant, and h is the reduced Planck constant.
The Fermi-function,
1
f(e, Ef, T)
(1.3)
=
can be simplified when the Fermi level is sufficiently far away from either of the bands,
E - Ef >> kT:
f(E, Ef, T)
=
-kT
14
+ 1
.
(1.4)
Using this last approximation, we can find the general property that the population of holes
and electrons is related to the temperature and the bandgap, Egap, and does not depend on
the Fermi energy:
np = Ne-(rc-EJ)kTPe~(cf -E)IkT= NPe-(c,-e,)kT = NPe-cgs/kT = n?.
(1.5)
In the Light
Now that we know the concentration of holes and electrons in the dark, we can move on
to what happens in the light. Under illumination, electrons and holes are both produced
in excess of their equilibrium values in the dark through absorption of light. This process
of an absorbed photon producing an excited electron and hole is called generation.
The
populations of these electrons and holes can still be described by a Fermi distribution, but
to represent this increase in population of holes in the valence band the Fermi level has to
move down closer to the valence band, while at the same time to represent the increase in
electrons in the conduction band, the Fermi level needs to move up closer to the conduction
band. These contradictory requirements are represented by splitting the Fermi levels into
two quasi-Fermi levels, as can be seen as the dashed blue lines in Figure 1-6(b). These are
then the electrochemical potentials of the holes in the valence band and the electrons in the
conduction band separately. In the light, Equation 1.5 can be rewritten as:
ip
=
N
e(cc-Ef,e)IkTP
= N Pe(c-/e(
,e-Ef,h)/kT
= nie(Ef,e-Ef,h)/kT.
(1.6)
Now we see that the population of holes and electrons depends on the populations in the
dark and the splitting of the quasi-Fermi levels. Just based on the amount of light incident
on a device, however, we do not yet know how to find this quasi-Fermi level splitting, so
we need another way to quantify the additional holes (in the valence band) and electrons
(in the conduction band) excited by light. This is given by the number of photons that are
15
absorbed to produced one hole and one electron each. The generation rate as a function
of position, x, through the device parallel to the direction the photons are traveling, and
photon energy, c, can be calculated as
g(E, x) = (1 - R(E))a(c)bs(E)e-fo '( ,x)dx
(1.7)
and then integrated over the energy of the solar spectrum to find the total generation rate
at a particular position in the cell:
G(x)
=
g(E,)dk.
(1.8)
This can then be integrated over the volume of the cell to find the total generation rate
for the cell, but it is often left in this position dependent form. In equation 1.7, R(E) is
the reflectivity of the cell's surface, b,(E) is the incoming flux of photons and a(E) is the
absorption coefficient. The incident radiation is determined by the output of the sun modified by the absorption and scattering of light as it passes through the earth's atmosphere.
Figure 1-7 shows the spectrum for AM 1.5 and AM 1.0 light, where the AM stands for
air mass and refers to how much atmosphere the light has passed through. Also included
in the calculation of b,(E) is the incident angle of the light and the refractive index of the
material.
Recombination
With more holes and electrons comes more opportunity for recombination. The most fundamental form of recombination is radiative recombination, where an electron and hole come
together and produce a photon to return to their ground state, see the leftmost image in
Figure 1-8. This is the opposite process of generation. Because this process requires both
a hole and an electron to be in the same place at the same time, the rate of recombination
is
16
I
I
I
I
2.0
2.0-
E
-
1.5
1.5
AM1.5 Global (ASTMG173)
-AMI.5 Direct (ASTMG173)
AMO (ASTM E490)
1.0
CL
0.5
-
l 0.5
0.0
0.0
500
1000
2000
1500
2500
3C
Wavelength (nm)
Figure 1-7: Solar spectrum incident at the earth's surface. AMO is the light when the sun
is directly overhead, and AM1.5 is the more commonly used spectrum representing more
of an average solar incident spectrum. Figure from http://pveducation.org/pvcdrom/
appendices/standard-solar-spectra.
EE
Auger
band-to-band trap-assisted
recombination
recombination
recombination
.
Figure 1-8: Forms of recombination from left to right: radiative recombination, recombination via a midgap state, Auger recombination, and recombination through interface states
at a metal contact. The left image is from http: //ecee. colorado.edu/~bart/book/book/
86
chapter2/ch2_8.htm and the right images is from [1211 p.
(1.9)
Rrad =
hi.
where R0 is the amount of radiative recombination in the dark.
17
Impurity recombination, also called Shockley Read Hall (SRH) recombination, happens
through trap states [93]. These are states that exist in the forbidden energy range between
the conduction and valence bands. These trap states are often localized, holding electrons
or holes and increasing the likelihood of recombination.
The image second from the left
in Figure 1-8 shows an electron and a hole meeting in a trap state.
This is the form of
recombination that is avoidable by making more pure materials with fewer trap states. The
rate for this type of recombination is
RsRH =
where
Tn,SRH
Tn,SRH (P +
np
Pt) + Tp, SRH(n
-+
nt)
,
(1.10)
is the lifetime for electron capture by the trap, and nt = nie(,t-e)/kT is the
occupation of the trap state.
Auger recombination occurs when two holes and one electron or two electrons and one
hole come together; this type of recombination therefore only becomes important at higher
concentrations. One electron and one hole recombine and give up their energy to the third
particle, which increases in energy, but then quickly loses that energy to the lattice in the
form of heat.
The third image from the left in Figure 1-8 shows this process with two
electrons and one hole. The rate for this type of recombination is
RAuger = nP(Cen + ChP),
where C, and
Ch
(1.11)
are constants.
Finally, recombination can happen at interfaces, especially those with metals. These have
many mid-gap states that allow this faster recombination of electrons and holes to take
place, see the rightmost image in Figure 1-8.
Charge Separation
Charge separation is a key feature of a solar cell that until now we have just assumed will
happen. There are two ways to get charge to move preferentially in one direction. The first
18
of these is to apply an electric field, as shown in Figure 1-9, and the second is to set up a
difference in concentration, as shown in Figure 1-10. We would like to quantify the electron
current on one side of the device and the hole current at the other side because this will tell
us what the total current is that we can expect to get from the cell.
Ce
x
C
FC
EFV
Figure 1-9: When there is an electric field present, electrons and holes will move due to the
drift caused by that electric field. The y-axis of this graph is the energy of an electron and
the x-axis denotes distance through a material with an electric field applied. The vacuum
potential, # is plotted as are the levels for the conduction band, fc, valence band, E&, and
the associated quasi-Fermi levels, ef,c and Ef,V. Image from [121]p.108.
x
A
-ew
EFC
EF,V
Ev
Figure 1-10: When there is a change in the population of electrons and holes, they will tend
to move from higher to lower population through diffusion. The y-axis is the electron energy,
the x-axis represents distance through the device. The vacuum potential, #, the conduction
band, Ec, valence band, ev, and the associated quasi-Fermi levels, Ef,c and Ef,v are plotted.
The quasi-Fermi levels move away from their associated levels on the right, meaning that
the concentration of holes and electrons is greater on the left side than the right side. There
will be a net drift of particles to the right. Image from [121]p.110.
Drift is the movement of charge due to electric fields, and the current due to drift can be
represented as
jQ,e =
OreVe#,
e
19
(1.12)
where ae is the conductivity and
#
is the potential.
The diffusion current caused by a difference in population is
(1.13)
eDeVn,
jQ,e =
where De is the diffusion coefficient for electrons in the valence band. The chemical potential
is another way to represent the carrier concentration, and is written as
(1.14)
-
Pe,o+ kT In
= ie
N
where pe,o is the chemical potential of electrons with no external voltage.
This formulation can be used to rewrite the diffusion current as
JQ,e
=
V/e.
e
(1.15)
All of these equations can also be written for holes, with just the reversal of the sign for
equation 1.12 because positive charge flows the opposite way in electric fields. The electric
potential whose gradient produces the electric field and the chemical potential that is responsible for the carrier concentration can be combined into a single variable, the electrochemical
potential, or quasi-Fermi level, Ef,e = pe - e# and Ef,h = Ph + e#. This variable represents
how charge will flow, and is the important variable to consider for charge separation. The
total electron current density can be written as:
JQ,e =
- (V e
e
-
Ve)
=
e
VEfe,
(1.16)
jQ=d~e
jQ = -VEf
e
+
and the total current density produced by a device is
+
20
h-Vf,h.
e
(1.17)
Now that we know the current, we would like to find the voltage so that we can calculate the
overall power of the device. The voltage across the cell is the driving force for this current,
which is the split in the quasi-Fermi levels across the device:
qV = 6e -
(1.18)
E6.
Current and voltage trade off with each other following a diode equation, such that the
maximum voltage, V0,,
occurs when there is no current, and the maximum current, ISc, is
extracted when V = 0. The maximum power from a solar cell can be found by looking at
the I-V curve and finding the point where P = VI is maximized. All of these are shown in
Figure 1-11. The maximum power can be written as
(1.19)
P = IscVocFF,
where FF is the fill factor, which is the ratio of how much power you get from the maximum
power point in comparison to the power you would get if your current was the same as the
short-circuit value, I,,, and if the voltage was the same as the open-circuit value, Vc.
ja
L
I
vnP
I
I
V
imp-.
- - - - - -
- -
-
-
VOC
Figure 1-11: A typical I-V curve for a solar cell. The general shape of the curve is given by
the diode equation, an d the intercepts are the open-circuit voltage Vc and the short-circuit
current, Ic. The maximum power given by the shaded grey rectangle. Figure from [121].
This maximum power that we can get out of our devices is an important number for quantifying the efficiency and determining the commercial usefulness of a device. We will talk
more about efficiency calculations in the next section.
21
1.1.2
Shockley-Quiesser Efficiency Calculation
In 1960, William Shockley and Hans Queisser published their famous detailed balance calculation of the maximum solar cell efficiency [94].
They wanted to find the theoretical
maximum of efficiency by considering the unavoidable losses of energy. There are the photons with energy below that of the gap which are not absorbed. Photons with energy above
the gap still only contribute Eg worth of energy. Because the cell is in quasi-equilibrium, it
also must lose energy due to radiative recombination. They calculate the number of photons
produced by the sun, incident on the cell, that have an energy greater than the gap:
Q8
= (27r/c2)
]E9 /h
exp(hv/kT,) - 1'
(1.20)
where v is the frequency of the light, c is the speed of light, Eg is the bandgap of the material,
h is Planck's constant, and T, is the temperature of the sun. From here, it is possible to
calculate the generation rate as
Grad =
where A is the area of the cell,
fw
AfwtsQs,
(1.21)
is the geometrical factor, having to do with the angle
between the sun and the cell, and t, is the probability that a photon with energy above
the gap which is incident on the surface will be absorbed and produce an electron-hole
pair.
If we replace the temperature of the sun, T, in equation 1.20 with the temperature of the
solar cell, Tc, this will now give us the number of photons above the energy gap emitted by
the solar cell. This relates to the amount of radiative recombination:
Rrad = 2AtcQc
(1.22)
where t, may be different from t8 because the blackbody radiation spectrum differs between
the two temperatures. The factor of 2 appears because the cell has two surfaces from which
22
to emit the photons, rather than just the one surface illuminated by sunlight. Other forms
of recombination can be written as some fraction of the total recombination, which can
therefore be written as a multiple of the radiative recombination:
where
fc
Rrad
-
(1.23)
,
Rtotai
is the fraction of the recombination that is radiative recombination.
Steady state happens when generation, recombination and current out of the device balance:
0 = Grad - Rrad(V) + Gnon-rad - R(O) - I/q.
(1.24)
Assuming the recombination has the form
R(V) = R(O)eqV/kT
(1.25)
then Equation 1.24 can be written as
Grad - Rrad(0) + [Rrad(0) - Rrad (V) + Rnon-rad(0) - Rnon-raA(V)] - I/q = 0
Gradj
-
Rrad(0) + Rtotai(0) - Rtotai(V) - I/q = 0
fe
I = q[Grad
-
Rrad(O)] + qRrad(0)/f[l1 - eqV/kTc]
I = Ise + Io[1
-
e VkTc ]
(1.26)
By plugging into this equation for I = 0, they find the open circuit voltage,
kT~
VOC = k ln[(Ise/ o) + 1].
q
23
(1.27)
They solve for the maximum power point by taking the derivative d(IV)/dt and setting it
equal to 0. They compare this to the total incoming solar radiation to find the maximum
efficiency as a function of the bandgap, see the left side Figure 1-12. Since their calculation,
solar cell developers have been striving to reach this theoretical maximum, and the right
side of Figure 1-12 shows the progress that has been made on different materials. There are
clearly materials challenges beyond just the theoretical maximum efficiency limit, and we
talk more about the different broad materials categories in the next section.
0 1.0
[%)
0.35
-
[volts]
V9 --.
W
0.300.25-
C
2etalled 9ell8.9
9 2
10-
/C-Si
mc-si
0.20-
CdTe
\0.15-
+~
JW .kIWnIdb
1ffilIencp for
0.10-*
i
GaSb
0icls00
Ge
Semi-
Umit
0
2
Gas
0
0
e!trc
|-
1.5G Effciency Unit
0.00__
0.8
6
4
a-Si
1.2
1.6
2.0
Bandgap/eV
--
Figure 1-12: Left: Maximum solar cell efficiency as a function of bandgap from the original
paper, [941. Right: Comparison of the efficiency of solar cells made from different materials
to the Shockley-Quiesser limit. Image from the Solar Energy Group at the University of
Sydney.
1.1.3
Materials for Photovoltaics
There are many different materials that are currently used as the semiconductors for solar
cells, as can be observed in the NREL chart, Figure 1-3. One distinction is between organic
and inorganic semiconductors. A basic structure for each can be seen in Figure 1-13. One
major difference between these two are the excitons, the attraction of the electron and hole.
In organics, the excitons are in general high energy Frenkel excitons, so the electron and
hole are bound closely together, perhaps within a single molecule. This very large binding
energy necessitates an equally large jump in energy between the electron and hole conducting layers. Inorganic semiconductors more frequently have larger dielectric constants and
24
therefore exhibit Wannier-Mott excitons. In this case, the exciton energy is often less than
25 meV, so the electron and hole can separate at room temperature.
Another major dif-
ference between these two types of solar cells is in the transport. In inorganic crystalline
semiconductors, the regular ordering leads to a band structure and faster transport, whereas
the organic molecules often have localized charges that get between molecules by the comparatively slower hopping mechanism. These differences lead to different geometries for the
cells. In the organic case, there are two types of molecule or polymer each with its own
band gap, conduction bands, valence bands, and exciton biding energy. The energy bands
must be aligned in a type II alignment, meaning they must be staggered, not straddling nor
disjointed. As mentioned above, the bands must be staggered enough to allow the excitons
to separate at the interface. Because hopping transport is slow, it is best to have the shortest possible distance for charges to travel to their respective contacts. Excitons also have
higher recombination rates because the electron and hole are already close together. Most
inorganic crystalline semiconductor solar cells consist of p-n junctions. Because the material
is doped, there are free charges that can rearrange and bring the cell into what appears to
be a type II interface, see Figure 1-13(b).
(a)
Sci
SC2
(Donor)
(Acceptor)
(b)
-wo
W.
PExcon
E
h mEo"
kn*KWBC W8 A
on* CCvoc
-W1 WP
X
Figure 1-13: (a) Organic solar cell with a type II interface. The bands need to be offset
enough so that electrons and holes with energy substantially lower than the HOMO and
LUMO levels (black bands) due to their exciton binding energy (red bands) can separate
at the interface. Image from [61. (b) A p-n junction: the top shows the charge transferred
to equalized the Fermi levels of the differently doped sides, and the bottom shows the band
energies and the dipole in the vacuum energy due to the charge transfer. Image from [1211.
25
Another major difference is a direct gap versus an indirect gap absorber material, see Figure
1-14. Materials with a direct gap allow absorption of a photon as long as there is an electron
in the valence band and a hole in the conduction band to be excited. To absorb a photon
with an indirect band gap material, there also needs to be a phonon to obey conservation of
momentum. This requirement greatly reduces the probabiliity of absorption, and therefore
a much thicker cell is required to absorb a substantial fraction of the light.
This extra
thickness also gives a greater potential for trap states and recombination throughout the
device.
Indirect
Direct
Figure 1-14: Light (orange) comes in to excite (yellow) an electron-hole pair. Light has
a high energy but low momentum, so for the direct gap, the light can directly excite the
electron-hole pair. In the indirect case, to get between the ground and excited states requires
not only a lot of energy but also more momentum than the light can provide, so a phonon
(blue) is needed as well to provide this extra momentum.
To overcome the problem described in Figure 1-5 of wasted energy because some photons
are too low energy to be absorbed and some are much higher in energy than the band gap
wasting the excess energy as heat, multi-junction cells combine multiple band gaps to utilize
a greater fraction of the solar energy, see Figure 1-15(a).
Let us now look back at the NREL chart, Figure 1-3 to see the current state of the different
types of solar cells.
purple curves).
