AN ABSTRACT OF THE DISSERTATION OF
Jason Francis for the degree of Doctor of Philosophy in Physics presented on
May 30, 2013.
Title: Growth and Characterization of the p-type Semiconductors SnS
and BiCuOSe
Abstract approved:
Janet Tate
BiCuOSe and SnS are layered, moderate band gap (ǫG ≈ 1 eV) semiconductors
that exhibit intrinsic p type conductivity. Doping of BiCuOSe with Ca results
in a slight expansion of the lattice and an increase of the hole concentration
from 1018 cm−3 to greater than 1020 cm−3 . The large carrier density in undoped
films is the result of copper vacancies. Mobility is unaffected by doping, remaining constant at 1.5 cm2 V−1 s−1 in both undoped and doped films, because
the Bi-O layers serve as the source of carriers, while transport occurs within
the Cu-Se layers. Bi possesses a 6s2 lone pair that was expected to hybridize
with the oxygen p states at the top of the valence band, resulting in high hole
mobility as compared to similar materials such as LaCuOSe, which lack this
lone pair. However, both LaCuOSe and BiCuOSe have similar hole mobility.
X-ray absorption and emission spectroscopy, combined with density functional
theory calculations, reveal that the Bi 6s states contribute deep within the valence band, forming bonding and anti-bonding states with O 2p at 11 eV and
3 eV below the valence band maximum, respectively. Hence, the Bi lone pair
does not contribute at the top of the valence band and does not enhance the
hole mobility. The Bi 6p states contribute at the bottom of the conduction
band, resulting in a smaller band gap for BiCuOSe than LaCuOSe (1 eV vs. 3
eV).
SnS is a potential photovoltaic absorber composed of weakly coupled layers
stacked along the long axis. This weak coupling results in the formation of
strongly oriented films on amorphous substrates. The optical band gap is
1.2 eV, in agreement with GW calculations. Absorption reaches 105 cm−1
within 0.5 eV of the band gap. The p type conduction arises from energetically
favorable tin vacancies. Variation of growth conditions yields carrier densities
of 1014 – 1016 cm−3 and hole mobility of 7 – 15 cm2 V−1 s−1 . SnS was alloyed with
rocksalt CaS, which was predicted to form a rocksalt structure when the calcium
content is increased past 18%. Films of Sn1−x Cax S with x from 0.4 to 0.9 adopt
the rocksalt structure with a band gap of 1.1-1.3 eV, with absorption greater
than 105 cm−1 within about 0.7 eV of the band gap. The lattice contracts as the
calcium content of the films is increased, reaching 5.7 Å when x = 0.93. Films
are highly insulating, but Seebeck measurements do indicate p type conduction.
c Copyright by Jason Francis
May 30, 2013
All Rights Reserved
Growth and Characterization of the p-type Semiconductors SnS and BiCuOSe
by
Jason Francis
A DISSERTATION
submitted to
Oregon State University
in partial fulfillment of
the requirements for the
degree of
Doctor of Philosophy
Presented May 30, 2013
Commencement June 2013
Doctor of Philosophy dissertation of Jason Francis presented on May 30, 2013.
APPROVED:
Major Professor, representing Physics
Chair of the Department of Physics
Dean of the Graduate School
I understand that my dissertation will become part of the permanent collection
of Oregon State University libraries. My signature below authorizes release of
my dissertation to any reader upon request.
Jason Francis, Author
ACKNOWLEDGEMENTS
The work presented here did not happen in a vacuum – well, strictly speaking, much of it did happen at ultra high vacuum – and would not have been
possible without the contributions of many others. I am foremost indebted to
my adviser, Janet Tate. Throughout my time at OSU, Janet was always eager
to listen, to offer guidance, and to help push experiments forward, all while
doing her best to make sure that I was ultimately responsible for driving the
research.
For the BiCuOSe work, I must acknowledge the previous work by Andriy
Zakutayev and Paul Newhouse, who established reasonable growth conditions
long before my arrival. Their work made it possible to get this project off the
ground quickly. Andrew Preston at the National Synchrotron Light Source was
very helpful when I first arrived, showing me around the X1B beamline and
getting me started taking measurements.
For the SnS work, I am again indebted to Andriy Zakutayev for his preliminary work with the material towards the end of his time at OSU.
Brady Gibbons was very helpful with x-ray measurements and with ellipsometry. Ram Ravichandran was eager to do early ellipsometry measurements
and help out with modeling. Chris Reidy invested considerable time doing electron microscopy of SnS and BiCuOSe. John Donovan and Julie Barkman at
CAMCOR were helpful in carrying out the electron microprobe measurements
and with analyzing and interpreting the data. Peter Eschbach was instrumental
in the TEM diffraction measurements of Sn1−x Cax S.
Everyone in the lab contributed to this work in some manner, whether it was
performing measurements or helping put the vacuum chamber back together.
The machine shop and electronics shop staff, particularly Mark Warner, provided invaluable assistance along the way.
CONTRIBUTION OF AUTHORS
The targets used for the BiCuOSe growths detailed in Chapter 2 and used
for the films in chapter 3 were prepared by Vorranutch Jieratum in Doug Keszler’s group in Chemistry..
In chapter 3, the LaCuOSe thin films were prepared by Hosono’s group at
Tokyo Institute of Technology. The x-ray absorption and emission measurements were carried out at National Synchrotron Light Source in collaboration
with Louis Piper’s group at Binghamton University.
In chapter 4, the theoretical results presented were performed by Julien
Vidal, Andriy Zakutayev, and Stephan Lany at National Renewable Energy
Lab.
In chapter 5, the theoretical work was performed at National Renewable Energy Laboratory by Stephan Lany and Julien Vidal. The targets were prepared
by Robert Kokenyesi and Jaeseok Heo from Doug Keszler’s group.
TABLE OF CONTENTS
Page
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Thin Film Photovoltaics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Electronic and Optical Properties of BiCuOSe:Ca . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3.1 Film Structure and Composition . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3.2 Transport Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3.3 Optical Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19
2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3 Soft X-Ray Spectroscopy of BiCuOSe and LaCuOSe . . . . . . . . . . . . . . . . . . . . 26
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2 Modified Lone Pairs Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2.1 Classical Lone Pairs Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2.2 Revised Lone Pairs Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.3 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.4.1 Electronic Structure of BiCuOSe and LaCuOSe. . . . . . . . . .31
TABLE OF CONTENTS (Continued)
Page
3.4.2 Ca-doped BiCuOSe and Mg-doped LaCuOSe . . . . . . . . . . . . 39
3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4 Electronic and Optical Properties of SnS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .48
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.2 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.3.1 Structural Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.3.2 Transport Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.3.3 Optical Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58
4.3.4 Comparison with Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5 (SnCa)S Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.2 Predicted Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.3 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.4 Experimental Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
TABLE OF CONTENTS (Continued)
Page
6.1 BiCuOSe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
6.2 Tin Sulfide and Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
A Pulsed Laser Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
A.2 Growth Parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .87
A.2.1 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
A.2.2 Fluence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
A.2.3 Pulse Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
A.2.4 Process Gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
B X Ray Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
B.1 Transition Rates and Selection Rules . . . . . . . . . . . . . . . . . . . . . 93
B.2 Decay Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
C Spectroscopic Ellipsometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
C.1 Ellipsometry Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
C.2 Dielectric Modeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .102
D Calculated Electron Diffraction Patterns . . . . . . . . . . . . . . . . . . . . . . . . . 106
D.1 Orthorhombic SnS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
D.2 Rocksalt (SnCa)S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
LIST OF FIGURES
Figure
Page
1.1 AM 1.5 solar spectrum with silicon direct (blue) and
indirect (orange) absorption regions indicated . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 A pn junction in the dark (top) and under illumination (bottom).