The most efficient cells are these multi-junction cells (many of the
The next most efficient (the lower purple curves) are GaAs cells.
This
is a direct band gap material, but suffers from high materials cost. This is why, despite
its lower efficiency on the NREL chart, silicon solar cells (blue in Figure 1-3 and Figure
1-15(b)), both mono- and poly-crystalline, dominate the commercial market.
Crystalline
silicon has a long history and has benefited greatly from the developments in the electronics
industry.
Current commercial cells have approximately a 20% efficiency; Figure 1-3 cites
26
(a)
Eco
.6 eV
0.95 eV
Ev
High energy gap
Low energy gap
Anti-weection
(c)
Inclap
.Top
Glam
1.4eVT"
11.06V
cd
Gbss
rft"
1cv
.9tJunction
-Tunnw Junction
*no*0*M
Mkkee Cdn/,
Junction
Mos
i u
PEDOTCOS
Junction 3
D"n
Figure 1-15: (a) Multi-junction cells absorb more than one wavelength of light. Image
from http: //www. nrel. gov/continuum/spectrum/awards. cfm. (b) A typical mono crystalline silicon solar panel. Image from http: //en. wikipedia. org/wiki/Monocryst alline_
silicon. (c) Schematic of an organic solar cell. Image from http: //energy. gov/eere/
sunshot/organic-photovoltaics-research.
a higher value, which demonstrates the difference between cells in the lab and modules
produced for commercial use. Silicon, however, is an indirect band gap material, and thus
large amounts are required. Manufacturing costs and energy input are high and require large
capital investment to produce. Glass, which is used to allow light to pass to the solar cell
while protecting the inner silicon from oxidation, is around 25% of the module cost; replacing
silicon with something that is not susceptible to oxidation from the atmosphere would greatly
reduce the cost. That is why, despite the advantages of being earth abundant and possessing
great manufacturing knowledge, we are trying to find alternatives to silicon.
The most obvious factor that we would like to change is the energy and capital requirement
of production.
Specifically, we want something that is low-temperature processable and
still earth abundant. This is why organics and quantum dots (orange curves in Figure 1-3)
have recently been investigated. This is a young field, but the efficiency is growing rapidly.
27
Currently the record efficiency is 11.1% for pure organics and 20.1% for perovskites cells.
Organic solar cells have the advantage that organic electronics are also being studied for
devices like light emitting diodes and sensors. They have the potential to be printed into
flexible sheets, and therefore very cheap and easy to manufacture [17, 29, 45, 89].
It may be that the future holds a place for many different types of solar cell depending on
the geography and the use. It is worth pursuing many different types of solar cells, but all
of them face similar challenges when it comes to improving the efficiency.
1.1.4
How to Improve Efficiency
What have we learned so far about solar cell efficiency? According to Shockley and Quiesser,
there will always be some amount of energy wasted, and that amount will depend on the
band gap of the material.
According to the image on the right in Figure 1-12, materi-
als today are still below this theoretical maximum in efficiency and have some room for
improvement.
Relaxation
Photo-ext tation
E) traction
ansport
CBW _
Extraction
Transpo rt
Rec
bination
VBM
0
External Load
Figure 1-16: This is our basic picture of a solar cell operation with the various places for
loss circled. These losses are discussed in the text.
Figure 1-16 shows the places where energy is lost in a way that we can do something
about. As indicated by the yellow circle, there is less energy absorbed from sunlight than
28
is theoretically possible. Some light is lost both to reflection and transmission through the
cell. To get around these losses, it is common to pattern the surface in order to get a lower
reflection and also cause scattering and longer path lengths through the material.
Some
cells have reflective material on the bottom, so that light will pass at least twice through
the cell and have more opportunity to be absorbed.
The red circle indicates that there are losses through recombination that could be avoided.
As already mentioned, it is possible to increase the purity of the material, thereby reducing
the number of trap states and reducing the SRH recombination.
Path length is also a
consideration - the longer electrons and holes travel, the greater chance for recombination.
This is at odds with the desire for a thicker cell to absorb more light, so these two concerns
need to be balanced with each other.
Finally, the purple circles indicate that energy is lost at the contacts where charge is extracted. If there is a barrier at this interface, less charge will be pulled out, and therefore
the device will have a lower current. As mentioned in the right-most picture of Figure 1-8,
this interface with the contact has many interface states and is a common place for recombination to occur. The longer charge sits at this interface before being pulled out, the more
likely it is to recombine.
There are a few other places that energy is lost that are not highlighted on the figure. For
example, if charge is not properly separated, there will also be a loss in performance. This
can be because of a lack of a type II alignment needed for charge separation. As previously
mentioned, another place where energy must be lost is from the electrons and holes excited
with photon energy much higher than the band gap relaxing down to the band edge. There
is an idea, called "hot carriers", that if we could pull these excited carriers out before they
relax, we could use this excess energy rather than wasting it as heat.
We will come back to these alternative ideas to get more energy out in Section 3.3, but the
bulk of this work focuses on the problem with energy loss at the interface of the semiconductor and the metal. In Section 1.2 we discuss the current understanding of these interfaces
and the different models that are used to analyze them.
29
1.2
Interface Energy Alignment
We begin by discussing some of the history and interface effects, show some of the experimental data motivating the different theories and then discuss the most important models
for describing these interfaces.
1.2.1
Metal-Semiconductor Interfaces
In 1874, Braun noticed the rectifying properties of contacts made by connecting a metal and
a semiconductor [121. The first person to try and explain this behavior was Schottky, who
said that at these interfaces a space charge region is formed on the doped semiconductor
side where the majority carriers are depleted [87]. Schottky assumed in his model that the
barrier height right at the interface could be found by simply aligning the energy levels as
they appear in vacuum with no modifications or dipoles. In the almost 80 years since, there
has been fierce disagreement about how exactly the alignment can be predicted, although
everyone agrees that Schottky's model is often too simplistic. Interface dipoles and surface
chemistry have been found to be important [28, 601.
Although a critical aspect of device operation is the nature of the interface between the
organic molecule or inorganic crystal and the metal contact, this interface is often portrayed
simply with Schottky's model by comparing the metal workfunction to the ionization energy
(IE) and electron affinity (EA) of the molecule or crystal, as shown in Figure 1-17 [19,
79].
Metal
organic
- vac
EA
EE
Figure 1-17: Simple band line-up model that neglects interface effects.
30
This simple picture of the metal-semiconductor interface ignores the complex interactions
that may change the performance of the device. It is often difficult to predict a priori what
effect the interface will have on the energy alignment, and these concomitant effects are
challenging to decompose and characterize experimentally.
1.2.2
Interface Effects
There are many possible interface effects which change of the expected energy alignment in
metal-organic interfaces [1, 37, 41]. In band alignment diagrams, it is the workfunction of
the metal and the IE and EA of the organic molecule that are considered. The workfunction
of the metal (OM in Figure 1-18a) sets the Fermi energy for the system, so we consider how
these various effects change the IE and EA of the molecules. Among the various possible
effects, many involve the formation of an interface dipole layer, which shifts both the IE and
EA of the molecule in the same direction, to either higher or lower energy relative to the
Fermi level. This effect will persist throughout the device because an interface dipole acts
like two infinite sheets of charge; the potential on one side differs from the potential on the
other.
Interface dipoles can arise from a number of different effects. First, a dipole can arise from
the charge separation caused by charge transfer from the metal to the organic or organic
to the metal [1, 41]. In this work we use the convention that electron charge transfer from
metal to organic will give a positive dipole moment, A (Figure 1-18a).
Another type of
dipole effect is caused by the compression of the metal's electron wavefunction tail due to
adsorption of a molecule. At a metal surface, there is an intrinsic dipole layer caused by
the lighter electron wave function extending into vacuum beyond the heavier positive nuclei.
When that vacuum is occupied by a material, such as an organic molecule, the electronic
wavefunction tail shortens, thus decreasing this natural dipole (Figure 1-18b) [1, 41, 1081.
This reduction in the preexisting dipole can be represented as a net negative dipole. A
third type of dipole is the natural dipole arising in the molecule itself (Figure 1-18c). Some
suggest engineering this dipole to change the energy levels in a favorable way [35]. Finally,
when the first layer of organics has either an electron or a hole, an image charge will be
induced in the metal, which stabilizes the presence of this charge, changing the EA or IE,
31
M==
b)
/
a--Ev-uum
O
A
wm===
Metal Vacuum
HOMO
d)
EvMuum
C)
Metal Molecule
0eta
Metal
Charged
Molecule
Figure 1-18: Interface effects on band alignment between metal contact and organic crystal.
a) Charge-transfer dipole (A) b) Dipole moment change due to compression of the metal
wavefunction tail c) Fixed molecular dipole d) Image charge due to the presence of an
electron on the molecule.
b)
aEvacuum
M
.
a)
0
~ 0.
*,O..--.
0
Metal
n0
Semiconductor
Metal Vacuum
C)
Metal Semiconductor
0
0
0
0
Metal
Charge on
Semiconductor
Figure 1-19: Interface effects on band alignment between metal contact and an inorganic
semiconductor. (a) Charge-transfer dipole (A) based on bonds forming at the interface. (b)
Dipole moment change due to compression of the metal wavefunction tail. (c) Image charge
in the metal stabilizes delocalized charge in the semiconductor.
32
respectively (Figure 1-18d) [30, 39, 67, 116].
For inorganic semiconductor-metal interfaces, the compression of the metal's wavefunction
tail still can cause a dipole, see Figure 1-19(b), but now there are also surface states of the
semiconductor to consider. These surface states are created by the dangling bonds and these
dangling bonds can form chemical bonds with the metal surface. This bonding produces
interface states that might give additional density of states for charge transfer, see Figure
1-19(a). These interface states might have a high enough density of states to pin the metal's
workfunction at one particular value; this will be discussed further in Section 1.2.5 below.
While charges are less localized, it is still possible for the image charge to stabilize charge
at the interface, see Figure 1-19(c).
1.2.3
Metal-Organic Interface Experimental Data
1.0
b1 A
1a0-
Mg
A
U.
PTCDA
IE6dV
PTCW
FKCNPC
1E-.2 *
IE-63
*
Potme
IE-SC
0
$A9535 4
4U5
$A s 45
2.5
9a
SmMgAg
'0
-
4.6
70
Zaft
A
Au
1..
1.O
as
insmesIt
-62 d
4A
4
4
0
35s
4S
55
s
s
Metal work function (eV)
Figure 1-20: Data that supports the IDIS model. The black lines represent qinterface as
defined in Figure 1-22 versus metal workfunction for a variety of different molecules. The
dotted blue lines show the Schottky-Mott limit for comparison. Taken from [42j.
There are many different behavior regimes seen in experimental data. When looking at the
workfunction of the metal-molecule system in comparison to the bare metal, people report
33
either a constant slope to the data with a slope between 0 and 1 (see Figure 1-20) or two
distinct parts where the slope is around 1 for one section and 0 for another section (see
Figure 1-21).
5.5
4.
--
35
3.5
-
-
--
4.0
4.5
50
"
5.5
-
-
C 45
60
-
--
35
6.0
4.0
4.5
5.0
5-5
6.0
bSUB (eV)
*suB (eV)
Figure 1-21: Data that supports the ICT model. The interface is plotted versus metal
workfunction and the slope is either 0 or 1 for different sections of metal workfunciton.
Taken from [15].
1.2.4
Schottky-Mott model
As mentioned above, the first and simplest model of energy alignments at an interface is
the Schottky-Mott model. This assumes absolutely no interactions between the metal and
semiconductor surfaces and alignment is achieved in the same way as depicted in Figure
1-17. In this very simple case, the bands are exactly where they are in the isolated metal
and organic or semiconducting systems, and the hole injection barrier is just
OB,p
= IE - OM
(1.28)
where OM is the metal work function and IE is the ionization energy. Similarly, the electron
injection barrier in this theory is
B,n
= Om - EA
(1.29)
where EA is the electron affinity. As will be discussed more below, this kind of behavior is
seen mostly on passivated metal surfaces, such as metals with an oxide layer 115, 26, 37, 56].
34
This type of alignment will only happen when none of the interface effects described above
take place.
Fermi level pinning
1.2.5
Fermi level pinning is the exact opposite of the Schottky-Mott relationship. In this case,
no matter what the workfunction of metal is, the workfunction of an organic or inorganic
semiconductor deposited on top of the sample will be the same, see Figure 1-22(a). The
origin of the pinning depends on the system and has been a constant source of confusion,
but all the models require some density of states on the semiconductor that can be filled
up to a point such that a dipole will form to bring the metal's workfunciton exactly in line
with pinning energy, see Figure 1-22(b).
(a)
()interface dipole
-
E
4(PM
Epin
"
"
W
E
pin
Interface
IE
(PM
Figure 1-22: Fermi pinning: (a) shows the behavior for perfect pinning, where, regardless
of the metal workfunction, the workfunction of the semiconductor on top of the metal is
the same. Compare this to Figure 1-21 which also has sections with a slope of 0. (b) The
mechanism behind Fermi-level pinning involves charge transfer to or from a pinning state in
the semiconductor that forms a dipole at the interface and aligns the Fermi-level with that
state.
The Schottky-Mott model and Fermi-level pinning are phenomenological models, but we
would like to have a physical explanation as well. In the next few sections, we will outline
the common models for interface behavior.
35
1.2.6
IDIS model for both inorganic and organic semiconductor-metal
interfaces
The induced density of interface states (IDIS) model, as the name implies, considers interface
states that are generated by interaction with the metal. It was originally proposed by Cowley
and Sze 121] to explain the behavior of semiconductor-metal interfaces, such as GaAs and Si
with various metals, and has since been used by many to explain both inorganic and organic
semiconductor-metal interfaces [1, 2, 15, 28, 33, 42, 54, 69, 70, 82, 95, 102, 108, 110, 111,
112, 1131.
The model assumes a constant density of states induced in the interface, defines a charge
neutral level ECNL in the semiconductor, and then compares this level to the workfunction
of the metal,
#M.
This ECNL acts like a Fermi-level in that if it is higher than the metal
workfunction, electrons will move to the metal from the induced interfacial states, and if
it is lower than the metal workfunction, electrons will move off the metal. This produces
a dipole at the interface that then tends to bring the ECNL and metal workfunction closer
together, see Figure 1-23.
(a)
(b)
organic
Metal
organic
Metal
16 Interface dipole
0
vac
SPM
(PM
E
vac
EA
ECNL
IE
ECNL
Filled IDIS states
Filled IDIS states
id-,
" WsIt
Figure 1-23: Basic picture behind the IDIS model. The left image shows the situation before
contact and the left shows what happens after charge has rearranged following contact of
the metal and semiconductor. The surface states on the semiconductor are previously filled
up to the charge neutrality level, ECNL, but after contact, they are filled up to the metal's
Fermi energy. The charge transferred because of this creates an interface dipole, A.
36
Charge neutrality level,
The
ECNL
ECNL
is found in calculations by integrating the density of states on the semiconductor
when in the presence of the metal up to the point of charge neutrality for the organic
or crystalline semiconductor alone. This is different than the Fermi level in the organic or
semiconductor because there is now a continuous density of states in the gap that will behave
differently than the bulk of the material. Experimentally, this quantity is the intercept of
the Schottky-Mott limit and the experimental data as long as there are no dipoles other
than the dipole from the IDIS charge transfer [54].
S parameter
In order to describe the ability of the interface states to change the energy alignment, a
parameter, S, is defined:
S = dB,n
d~bM
_
M/organic
(1.30)
- EA) + (1 - S)ECNL-
(1-31)
d4B,p
d(Dm
_ d
d4DM
The electron injection barrier is now
=B,nS(OM
In the case of Fermi pinning, S
=
0, and for Schottky-Mott behavior, S = 1. In general
S can be anywhere in between. This parameter is sometimes also defined with respect to
electronegativity, SX, instead of workfunction, Sp, but for organics, these two are found to
be fairly close in value [124].
To calculate this S parameter, we can think about the picture that we had of the induced
states giving or receiving excess charge in order to create a dipole that will realign the metal
and molecule energy levels.
Some amount of charge is transferred either to or from the
IDIS states from or to the metal, and this sets up two infinite sheets of charge with charge
density
37
- = eD(EF)(M - ECNL -
A) /A.
(1.32)
We can calculate the dipole produced by these sheets of charge and in this way find S:
S = 1/(1 + 47re 2D(EF)d/A),
(1.33)
where d is the distance between the molecules and the metal surface, A is the area of a
molecule on the surface, and D(EF) is the density of induced states at Fermi level. The
dipole at the interface will be
AIDIS
=
(1
-
S)(OM
-
ECNL).-
(1.34)
Accounting for other interface dipoles
There are other effects besides just this induced density of states that might create a dipole
at the interface. In both the case of metals and semiconductors, there is the effect of the
compression of the tail of the metal wavefunction that creates a dipole, and organic molecules
may also have permanent dipoles across them. The IDIS model has been updated to include
these effects [27, 108, 109, 110]:
EF - ECNL = S(OM
- ECNL
-
Anon-IDIS).
(1.35)
This Anon-IDIS could be compression of the metal wavefunction tail or permanent dipoles
of the molecules.
It can be found from experimental data as the difference between the
workfunction predicted by the IDIS model without this dipole and the experimental value
of the workfunction at ECNL [54].
The total dipole in this case is
38
ATotal
+ (1
= Anon-IDIS
-
S)(ObM
-
ECNL _
Anon-IDIS)
(1.36)
Extending to organic-organic interfaces
This model has also been used to explain organic-organic interfaces [110, 112]. The benefit
of this extension is that, in theory, the ECNL of each organic is already known. The organic
molecules do not accept charge as redly as a metal surface, and so the S parameter is
different, here related to the dielectric constants:
1
S= -
2
1
1
-+
-
,E1
E2)
,(1.37)
where 1 and 2 refer to the two different organics. The dipole across these interfaces can be
calculated as
A
1.2.7
=
(1
- S)(ECNL,1 - ECNL,2).
(1-38)
ICT model for organic-metal interfaces
In other cases, such as Figure 1-21, people observe only vacuum level alignment (SchottkyMott limit) or complete Fermi-level pinning.
This behavior is described by the Integer
Charge-Transfer Model (ICT) [11, 13, 14, 15, 18, 22, 26, 56, 88, 102, 103]. For metals that
are passivated by something like an oxide layer, there are no interfacial dipoles formed at
the interface with an organic molecule. However, when the workfunction of a substrate falls
below the IE or above the EA, the fermi-level is completely pinned to an energy associated
with the HOMO or LUMO. This energy level, however, is not that of the HOMO or LUMO
in vacuum, and instead falls inside the gap of the molecule. Many argue that this is the
polaronic energy of that state [15, 22, 102, 103]. Because the energy can differ from the
HOMO or LUMO by up to 1eV, it has been argued that this effect cannot be due to simple
molecular relaxation and instead must come from something else [111. It is possible to think
about this model as an extension of the IDIS model where the interaction is always weak
39
enough when the workfunction of the metal is in the gap of the organic such that S = 1
[27].
1.2.8
Unified Defect Model for inorganic semiconductor-metal interfaces
In some inorganic semiconductor-metal interfaces, there are defect states at specific energies
within the gap that dominate over the induced states to pin the Fermi level; this is the basis
for Spicer's defect model [98]. Many experimentalists have used this model to analyze their
interface energy alignment data [60].
Sometimes defects are created during the deposition process, and sometimes there are intrinsic surface defects [16]. Inorganic semiconductor surfaces have unpassivated dangling bonds
and these dangling bonds can create gap states that pin the Fermi level. One example is
GaAs, which has a Ga-induced gap state which pins the Fermi-level to an energy just below
that of the conduction band; this gap state can be passivated and therefore the Fermi energy
unpinned by adding Se to the interface [8].
It has been suggested that this model is often experimentally indistinguishable from the
IDIS model, but that it seems clear that this is the correct model to use for a few layers
of metal deposited on an inorganic semiconductor [28]. The model has been shown to be
important when the deposition is more likely to create defects. Analysis of high and low
temperature deposition showed that at higher temperatures, it is more likely to be defect
states that pin the Fermi energy [96].
In inorganic semiconductor-metal surfaces, it is probable that both this and the IDIS model
contribute to some extent, and must examined on a case-by-case basis [96].
1.2.9
Challenges for Predicting Interface Energy Alignment
We saw in Subsection 1.1.4 that metal-semiconductor interfaces are one place that energy
can be lost and reduce the efficiency of a solar cell below that of its theoretical maximum
efficiency. We have now seen the vast array of interface effects that can change band alignment. The models that have been used sometimes work and sometimes fail, and we see a
40
challenge to better, more reliably predict the interface energy alignment.
In the IDIS model, it is assumed that S only depends on the molecule used, but in the
calculation for S, the value depends on the induced density of states and the metal-organic
separation distance. Others have noted this [28, 111, 1241, and so have started averaging S
and
ECNL
for a variety of metals. This, however, reduces the effectiveness of the approach.
While we agree that this approach is grounded in fundamental interface physics, we do not
suggest using it to predict interfaces where alignment is crucial. The Unified Defect Model
and the Integer Charge Transfer model also seem to explain the data, but do not predict it
a priori, and are therefore not necessarily helpful for prediction purposes.
In this work, we propose using Density Functional Theory (DFT), described in Chapter 2,
to analyze interface behavior and take apart the different interface effects. We examine both
an ionic crystalline semiconductor, CdSe, as well as a few organic molecules interfaced with
various metals and find that through this approach, we are better able to understand the
behavior of these interfaces.
41
1.3
Motivation
When designing electronic devices, we would like to be able to predict the behavior of the
device, the efficiency, the open-circuit voltage and short-circuit current. In order to predict
these things, we need to know the band alignment, which is a combination of the electronic
properties of the materials in bulk and the interface behavior. This is shown in Figure 1-24.
The bulk properties of materials are fairly well known and straightforward to measure. It is
clear how to go from the two boxes on the left to the center box of energy level alignment,
and from there to the box on the right, the device properties that we are interested in
probing. The interface properties, the purple box, however, are much more complex. The
motivation for most of this work centers on trying to understand and calculate this interface
behavior to complete this picture.
Mewi
-
Device Performance
-m
Electronic
Energy Alignment
owl~
1Kbp
Figure 1-24: We are interested in the device properties (green) which can be predicted from
the device energy alignment (orange) as well as some properties like mobility. The overall
device energy alignment comes from the bulk properties (blue) plus what happens at the
interface (purple). It is this last box that is still not well known, and better predicting these
properties is the motivation for the majority of this work.
42
Chapter 2
Methods
In this chapter, we discuss the methods used to conduct the work in this thesis. We used
Density Functional Theory, which will be discussed first. We online various methods used
for the work in general and the individual aspects of each study independently. We studied metal-CdSe interfaces to examine the effect of semiconductor surface states on metalsemiconductor Fermi level pinning.
To explore organic-metal interfaces, we conducted a
large study with a few different organic molecules and metals.
43
2.1
Introduction to DFT
There are many computational tools used to calculate properties of materials. Since we are
interested in the electronic properties of the material, we need to be able to account for
quantum mechanics, and for this we use density functional theory (DFT). Figure 2-1 shows
that DFT is only able to simulate short time scales and small volumes in comparison to its
classical mechanical counterparts. We are only able to calculate small systems with at most
a few hundred atoms, so we need to choose our systems carefully to be representative of the
real system we are interested in.
Time scale
M(deM
"Empirical"
or experimental
parameter
feeding
Quantum
mechanics
Length scale
Figure 2-1: Computational scaling of time and length scales that can be calculated with
different computational methods. DFT can only simulate a short time and small volume in
comparison to molecular dynamics (MD) and continuum modeling, but it takes into account
the quantum mechanics of the system, instead of just classical mechanics. Figure courtesy
of Jeffrey Grossman.
DFT aims to solve the Schr6dinger equation, fH4 = E0 for a system of atoms to find
the lowest energy state, or ground state. These atoms consist of electrons and nuclei. An
electron is approximately 1800 times less massive than a proton, and therefore much lighter
than even the smallest nucleus. This is the basis of the Oppenheimer approximation; the
electrons are able to respond much faster than nuclei allowing us to separate the equations
for electrons and nuclei and solve for each independently. This approximation still leaves us
with the difficult problem of solving for all, N electrons in the system at once:
44
2
H
=
2m
2mi=1
N
N
N
V?+EV(rj)+E E U(rjrj)
z
i=1
i=1 j<i
O=Eo
(2.1)
where the first term gives the kinetic energy, the second term is the interaction of electrons
with the nuclei, the third term in the electron-electron interaction term, and the solution
4'
= 0(ri,
... , rN)
is only for electrons. We make the further approximation, originally made
by Hartree, that this multi electron wave function, 0 can be written as the product of N
single electron wave functions, 4 = 0j(rl)02(r2)...ON(rN). Even with all these simplifications, we are still facing a very challenging problem. For example, if we are interested in
a single molecule of anthracene, with chemical formula C 14 H10 , we have 94 electrons, each
represented by a wave function with three spacial dimensions. All of these electrons interact
with each other through the third term of Equation 2.1, making this a very tricky set of
coupled equations.
If we look to experiments for inspiration we notice that what is measured is not the individual
wave function of an individual electron, but instead the total electronic density which is
related to these wave functions by:
n(r) = N
(r)4i(r).
(2.2)
This quantity is much more straightforward to calculate, and is the inspiration for the
Hohenberg-Kohn theorems. The first theorem says that the ground-state energy is a unique
functional of the electron density. A functional is a function of a function, in this case, the
electron density, n. This functional is uniquely determined by the external potential and
will only produce the ground state energy when the input is the ground state density no.
This ground state density then determines the important properties of the system, and we
can solve for this instead of for the full wave function, V'. This means that for our system
of anthracene given above, instead of solving for 94 x 3 = 282 variables, we now only have
the three spacial dimensions of the charge density.
The second Hohenberg-Kohn theorem states that we can find the ground state by varying
45
the density and finding the one that minimizes the energy. Now it seems we have a recipe
for success; all we need is the exact functional and we can get to work finding the ground
state. We turn back to Equation 2.1 and split it into one-electron equations - these are now
called the Kohn-Sham equations:
V2
+ V(r) + VH(r) + Vxc(r)] O i(r) = ei i(r).
(2.3)
In this equation, V(r) is the external potential which includes the interaction with the nucleii,
VH(r) is is the Hartree potential which gives the interaction with the other electrons on
average, VH(r) = e 2
f
n(r d3 r, and Vxc(r) is exchange-correlation potential. The exchange
terms accounts for the fact that electrons with the same spin cannot exist in the same place
because of the Pauli exclusion principle, and so will spend less time close to each other.
Correlation energy is always negative for the ground state and accounts for the fact that
electrons will avoid each other due to Coulomb repulsion. The one-electron energies are the
eigenvalues, Ei, associated with the one-electron wave functions, O4.
It is this last term, the exchange-correlation potential, that is the major challenge of DFT.
We do not have the exact functional that captures these effects in the general case.
In
the simplest case, a uniform electron gas, the exchange-correlation functional is known,
and this can be used to approximate results in more complex system - this approximation is
called the local density approximation (LDA). A more complex group of exchange-correlation
functionals use not only the information about the local density, but also information about
the first derivative of the density - called the Generalized Gradient Approximation (GGA).
Because there are different ways to use the information given in the first derivative, there
are different GGA functionals.
Even after we have picked an exchange and correlation potential to use, we still do not have
a complete functional to solve. This is because the functional itself depends on the electron
density. We need to start with guesses for the electron density, construct the functional,
solve it for the new electron density, use that to update our functional, and continue this
process until our calculated electron density approximately matches the one we used to
construct the functional.
46
These equations can be solved either in real space or in k-space. If the system we have has
a periodic potential in real space, as does a crystalline solid, it is much faster to Fourier
transform and solve in k-space. If, however, we are just interested in a single molecule with
isolated orbitals in vacuum, it is faster to solve in real space. This is one of the common
differences between chemistry and physics codes.
Once the code has been chosen, there are still many parameters that need to be set and the
properties that we are interested in need to be converged with respect to these parameters.
Properties are integrated in k-space, so we need to use an appropriate number of points in
k-space so those integrals are meaningful. We need to pick how big the basis for our wave
functions will be - this is again a trade-off between time and accuracy. The cutoff value for
the basis size is often given as the energy of the fastest-varying wave function included in
the basis set. To reduce the number of atoms that need to be included in the calculation,
we often use pseudopotentials that mimic the behavior of the core electrons while we focus
only on the valence electrons.
2.1.1
DFT packages
There are many different codes written to perform DFT calculations in different ways. In
the studies discussed here, we have used several different codes.
For the CdSe-metal study, we used Quantum ESPRESSO [311.
Quantum ESPRESSO is
an open-source plane wave code that uses pseudopotentials. ESPRESSO stands for opEnSource Package for Research in Electronic Structure, Simulation, and Optimization. Because
it is open-source, there are many add ons that are meant to calculate different properties
and is very versatile. For a part of the metal-organic study, we used one of these add-ons in
the BerkeleyGW code [24, 38, 84].
For the metal-organic study, we used the Vienna ab initio Simulations Package (VASP) [48,
49]. It is also a plane wave code that uses pseudopotentials, but it is not open-source.
To do some comparison of molecules, we also used a quantum chemistry code called Gaussian
09. This is the updated version of a code originally released in 1970 by John Pople, who won
the Nobel Prize in 1998 with Walter Kohn for their work on computational chemistry.
47
Quasiparticle Gap and Optical Gap
2.2
Semiconductors have a band gap - a range of forbidden energy between the valence and
conduction bands (or the HOMO and LUMO). To excite an electron from the ground state
to the lowest excited state requires a certain amount of energy, called the exciton or optical
gap,
(2.4)
Eex= E(N, e + h) - E(N).
This energy is lower than the quasiparticle or transport gap,
(2.5)
Egap,qp = IE - EA,
by the exciton binding energy. Excitons are a bound state of the excited electron and hole
and were discussed further in Section 1.1.3.
2.2.1
Optical Gap Calculation
ground state
triplet
singlet
Nf +
I/V'
44
Figure 2-2: Ground, singlet, and triplet states of a two electron system.
There are a few different ways to try to calculate excited states, such as a configuration
interaction approach, time-dependent DFT, and A- self-consistent-field theory. ASCF is a
method that is only a slight variation on ground state DFT. In this method, the ground
state is calculated first, and then an excited occupation of the Kohn-Sham energy levels is
enforced. The basic ground state of a two electron system can be seen on the very left of
48
Figure 2-2. The singlet state is in the middle, and the three triplet states are on the right.
A system with more than two electrons can be represented by these same figures with some
number of fully-occupied states below.
The excited states that we are able to enforce are the triplet state (THOMOTLUMO)
a mixed singlet-triplet state (tHOMOLuMO).
and
This mixed singlet and triplet state can be
written as:
14
+ 41)
_(t4-
2
which is the same as saying 14= jtriplet
energy from the
tt state,
+
(14 -2 41)
(2.6)
22
+ isinglet.
We are able to calculate the triplet
so now using this mixed state, we can solve for the singlet energy
as
Esinglet = 2ET
(2.7)
- Etriplet.
This method was demonstrated to agree with experiments in a paper by vanVoorhis' group
[47].
They relaxed the ground state of the molecules using B3LYP and then found the
vertical excitations of the ground state, calculated with the PBEO hybrid functional. We
mimicked this process by using Gaussian09 to relax the structures using B3LYP, and then
calculated the forced occupation triplet state and mixed singlet/triplet state of the molecule
without relaxing the ionic structure (vertical transition) in VASP. We found reasonable
agreement with experiment and with the numbers from [47], see Table 2.1.
Table 2.1: Comparison of calculated singlet and triplet energies using ASCF. Our results
compared to the computational results of [47]. All energies in eV.
molecule
triplet
singlet
experimental triplet from singlet from
from [47] from [471
value
our ASCF
our ASCF
anthracene
porphine
2.10
1.89
3.32
2.63
3.21
2.01
2.13
1.75
3.29
2.55
phthanocyoninato
1.12
1.96
1.88
1.25
1.92
We also calculated the triplet energy of Alq 3 excitations and compared to experiment, see
Table 2.2.
49
Table 2.2: Comparison of the experimental values for excitation energies of the two isomers
of Alq 3 to our A-SCF method and to the Kohn-Sham LUMO - HOMO energy.
Alq 3
facial triplet excitation (eV)
meridional triplet excitation (eV)
2.2.2
experimental [201
ASCF
KS LUMO-HOMO
2.16
2.11
2.18
2.07
2.10
1.77
Ionization Energy and Electron Affinity
In order to calculate the quasiparticle gap, the ionization energy (IE) and electron affinity
(EA) are needed (see Equation 2.5). The individual ionization energy and electron affinity
can be calculated by comparing the energy of the neutral state to the state with an extra
electron or hole.
IE = E(N - 1) - E(N)
(2.8)
EA = E(N) - E(N + 1)
(2.9)
In the DFT calculation a charged system repeated throughout all space would give an
infinite energy, so to correct for this, the program adds a neutralizing background charge.
This background charge interacts with the charged system, adding an unphysical term to
the energy [1201. To correct for this, we vary the size of the system and extrapolate the value
of the energy for an infinite-sized unit cell. This was done for the anthracene, anthracene
derivatives, and Alq 3 , and the comparison to experiment is shown in Table 2.3.
Table 2.3: Electron Affinity (EA) and Ionization Energy (IE) of the various molecules calculated and compared to experiments. All values in eV.