The p type material is on the right. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1 BiCuOSe crystal structure showing stacking along c axis.. . . . . . . . . . . . . .10
2.2 X-ray diffraction pattern of BiCuOSe grown on (a) h001i SrTiO3
and (b) h001i MgO. Substrate reflections are labeled in blue.
* denotes impurity peaks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 Rocking curve around the (003) peak of BiCuOSe on MgO . . . . . . . . . . . . 14
2.4 Burgers vector for an edge dislocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.5 SEM image of BiCuOSe thin film deposited on h100i MgO . . . . . . . . . . . . 15
2.6 Expansion of the BiCuOSe lattice as calcium is substituted on the
bismuth site. Asterisk indicates that calcium content is estimated
from measured content in other films.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16
2.7 Calcium content of films grown from 6% Ca-doped target under
different laser fluences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.8 Carrier density of doped BiCuOSe films (black - measured, red
- calculated) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.9 Conductivity and Seebeck coefficient of BiCuOSe films . . . . . . . . . . . . . . . . 19
2.10 Transmission spectra of undoped and doped BiCuOSe thin films
on MgO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.11 Transmission spectrum of BiCuOSe single crystal . . . . . . . . . . . . . . . . . . . . 21
3.1 Schematic of revised lone pairs model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
LIST OF FIGURES (Continued)
Figure
Page
3.2 Calculated density of states for BiCuOSe. The major orbital
contributions are labeled. Asterisks indicate unoccupied orbitals. . . . . . . 31
3.3 Calculated density of states for LaCuOSe. The major orbital
contributions are labeled. Asterisks indicate unoccupied orbitals. . . . . . . 32
3.4 BiCuOSe O K-edge XES and XAS spectra. Inset: The contribution
of O 2p below the main peak in the valence band
XES spectrum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.5 LaCuOSe O K-edge XES and XAS spectra. Inset: Oxygen 2p
emission spectrum below the main peak in the valence band . . . . . . . . . . . 35
3.6 Calculated oxygen K edge emission spectra for LaCuOSe and
BiCuOSe. A peak corresponding to a Bi 6s – O 2p bonding state
is observed at 11 eV below the valence band maximum. . . . . . . . . . . . . . . . . 36
3.7 BiCuOSe emission spectrum and broadened DFT calculation of
the partial density of states, showing the existence of bonding
(B) and anti-bonding (AB) states in the valence band. . . . . . . . . . . . . . . . . 37
3.8 Bi s and p partial density of states within the valence band. The
majority of the weight of the p states is at lower energy than
the s states. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.9 LaCuOSe emission spectrum and calculated density of states. Weak
bonding and antibonding states are observed between the La and
O p states. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.10 Measured absorption spectrum and Gauss-broadened calculated
density of states for BiCuOSe, showing that the O 2p density of
states reflects the cation density of states. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.11 Measured absorption spectrum and Gauss-broadened calculated
density of states for LaCuOSe, showing that the O 2p density of
states reflects the cation density of states. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
LIST OF FIGURES (Continued)
Figure
Page
3.12 XAS scans of the Ca L3,2 edge in undoped and 6% Ca-doped
BiCuOSe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.13 O K edge x ray emission of doped and undoped BiCuOSe films. . . . . . 44
3.14 Cu L3,2 emission spectra for undoped and Mg-doped LaCuOSe
thin films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.1 Layered orthorhombic structure of SnS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.2 Diffraction pattern of target used for SnS depositions . . . . . . . . . . . . . . . . . 51
4.3 θ-2θ scan of SnS film deposited on fused silica. Only (0k0) peaks
are present . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.4 θ-2θ scans of SnS (131) peak, with sample tilted for
(010) orientation and (111) orientation (inset).. . . . . . . . . . . . . . . . . . . . . . . . .54
4.5 SnS x-ray reflectivity pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.6 TEM cross section of SnS thin film deposited on fused silica. . . . . . . . . . .56
4.7 Electrical transport properties of SnS thin films grown on fused
silica . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.8 Optical absorption spectrum for SnS thin films deposited on
fused silica . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.9 Refractive index and extinction coefficient for SnS thin films on
fused silica.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60
4.10 Experimental (solid, gray) and calculated absorption with (solid,
black) and without (dashed, black) excitonic effects included . . . . . . . . . 62
4.11 Calculated formation enthalpies for SnS under tin-rich and sulfurrich growth conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
LIST OF FIGURES (Continued)
Figure
Page
4.12 Experimental (squares) carrier densities for SnS thin films and
calculated (solid curves) carrier densities under tin and sulfurrich growth conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.1 Formation energy for Sn1−x Cax S for rocksalt (SG 225) and
orthorhombic (SG 62) structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.2 Calculated absorption spectra for Sn1−x Cax S . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.3 X ray diffraction patterns powder removed from (SnCa)S targets . . . . . . 71
5.4 Calcium content of (SnCa)S films grown at different temperatures . . . . . 72
5.5 Glancing incidence x ray diffraction of (SnCa)S deposited on thermal
oxide silicon. Asterisks denote substrate reflections. . . . . . . . . . . . . . . . . . . . . 73
5.6 X ray diffraction of the (002) peak of Sn1−x Cax S thin films
with different compositions. The numbers on the plot indicate x. . . . . . . 75
5.7 Lattice parameter of Sn1−x Cax S films as a function of calcium
content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.8 Electron diffraction pattern of SnCaS thin film looking along the
h100i zone axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.9 Electron diffraction pattern of SnCaS thin film looking along the
h011i zone axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.10 Absorption spectra of Sn1−x Cax S thin films deposited on fused
silica. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .78
B.1 Energy spectrum of x-rays emitted from a synchrotron . . . . . . . . . . . . . . . 93
B.2 Schematic of three basic x-ray spectroscopy techniques. (a) XES,
(b) XAS, (c) XPS. In XAS and XES, a core hole is created and the
decay products measured. In XPS, the ejected core electron itself is
measured. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
LIST OF FIGURES (Continued)
Figure
Page
B.3 1s2p2p Auger decay process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
B.4 Percentage of decay via x ray fluorescence as a function of binding
energy. Figure taken from [3] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
C.1 Polarization ellipse. The position on the ellipse gives the s and p
components of the electric field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
C.2 Schematic of spectroscopic ellipsometry experimental setup . . . . . . . . . . 102
D.1 Electron diffraction pattern of orthorhombic SnS viewed along the
h001i zone axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
D.2 Electron diffraction pattern of orthorhombic SnS viewed along the