System
Property Experimental Value Calculated Value
Alq3
anthracene
dca
daa
IE
5.9 [92]
6.14
EA
2.1 [921
2.19
IE
EA
IE
EA
IE
7.439 [72]
0.53 [721
7.58 [73]
7.49
1.0
7.39
1.26
6.14
5.81 [51]
0.75
EA
50
2.3
Metal Workfunction
The workfunciton of a metal is the energy needed to extract an electron from the metal
and bring it infinitely far away. This is the difference between the Fermi energy and the
vacuum energy. When there is sufficient vacuum in our unit cell, it is possible to find the
workfunction simply by comparing the Fermi energy to the vacuum energy level, as seen in
Figure 2.3. This method has been used by others [35, 115].
-P
lkm
-I
A
-
i-
11
d
4PM
Ef
VI
-
0
-5
-10
-15
~~n
'U1
10
.
I
30
20
I
I
I
40
distance
Figure 2-3: The blue curve shows the potential surface for 6 layers of Al next to anthracene
and the black line shows the Fermi level. The difference potential off the metal side and the
Fermi level gives the metal workfunction from the metal side, OM, shown in dark red.
2.3.1
Metal Workfunction versus thickness
For these studies, we wanted the appearance of bulk metal, and one way to test if we had
enough layers of metal is to ensure that workfunction on the back end matches the bulk
value. Figures 2-4 and 2-5 show the work function of Magnesium and Aluminum versus the
number of layers, and we see that it takes six layers to accurately represent the metal.
51
-3. -3.'
I
I
I
I
I
I
I
I
I
I
I
I
i
i
I
i
c--3.5
-3.6
-3.7
0
0
7
8
0
ci
-3.81-
0
1
2
3
4
6
5
Number of Layers
Figure 2-4: Mg workfunction versus number of layers.
5
I
I
I
4. 8-
> 4.60
o4..40
:4..2-
-
4
32
.
0
0
3
b2 4
5
6
7
Number of layers
Figure 2-5: Al workfunction versus number of layers.
52
2.4
CdSe-metal study
To explore semiconductor-metal interfaces, we looked at one semiconductor in particular,
CdSe.
We interfaced CdSe(0001) with both Al(111) and Au(111) surfaces and studied
different numbers of layers of each to make sure the various properties converged.
We
also looked at these interfaces with a Cd vacancies. Because the unit cell is repeated, this
translated to one in four Cd removed from the interfacing layer of Cd with the metal. See
Figure 2-6 to see examples of these systems.
00
0
*
0*
0
.0.0
(
00000
00000
00000
00800
00000
Figure 2-6: Left: Top view of the CdSe structure; Cd atoms are cyan, and Se atoms are
yellow; the unit cell is shown in blue, which is one-quarter of our unit cell. Right: 5 layers of
Al with 6 layers of CdSe. The bottom layer of CdSe has a Cd vacancy. Aluminum is shown
as blue spheres, pink is cadmium and green is selenium.
In this study, we used ultra-soft pseudopotentials to model the ionic cores, and the generalizedgradient approximation (GGA) for the exchange-correlation functional, with the PerdewBurke-Ernzerhof scheme [74, 75]. The energy cutoff for our wavefuncitons is 82 Ryd and we
used a 6 x 6 x 2 Monkhorst-Pack k-point grid [61].
53
Convergence and check of basic properties
To test that our calculations compare to experiment, we compare several values to experiment in Table 2.4.
System
Au
Al
CdSe
Table 2.4: comparison to experiment of many basic properties.
Property
Experimental Value Calculated Value
bulk lattice parameter (A)
4.07
4.1
(111) surface workfunction (eV)
5.47
5.25
surface energy (eV)
0.08
bulk lattice parameter (A)
4.05
4.051
(111) surface workfunction (eV)
4.26 [55]
4.13
2
surface energy (eV/A )
0.07
0.09
bulk lattice parameter, a, (A)
4.30
4.38
c/a
1.632
1.635
The calculations were done with a repeated cell of metal-CdSe-metal, so that both the sides
of the CdSe could interface with the metal. The CdSe (0001) surface was chosen because
nano-rods made from these chalcogenides tend to grow in the [0001] direction, so these are
most likely the surface that is interfacing with metal electrodes [25].
Each bilayer of CdSe had 4 unit cells (see the left image in Figure 2-6); this allowed minimal
reconstruction of the formation of the Cd vacancy. To minimize the strain due to lattice
mismatch, we used a 3 x 3 surface unit-cell for both metals. The resulting strain was 2.2% for
Al and 0.3% for Au and the work function changed by leads than
54
0.1eV in either case.
2.5
Metal-organic study
We explored two different organics that exemplify the spectrum of small organic molecules:
tris(8-hydroxyquinolinato) aluminum, often referred to as simply Alq3 , which includes electronegative atoms such as oxygen and has an intrinsic dipole, and anthracene, a stable, flat
molecule with no intrinsic dipole. It has been found in previous DFT studies that oxygen
atoms tend to allow more charge transfer than other atoms [801, but aromatic rings tend
to screen charge better [53], so we thought these two systems were an interesting comparison. We examine the interfaces between these molecules and three metal surfaces, Ag
(111), Mg (0001), and Al(111), with a variation in workfunction (4.4, 3.7, and 4.1eV respectively). In addition to those two molecules, we also briefly studied the effect of ionization energy of the molecule by looking at 9,10-dichloranthracene (dca) and 9,10-diaminoanthracene
(daa).
Both Alq 3 and anthracene are used in electronic devices. Alq 3 is used as a green emitter in
organic light emitting diodes (OLEDs) and is also often used as the electron transport layers
in organic electronics [66]. Polycyclic aromatic hydrocarbons, such as anthracene, and their
derivatives are also used in organic electronics [4, 59]. Both Alq 3 [7, 123] and anthracene
derivatives [107] have been used in solar cell devices.
Alq 3 has two different isomers, as is shown in Figure 2-7. The lower energy meridianal isomer
has the three oxygen atoms in the same plane as the aluminum, and the metastable facial
isomer has all of the oxygen atoms on one side of the aluminum. We consider the facial isomer
of Alq 3 , which has been demonstrated by ourselves (see Table 2.5) and others ([115, 122])
to be the most stable isomer next to a metal surface. Near a surface the meridianal isomer
will isomerize into the facial isomer so all the oxygen atoms face the surface .[122].
The
bulk Alq 3 will have alternating dipoles so that the net dipole across a patch of bulk will be
zero [40]. A planar conjugated molecule such as anthracene often prefers to lie flat on metal
surfaces [65, 80, 81, 108, 110] as an isolated molecule on the surface or a monolayer; however,
the second layer of anthracene starts to tilt [58, 119]. Figure 2-8 shows anthracene and the
two derivatives we studied. Figures 2-9, 2-10, and 2-11 display some of the metal-organic
systems studied.
55
Figure 2-7: Left: meridianal and Right: facial isomers of Alq 3 . In this figure, brown atoms
are carbon, pink are hydrogen, red are oxygen, silver are nitrogen, and blue is aluminum.
Table 2.5: Energy of various positions of a six-silver-atom cluster near Alq 3 . This table
shows that Alq3 is more stabilized the closer the oxygen is to the metal surface.
energy (eV) binding energy (eV)
Ag position
-0.285
-372.764
Ag 6 above ring near 0
-0.118
-372.597
Ag 6 on the edge of a ring near 0
-0.207
-372.686
Ag 6 near one 0
(a)
-0.175
-0.742
-372.654
-373.221
Ag 6 near 3 N's
Ag 6 near 3 O's
(b)
(c)
Figure 2-8: (a)anthracene (b) daa (c) dca. Brown atoms are carbon, pink are hydrogen,
bluish silver are nitrogen, and green are chlorine.
We examined several combinations of these metals and organic molecules. We have single
molecules of Alq 3 or anthracene on top of each of the different metals (both smooth and
rough metal surfaces). We also had full single layers and full double layers of each molecule
on top of Al (smooth surface only). The metals were all 6 layers thick in the z-direction
with only the top layer allowed to relax from bulk. Six layers of metal were chosen because
this was the point where the workfunction of the unrelaxed side of the metal matched the
experimental value of the workfunction (see Section 2.3.1).
56
a)
0pp-000--W001
o
00P
000000000
0 00000000
0000000000
0 00
00
00
00
d)
C)
@000
0000000000000
0000000000000
0000000000000
0000000000000
0000000000000
0000000000000
0000000000000
000000000000000
Figure 2-9: (a) 1 full monolayer of Alq 3 on a smooth Al surface (b) 2 monolayers of anthracene on a smooth Al surface (c) Alq 3 on a smooth Ag surface (d) Alq 3 on a rough
Mg surface. In these figures, brown spheres are carbon atoms, pink are hydrogen, red are
oxygen, bluish silver are nitrogen, blue are aluminum, orange are magnesium, and silver
spheres are silver atoms.
0c
0
Af
0
0
00
0c
%00*
0
0 00
06
0000o
*
0000o
00000
0
0 0
0
0
Figure 2-10: Left: Alq 3 on Mg. Right: single layer of Alq 3 on Al. The different atoms follow
a color scheme where brown represents carbon, pink is hydrogen, red is oxygen, bluish silver
is nitrogen, blue is aluminum, and orange is magnesium.
57
4311.:000
0 0 0 0 000000
a)
0 00
0a
0
00
0 00
0
0
0
0000
0000
0
000000
0 000
ooooo
b)
b)0
0
0 0 000000 0
@0000000
0 0 0 0
O
0
0 0 0 0 0 0*0 0 00
0000000000000000
0000000000000
0000000000000000
000000000000
0000000000000000
Figure 2-11: (a) Anthracene on top of Al (b) anthracene on top of Mg. Anthracene has
carbon (brown spheres) and hydrogen (pink spheres). Aluminum is represented by blue
spheres and magnesium is orange.
The single molecules were first sampled at different distances to identify an optimum starting
distance. We then sampled several starting positions of molecules and allowed the molecules
and the layer of metal closest to the molecule to relax while holding the rest fixed at bulk
positions. For each system, the lowest energy structure was used for further analysis. For the
2
isolated molecule on a metal surface calculations we used one organic molecule per 1.86nm
for Ag, 2.23nm 2 for Mg, and 1.77nm 2 for Al.
For the one and two monolayer of molecules on a metal surface, we started the systems at
58
the optimal distance found for the single molecule and again relaxed the organics along with
the top layer of metal. For the full layers on Al we have a density of one molecule of Alq 3
per 1.24nm2 and one molecule of anthracene per 0.71nm2
To. keep layers from interacting with each other in the z-direction, we used a potential
correction and at least 20 Aof vacuum between the top of the organic molecules to the
bottom layer of the metal. The potential correction produces an electric field in the vacuum
to flatten out the vacuum energy level. This prevents the natural dipole from the top and
bottom of our system from producing an electric field that interacts with the system. Others
have demonstrated the necessity for this correction [115].
A few other computational details: we used the projector augmented wave (PAW) approach
[10, 50], a cutoff energy of 550 eV, Gaussian smearing of 0.2 eV, and a 5 x 5 x 1 MonkhorstPack k-point grid.
Convergence and check of basic properties
To make sure our pseudopotentials and parameters were reasonable, we checked some basic
properties with experimental properties, see Table 2.6. The results give us confidence in the
results of our calculations exploring properties that cannot be checked by comparison with
experiment.
Table 2.6: Comparison of calculated values to experiment for many basic properties.
Experimental Value Calculated Value
Property
System
4.14
4.09
bulk lattice parameter (A)
Ag
4.74 [55]
4.48
(111) surface workfunction (eV)
0.084
0.078
surface energy (eV)
3.21
3.21
bulk lattice parameters (A)
Mg
3.73
3.66 [55]
(0001) surface workfunction (eV)
4.04
4.05
bulk lattice parameter (A)
Al
4.06
4.26 [55]
(111) surface workfunction (eV)
Alq3
7.7
Dipole moment (D)
59
7.5
2.5.1
Choice of Functional
The different functionals have been studied with many test cases, and each has its own
strengths and weaknesses. For example, GGA often outperforms LDA in the calculation of
metal workfunctions, bond lengths, and binding energies [85]. For a molecule on a metal
surface, LDA and GGA have been found to give nearly identical relaxed structures [85].
The GGA functional always underestimates the band gap of materials. However, the image
charge effect reduces the bad gap of materials at the interface with metals. This reduction
is often comparable to the underestimation of the bandgap by DFT [9, 27].
Van der Waals correction
Van der Waals forces come from the spontaneous polarization of one atom or molecule inducing a polarization in another and then being attracted by the dipole-dipole interaction.
These forces are very small, often around 0.004 to 0.04 eV per atom, and yet also very important for understanding the forces between organic molecules. Because van der Waals forces
are due to long-distance electronic correlation, they are not well captured by traditional
DFT methods. To include them in our calculation, we used the van der Waals functional
proposed by Grimme [321. It has been found that this functional is able to predict metalorganic distances better than other functionals [105]. Comparing results of this functional
and the uncorrected PW91 functional [76, 77], we found no change in the magnitude of
the charge transfer or the interface dipole; however we observe significant changes in the
metal-to-molecule distance and in the binding energy.
Table 2.7: Relaxed distance from the surface (in A) for the regular GGA PBE function and
the GGA functional with the van der Waals correction.
System
without van der Waals with van der Waals
Alq 3 /Ag, smooth
Alq 3 /Ag, rough
Alq 3 /Mg, smooth
5.09
3.27
5.24
3.8
3.16
4.9
Alq 3 /Mg, rough
3.0
2.8
Alq 3 /Al, smooth
Alq 3 /Al, rough
5.59
3.45
4.1
3.18
anth/Ag, smooth
anth/Mg, rough
3.9
2.14
3.0
2.50
anth/Al, rough
3.49
3.67
60
2.5.2
Binding Energy
The binding energy, which quantifies the strength of the interaction of the organic molecule
and the metal surface, is calculated by comparing the total system to each individually:
Eorganic,relaxed -
Ebinding = Etotalsystem,relaxed -
2.5.3
Emetal,relaxed.
(2.10)
"Isolated" molecules
In this study we wanted to look at molecules that were either isolated on a metal surface
or in one or two monolayers. Because of our repeating unit cells it is impossible to study a
single molecule on a metal surface, but the molecules are separated by enough distance to
not substantially interact. To show that they indeed do not interact, we observe the energy
of the relaxed molecule as function of unit cell size, see Figures 2-12 and 2-13. For this
comparison, we keep a constant distance in the z-direction, and just change the x- and yvalues.
-50 I-
C
-100 I-
w
-150
0
i
0
0
500
0
0
1000
Cell Area (AA2)
1500
2000
Figure 2-12: Energy of the anthracene molecule versus the cell area (in the same plane as
the anthracene). Because the energy does not change as a function of cell size, this spacing
of anthracene molecules is enough to simulate isolated anthracene molecules.
61
-
UI
I
I
-361
-362-
-
> -363
-364-
-365-
0
-360
0
0
00
500
1000
1500
Area (AA2)
Figure 2-13: Energy of the Alq3 molecule versus the cell area (in the same plane as the
Alq 3 ). This shows that we can treat the Alq 3 as if it is isolated on the metal surface.
2.5.4
Interface Dipole
The interface dipole was calculated by examining the potential in the direction perpendicular to the surface of the metal in a system with enough vacuum and employing a dipole
correction. The image on the left in Figure 2-14 shows this plot for the case of a single
molecule of Alq 3 on the surface of Mg. The value of the discontinuity of the vacuum level
indicates the energy of the total dipole across the combined system of the metal, the interface dipole and the dipole across the molecule. To get just the dipole present at the surface,
we subtract off the dipoles across the metal individually and the Alq 3 alone. This process
is represented in the bottom part of figure 2-14.
This method only gives the potential energy difference, so to get the value of the dipole in
Debye it is necessary to take this potential energy difference and multiply by the area of the
x-y plane (in units of A2) and a factor of 0.0265.
As a check, we turned off the potential correction and calculated the charge distribution for
Alq 3 . We then integrated pz = f zA(z)dz, where A(z)
=
f pdxdy is the linear charge density
in the direction in which we want to calculate the dipole. This result was only 1% different
from the method using the potential corrected for the dipole.
62
-0.024
1.004eV
o
'02
0
dimanv i A
---- ---
-
-----
40
1.058eV
-1.004
-(-1.058+0.024)
=O.O3OeV
Figure 2-14: Potential energy curves for various systems plus vacuum. The drop in potential
in the vacuum is from the potential correction and gives the total dipole for the system. Left:
Mg + Alq 3 system, upper right: Mg alone and lower right: Alq 3 alone. The dipoles from
the metal and molecule alone are subtracted from the dipole of the combined system, and
this is the dipole present at the surface. To turn this into units of Debye, it is necessary to
multiply this potential energy difference by the surface area in A 2 by a constant value of
0.0265.
2.5.5
Bader Charge
We are interested in probing how much charge is associated with the molecules on a surface
or with a particular atom. To do this, we need some way of dividing up real space to assign
the charge density in a particular place as associated with a particular atom. This is not a
straightforward problem, so there are many methods commonly used to assign the volume
of each atom. The method we use is called Bader Charge Analysis [5, 1011. The boundaries
between atoms are assigned to be the places with the minimum of charge density in any
particular direction.