h010i zone axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
D.3 Electron diffraction pattern of orthorhombic SnS viewed along the
h100i zone axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
D.4 Electron diffraction pattern of orthorhombic SnS viewed along the
h111i zone axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
D.5 Electron diffraction pattern of orthorhombic SnS viewed along the
h011i zone axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
D.6 Electron diffraction pattern of orthorhombic SnS viewed along the
h101i zone axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
D.7 Electron diffraction pattern of orthorhombic SnS viewed along the
h110i zone axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
D.8 Electron diffraction pattern of rocksalt (SnCa)S viewed along the
h001i zone axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
D.9 Electron diffraction pattern of rocksalt (SnCa)S viewed along the
h011i zone axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
LIST OF FIGURES (Continued)
Figure
Page
D.10 Electron diffraction pattern of rocksalt (SnCa)S viewed along the
h111i zone axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
LIST OF TABLES
Table
Page
2.1 Stoichiometry of BiCuOSe:Ca Thin Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.1 X ray binding energies of Bi, La, Cu, O, Se, and Ca. . . . . . . . . . . . . . . . . . . 27
4.1 Stoichiometry analysis of SnS thin films grown under different
conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.1 Calculated peak positions and intensities for rocksalt Sn0.38 Ca0.62 S
and orthorhombic SnS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
1 — Introduction
1.1 — Overview
Work on two moderate gap (EG ≈ 1 eV) p-type semiconductors, BiCuOSe and
SnS, is presented. Interest in these materials sprang out of past work in the
group and within the materials community on transparent p-type conductors
suitable for use in transparent electronics and as window layers in thin film
photovoltaic devices. Such materials are of important technological interest
because while there are many suitable transparent n-type conducting oxides
such as In2 O3 :Sn and SnO2 :F, transparent p-type materials have remained elusive. Interest in such materials evolved into investigations of moderate gap
p-type semiconductors that may be of technological interest.
SnS is an indirect material with a large absorption coefficient (> 105 cm−1 ),
appropriate band gap for solar absorption (1.16 eV), and strong onset of absorption, reaching 105 cm−1 within half an electron volt of the gap. BiCuOSe
is a somewhat smaller band gap ( 0.9 eV) material whose electronic properties
are of considerable interest, especially as compared to the transparent p-type
conductor LaCuOSe, which shares the same crystal structure. BiCuOSe may
also be useful as a thin film photovoltaic material, particularly if it can be alloyed with another, wider gap material such an LaCuOSe in order to increase
the band gap. However, the primary interest with BiCuOSe is in understand-
2
ing the reason why it possesses a smaller optical gap than, but nearly the
same electrical properties as LaCuOSe. Some of the properties of BiCuOSe
may also translate to its zero-gap telluride analog, which may be useful as a
thermoelectric material due to its quasi-two dimensional structure.
1.2 — Thin Film Photovoltaics
Currently, most commercial photovoltaic devices are based on either crystalline
or amorphous silicon technology. This is rather disconcerting, as silicon is quite
the poor absorber since it is an indirect material with a fairly low absorption
coefficient of around 104 cm−1 . The direct transition does not occur until
3.4 eV, so virtually the entirely solar spectrum must be absorbed via indirect
means, as shown in Figure 1.1 [1]. This necessitates that photovoltaic devices
have an active layer hundreds of microns thick. This, in turn, requires high
quality material so that carriers can diffuse out of the absorber layer before
recombining. Despite these drawbacks, silicon is still an acceptable absorber
material because it is well developed and very high quality material can be
prepared with carrier lifetimes of order 1 ms at room temperature [2].
By using materials which absorb strongly and have a suitable band gap,
it is possible to drastically reduce the amount of material needed to make a
photovoltaic device and relax some of the requirements on the carrier transport properties. For example, a material with an absorption coefficient of
1 × 105 cm−1 will absorb 95% of incident light within 300 nm. Absorption of
that same percentage of incident light would require 3 µm of material with an
absorption coefficient of 104 cm−1 .
A photovoltaic cell is, in essence, merely a pn junction. Analysis of a pn
Irradiance (W/m2 nm)
3
AM 1.5
2
Indirect
1
Direct
0
500
1000
Wavelength (nm)
2000
3000
Figure 1.1: AM 1.5 solar spectrum with silicon direct (blue) and indirect (orange) absorption regions indicated
junction leads to some general design principles for thin film photovoltaics.1
A simple homojunction is depicted in Figure 1.2. Under no illumination, the
system is in equilibrium and the Fermi level is the same across the interface.
The alignment of the Fermi level across the interface lowers the vacuum level
in the n type material, resulting in a built-in voltage Vbi across the junction.
This built-in bias is necessary in order to separate charge carriers. Under
illumination, carriers are excited and electrons build up on the n type side,
while holes build up on the p type side. This splitting of the Fermi level results
in an open circuit voltage
VOC =
Ef,n − Ef,p
q
(1.1)
. The open circuit voltage thus is limited by the band gap of the material for
1
For a much more detailed analysis of solar cells, see [3]
4
Figure 1.2: A pn junction in the dark (top) and under illumination (bottom).
The p type material is on the right.
a homojunction. The short circuit current is given roughly by
JSC = qG(Ln + Lp )
(1.2)
where q is charge, G is the carrier generation rate, and Ln and Lp are the diffusion lengths for electrons and holes. The generation rate G can be obtained by
differentiating Beer’s law I = I0 e−αx and assuming that every photon absorbed
results in the generation of an electron-hole pair.
G = αΦ0 e−αx
(1.3)
where Φ0 is the number of photons per unit area per unit time incident on the
surface.
The solar cell efficiency is given by
η = FF
JSC VOC
PS
(1.4)
5
where F F is the fill factor which describes the sharpness of the J-V curve and
PS is the incident power.
Using this, we can arrive some general design principles for solar cell absorber materials. In order to optimize the open circuit voltage, we need a
material with a large band gap. However, as the band gap is increased, the
short circuit current will decrease as fewer photons are absorbed and thus fewer
carriers are generated. The optimal gap, calculated by Shockley and Queisser,
is 1.34 eV, with a maximum conversion efficiency of 33.7% [4]. It should be
noted that the optimal gap obtained by Shockley and Queisser assumes a step
function absorption. That is, all the photons below the gap get through without
being absorbed, and all the photons above the gap get absorbed. In practice
this is not true and the absorption typically turns on to some maximum value
within about half an eV of the band gap. Materials with slower absorption
onsets exhibit notably lower efficiencies than those with rapid onsets [5]. High
mobility is needed so that photo-generated carriers can be extracted before recombining, so the material should have a low carrier density – in practice this
often means using a pin structure, where the absorption takes place within the
intrinsic layer.
Current thin film technologies such as CdTe and CuInGaSe2 (CIGS) meet
these requirements. CdTe has a band gap of 1.44 eV and a room temperature
mobility of about 70 cm2 V−1 s−1 [6]. The absorption coefficient is in excess of
105 cm−1 within about 0.5 eV of the gap. [7] [8][9]. CIGS has a tunable direct
band gap of 1.0 - 1.7 eV, depending on the ratio of In to Ga and, like CdTe,
reaches absorption in excess of 105 cm−1 within about half an electron-volt of
the gap [10][5].
While CdTe and CIGS are suitable purely from a materials properties per-
6
spective, both have serious drawbacks that may limit their commercial penetration. CdTe is made from elements that are toxic and not earth abundant.
CIGS has a complex stoichiometry that makes manufacture more difficult, and
may have cost issues due to the use of indium and gallium. What is needed
are materials made from earth-abundant elements which possess the materials
properties needed for efficient solar cells.
7
Bibliography
[1] R Soref and B Bennett. Electrooptical effects in silicon. IEEE Journal of
Quantum Electronics, 23(1):123–129, 1987.
[2] Rolf Häcker and Andreas Hangleiter. Intrinsic upper limits of the carrier
lifetime in silicon. Journal of Applied Physics, 75(11):7570, 1994.
[3] J Nelson. The Physics of Solar Cells. Imperial College Press, London,
2003.
[4] William Shockley and Hans J Queisser. Detailed Balance Limit of Efficiency of p-n Junction Solar Cells. Journal of Applied Physics, 32(3):510,
1961.
[5] Liping Yu, Robert S Kokenyesi, Douglas A Keszler, and Alex Zunger.
Inverse Design of High Absorption Thin-Film Photovoltaic Materials. Advanced Energy Materials, 3(1):43–48, August 2012.
[6] I Turkevych, R Grill, J Franc, E Belas, P H schl, and P Moravec. Hightemperature electron and hole mobility in CdTe. Semiconductor Science
And Technology, 17(10):1064–1066, September 2002.
[7] Sadao Adachi, Toshifumi Kimura, and Norihiro Suzuki. Optical properties of CdTe: Experiment and modeling. Journal of Applied Physics,
74(5):3435, 1993.
[8] Kim Mitchell, Alan L Fahrenbruch, and Richard H Bube. Photovoltaic
determination of optical-absorption coefficient in CdTe. Journal of Applied
Physics, 48(2):829–830, 1977.
[9] T H Myers. Optical properties of polycrystalline CdTe films. Journal of
Applied Physics, 52(6):4231, 1981.
[10] T Tinoco, C Rincón, M Quintero, and G Sánchez Pérez. Phase Diagram
and Optical Energy Gaps for CuInyGa1ySe2 Alloys. physica status solidi
(a), 124(2):427–434, April 1991.
8
2 — Electronic and Optical Properties of BiCuOSe:Ca
Thin films of the moderate gap p-type semiconductor Bi1−x Cax CuOSe (x =
(0 − 0.1)) have been prepared on MgO and SrTiO3 single crystal substrates by
pulsed laser deposition. X ray diffraction indicates that the films are strongly
oriented and well crystallized. All films exhibit p type conduction. Undoped
films have a carrier density of 7 × 1018 cm−3 as the result of copper vacancies,
and the hole concentration rises to 5 × 1020 cm−3 in films with x = 0.1. The
mobility is not significantly impacted by the introduction of dopants into the
[Bi2 O2 ]2+ layers, remaining constant at 1.5 cm2 V−1 s−1 . An optical band gap
of about 1 eV was measured, as compared to 0.84 eV in single crystals.
2.1 — Introduction
BiCuOSe is a tetragonal, layered quaternary oxychalcogenide composed of alternating [Bi2 O2 ]2+ and [Cu2 Se2 ]2− layers stacked along the c axis (space group
p4/nmm) (Figure 2.1). It belongs to a diverse family of copper-containing
layered compounds that exhibit behaviors that are of potential technological
interest. BaCuTeF, BaCuSeF, LaCuOS, and LaCuOSe possess large optical
band gaps and display p-type conduction, making them of interest in transparent electronics and as window layers in thin film photovoltaics.[1][2][3] The
narrow gap materials within this family, including BiCuOTe and BiCuOSe, may
prove to be useful thermoelectrics due to the quasi two-dimensional transport
9
within layers.
Interest in BiCuOSe sprang out of work on LaCuOS originated by Hosono
et al. in 2000, despite the bismuth compound being discovered considerably
earlier [4]. Sputtered thin films of LaCuOS:Sr demonstrated optical transmission in excess of 70% throughout the near infra-red and visible. The band
gap was determined to be 3.1 eV. Electrically, the films demonstrated p-type
conduction, but had fairly poor conductivity of 10−2 - 10−1 S/cm.[5]
This was followed by the reporting of LaCuOS1−x Sex powders, in which a
clear shift of the band gap from 3.1 eV for the sulfide to 2.8 eV for the selenide
was observed. [6] In 2003, epitaxial films of LaCuOS1−x Sex were reported. The
selenide displayed a mobility of up to 8.0 cm2 /Vs. Conductivities of 140 S/cm
were measured in Mg-doped (20%) LaCuOSe films.[7]
BiCuOSe powders were synthesized considerably earlier than LaCuOSe,
but attracted little attention at the time. The synthesis and crystal structure
of BiCuOSe was first reported in 1993 by Kholodkovskaya et al.[4] This was
followed by Rietveld analysis of the structure, along with reporting of the sulfide
analog.[8]
BiCuOSe garnered interest as a p-type semiconductor expected to have
high hole mobility resulting from the hybridization of the Bi 6s electrons with
the Ch p electrons at the valence band maximum [9]. However, the transport
properties of BiCuOSe are actually quite similar to the electronic properties of
LaCuOSe [10]. The details of the BiCuOSe electronic structure and the role of
the 6s2 lone pair electrons is explored in detail in the next chapter.
10
Figure 2.1: BiCuOSe crystal structure showing stacking along c axis.
2.2 — Experimental Details
Thin films of BiCuOSe:Ca were prepared by pulsed laser deposition on single
crystal h100i MgO and SrTiO3 . Epitaxial films of BiCuOSe (a = 3.93 Å) were
prepared on single crystal SrTiO3 (a = 3.905Å) – 0.64% mismatch – and MgO
(a = 4.216 Å) – 7% mismatch. Phase-pure targets prepared by Vorranutch
Jieratum in Doug Keszler’s group at OSU were ablated using a 5 eV KrF
pulsed excimer laser at a pulse rate of 7 Hz. The target-substrate distance was
fixed at 5.4 cm. Films were prepared at substrate temperatures of 450 - 550 ◦ C
under ultra high vacuum (base pressure 10−9 Torr, deposition pressure 10−8 –
10−7 Torr). Laser fluence was varied from 1 - 1.75 J/cm2 .