63
2.5.6
Image Charge
Because metals have seas of mobile electrons (high dielectric constants) when a charge is
brought near the surface of a metal, the electrons in the metal will rearrange themselves
to to exclude the electric field. This in effect brings an opposite charge to the surface and
this will stabilize that charge near the surface. When the metal surface is like an infinite
plane, this effect can be modeled with the concept of image charges.
The space above
the metal's surface will have the same electric properties as if the metal had a charge of
the same magnitude and opposite sign exactly the same distance below the surface as the
original charge is above it (see Figure 2-15).
@
00
0
0000000000000
Figure 2-15: The LUMO of anthracene and its image charge reflected in the metal below.
The wave function of anthracene is made up of blue (negative) and yellow (positive) lobes.
The atoms colors are brown is carbon, pink is hydrogen, and orange is magnesium.
For a point charge, the image charge reduces the energy by E
=
= e,
where e is the
charge of an electron and d is the distance from the image plane to electron's location. The
factor of -1 comes from the fact that this picture is only valid in the top half of space, above
the metal surface, and the electric field is zero below. The magnitude of this effect is very
large, shifting bands by around 1eV and changing band gaps significantly.
In DFT, the exchange-correlation energy is not long-range enough to be able to account for
this correction. To calculate this correction to the Electron Affinity and Ionization Energy
64
(see earlier section 2.2.2), we started with the electron density of the HOMO and LUMO
of the molecule. The value of the image charge was found using the ICM code in Quantum
Espresso [24, 31, 38, 84] where the HOMO or LUMO of the molecule is reflected at the
image plane into the metal [52], and this image is given the opposite charge. The image
charge energy correction is calculated by a classical electrostatic integration of the reflected
charge with the original charge [67].
Finding the image plane involves some work.
One might naively assume that the plane
ought to just be the position of the top layer of atoms plus half the interlayer spacing.
However, as we saw earlier (see Section 1.2.2), at the boundary of a metal, the electronic
wave function extends out farther into space than just half the interlayer spacing.
This
method is outlined by Lam and Needs in [52]. They first describe the potential close to the
metal surface when there is an applied electric field, and the result is shown in Figure 2.5.6
and described by
Zo= ZB -AV
Dz
(2.11)
av.
AV
ZA~Zo
Z
Figure 2-16: The sloped line represents the potential from an applied electric field and the
wiggles represent what happens to that field at a metal surface. The value of zo is where
the metal surface seems to end for that applied electric field. Figure from [52].
We apply an electric field in the vacuum between a two metal surfaces and analyze results
such as seen in Figure 2-17 by fitting the slope to a line as shown. Using these parameters,
we rewrite equation 2.11 in the following way to solve for zo:
ZO = dmetalnudeus
65
-
- a
(2.12)
I
/1
/
/
-
0.4
V=a+bxd
/
/
0.2
0
V
=Von
-0.2 [-
.I
,
0.6
0.2
6
I
0.8
I
Distance
Figure 2-17: Example of an electric field applied outside of a metal surface and extrapolated
to find its surface under this electric field. This is a plot of the potential of the applied
electric field case with the zero electric field case subtracted off. The value of the slope is
then fit to Equation 2.12.
The zo that we want for the image plane is the one with zero applied field. We do not get
the nice linear relationship with no applied electric field, so we need to plot zo as a function
0.005
-
of electric field and extrapolate to the zero-field case as is shown in Figure 2-18.
0
w
-0.(X)5
1
I
1.55
1.6
distance
Figure 2-18: Electric field as a function of distance. This differs from just a linear electric
field because of the screening from a metal.Taken from [521
66
Our results are shown in Table 2.8. Our value for Al is not too far away from the 1.67 value
found in [52].
Table 2.8: Distance away from the metal plane where the metal electron density is said to
end for the purpose of assigning a metal plane to reflect the charge density over and find
the image charge interaction energy.
zo (A)
Al
1.59
67
Mg
1.63
Ag
1.49
Chapter 3
Results and Discussion
In this chapter, we now turn to the results of our various studies. We start by discussing
the results of the CdSe-metal study to observe if surface states predict Fermi-level pinning.
Then we discuss the metal-organic study, where we dissect all the different contributions
to interface alignment for different types of molecules.
discussion of a novel idea for solar cell efficiency.
69
We end this chapter with a brief
3.1
CdSe-metal interfaces
We begin our exploration of metal-semiconductor interfaces with a metal-crystalline inorganic semiconductor example. The expected interface effects for this type of system were
given in Figure 1-19. As was discussed in Section 1.2.8 the interface properties of metalcrystalline semiconductor interfaces are thought to be determined by the surface states
present on the semiconductor [21, 96]. One of the most commonly cited examples of this
is GaAs. Doped GaAs exhibits Fermi-level pinning; this can be seen in Figure 3-1, which
is from Spicer et al.'s paper [96], the left side of which is a plot of the Fermi pinning levels
of p- and n- type GaAs with various metal surfaces.
At first, these pinning levels were
misattributed to vacancies, however Allen and Dow [3] realized that anti-site defects were
more probable than vacancies.
An anti-site occurs when two elements switch place in a
crystal structure, and thereby create a local defect energy level in the bandgap. Weber et
al. [117, 118] found that the anti-site energies for AsGa match the pinning levels, as shown
in the right side of Figure 3-1.
on
&P
FERMILEVEL
PINNING
AsGa ANTISITE
CBM
r
eV
1.2-
CB
GaAs (110)
0
n
n
n
0
0
0.4
----- 0.75
eV
050.75
-
1k 0. 6
w
-42U
1.00 eV
eV
0.52 eV
W/X
V/i?/V/A
i
nV/Axy:A VBM
Spicer et al., 1979
D+/D 2 +
D +/DD
Weber et al., 1982
Figure 3-1: On the left is the Fermi-level pinning energy for n-type (circles) and p-type
(triangles) GaAs on different metal surfaces; this images is from [97]. On the right is the
comparison of these energies to the anti-site vacancy energy levels which match the Fermipinning energies; this image is from [117].
Another example is the case of HfO 2 , where Fermi-level pinning due to an oxygen vacancy
has been observed [83].
This pinning is illustrated in the left image of Figure 3-2.
70
To
overcome this Fermi-level pinning, it is possible to passivate that surface oxygen vacancy
with the addition of lanthanum [57]. This idea is cartooned in the diagram on the right side
of Figure 3-2.
(a)
(b)
vacuum
-------- YgttUM
0
-27
e
CS
-2
20
.4
-6
0
.8
8 -88
81
s$10
8tSiS02
Bf2
m
e
02
HfO2
f0
HfO 2 onty
ea
LaHf oxide
Figure 3-2: (a) Example of band bending due to Fermi pinning of the oxygen vacancy states
in HfO 2 . Image from [83]. (b) On the left is the image of the oxygen vacancy state giving
charge to a metal surface to pin the Fermi energy to the vacancy energy level, while the
right shows this oxygen vacancy being passivated by electrons donated from La. Image from
[57].
The above examples show two cases of surface states from different origins pinning the
Fermi energy when these semiconductors are interfaced with a metal. We intend to explore
if other types of surface states will pin the Fermi level. To do this, we simulate CdSe-metal
interfaces. The computational details and some images of the system are given in Section
2.4. CdSe is a II-IV semiconductor with a wurtzite crystal structure. It has been used in
solar cells as nanorods [63, 99, 100], quantum dots [621, and polycrystalline films [231. This
system is a good case study because there is a surface state on the CdSe (0001) surface
that is removable through a Cd-vacancy. We explore both the defect-free CdSe surface and
the Cd-vacancy surface interfaced with metals.
Our expectation is that the Fermi level
should therefore be pinned to this surface state energy when a metal is interfaced with the
defect-free surface, but pinning should not occur when the metals are interfaced with the
Cd-vacancy surface.
Before interfacing CdSe with a metal, let us explore the surfaces of the defect-free and the
Cd vacancy cases. Figure 3-3 shows the projected density of states (PDOS) of the defectfree CdSe. The yellow curve represents the density of states of the atoms in the outermost
bilayer of CdSe where the Cd is in contact with vacuum. The peak around the Fermi energy
71
75 75
I
I
-
60
\
I
30
CdSC I
CdSc 4
CdSC 2
-CdSC 3
-
\------s---
004
-2
24
0
1P1
0
E -Ef (eV)
Figure 3-3: Layer by Layer PDOS of CdSe. The corresponding structure is given on the
right, where purple is Cd and green is Se. The yellow PDOS is for the top layer of CdSe on
the Cd side, the surface layer, the red and blue are for the middle two layers shown and the
black is for the bottom layer shown, which is the side where Se is interfaced with vacuum.
is a surface state that we expect will form an interface state when interfaced with a metal
and will pin the Fermi energy to this level. Just as a comparison, we also examine the Cdvacancy case, shown in Figure 3-4. The purple curve now represents the density of states
of the outermost layer of CdSe on the Cd side, and the surface state has disappeared. In
this case we expect a very different interface behavior when in contact with a metal because
there are no surface states to pin the Fermi energy.
To test our predictions of pinning, we look at the density of states for the different Cd and
Se levels when interfaced with the Al surface. Figure 3-5 shows the density of states of the
bilayers in an 8 bilayer structure of CdSe interfaced with Al. The yellow PDOS represents
the interface layer of CdSe on the Cd side. There is essentially a continuous density of states
localized at the CdSe interface with the Al. This is in contrast to the bare CdSe surface
shown in yellow in the graph of Figure 3-3 where there is an interface state but otherwise
the density of states goes to zero in the gap. The presence of a metal can broaden a surface
state, so it could be that this continuum comes from the interaction of the CdSe surface
state with the metal surface.
To compare, Figure 3-6 shows the density of states of the various layers of an 8 bilayer CdSe
72
-Z0
=
-Z
F
60
ri
- -Full
(Se end)
= 3 (Cd vac end)
surf. (Cd end)
I090
S
*999o'W
40
0999*0
2E20
Ott99*
-4
E -Ef (eV)
Figure 3-4: Layer by Layer PDOS of CdSe with a Cd vacancy at the Cd side. Again, the
structure is given on the right where purple is Cd and green is Se. The purple line represents
the PDOS of the top CdSe layer with the Cd vacancy. Again, the blue and the red curves
represent the next two bilayers of CdSe. The black line is the PDOS of the Se end. The
dotted black line in the structure on the right represents the Cd vacancy, and the PDOS of
the defect-free surface is plotted as a dotted black line.
0000000
-- Z=0 Se cnd
-_ I
0000000
_
_
00,,0
-A 0000000
45
0999*
*999,
09990
15
EL I
-4
Lg&.
0
-2
E-Ef(eV)
2
0 Otte
4
O@,.
*1990
Figure 3-5: Layer by layer PDOS for 8 bilayers of CdSe interfaced with 8 layers of Al. The
silver blue colored atoms are Al, Cd is purple and Se is green. This is just a single unit cell,
so the metal is interfaced with both sides of the CdSe. The curves on the left represent the
PDOS of each individual bilayer of this structure; the two interface bilayers are the yellow
on the Cd side and the black on the Se side.
73
-
Z= I(Se end)
-
Z=-2
Z=3
-
00000
0000000
40
0000000
33MO
.0 9
I9990
20
0999*
0
999t0
0 999.1
10
*999o0
-6
-4
2
-2
0
E-Ef(eV)
4
0@999.l
0999.
Figure 3-6: Layer by layer PDOS for 8 bilayers of CdSe with a Cd-vacancy on the outermost
Cd-layer interfaced with 8 layers of Al. The silver blue colored atoms are Al, Cd is purple
and Se is green. The curves on the left represent the PDOS of each individual bilayer of this
structure; the two interface bilayers are the yellow on the Cd side (with a vacancy) and the
black on the Se side.
structure interfaced with the same Al surface.
The yellow line here represents the same
CdSe bilayer on the Cd side, however this time with a Cd vacancy. Notice here we see the
same interface density of states as in the case without the Cd vacancy (see the yellow line in
the graph on the right in Figure 3-5). The Cd-vacancy surface does not have the interface
state (see Figure 3-4). This contradicts our hypothesis and implies instead that the origin
of these interface states are metal-induced and are not related to the intrinsic surface states.
Therefore, although CdSe has a well-known surface state, the Fermi level will not be pinned
.
to this level, unlike in the cases of GaAs and HfO 2
We also examined the interface with Au.
Figure 3-7 shows a similar density of states
induced at the interface. The Fermi-level is in a different place, lower by less than 1eV. The
workfunction difference between Al and Au is more than 1eV. This indicates that the Fermi
level is somewhat pinned - that the value of S in the IDIS model (Section 1.2.6) would be
somewhere between 0 < S < 1. This is exactly as we predicted - the surface state seen in
yellow in Figure 3-3 does not pin the Fermi level. However, the alignment is not completely
74
-
I(Se end)
00000W0
-Z=2
-_4Z--3
60
000000
45
09990
30
099,
*Otto
15
99990
Al
-6
-4
-2
0
2
4
E-Ef (eV)
00 999
Of1too
Figure 3-7: Layer by layer PDOS for 8 bilayers of defect-free CdSe interfaced with 5 layers of
Au. Again, the yellow and black curves represent the two interface layers, where the yellow
curve is for the Cd end and the black is the Se end. The structure of the unit cell is shown
on the right where Cd is purple, Se is green, and Au is gold-colored.
described by the Schottky-Mott model (Section 1.2.4) because of the continuous density of
states induced from the interaction of the CdSe and metal surfaces.
This study warns us of the dangers of assuming that knowing about a surface state will
allow us to predict metal-semiconductor energy alignment behavior. Instead, it is crucial to
always check how strongly a surface state is able to persist in the interface. In this case,
the IDIS model will describe well the behavior of this interface, with the density of states
induced by the metal given by Figures 3-5, 3-6, and 3-7.
75
3.2
Metal-Organic Interfaces
Another common class of semiconductors used in photovoltaics is organic molecules, so we
now consider metal-organic interfaces. Organic molecules do not have dangling bonds, and
are therefore expected to react much less with the metal surface. However, organic molecules
can also be floppy and can interface with metal surfaces at different angles. They sometimes
carry their own dipoles. Different interface effects for organic-metal interfaces were described
in Figure 1-18. While for inorganic crystal-metal interfaces, the behavior seems to be welldescribed by either pinning to a strong interface state or by the IDIS model with the density
of induced states from the interaction of dangling bonds on the metal and semiconductor,
the behavior of metal-organic interfaces is not as clear. Our aim is to discover what we can
about these interface energy alignments.
As a reminder of why this is important, see Figure 3-8. This diagram is drawn in an attempt
to find the electronic properties of this system, but it uses the Schottky-Mott assumption
where vacuum energy alignment is assumed, as illustrated in Figure 1-17.
Any interface
dipoles or other changes to the electronic structure will change this picture and therefore
the predictions made from such a model.
5.0 eV
3.4 eVj
.2e
4.28 eV
ZnPC
Alq3
Ag
5.2 eV
5.83 eV
ITO/PEDOT:PSS
Figure 3-8: An example band line-up diagram where the workfunction of contacts is compared to the IE and EA of the semiconductors making the Schottky-Mott assumption - used
to predict electronic properties of the hypothetical device. Image from [19].
With this motivation, we first present the results from the isolated molecules in vacuum and
on smooth surfaces, then we discuss one and two full monolayers of organic molecules on
metal surfaces. We also discuss the difference between a smooth and rough metal surfaces
76
and examples of anthracene bending on metal surfaces. We summarize with a look at how
the models currently used are not well substantiated by this data.
3.2.1
Alq 3 and anthracene
For this study we have chosen to explore two different types of organic molecules, represented
by Alq 3 and anthracene. These systems were introduced in Section 2.5. Alq 3 has reactive
elements like oxygen as well as a permanent dipole. It is floppy because each of the three
8-hydroxyquinolate sections can move a bit relative to each other. Anthracene, on the other
hand, is a flat, aromatic molecule. This aromaticity means that anthracene is expected to
stay flat and has a lot of electron density above and below the molecule in long, conjugated
ir-systems. These large orbitals are expected to be able to interact with the metal better
than the orbitals of a molecule like Alq 3 which are more contained within the molecule. This
difference in orbitals is expemplified in Figures 3-9 and 3-10, which show the HOMO and
LUMO of Alq 3 and anthracene.
HOMO
A
Q3
LUMO
Figure 3-9: Top and side views of the HOMO (left) and LUMO (right) of Alq 3. In the
center molecule, brown atoms are carbon, pink are hydrogen, red are oxygen, silver-blue are
nitrogen, and blue is aluminum. The yellow lobes are the positive and blue are the negative
lobes of the wave function.
77
HOMO
x0
Anthracene
LUMO
0
Figure 3-10: Top and side views of the HOMO and LUMO of anthracene. The atom colors
are brown for carbon and pink for hydrogen. The wave function has positive lobes (yellow)
and negative lobes (blue).