Stoichiometry analysis was performed using a Cameca SX 50 electron microprobe at accelerating voltages of 10, 15, and 20 kV. Magnesium, calcium,
11
oxygen, and copper Kα emission were measured, along with selenium Lα and
bismuth Mα . All films were coated in a 20 nm conductive carbon layer. Se, Cu,
and Bi metals were used as standards, along with diopside (MgCaSi2 O6 ), and
MgO. The resulting K ratios (unknown intensity / reference intensity) vs accelerating voltage were modeled in Strategem to obtain the film stoichiometry,
using known film thicknesses. Such modeling and measurements at various accelerating voltages are nececessary because an inhomogeneous volume is being
excited.
X-ray diffraction measurements were collected in 2θ − ω mode using the
parallel beam geometry to reduce peak position sensitivity to height misalignment (as compared to the Bragg-Brentano geometry) with Cu Kα radiation
using a Bruker D8 Discover x-ray diffractometer with a scintillation counter.
Electron micrographs were collected using an FEI Quanta 3D dual beam
scanning electron microscope. Films were coated with a Au/Pd layer prior to
imaging.
Electrical characterization was performed using a LakeShore Cryotronics
7504 Hall effect measurement system with pressed indium contacts in the van
der Pauw geometry, which gave Ohmic IV curves. Data was collected at magnetic fields of 1 – 2 Tesla. Room temperature Seebeck coefficients were obtained
using a custom made system.
2.3 — Results and Discussion
2.3.1
Film Structure and Composition
X-ray diffraction shows that films are highly oriented BiCuOSe when deposited
on both MgO and SrTiO3 , as shown in Figure 2.2. Films grown on MgO appear
12
(002)
(001)
(a)
(001)
(003)
(004)
(005)
(006)
*
(002)
*
ytisnetnI
(002)
(b)
(003)
(001)
(004)
(005)
(006)
(002)
10
20
30
40
50
60
70
2q
Figure 2.2: X-ray diffraction pattern of BiCuOSe grown on (a) h001i SrTiO3
and (b) h001i MgO. Substrate reflections are labeled in blue. * denotes impurity
peaks
phase pure, showing only the (00l) peaks of BiCuOSe and MgO. However, in the
films grown on SrTiO3 , the formation of an impurity phase occurred, showing
peaks at 27
◦
and 43.5◦ . The impurity phase could be readily identified, but
is likely a M − Ch binary. This happens despite the notably better lattice
matching with SrTiO3 .Visually, the films appear black, shiny, and smooth.
X ray rocking curves of the (003) peak of BiCuOSe grown on MgO were
used to characterize the quality of the film. The rocking curve has a full width
13
at half max of 0.95◦ , as shown in Figure 2.3, indicating that the films are
strongly oriented. An upper limit on the dislocation density can be established
by following the model proposed by Gay et al and setting the non-dislocation
broadening to zero [11][12].
ρd ≈
β2 − B2
9b2
(2.1)
where ρd is the defect density per square centimeter, β is the rocking curve
width, B is the rocking curve broadening due to other factors, and b is the
√
Burgers vector b = a h2 + k 2 + l2 /2, which is depicted in Figure 2.4 for an
edge dislocation. The omission of the other broadening effects can be justified because the grain size is too large to explain the observed broadening.
Substrate-film lattice mismatch also appears to play little role, as the peak
widths in films grown on both MgO and SrTiO3 are quite similar, despite the
much better lattice matching with SrTiO3 .
A typical dislocation defect would displace the lattice by a lattice constant,
so the Burgers vector can be approximated as simply the lattice parameter.
Applying this to the rocking curve of the (003) peak and using the 3.94 Å base as
the dislocation size, we get a dislocation density of 2×1010 cm−2 . This approach
is known to overestimate the dislocation density by as much as an order of
magnitude [13]. Taking this into consideration, this dislocation density upper
bound is not entirely unreasonable, being comparable to reported dislocation
densities in other materials such as GaN and YBa2 Cu3 O7−δ [14][15].
Scanning electron microscopy images of BiCuOSe on MgO show that the
underlying substrate lattice structure carries over into the films. BiCuOSe
growth on MgO is characterized by blocky segments with nearly right angle
14
Intensity
1.0
0.5
0.0
-4
-2
0
2
4
ω
Figure 2.3: Rocking curve around the (003) peak of BiCuOSe on MgO
Figure 2.4: Burgers vector for an edge dislocation
15
Figure 2.5: SEM image of BiCuOSe thin film deposited on h100i MgO
corners, with voids in between grains. The alignment of the edges matches
the structure of the underlying substrate. The grain size is roughly 250 nm,
although significantly larger grains are observed, as illustrated in Figure 2.5.
A slight expansion of the lattice by 0.6% is observed when calcium is substituted onto the bismuth site (x = 0.16), as shown in Figure 2.3.1, likely the
result of calcium’s slightly larger ionic radius (1.80 Å vs 1.60 Å) [16].
Electron probe microanalysis indicates that the films generally preserve the
target cation ratios faithfully, as shown in Table 2.1, although all films show
some preference for copper over bismuth. A significant deviation from 1:1 is
observed in the 3% film. This is likely the result of the lower melting point and
higher vapor pressure of bismuth (271.5 ◦ C) relative to copper (melting point
1085 ◦ C). The Cu:Se ratio is also preserved fairly well, although there is a significant copper deficiency. The observed copper deficiency relative to selenium
16
8.93
8.92
*
8.91
)( c
8.90
8.89
8.88
8.87
0
2
4
6
8
10
12
14
16
% Ca
Figure 2.6: Expansion of the BiCuOSe lattice as calcium is substituted on
the bismuth site. Asterisk indicates that calcium content is estimated from
measured content in other films.
Fluence (J/cm2 )
Target CaBi (%)
Film CaBi (%) Bi:Cu
Cu:Se
1
1
1
1
0
1
3
6
0.4
1.32
2.2
5.16
1.18
1.12
1.17
1.14
0.96
0.95
0.76
0.87
Table 2.1: Stoichiometry of BiCuOSe:Ca Thin Films
likely explains the fairly high carrier densities observed in nominally undoped
films. Copper vacancies have been identified as the source of p type conduction in other materials within the same family that have not been extrinsically
doped [17][18][19]. The thin film thickness (less than 100 nm) and presence of
an oxide substrate made quantification of the oxygen content unreliable.
As illustrated in Figure 2.7 for films grown from a 6% Ca-doped target,
the calcium content of the films depends strongly on laser fluence. At 1 J/cm2
fluence, the calcium content is only 7%. The calcium content rises rapidly to
17
Calcium Substitution
0.095
0.090
0.085
0.080
0.075
1.00
1.25
1.50
1.75
2
Fluence (J/cm )
Figure 2.7: Calcium content of films grown from 6% Ca-doped target under
different laser fluences
9% at 1.25 J/cm2 , before slowly rising to 9.5% at a fluence of 1.5 J/cm2 and
leveling off. Such dependence of the film stoichiometry on laser fluence has
been reported in other systems such as SrTiO3 and YBCO [20][21].