3.2.2
Single molecules on the metal surface
In this section we discuss the interface energy alignment of effectively isolated molecules
that are on metal surfaces. We are interested first in the effects that occur only due to the
interaction of the metal and the molecule ignoring a molecule's effects on other molecules.
Because the unit cell repeats, it is impossible to get a truly isolated molecule, but we examine
effectively isolated molecules. This means that the molecules are far enough away from each
other that they do not influence the behavior of their neighbors and is quantified in Section
2.5.3. For images of these unit cells, see Figure 2-9 (c) and (d), 2-10(a) and 2-11.
First, we check that we are indeed in the physisorbed regime instead of the chemisorbed
regime. Chemisorption is when a strong chemical bond forms and is unlikely for a moleculemetal interaction since there are no dangling bonds on the molecule. Chemisorption may
create pinning states in the gap and may cause changes in the molecules themselves. The
energy for chemisorption of a molecule should be multiple eV/molecule. Physisorption bonds
are van der Waals bonds (see Section 2.5.1), and are therefore much weaker and lead to much
less disruption of the molecule. This bond strength should be between 10-1000 meV and
charge transfer should be low. In our systems, the binding energy is around 1eV (see Table
78
3.1) and the charge transfer is significantly less than a whole electron per molecule. That no
chemical bonds have been formed can also be observed in the PDOS (see Figure 3-14 and
3-15) where there is a general broadening of states, but no new states formed in the gap.
Notice that the binding energy is a bit higher for the aromatic compound, as was predicted
from the large aromatic orbitals that can overlap with the metal states.
Table 3.1: Relaxed interface properties for the systems studied. Binding energy is given per
molecule; Bader charge [5] is the fractional charge that has been transferred per molecule,
the negative indicates the molecule has a negative charge; the dipole at the interface is the
dipole between the metal and the molecules and the structural dipole change is due to the
relaxation of the molecule in the environment of the metal and other molecules.
System
Binding
Bader charge
dipole at
structural relax.
Energy (eV) (on molecules) interface (D) dipole change (D)
Alq 3 /Ag
-1.9
-0.2
-2.3
1.3
Alq3/Mg
-0.3
-0.2
0.2
1.2
Alq 3 /Al
1 ML Alq 3 /Al
2 ML Alq 3 /Al
-0.2
-1.1
-1.4
-0.3
-0.4
-0.4
-0.3
0.4
0.8
1.2
1.9
3.8
anth/Al
-1.2
-0.3
-1.2
0.01
1 ML anth/Al
2 ML anth/Al
-0.6
-0.6
-0.3
-0.3
-1.2
-0.9
0.01
-0.08
Now that we have established that we are dealing with a case of physisorption as expected,
we can start dissecting the various effects that shift the interface energy alignment. In Figure
3-11, the single molecule shifts in the band alignment are decomposed into the effect from a
dipole shifting the vacuum energy (red) and the image charge effect (blue), and numerical
results are presented in Tables 3.1 and 3.2.
For single molecules on the surface, the image charge is the strongest effect, causing a
significant reduction of the gap (see the blue arrows in Figure 3-11 and Table 3.2). The
shift seen in anthracene is larger than in Alq 3 because in the planar anthracene's HOMO
and LUMO are both closer to the surface, partially because anthracene is flat and partially
because anthracene's relaxation distance is slightly closer as can be seen in Figure 3-12 and
Table 3.2. In the case of Alq 3 , the correction to the EA is always smaller than the correction
to the IE because the LUMO has a large electron density on the nitrogen atoms farther away
from the surface, whereas the HOMO is concentrated on the oxygens closer to the surface.
Figure 3-9 shows these orbitals, and it can be seen that the HOMO has more electron density
on the bottom near the oxygen atoms, while the LUMO has a greater density at the top
79
01
Dipole
Image Charge
V
Electron
Affinity
-2
0
0)
0
-4
I
4.5
4.06
3.72
WMMmWinmM
C
w
-6
Ionization
Energy
AkM
A9
mm
l
t"l
Figure 3-11: Single molecule IE and EA energies of Alq 3 and anthracene on various metals
adjusted for dipole at the interface (red) and image charge (blue). The green lines represent
the IE and EA of the molecules in vacuum, the purple levels are the corrected values and
are relative to the metal workfunction given by dotted black lines.
near the nitrogen atoms.
(b)
(a)
OOO000OOOOOO
ooooooooooooo
ooooooooooooo
ooooooooooooo
00000
00000
00000
ooooooooooooo
ooooooooooooo
Figure 3-12: (a) Alq3 and (b) anthracene on top of Al. The atom colors are the standard:
brown atoms are carbon, pink are hydrogen, red are oxygen, silver are nitrogen, and blue is
aluminum.
80
Table 3.2: Relaxed distance is measured between the Al of Alq 3 or the average plane of
anthracene and the image plane for the metals in the various systems; image charge refers
to the relative shift in the IE and EA (respectively) due to the image charge effect. ML
stands for monolayer and anth is anthracene.
System
distance between metal
Image charge
Image charge
surface and molecule A for holes (eV) for electrons (eV)
Alq 3 /Ag
Alq 3 /Mg
Alq 3 /Al
1 ML Alq 3 /Al
2 ML A1 3 /Al
2.1
3.3
2.5
2.1
2.4
1.1
0.6
0.8
0.7
0.6
-0.4
-0.2
-0.3
-0.3
-0.4
anth/Al
1 ML anth/Al
1.7
1.8
1.3
1.2
-1.3
-1.2
2 ML anth/Al
1.6
1.5
-1.5
The other class of change to the electronic structure is the dipole shift (the red arrows in
Figure 3-11). As can be seen in Table 3.1, if we compare the Alq 3 cases, the charge transfered
to the molecule is roughly the same for each case. Because the organic is negatively charged,
we would expect the dipole shifts to be positive. However, for Alq 3 on both Al and Ag the
dipole is negative. While the magnitude of the dipole is small on Al, it is substantial on Ag.
As previously stated, the compression of the tail of the wavefunction will cause a negative
dipole, and as expected, this negative dipole from this wavefunction compression dominates
,
for metals with larger work functions [42]. Anthracene is closer to the Al surface than is Alq 3
and this both reduces the dipole from charge transfer and increases the effect of the metal
wavefunction tail compression. As we will discuss below, we cannot know if this dominance
of one type of interface dipole effect over the other will hold for all metal surface-molecule
distances.
Table 3.1 lists the difference of the dipole of the molecule isolated in vacuum from the
geometry it takes when relaxed in the presence of the metal surface. For example, Alq 3 in
its facial form, when isolated and relaxed, has a dipole of 7.5 D but in the environment of
the Ag surface only has a dipole of 6.2 D. This effect for Alq 3 is roughly the same for all
cases of the single molecule/metal surface interface. In contrast, anthracene in isolation has
no dipole, and relaxation on the surface has very little effect.
81
3.2.3
Further distinguishing dipoles at the interface
It is possible to separate the effect of the dipole due to charge transfer and the dipole due
to the compression of the metal wavefunction by looking at these as a function of distance.
Here we looked at this for three different systems, anthracene, 9,10-dichloroanthracene (dca),
and 9,10-diamino-anthracene (daa) on an unrelaxed Al surface and our results are shown in
Figure 3-13. We varied the distance between Al and the various anthracene derivatives; as a
function of distance we look at the total dipole across the interface and the charge transferred
multiplied by twice the distance. This second quantity, the charge transferred multiplied
by twice the distance of the molecule to the image plane would be the dipole energy if the
transferred charge was transferred to a single point. The real charge transferred is more
disperse, and so this is not the right value for that dipole, but it is related. Therefore we
can observe the trends as a function of separation distance. We also check if the position
of the molecule on the surface makes a difference; Figure 3-13 (c) and (d) show different
positions of dca on Al and show that where the molecule is on the surface does not change
the result.
Looking at all of these graphs, it seems that in the case of anthracene and dca on Al, the
charge transfer dipole and the compression of the metal wavefunction tail keep pace with
each other, canceling each other out except for a nearly-constant value, at least in the region
of expected molecule-metal separation. However, in the case of daa on Al, the total dipole
becomes more negative as the molecule approaches the surface, meaning that compression
of the metal wavefunction tail grows faster than the charge transfer dipole. Morikawa et al.
found that the dipole varies greatly as a function of ditstance for n-alkane-metal interfaces
[64]. Therefore, in some cases, the dipole at the interface will be very sensitive to the
separation distance, and at other times it will not be.
3.2.4
Projected Density of States
There is much information to be extracted from the projected density of states plots. All of
the Alq 3 Projected Density of States (PDOS) plots are shown in Figure 3-14. The purple
line gives the full Alq 3 PDOS, and the blue and red show the density of states localized
82
(a) 2oal
Interface dpole
(b)
A
Charge'diSta
A charge transferdstance
0 total dipole at me interlace
0.
S0
<
00000
121416
2
8
3
4262o3
2
A
0.
3
-0.'4 -
8
000
A
0
0:: 0 o
A
0
o
1
a
distance (A)
-0.
0
4.
3.2 3 4 3636 '4
3
2.2 24 26 2.8
1.2 1.4 1.6 182
AA
4
3
2
distance
I'AI
IC)
AAAAA00
A
600-
00
1 1(
1
1 0o total nterlace dpole
0 charge transferdastance
10 total Interface doe
-A
0 0 0 0
0
0A
0
0.5
13
0 0 0
0
A
0 00 0
0~i
1.
2.5
A
00
2
0 000
00 0 0000
00
0 0 00
0O
A
A
A
A
0 00 0
00
00
00 00
0 00 0 0000
0A
00
0 0000 oooooooo
A
2.5
A
0.5
1 1
AAAI
0
0 0
000
000
1.5
2
0
25
3
0 **
.
1 0' 01010 j0 0 0 010 .1
35
-0.e
4
12 14 16
18
distance (A)
2
22 24 26 2.8
distance (A)
32
34 36 38
4
Figure 3-13: Dipole due to charge separation and versus the total dipole as a function of
distance away from the surface for (a) anthracene on Al, (b) daa on Al, (c) and (d) different
positions of dca on Al. The total dipole is measured in the way described in Section 2.5.4 and
the charge*distance category is given by twice the molecule to metal image plane times the
Bader charge transferred to the molecule. Atom colors are the standard: brown atoms are
carbon, pink are hydrogen, silver-blue is nitrogen, green is chlorine, and blue is aluminum
on nitrogen and oxygen, respectively. First of all, we can use the relative strength of the
oxygen over nitrogen to identify the HOMO state, and more nitrogen than oxygen density
to locate the LUMO. This indeed confirms that the Fermi energy (0 eV on the x-axis) is
between the HOMO and LUMO of Alq 3 . We also note that there is a bit of hybridization
between the organic and metal in the interface, but the interaction is very small. This can
be seen by the low-level induced density of states in the band gap. Oxygen plays a bigger
part in these induced states in the gap than does nitrogen.
This is due to the fact that
oxygen is physically closer to the metal surface as well as the fact that it reacts much more
strongly with metal surfaces than does nitrogen.
The middle right graph in Figure 3-14 shows the PDOS for a full monolayer of Alq3 on Al.
This looks very much like the PDOS plot of a single molecule of Alq 3 on the Al surface
83
Atq3
nitrogen
-
-
oxygen
Atq3
nitrogen
oxygen
C,,
C,,
0
0
0~
-4
-2
4
2
0
0
-2
-4
4
2
Energy (eV)
Energy (eV)
-
Atq3
nitrogen
-
oxygen
Atq3
nitrogen
oxygen
U),
0
C
a.
Energy (e V)
4
2
Energy (eV)
-
-
---
2
4
bottom Atq3
bottom nitrogen
bottom oxygen
top Alq3
top nitrogen
top oxygen
(C)
-2
0
2
Energy (eV)
,
Figure 3-14: Top left: Alq 3 on Ag; top right: Alq3 on Mg. Middle left: isolated Alq 3 on
Al; top right 1 monolayer of Alq 3 on Al; bottom: 2 monolayers of Alq 3 on Al. In all of the
diagrams, the total density of states for Alq 3 is given by the purple line, nitrogen is blue
and oxygen is red. For the bottom PDOS, the full lines are the Alq 3 molecules closest to
the metal, and the dotted lines are the next layer of Alq 3 . Notice for the two layers of Alq 3
the layer of molecules farther away from the metal have no density of states in the gap.
given in the figure just to the left of it. The bottom graph represents the PDOS of the first
and second layers from the 2 monolayers of Alq 3 on Al case. The dotted line represents the
Alq 3 that is farther away from the metal, while the solid lines are the layer closest to the
84
metal. Notice that this layer again looks like the full monolayer and the single molecule on
Al shown in the two graphs above. The second layer has a density of states that goes to
zero in the gap, just like the bulk case of Alq 3 . This indicates that by the second layer, we
can tread Alq 3 like bulk.
-
isolated anthracene
1 ML anthracene
2 ML anthracene - top layer
2 ML anthracene - bottom layer
CO
0
0
a.
-4
-2
0
2
4
Energy (eV)
Figure 3-15: Anthracene on Al. Blue curve: isolated molecule, red: one monolayer, green
and purple: 2 monolayers. The Fermi energy is set to be at the point E = 0 on the x-axis.
The 2 monolayer case has density of states in the gap for the purple curve which represents
the layer of anthracene closer to the metal, whereas the density of states goes to zero in the
gap for the layer of anthracene farther away from the metal.
The PDOS of anthracene, isolated on the metal surface (blue curve), one monolayer (red
curve) and 2 monolayers (green and purple curves) is shown in Figure 3-15. We notice many
of the same trends for this case. First of all, going from the isolated anthracene on Al to one
and two monolayers on Al does not substantially alter the PDOS. We also see that in the 2
monolayer case, the layer that is farther away from the metal (green curve) has no density
of states in the gap, meaning we can treat this like bulk.
85
3.2.5
Smooth versus Rough metal surfaces
We also explored the effect of surface roughness on energy alignment. Often when metals are
deposited on organic molecules, they form a much rougher surface than depositing organic
molecules on metals. Small molecules and polymers can be vacuum deposited or spin coated
on the metal surface, whereas the top metal is often done by evaporation deposition, so the
metal atoms have a high energy when they land on the surface and each metal atoms is also
smaller than the molecules, and so they can insert themselves in between, as depicted in
Figure 3-16. The difference in surface roughness often leads to different electron injection
behavior when the top and bottom contacts are made from the same metal [33], see the
right side of Figure 3-17. However, this is not the case with Alq 3 as long as one contact has
not been oxidized [901, see the left side of Figure 3-17.
Organic on metal
abrupt
interface
Metal
on organic
High-T
asource
source
0;
0
g 0 0 00 0
..0
0
00
g
ggggggooggggggg
Figure 3-16: (a) Organic-on-metal surfaces are often smoother than (b) metal-on-organic
surfaces. The yellow circles represent the metal atoms, and the red and green ovals are
organic molecules that have or have not interacted with metal atoms, respectively. Image
from [37J.
Figures 3-18 and 3-19 show the difference in the PDOS of Alq3 on Mg and Al smooth
and rough surfaces. The surface density of states does not change substantially. Table 3.3
also shows that Alq 3 -metal interfaces have a very similar dipole between the smooth and
the rough cases. Our results here confirmed that, for Alq3 , the surface roughness will not
dramatically affect the interface behavior. This corresponds with the result that metal-onorganic and organic-on-metal electronic characteristics resemble each other.
Notice in Table 3.3 that the values of the dipole across anthracene do not remain constant
86
101
AUAtqg Al
10'
10.1
w knjecionf -omtop Al
10A.
I I
E
i
9:0M
W0.
PtTFSWPt
102
* injection from bottom Al
Injection from bosom Pt
10.2
U
10-2
10-4
S
0
S
10-5
hnjection from top Pt
10-4
10-8
0.1
10
1
01
10
Applied Voltage (V)
Applied Voltage (V)
Figure 3-17: I-V curves from current injected from the top and bottom of a device with
the same metals sandwiching Alq 3 on the left and poly(9,9'-dioctylfluorene-co-bis-N,NO(4-butylphenyl)diphenylamine) (TFB) on the right. The top and bottom metal layers are
produced in different ways and so have different surface roughness. This does not change
the interface electronic structure in the case of Alq 3 but does for TFB. Image from [37]
i lr
-
smooth Mg
0000
0000000000000
rough Mg
0000000000000000
C,,
00000000000
000000000
00000000000000
000000000000000
000000000ooo000
@0000000000000
000000000000000
S
..
0000000000000
0
Energy (eV)
Figure 3-18: PDOS of Alq 3 on smooth (blue curve) and rough (red curve) Mg surfaces.
To the right are the unit cells for these two calculations where orange spheres represent
magnesium atoms, brown is carbon, pink is hydrogen, red is oxygen, silver is nitrogen and
silver-blue is aluminum.