2.3.2
Transport Properties
BiCuOSe exhibits p-type conduction with hole concentrations in excess of 1018
cm−3 even in nominally undoped samples. A dramatic increase in carrier density is observed when films are doped with Ca (Figure 2.8), increasing by nearly
two full orders of magnitude. The conductivity also increases notably, while
the Seebeck coefficient decreases (Figure 2.9). Undoped BiCuOSe has a carrier
density of approximately 7 × 1018 cm−3 , conductivity of 1.7 S/cm, and Seebeck
coefficient of 240 µV/K. Films become increasingly conductive upon substitution of Ca2+ on the Bi3+ site. In 1.6% doped films, the carrier density rises to
1.4 × 1020 cm−3 , compared to a theoretical carrier density of 2.3 × 1020 cm−3 ,
18
-3
Hole Concentration (cm )
21
10
6
4
2
20
10
6
4
2
19
10
0
2
4
6
8
10
Calcium Substitution (%)
Figure 2.8: Carrier density of doped BiCuOSe films (black - measured, red calculated)
indicating to a doping efficiency of about 61%, assuming all holes come from
the substitution of calcium for bismuth. In films with 9.6% Ca content as measured by electron microprobe, a carrier density of 5 × 1020 cm−3 is observed,
with a doping efficiency of 36%.
While carrier density and conductivity increased notably, there is little
change in the mobility of doped films. Both undoped and 6% Ca-doped BiCuOSe films grown under the same conditions give a mobility of 1.5 cm2 V−1 s−1 .
The introduction of additional defects into the Bi-O layers has negligible impact on the transport properties because it is the Cu-Se layers that serve as
hole transport paths. The same observation was noted in LaCuOSe:Mg films,
in which the introduction of large numbers of defects into the metal oxide layers
did not impact the mobility.[3]
19
250
Conductivity (S/cm)
8
6
200
4
2
150
10
8
6
100
4
50
2
Seebeck Coefficient (µV/K)
100
1
0
2
4
6
8
Calcium Substitution (%)
Figure 2.9: Conductivity and Seebeck coefficient of BiCuOSe films
2.3.3
Optical Properties
Transmission measurements of BiCuOSe thin films reveal an optical band gap
of around 1 eV, as seen in Figure 2.10. The optical behavior of the 1% and 3%
nominally doped films is essentially the same as in the undoped case. Films
prepared from the 6% target show a smearing out of the band gap with a much
slower onset of absorption. For comparison to the bulk material, transmission
measurements of BiCuOSe single crystals indicate an optical band gap of 0.84
eV, determined from the minimum of the derivative of the transmission spectrum, as shown in Figure 2.11. This value is about 0.2 eV smaller than the
band gap observed for BiCuOSe thin films. This is likely due to the difficulty of
detecting the weak indirect absorption near the band gap when there is comparatively little material present, leading to an overestimation of the gap in
the thin films. Thin film interference near the band edge also introduces some
20
0.4
Undoped
1%
3%
noissimsnarT
0.3
6%
0.2
0.1
0.0
1
2
3
4
5
Energy (eV)
Figure 2.10: Transmission spectra of undoped and doped BiCuOSe thin films
on MgO
ambiguity into the thin film optical gap.
2.4 — Conclusions
Strongly oriented (001) BiCuOSe thin films are easily formed on MgO and
SrTiO3 at substrate temperatures above 450 ◦ C. Films grown on SrTiO3 show
the presence of a secondary phase, despite better lattice matching. Calcium
doping results in a large increase in carrier density to greater than 1020 cm−3 .
Despite the introduction of large numbers of defects into the [Bi2 O2 ]2+ , the
mobility is unchanged due to the preservation of the Cu-Se layers that act as
hole transport paths. BiCuOSe thin films show a band gap of about 1 eV, in
reasonable agreement with single crystal results that indicate a band gap of
0.84 eV.
21
0.3
0.2
Ed/Td
0.1
0.0
-0.1
-0.2
-0.3
-3
40x10
30
T
20
10
0
0.6
0.7
0.8
0.9
1.0
1.1
Energy (eV)
Figure 2.11: Transmission spectrum of BiCuOSe single crystal
1.2
22
23
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Masahiro Hirano, and Hideo Hosono. Heteroepitaxial growth of a wide-gap
p-type semiconductor, LaCuOS. Applied Physics Letters, 81(4):598–600,
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[3] Hidenori Hiramatsu, Kazushige Ueda, Hiromichi Ohta, Masahiro Hirano,
Toshio Kamiya, and Hideo Hosono. Wide gap p-type degenerate semiconductor: Mg-doped LaCuOSe. Thin Solid Films, 445(2):304–308, 2003.
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A B Popovkin. Materi. Sci. Forum, 693:133–136, 1993.
[5] K Ueda, S Inoue, S Hirose, H Kawazoe, and H Hosono. Transparent ptype semiconductor: LaCuOS layered oxysulfide. Applied Physics Letters,
77(17):2701–2703, 2000.
[6] K Ueda and H Hosono. Band gap engineering, band edge emission, and
p-type conductivity in wide-gap LaCuOSSe oxychalcogenides. Journal of
Applied Physics, 91:4768, 2002.
[7] Hidenori Hiramatsu, Kazushige Ueda, Hiromichi Ohta, Masahiro Hirano,
Toshio Kamiya, and Hideo Hosono. Degenerate p-type conductivity in
wide-gap LaCuOS1−x Sex (x=0–1) epitaxial films. Applied Physics Letters,
82(7):1048, 2003.
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BiOCuS: Syntheses and Crystal Structure. Journal of Solid State Chemistry, 112(1):189–191, September 1994.
[9] H Hiramatsu, H Yanagi, T Kamiya, K Ueda, M Hirano, and H Hosono.
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24
of Electronic Configures of M3+ Ions. Chemistry of Materials, 20:326–334,
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[10] A Zakutayev, P Newhouse, R Kykyneshi, and P Hersh. Pulsed laser deposition of BiCuOSe thin films. Applied Physics A, 2010.
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26
3 — Soft X-Ray Spectroscopy of BiCuOSe and LaCuOSe
Density functional theory calculations and x-ray emission and absorption spectroscopy have been used to determine the influence of the stereochemically
active Bi 6s lone pair on the electronic and optical properties of BiCuOSe,
which shows a distortion of the [Bi2 O2 ]2+ layers as compared to the [La2 O2 ]2+
layers in LaCuOSe. BiCuOSe shows a smaller band gap of approximately 0.9
eV, as compared to the 2.8 eV gap measured for the transparent p-type semiconductor LaCuOSe. Measurements of the electronic properties of BiCuOSe
and LaCuOSe show very similar p-type conduction, indicating that the Bi 6s
states contribute minimally to the top of the valence band, which is largely
derived from Cu 3d and Se 4p. The reduced band gap is determined to be the
result of an increased valence band maximum due to the presence of an antibonding Bi 6s - O 2p state, and a lowering of the conduction band minimum
arising from the unoccupied Bi 6p level.
3.1 — Introduction
LaCuOSe is a wide gap (εg ≈ 3 eV) p-type transparent semiconductor, while
BiCuOSe is a narrow-gap (εg ≈ 1 eV) p-type semiconductor. The difference in
the optical properties of these two materials is explained by the difference in
electronic configuration of the metal ion in the [M2 O2 ]2+ layers. While La3+ has
the closed shell configuration [Xe], Bi3+ has the pseudo-closed shell configura-
27
O
Cu
Bi
La
Se
Ca
K
543.1
8979.0
90524
39925
12685
4038.5
L1
41.6
1096.7
16388
6266
1652
438.4
L2
L3
M1
M2
M3
M4
M5
952.3
15711
5891
1474
349.7
932.7
13419
5483
1434
346.2
122.5
3999
1362
229.6
44.3
77.3
3696
1209
167
25.4
75.1
3177
1128
161
25.4
2688
853
56
2580
836
55
Table 3.1: X ray binding energies of Bi, La, Cu, O, Se, and Ca.
tion [Xe]4f 14 5d10 6s2 . While it was initially believed [1] that the presence of the
6s2 electrons would result in improved hole transport, the two materials actually have nearly identical transport properties, indicating that the 6s2 electrons
have very little role in determining the electrical properties of BiCuOSe.
Bulk-sensitive O K-edge x-ray emission spectroscopy (XES) and corresponding electron yield x-ray absorption spectroscopy (XAS) were used to determine the electronic structure of BiCuOSe and LaCuOSe, with the goal of
understanding the role of the Bi lone pair. Dipole selection rules dictate that
only the O 2p character is measured. It has been established that measurement
of the O 2p partial density of states (PDOS) is a valid way to determine the
hybridization of the metal s and O 2p states, for example in studies of Pb and
Bi oxides [2][3]. The oxygen p partial density of states in the conduction band
was determined from O K edge x ray absorption measurements.
Additionally, the Cu and Ca L edges and La M edges were measured to
determine the effect of calcium and magnesium doping on the electronic structure of BiCuOSe and LaCuOse. The binding energies for the relevant elements
are given in Table 3.1 [4].
28
3.2 — Modified Lone Pairs Model
The results that follow are consistent with the “revised lone pairs” model developed by Walsh and Payne [5]. This revision came about because the classical lone pairs model fails to explain the non-symmetric structure observed
in many metal oxides that is not observed in the chalcogenides. For example,
PbO adopts the litharge structure, while PbS is rocksalt [6][2]. SnO and the
tin monochalogenides also undergo structural changes as one works down the
column. SnO is litharge, while rocksalt is the stable phase of SnTe. The distortion of the crystal structure decreases with the progression from the oxide to
the telluride, as a result of the weakening interaction between the Sn 5s states
and the anion p states as the cation s states and anion p states become more
separated energetically [7].
3.2.1
Classical Lone Pairs Model
In the classical lone pairs model, there is on-site mixing of non-bonding s and
p states, with the anion playing no role [8]. These lone pairs do not take part
in bonding, but nonetheless may be stereochemically active. The most well
known example of such an effect is perhaps H2 O, in which the 104.5◦ bond
angle is explained by the presence of two lone pairs on the oxygen site.
3.2.2
Revised Lone Pairs Model
While the classical lone pairs model is sufficient to explain the observed structure of some materials, the model clearly does not adequately describe the
general behavior. The presence of s2 electrons in heavy metals such as lead
and tin are expected to result in stereochemically active lone pairs, and indeed
this is the case in the oxides. However, there is no observed distortion in either
29
AB
Mp
Ms
B
Op
Figure 3.1: Schematic of revised lone pairs model
SnTe or PbS. Clearly, on site mixing alone is not the complete explanation,
as this would predict that, for example, PbO and PbS have the same structure. The classical lone pair model of purely on-site mixing is not sufficient
to explain the observed stereochemical changes, or the lack thereof. Instead
of simple on-site mixing of the metal s and p states independent of the anion,
the cation s and p states mix via interactions with the anion p states. This is
depicted in Figure 3.1. The metal s state mixes with the anion p state, then
the resulting anti-bonding sp∗ state mixes with the metal p state. In order for
this to happen, the cation s and anion p states must be energetically similar
so that there is overlap between the s and p states [9].
We expect from the revised lone pairs model that the the Bi 6s states will
hybridize with the O 2p states to form bonding and antibonding states deep
within the valence band (of order 10 eV below the band edge) and within a
few eV of the valence band maximum, respectively. We also expect that the
Bi p partial density of states will contribute at energies just below the Bi 6s –
O 2p antibonding state and at the conduction band minimum, resulting in a
lowering of the CBM and reduced band gap.
30
3.3 — Experimental Details
Epitaxial films of LaCuOSe and BiCuOSe were prepared on h001i MgO single
crystal substrates by reactive solid phase epitaxy – which uses pulsed laser deposition – and pulsed laser deposition, respectively. The details of the BiCuOSe
growth are described in Chapter 2. Details of the reactive solid phase epitaxy
method and its application to LaCuOSe can be found elsewhere [10][11][12].
X-ray emission and absorption spectroscopy measurements were carried out
at the National Synchrotron Light Source, beamline X1B, using a spherical
grating monochromator and spherical grating spectrometer. Oxygen K edge
emission measurements were performed at near-normal incidence with a beam
energy above 540 eV. For the emission measurements, the resolution was 370
meV. Second order Zn metal Lα,β emission was used as an energy calibration.
The experiment geometry was optimized by tilting the films to minimize signal
from the MgO substrates and maximize signal from the films, as evidenced by
maximization of the Cu Lα,β second order emission signal from the films.
X-ray absorption measurements were performed by measuring the surfacesensitive total electron yield, which probes approximately the top 10 nm of
the film, via the detection of nanoamp scale current variations. Electrical
contact was made to the films using tantalum foil. The energy resolution for
the absorption measurements was 190 meV. Ti L3,2 absorption of TiO2 was
used to determine the energy scaling.
Density functional theory calculations were performed in WIEN2k using
the PBE-GGA exchange correlation functionals with a k mesh of 500 points
[13]. The partial density of states was broadened for comparison to the experimental results in order to approximate the instrumental resolution - 0.4
31
Bi total
)stinu .bra( setatS fo ytisneD
Cu total
Cu 3d
O total
Se total
Se 3s
Se 4p
Bi 6s
-15
-10
O 2p
-5
Cu 4s*
Bi 6p*
0
5
Binding Energy w.r.t. VBM
Figure 3.2: Calculated density of states for BiCuOSe. The major orbital contributions are labeled. Asterisks indicate unoccupied orbitals.
and 0.2 eV for the emission and absorption spectra, respectively. The calculated BiCuOSe and LaCuOSe partial density of states is given in Figures 3.2
and 3.3. Calculated x ray spectra were obtained using the XSPEC package.