87
6
4
a .z
0000
0 0cQ0000000
0000000000000
smooth Al
-
8
-
rough Al
0000000000000
0000000000000000
0000000000000
0000000000000
K
0000600000000
2--
Fiue
0000000000000
-3- 2 -1 0 1
0000000000000
3 0000000000000
2
0000000000000
Energy (eV)
Figure 3-19: PDOS of Alq 3 on a smooth (blue curve) and rough (red curve) Al surface.
The geometry of the smooth and rough surfaces with Alq 3 are on the right side, where blue
spheres are aluminum, brown is carbon, pink is hydrogen, red is oxygen, and silver-blue is
nitrogen.
Table 3.3: Total dipole and binding energy for the interfaces of Alq 3 and anthracene on
smooth and rough metal surfaces.
binding
total surface
System
energy (eV)
dipole (D)
Alq 3 /smooth Ag
Alq 3 /rough Ag
Alq 3 /smooth Mg
Alq 3 /rough Mg
Alq 3 /smooth Al
Alq 3 /rough Al
-8.5
-8.9
-5.9
-6.0
-6.8
-6.6
-1.9
-0.9
-0.3
-1.8
-0.2
-1.1
anth/smooth Al
-1.3
-1.2
anth/rough Al
-0.3
-0.8
anth/smooth Mg
-1.1
-0.9
anth/rough Mg
2.3
-0.6
going from the smooth to the rough surface. The density of states, shown in Figure 3-20
is also not similar going from the smooth to the rough Al surface. In fact, the geometry of
this molecule depends on the underlying system, as can be seen by the bending we see on
the rough metal surface.
88
0
0000
-
0o0o06060ooo0
0000000000000
000000000000
0000000000000
o:OO
:szzO
0000000000000
00000OOOO
000000000000
00000OOOO
00000OOOOO
900000OOOO
00000OOOO
anthracene on rough Al
anthracene on smooth Al
4
3
W
2
00900Q
0
2
4
Energy (eV)
Figure 3-20: PDOS of anthracene on a smooth (orange) and rough (purple) Al surface. The
geometries are to the left where blue sphere are aluminum, brown is carbon, and pink is
hydrogen. Note that anthracene bends when on the rough metal surface.
3.2.6
Difference between 1 and 2 full layers and single molecules
Now we move on to explore how the energy level alignment changes where there is more than
an isolated molecule on a metal surface. We do this by looking at one and two monolayers of
molecules on the surface. In a real device there are will be a substantial thickness of organic
molecules of 10-1000's of nm. We are interested in the interface effects rather than the bulk
effects, but we also recognize that the environment may affect how the individual molecules
interact with the metal surface.
In the systems with one or two full monolayers, many of the properties remain the same
(see Tables 3.1 and 3.2). The image charge is still the largest effect. This value does not
change substantially as we go from the isolated molecules to one and two layers, with small
variations caused by a change in the molecule to metal equilibrium distance. Only the case
of two monolayers of Alq 3 stands out, and will be discussed below.
For anthracene, the other properties, such as binding energy, charge transfer from metal to
molecule, and the dipole at the interface, remain similar between a single molecule and one
89
and two monolayers. From the density of states, we observe no midgap states in the second
layer of anthracene (see the two blue curves in the bottom image of Figure 3-15) indicating
that when modeling the anthracene/metal interface properties, a second layer of anthracene
is not necessary.
For Alq 3 , while the binding energy and charge transfer do not vary dramatically, the dipole
at the interface and the amount of structural relaxation are notably different. Observing the
absence of midgap states on the second layer of Alq 3 (see the blue line in the bottom left
image in Figure 3-14) again illustrates that this second layer of molecules does not interact
with the metal surface. Instead, this difference is due to the presence of the second layer of
molecules changing the relaxation position of atoms within the first layer of molecules. In
the two monolayer case, the bottom layer of molecules compress, explaining the large change
in dipole in Table 3.1. This brings the HOMO and LUMO closer together and explains why
the image charge corrections are closer together in this case (see Table 3.2). We see that
the molecular geometry and therefore its dipole moment of Alq 3 depend strongly on the
chemical environment.
In Kelvin probe experiments with Alq 3 , it has been observed that there is an initial shift
observed in the workfunction after the deposition of the first layer of molecules but no further
shift with increasing thickness [36, 40]. This parallels our finding of a dipole at the interface
and potentially across the first layer of molecules, but then further layers acting like bulk.
We therefore justify ending our simulation with two monolayers of Alq 3 . Therefore, unlike
anthracene whose properties we can predict with just a single molecule on a surface, Alq 3
requires at least two full monolayers to correctly predict the interface energy alignment.
This type of behavior has been seen in other simulations, where the a full monolayer was
required to model the depolarizing effect of the neighbors {104.
3.2.7
Correction for Band Alignment
One goal of studying the interface dipole formation and image charge correction was to be
able to make better band line-up diagrams such as the one in Figure 3-8 so that we can
better predict the behavior of devices that include these interfaces. Figure 3-21 shows the
corrected band line-up diagram for the interfaces we have studied based on our results. The
90
workfunction of the metal is aligned with the corrected IE and EA of the first layer of the
molecule; the corrections include both the interface dipole and the image charge effect. This
will transition to the bulk values, with dipole shift still affecting the vacuum energy, but the
image charge effect falling off rapidly. In anthracene, the effect is not as important, but in
Alq 3 molecules, the dipole shift from all Alq 3 being oriented in the same direction on the
surface adds an additional dipole shift, called the first layer dipole in the figure. The bulk
values of IE and EA in this figure are what is traditionally used in a band alignment picture
[19, 431. It is also possible to calculate the correct IE and EA for thin films [104] and bulk
[34].
This figure will give very different results than a traditional band line-up diagram; the
calculation of the barrier to extract or inject electrons or holes, recombination velocity, and
even open circuit voltage of the device will all be affected. For example, electrons will face
a barrier going to Al from Alq 3 . Since Alq 3 is used as an electron-transporting layer, this
could cause problems in a solar cell made with this molecule.
The alignment shown in Figure 3-21 is in good agreement with experimental data.
We
compare the metal workfunction to the bulk values corrected by the total dipole across both
the interface and first molecule layer because in experiments there are many layers of the
organic on the metal surface. One of the common techniques to measure these energy levels
is called ultraviolet photoemission spectroscopy (UPS), and it to this type of experimental
data that we compare our values. In Figure 3-21 (b), the total dipole at the interface of
Al and Alq 3 is 0.9eV, which matches closely the experimentally found 1.0eV [41, 42] or
the 0.8-1.0eV [92].
The distance between the LUMO of Alq 3 and the Al workfunction is
about 1.0eV, exactly matching that of [42], and the distance between the HOMO and Al's
workfunction, 2.9eV, is just a bit larger than the experimental 2.6eV [42] or 2.5eV [91].
In this section we have demonstrated that we can use our calculation of dipoles and image
charge correction to better predict the energy alignment at interfaces. In the following section, we discuss another issue that can complicate band alignment calculations that certainly
goes beyond the simple picture of vacuum-level alignment.
91
(a)
-U
I.~u.
j
Interface
dipole
First layer dipole
I
-2 k
(PM
(D
--
TEA
-
-
-
-4
I
Evac
-
0
anthracene
bulk
first layer
anthracene
0)
IE
-
-6
-8
(b)
first layer A1%3
Al
0
diple \
bulk Alq3
First layer dipole
Evac
-2k
EA
(PM
0)
Ia)
C
-4
-
a)
.*m...
-
m
m
M
w
XE
-6-
Figure 3-21: Band Alignment including surface effects for (a) anthracene on Al and (b) Alq 3
on Al. OM is the metal workfunction, IE and EA are the ionization energy and electron
affinity, respectively, of the organic molecule.
3.2.8
Bending of anthracene on Mg
When we relaxed anthracene on top of the Mg surface, to our surprise, we found that the
anthracene molecule spontaneously bends, see Figures 2-11 (b) and 3-23. This disruption
92
in the aromaticity of the anthracene system should destabilize the molecule, so it must be
compensating for this loss in stabilization by favorable interaction with the Mg surface. The
relaxed anthracene on Al, however, hardly bends at all. To explore what happens with
the anthracene derivatives, daa and dca, we also examined those on Al. We relaxed many
different starting positions of the molecules. For these systems, we calculated the binding
energy, Equation 2.10, and the stabilization energy:
Estabilization = Ebinding + Edistortion = Etotalsystem - Emetal,relaxed - Eanthracene,unrelaxed- (3.1)
Table 3.4 shows the binding energy, stabilization energy, and charge transferred to the
molecule. The last two columns give the variance of the height of the molecules and the
distance to the surface. The variance of the height is related to the bending of the molecule,
although it is not directly comparable across different molecules. For a comparison of bending between the different molecules, see Figure 3-23 which shows the side views of a few of
these.
Table 3.4: Data for bending of anthracene. Binding energy is defined in Equation 2.10,
Stabilization energy is Equation 3.1, Bader charge is described in Section 2.5.5.
System
Ebinding Estabilization Bader charge variance in height dist to surface
anth/Al (a)
anth/Al (b)
dca/Al (c)
dca/Al (d)
daa/Al (e)
daa/Al (f)
anth/Mg (g)
-1.49
-1.19
-1.35
-1.30
-1.59
-1.53
-1.10
anth/Mg (h)
-1.07
-1.50
-1.21
-5.09
-1.48
-1.61
-1.55
-1.77
-0.34
-0.40
1.44
0.55
0.26
0.25
2.00
0.0048
0.0005
0.057
0.003
0.025
0.023
0.049
1.36
1.46
1.41
1.49
0.95
0.95
0.95
1.68
0.073
1.19
This unexpected bending complicates the interface energy alignment.
In the case of an-
thracene on Mg, the LUMO is almost filled; this can be observed from the charge transfer
in Table 3.4 or the position of the LUMO relative to the Fermi energy in Figure 3-24. If
the LUMO is filled or almost filled, it is now the LUMO+1 that is important for transport
through this layer. Therefore predicting band line-up in this case requires more than just
the IE and EA of the molecule plus interface effects.
93
This charge transfer also creates a
(b)
S.oooooo
0000
0
R2A
0000000000
0
000 0
00
00
01
00
(d) 0
k
Q
00000000000
a
00
0h
0
000
0 o0
0O
0
oooooL 00
0 00 00 ft0o0
0000#0000
0 0
(C) 000
0000000000
00000
(g)~
0 00
000
0~
00000000000
0
0 0
0
0IW~0
*o~0oo6 o
Figure 3-22: Top view of various relaxation positions from different starting positions of
anthracene and its derivatives on Al and Mg: (a) and (b) anthracene on Al; (c) and (d) dca
on Al; (e) and (f) daa on Al; (g) and (h) anthracene on Mg. The colors of the atoms are
brown for carbon, pink for hydrogen, green for chlorine, silver-blue for nitrogen, blue for
aluminum, and orange for magnesium.
94
<
(d)
-(c)
000000
00000
00000
000000
OO O
00000
00000
-0
O O
00000
00000
00000
0-0a0 00(B) 00OO
00000
00000
_eaa
00000
00000
00000
00 O 00
00000
00000
0 0 000
00 0 00
a0 0000
00
0 00
00 0 00
000
00
00
0
0 00
0
00
00
00
0
0 00
00
0
00
0 0 000
0 00
00
.
(b)
0
0
Figure 3-23: Side views of the different systems in Table 3.4 and Figure 3-22 to see which
bend and which stay flat; (b) anthracene on Al, (c) and (d) dca on Al, (f) data on Al, and
(g) anthracene on Mg. The colors of the atoms are brown for carbon, pink for hydrogen,
green for chlorine, silver-blue for nitrogen, blue for aluminum, and orange for magnesium.
large dipole at the interface.
Previously the only observed anthracene bending on a metal surface was on Pt, and this
was ascribed as being due to bonding with the d states of the metal [651. See figure 3-25 to
see the charge density difference on top of Pt as compared to the charge density difference
we see for both the case of on top of Mg and Al. However, neither Al nor Mg have d states,
so this bonding is taking place to the surface states that are just s and p.
We can also compare these observations to results on longer aromatic hydrocarbon chains.
Pentacene on A,(001) was studied with similar results 1106]. They found that in the most
stable structure the LUMO was filled and the pentacene molecule bows down in the middle
in the same way that we see. In their DFT model, the angle of bending around the central
two atoms is 155 degrees, and the deformation energy is about 1.35 eV. They also observed
the bending with scanning tunneling microscopy, although the total amount of bending was
a bit less.
95
-
anthra cnc on Mg
anthracene on Al
2
LUMO
HOMO
1
4
3
-2
0
-1
1
2
Energy (eV)
Figure 3-24: PDOS of anthracene on Al (green curve) and Mg (red curve). Notice that the
LUMO is mostly below the Fermi energy for anthracene on Mg, but not for anthracene on
Al.
0 0 0000000000
negative
positive
Figure 3-25: Charge density differences. top left: anthracene on Al, top right: anthracene
on Mg, bottom: positive and negative charge density differences of pentacle on Al(001) from
[651 In the top figures, the yellow corresponds to negative charge transfer and the blue is
positive charge transfer. The charge differences for anthracene on Mg more closely match
the charge differences of pentacene than does anthracene on Al.
To explain these results, we look at the energetics of the LUMO compared to the workfunction. The flat anthracene on top of Al produces the alignment shown in Figure 3-11.
However, on top of Mg, if the anthracene bends, the LUMO decreases by around 0.5eV, as
can be seen from the PDOS, see the left side of Figure 3-26. If this shift in the LUMO is
compared with the greater shift of the image charge, 2.4eV, due to the fact that anthracene
96
is closer to the Mg surface, this drops the LUMO level below that of workfunction of Mg,
see the right side of Figure 3-26.
Mg
-
anthracene
bent anthracene
flat anthracene
6vac
4PM
Image
charge
energy
10-
IE
-3
-2
-1
0
1
3
2
Energy (eV)
Figure 3-26: Left: PDOS of anthracene when flat (purple curve), and when bent as it is on
Mg (yellow curve). The HOMO is centered around -1eV for both curves, but the LUMO
is shifted down about 0.5eV on the bent anthracene in comparison to the flat anthracene.
Right: Energy level comparison of the LUMO of anthracene and the workfunction of Mg,
Om. The LUMO drops due to the image charge (red arrow) and due to the bending of
anthracene (green arrow). The LUMO drops far enough to be compatible in energy to the
workfunction of Mg, and therefore charge transfer is expected from Mg to anthracene.
3.2.9
Modeling Metal-Organic Interfaces
Our results give insight into what kind of modeling needs to be done to more accurately
represent energy levels in band alignment diagrams for metal/organic interfaces.
These
results are summarized in Figure 3-27. Localized charge on the layer closest to the metal will
experience an image charge correction to its energy level and the more localized the charge
and the closer to the surface, the stronger this effect will be. The first layer of molecules will
slightly hybridize with the metal, and the charge transfer from this in conjunction with the
compression of the metal wave function tail will produce a dipole right across the interface.
This effect of the compression of the metal wave function tail becomes more important the
higher the metal workfunction. The molecule may have a natural dipole, such as Alq 3 , and
if the molecules align, this dipole will further influence the vacuum level. It is also possible
for molecules to relax into a position where they develop a dipole moment, and this can
97
happen either from interaction with neighboring molecules or interaction with the surface.
When modeling more flexible molecules, it is important to relax them in an environment
that includes their neighbors, but rigid molecules do not need this environment to give good
predictive results. Rigid, aromatic molecules may interact more strongly with the metal,
with a stronger binding energy, and this stronger interaction may lead the molecule to relax,
as in the case of anthracene on Mg.
Interface dipole
Molecule has dipole
if the molecule has an
inherent dipole, It may
further shift the vacuum level
" Charge transfer dipole
ave uncionta
" Meal
Rigid or elastic
* Elastic molecules are
Charge Is localzed
If hopping transport
of charges localized
on molecules, image
EA
tE
charge effects will be
OeO.n
Influenced by
neighboring
molecules, so need tc
model multiple layern
* Rigid molecules do
Aromatic
- if the molecule is
aromatic may
react more with the metal states
" Stronger binding energy
" Pass"bitv of shiftinir strucsre
Figure 3-27: This diagram shows all the considerations for predicting a metal-organic interface.
Following this method, future calculations of metal/organic interfaces can be performed and
used to make better predictions of organic devices. The search space for new combinations of
materials is huge, but these predictions are only useful if they correspond to the experimental
device physics, and this method can bring calculations one step closer to this goal.
98
Comparison to IDIS Model
It has been predicted that flat molecules with have a small value of S in the IDIS model
because they should be able to take on more charge density from the metal, whereas more
3-dimensional molecules like Alq 3 will have S ~ 1 because they will not interact as strongly
with the metal surface [54]. Our results in Table 3.1 indicate that anthracene binds more
strongly to the surface than Alq 3 , but that the charge transfer is about the same for both
molecules, so this stronger interaction does not result in a stronger dipole at the interface.
(There is more charge transfer in the case where the LUMO partially fills and the molecule
bends, described in section 3.2.8.)
Alq 3 has been found experimentally to have S = 0.96 [54] and ECNL = 3.8eV [112]. Others
have found S = 0.8 [42]. Table 3.5 compares our experimental values of the interface dipole
to the dipoles obtained from these two values of S; Figure 3-28 plots out what the band
line-up diagram would be for these two cases, and should be compared to Figure 3-21 (b).
We can see that the trend agrees, but the values do not. Part of this disagreement comes
from the importance of the compression of the metal wave function. We used the simple
expression, Equation 1.34, however, looking instead to use Equation 1.36 does not fix all the
problems, such as the fact that there is disagreement on the exact value of S in the literature;
this should signal the IDIS method is not useful for predicting metal-Alq 3 surfaces. The
more complex equation also requires more calculation of properties that depend on metalto-molecule distance, density of states, and are just as complex as our calculations for less
physical insight.
Table 3.5: Interface dipoles for different experimental values of S using the IDIS model
compared to our data. All values are for complete coverage of surfaces and are in eV.
system
dipole for dipole for calculated
S = 0.8
value
S = 0.96
Alq3 /Ag
Alq 3 /Mg
Alq 3 /Al
0.14
-0.02
0.05
0.028
-0.004
0.01
0.72
-0.05
0.10
From our analysis of the different interface effects, we have seen that this model should not
hold all the time. One of the assumptions is that the metal-to-molecule distance should not
matter. We have seen that this is not necessarily true (see Figure 3-13). We also have seen
99
-2
-
-2
Wa
-2-
-
we-3-3--
I aV
-4 -
-4
0.96 on the left and S = 0.80 on
Figure 3-28: Band line up diagrams for Alq 3 on Al for S
the right. The solid black line is the vacuum level, the dotted black line is the workfunction
of Al, and the red and blue lines are the IE and EA of Alq 3. Compare how different this
model is from the one produced by our method shown in Figure 3-21 (b).
that the molecular dipole is not necessarily the dipole that will be present at the interface
(see the Alq 3 relaxation with two layers above). Finally, with the bending of the anthracene
and anthracene derivatives, and subsequent charge transfer, we have seen that we cannot
assume that we know the electronic structure and important electronic levels for energy
alignment. Therefore, while this model can work in some cases, it is hard to predict ahead
of time if it will in a particular case.
Comparison to ICT Model
The ICT model works well for molecules on metal surfaces that are already passivated, and
therefore should not apply to these systems. Alq 3 has been found to have EIcT,+ = 4.3eV
and a permanent dipole of A = 0.4eV [56]. Because this is using the ICT model, these
numbers are only relevant to Alq 3 on passivated metal surfaces where the interaction will
not be strong enough to isomerize the meridional molecules.
None of our work functions
were deep enough to see this charge transfer state, and our dipole moment was large due to
the facial structure, which, as we discussed in the introduction, is more likely because of the
interaction with a metal surface. On a passivated surface, the Alq 3 molecules would stay in
their meridianal form.
Our discussion above about bent anthracene (derivatives) dropping the LUMO below the
metal workfunction, and therefore filling is related to the ICT model. We also looked at the
100
energy of the charged state and not just the empty LUMO level. However, we still expect to
see a dipole at the metal-anthracene interface that depends on compression of the metal wave
function tail and we will still need to consider the dipole from charge transfer. Therefore,
while there are similarities, the ICT model should only be used for organic molecules on
passivated metal surfaces.
101
3.3
Photovoltaic Efficiency in Indirect Bandgap Materials
In the previous two sections we were focused on the behavior of metal-semiconductor interfaces. While improving the behavior of contacts is one part to the overall efficiency of
a photovoltaic device, in order to improve the behavior of solar cells, it is important to
search for new methods of improving overall efficiency. In this section, we explore one idea
to possibly increase the efficiency: using a material that has both a direct and indirect gap.
This idea has been discussed in many informal conversations, but as far as we are aware,
has never been written up in an formal way. To give this problem more context, we first
discuss the idea that is most similar - hot carriers. Then we move on to talk about why our
idea might work, and use a Shockley-Quiesser-like approach to show that it does not.
3.3.1
Hot Carriers
There are many ideas to improve the efficiency of solar cells and get around the ShockleyQuiesser limit, such as multilayer cells, hot carriers and intermediate band gap materials
[68, 121]. Here we discuss the use of hot carriers briefly. As discussed in Section 1.1.1, we
assume that when an electron and hole are excited, all the excess energy above the band
gap of the material becomes wasted heat (see Figure 1-5). This assumption was used in the
Shockley-Quiesser efficiency calculation (see Section 1.1.2), and so if we can do better than
this assumption, we have the potential to go beyond the Shockley-Quiesser limit.
(0 (1)
2)
po"ron
tkA
tko
formation
t: <0 =0
v10fs
;100 fs
(5)
(6)
20 ps
1 ns
(4)
(3)
1ps
(0)
tk+ T
Figure 3-29: After excitation, (1) the distribution of electrons and holes mimics the distribution of photons, (2) this distribution is spread out by carrier-carrier scattering, (3) - (5)
the optical and acoustic phonons are formed, taking energy from the excited distribution
of electrons and holes, and (6) finally thermal equilibrium within the bands and carrier
recommendation within bands starts to happen. Image from [46].
102
In a typical photovoltaic device, this process of cooling down to the band edge happens on
the order of picoseconds, as can be seen in Figure 3-29, and the process of extraction of the
carriers takes much longer. However, if there were some way to make them take the same
order of magnitude, we would be able to extract more energy from the photons with energy
greater than the bandgap of the material. This point is illustrated by Figure 3-30.
CB
g
er
Figure 3-30: The idea of "hot" carriers - electrons from higher energy photons were extracted
before that extra energy was dissipated as heat, the device would have a higher current.
Image form [86].
3.3.2
Direct and Indirect Bandgap Material
Along these lines, we wanted to investigate a cell that has both a direct and an indirect
band gap in hopes of combining the favorable properties of each. Direct band gap materials
have good absorption and therefore require less of the material to absorb all the light, which
also leads to shorter path lengths for electrons and holes to travel before exiting the cell to
do useful work. Indirect band gap materials have low radiative recombination rates, and
therefore longer lifetimes. If a solar cell could combine these two, is it possible to increase
the efficiency above the old limit?
Some materials, like SnS (see Figure 3-31), have a direct bandgap that is very close in energy
to the direct gap, so when absorbing through the direct gap and relaxing down to the indirect
gap state, there is not a significant loss of energy. In the best case, photons would excite
electrons and holes across the direct gap, the holes would quickly jump to the indirect gap
state and therefore be protected against recombination, thus increasing the lifetime of the
cell.
103
4
0
C.)
0
0
-2
xr
Y
z
r
b ,
c
Figure 3-31: On the left is the band structure for SnS, whose crystal structure is shown on
the right. Yellow spheres are sulfur and grey are tin. Notice how the direct band gap is only
slightly larger than the indirect band gap. Image from [114].
Simple Model
We first want to try to do a calculation in the same style as Shockley and Queisser [94] (see
Section 1.1.2). Our model is represented by Figure 3-32.
S
CBM
R
--
-- Din direct Gap
- -
Direct Gap
0
Figure 3-32: Processes happening in a solar cell. G (yellow) is generation and depends on the
number of photons; R (red) is recombination, here we only consider radiative recombination;
U (dark green) is the phonon assisted tradition of a hole from the direct to the indirect state,
and D (dark purple) is the transition of a hole back from the indirect to the direct gap state.
We ignore absorption across the indirect state. We assume the Fermi level has split into
quasi-Fermi levels (blue dashed lines) that are flat across the device, and the dark blue and
light green levels indicate the energy at which we pull holes and electrons, respectively, out
of the device.
In this model, we have a direct and indirect gap. To simplify the model, we assume there is
only absorption and recombination between the direct gap and the conduction band. Holes
go between the direct and indirect band state with the aid of phonons. Figure 3-32 assumes
104
that these two populations are in thermal equilibrium, but we will start by writing out the
general equations.
We start with the total Generation which we write out as a constant that could be calculated
by integrating Equation 1.8 over the cell.
(3.2)
G = Gsun = AG - Gdark
Looking only at radiative recombination, we have Equation 1.9 rewritten to reflect the new
variables
Rrad =
Ro
(3.3)
nPd
noPd,o
We also need to write the rates of transition between the direct and indirect states.
U = UOf(Qs)[1 - f(6)]
(3.4)
D = Dof(Ei)[1 - f(6)]
(3.5)
Making the common assumption of very low hole populations, the [1 -
f(E)] terms drop out
and these equations can just be written as
U = UO Pd
(3.6)
D = Do
(3.7)
Pd,O
and
Pi,o
105
Solving the System of Equations
Charge conservation tells us
Iholes,direct + Iholes,indirect
=
-
Ielectrons
(3.8)
The time dependence of holes and electrons is
dn
= G-Rdt
I
(3.9)
dpd= G- R- Id- U+D
dt
dpi
-=
dt
U - D - It.
(3.10)
(3.11)
Under steady state,
dn
dt
dpd
dt
dpi
dt
0.
(3.12)
We can plug these zeros into Equations 3.10 and 3.11 to get
U - D - Iz = 0
I,= U - D
106
(3.13)
G-R-Id-U+D=O
G- RG- R-
-
Ij
=
0
(3.14)
I= 0.
I=G-R
I= G-R
I=N
Pd
noPd,o
Edirect)/kT]
exp[-(ECBM - Ef,right) /kT]Pd exp[-(Ef,1eft N exp[-(ECBM - Ef )/kTPd exp [-(ef - Edirect)/kT]
exp[-(ECBM -
Edirect)/T] expl-(Ef,left - Ef,right)/kT]
exp[-(ECBM - Edirect)/kT]
I = (AG + Ro) - Ro exp[-(Ef,eft
-
Ef,right)/kT]
I = AG + Ro(1 - eqV/kT)
(3.15)
This clearly has nothing to do with an indirect gap, and is the same diode equation that
we would get from solving system of equations for a direct bandgap material. This is not a
surprising result, since the assumption of thermal equilibrium between the direct and indirect
states means that this functions the same way any direct-gap solar cell would.
There are a few assumptions that we have made in this very simple picture, such as ignoring
forms of recombination besides radiative recombination.
If we were to add that in, just
like in the Shockley-Quiesser case, the total recombination would just be off by a constant,
indicating what fraction of the recombination is due to radiative recombination, but it would
not change the conclusion. We also assumed flat bands all the way across the cell and perfect
electron- and hole- accepting layers. This again would change the exact result and lower the
voltage that we could extract, but would still show no additional benefit to using an indirect
and direct band gap material.
So from this analysis, we have shown that introduction of an indirect band into a direct
band gap material does not improve the overall efficiency as long as those two states are
107
allowed to reach thermal equilibrium. The next step is to examine what happens when these
two states are no in thermal equilibrium, but that would require very short lifetimes in the
cell or suppression of the phonons that assist transitions between the two states.
108
Chapter 4
Conclusion and Outlook
The world is currently using about 16 TW of power and this number is only growing. We
are already experiencing extremes in climate, and melting ice caps; we need to look to
renewable energy sources. The sun seems to be the most promising resource available to
us. Although solar thermal power for heat generation is currently being used in much of the
world, photovoltaics only provide about 1% of the world's electricity production. There is
therefore much room for improvement of photovoltaics for electricity generation.
In order to expand solar to electricity production, we need to find new materials and construct new devices.
These materials would ideally be low-cost, require small amounts of
energy to produce, and be earth abundant and non-toxic. Once we have promising materials, we will need to construct a device with them that gets the highest possible efficiency.
There are many ways to address this problem; we can look as broadly as the looking to
change overall device structure or as narrowly as attempting to understand and improve the
electronic properties of individual parts of the device.
Efficiency gains involve minimizing loss. Energy is lost throughout in different ways through
the device - photons with energy below the bandgap fail to be absorbed, photons with with
energy much higher than the band gap lose that excess energy to heat, excited carriers
undergo various forms of recombination throughout the semiconductor region, and other
losses occur at the interface with the contacts. It is this last piece, the loss of energy that
occurs at the interface of a semiconductor and metal, that we find is often not addressed,
109
and so we aimed to fill this gap.
These interfaces host states within the band gap that
allow recombination. Depending on energy alignment, they might also provide barriers to
electrons or holes exiting the device.
In this work, we dissected the different complications that occur at an interface.
In the
CdSe study, we found that not all surface states serve to pin the Fermi energy.
In our
organic-metal work, we explored the complexity and challenges of modeling these systems.
For example, we confirmed that aromatic compounds indeed have stronger interactions with
metal surfaces, but this may lead to the geometry changing as a result of the interaction, as
in the case of anthracene on Mg and others. We also found that molecules that are not rigid
are strongly affected by their neighboring molecules, such as Alq 3 , which relaxed in the two
monolayer case to have a different inherent dipole than the molecule in vacuum. We found
that surface roughness will have an effect on molecules that more strongly bind to metal
surfaces.
Despite all these challenges, we were able to dissect the pieces of interface energy alignment
into their various contributions. The dipole at the interface was decomposed into its contribution from the charge transfer and the contribution from the compression of the metal
wave function tail, and found that the latter was larger for metals with larger workfunctions.
We found that the interface dipole sometimes surprisingly does not depend strongly on the
metal-to-molecule distance, whereas, in other cases it does. We also were able to predict the
image charge stabilization of electrons or holes localized on the molecules at the interface.
Taken all together, we were able to construct band line-up diagrams that better describe
the electronic characteristics of the interface.
It is our hope that this work is used to improve predictions of future devices, thus better
guiding the search for new viable solar cells. Currently the methods used to predict interface
energy alignment are inadequate to predict the behavior.
This work so far only served
to better understand the metal-semiconductor interfaces.
In a real device, there will be
the contact of the metal contact on two sides, but there are often two or more layers of
semiconductors or insulators serving as absorbers and carrier-selective layers. To be able to
fully construct a band line-up diagram with predictive power, these other interfaces need to
be better characterized as well.
110
Taking this to the next level, we would like to see the predictive powers continue to improve
with an even more nuanced understanding the the interface behavior. This work is just an
introduction to the variety of effects that are possible, but a more systematic classification of
different types of organic molecules and inorganic semiconductors is needed. We hope that
with a better understanding of semiconductors, we may predict - without DFT - which
surface states will and will not pin the Fermi energy, how rigid a molecule will be, how
strongly the surface roughness will affect the electronic properties, and overall band line-up
diagrams.
With better predictive power, it will become possible to do high throughput
screening of materials for better devices.
In this way, we could bring new photovoltaic
devices to market faster.
Finally, this work aimed to address a potential new idea to go beyond the Shockley-Quiesser
efficiency limit. While this idea fails in the case of quasi-equilibrium, it is possible that there
is a place for it to work out of equilibrium. If not, we believe that taking a step back to
observe the field of solar cell design is a useful exercise. The next big idea for going beyond
Shockley-Quiesser is out there just waiting to be discovered, and exploring failed ideas to
see why they failed is just as important as understanding why others work.
While it has come a long way, we see there is much work left to be done in the field of
photovoltaics. This is an exciting challenge with interesting physics and materials questions
that are worth studying for their own merit. Additionally, they are important questions
to be answered for the successful deployment of solar cell technology that is needed. It is
certainly an exciting time to be working in the field of photovoltaics.
111
Chapter 5
Acknowledgements
There are so many people who have contributed to this thesis. Jeff has been wonderful to
work with, allowing me a lot of freedom to explore what I found interesting and always being
supportive. He has gathered around him an amazing group of people, and I cannot think
of a group with whom I would rather have spent this period of my life. I especially need
to thank Alexie Kolpak and David Strubbe for discussions about this work and Alexie in
particular has acted as a mentor and friend throughout my time at MIT. The SnS project
was inspired by a conversation with my friend from high school and fellow MIT graduate
student, Katy Hartman. Niall Mangan helped me learn the basics of solar cell operation
and discussed the efficiency calculation; she always allowed me to ask stupid questions that
really forced me to confront what I did not understand.
In the physics department, Bo Zhen has always been a good friend and was invaluable
in helping me prepare for Part III and my thesis defense.
Cathy Modica was incredibly
supportive during tough times and always stood behind me with the other wonderful people
in the physics office always lending their support as well. Janet Conrad helped me through
the tough period of changing advisors, and she along with Kazu Terao and Peter Fisher
helped me prepare for my Part II exam. Janet Conrad, Andy Neely and Bob Redwine have
been wonderful to work with in 8.02, and I have learned to love teaching while woking with
them.
Finally, my family and friends are the ones who deserve the most credit for making my time
113
at MIT as wonderful as it has been. My husband, Andrew Cheng, and my friends, Jenny
Barry, Ani Nguyen, Yusra Naqvi, Alev Atalay, Saurav Dhital, Kei Fukuda, my roommates,
Apratim Sahay and Liz Sefton, and my mother, Betty Ketcham, and father, Steve Tomasik,
are incredibly caring and loyal people who always manage to brighten any day.
Part of my funding came from the NSF GRFP.
114
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