Lorentzian broadening was applied to the calculated spectra in order to correct
for spectrometer resolution and lifetime broadening.
3.4 — Results
3.4.1
Electronic Structure of BiCuOSe and LaCuOSe
DFT calculations indicate band gaps of 0.3 eV and 1.5 eV for BiCuOSe and
LaCuOSe, respectively. The valence band maximum is of predominantly Cu d
and Se p character, with the bismuth and lanthanum contributing minimally.
32
La total
)stinu .bra( setatS fo ytisneD
Cu total
Cu 3d
O total
Se total
La 5p
Se 3s
O 2p
Se 4p
Cu 4s*
-15
-10
-5
0
5
Binding Energy w.r.t. VBM
Figure 3.3: Calculated density of states for LaCuOSe. The major orbital contributions are labeled. Asterisks indicate unoccupied orbitals.
33
The lack of contribution by the [M2 O2 ]2+ layers to the VBM results in similar
transport properties for both the lanthanum and bismuth compounds.
The band gap can be determined experimentally by examination of the
oxygen K edge x-ray emission and absorption spectra. The x-ray absorption
spectra were shifted to 0.6 eV higher energy than measured in order to account
for the lower photon energies measured in XAS as a result of the core hole final
state, which shifts the energy levels downward [14]. The oxygen 1s level (528.9
eV) was used as the reference for both LaCuOSe and BiCuOSe measurements.
The experimental spectra were fit to Gaussians and the second derivative of
the resulting functions was used to determine the band edge, with maxima in
the second derivative of the emission and absorption spectra being identified as
the valence band maximum and conduction band minimum, respectively. Using
the core-hole corrected absorption spectra, the band edge separations change
from 0.3 and 2.2 eV in the unshifted case to 0.9 and 2.8 eV for BiCuOSe and
LaCuOSe (Figures 3.4 and 3.5), respectively, bringing the measurements into
agreement with optical measurements of the band gap. Similar corrections for
the shift in the absorption spectrum arising from the final state core hole have
been applied to other materials such as BiVO4 [14]. It should be noted that
the exact shift applied to the absorption spectrum was arbitrary; however, the
same shift was applied to both BiCuOSe and LaCuOSe and shifts of order 1
eV have been applied to oxygen XAS data from other materials.
As can be seen by comparing the combined XES and XAS spectra in Figures
3.4 and 3.5, the smaller gap of BiCuOSe as compared to LaCuOSe is primarily
the result of a lowering of the conduction band minimum, with some raising of
the conduction band maximum contributing as well.
Focusing on the emission spectra and the density of states below the va-
34
ytisnetnI
x 10
512
516
520
dnoceS
evitavireD
510
515
520
525
530
535
540
545
Photon Energy (eV)
Figure 3.4: BiCuOSe O K-edge XES and XAS spectra. Inset: The contribution
of O 2p below the main peak in the valence band XES spectrum.
35
ytisnetnI
x 10
512
516
520
dnoceS
evitavireD
510
515
520
525
530
535
540
545
Photon Energy (eV)
Figure 3.5: LaCuOSe O K-edge XES and XAS spectra. Inset: Oxygen 2p
emission spectrum below the main peak in the valence band
36
LaCuOSe
BiCuOSe
ytisnetnI
x 10
-14
-12
-10
-8
-6
-4
-2
0
2
Energy w.r.t. Valence Band Maximum (eV)
Figure 3.6: Calculated oxygen K edge emission spectra for LaCuOSe and BiCuOSe. A peak corresponding to a Bi 6s – O 2p bonding state is observed at 11
eV below the valence band maximum.
lence band maximum, there is one important difference between BiCuOSe and
LaCuOSe. DFT calculations of the O K edge x ray emission spectra indicate
the presence of a peak at 11 eV below the main valence band maximum in
BiCuOSe which is not present in LaCuOSe, as shown in Figure 3.6, but otherwise the character of the two spectra is similar. Comparison of the density
functional theory calculations of the O 2p partial density of states shows that
at the top of the valence band, both BiCuOSe and LaCuOSe exhibit essentially
the same behavior. The top of the valence band is derived primarily from Cu
3d and Se 4p states, with oxygen 2p having its major contribution a few eV below the valence band maximum. The Bi 6s states contribute minimally to the
valence band maximum. In the experimental spectra, it can be seen that the
character of the two compounds differs as one goes away from the valence band
maximum, with BiCuOSe showing a peak in the O K edge emission spectrum
37
XES
p
Bi 6s
O 2
ytisnetnI
B
AB
510
515
520
525
530
535
540
545
Photon Energy (eV)
Figure 3.7: BiCuOSe emission spectrum and broadened DFT calculation of the
partial density of states, showing the existence of bonding (B) and anti-bonding
(AB) states in the valence band.
at about 11 eV below the valence band maximum (518.5 eV), corresponding to
the Bi 6s – O 2p bonding state, as shown in Figure 3.7, in agreement with the
calculated emission spectrum and partial density of states. The corresponding
anti-bonding state at 526.5 eV is contained within the main oxygen peak in
the emission spectrum. The positioning of both the bonding and antibonding states as predicted by DFT and evidenced in the emission spectra is in
agreement with the predictions of the revised lone pairs model.
The validity of the modified lone pairs model can be further tested by examination of the oxygen 2p partial density of states. The oxygen 2p contribution
to the Bi 6s – O 2p bonding state was determined by comparing the area of
38
the fitted peak to the total area of all the oxygen 2p peaks in the emission
spectrum, using the relation
fO
2p
=
Apeak /Atotal
n/p
(3.1)
where p is the total number of valence electron pairs per formula unit and n is
the number of metal atoms per formula unit.[15][5] For BiCuOSe, the number
of metal atoms is n = 2 for Bi and Cu and
p=
d10 [Cu+ ] + s2 [Bi3+ ] + p6 [Se2− ] + p6 [O2− ]
2
(3.2)
= 12
This analysis leads to an oxygen 2p character of fO
2p
= 0.23, in good
agreement with the 0.31 value obtained from density functional theory calculations. Above 526 eV, BiCuOSe shows increased O 2p character as compared
with LaCuOSe, consistent with the Bi 6s – O 2p antibonding state. There is
significant mixing of the Bi 6s – O 2p antibonding state with Bi 6p according
to the DFT calculations, which is again consistent with the revised lone pairs
model. Examination of the bismuth PDOS below the valence band maximum
shows that the major Bi p contribution to the density of states lies at about 3
eV lower than the antibonding Bi 6s – O 2p state as shown in Figure 3.8, again
consistent with the revised lone pairs model.
In the lanthanide, a very small peak is observed at about 15 eV below the
valence band maximum, associated with a La 5p – O 2p bonding state, again in
agreement with the DFT calculations, as shown in Figure 3.9. The antibonding
state lies deeper within the valence band region, in contrast to BiCuOSe, in
39
)stinu .bra( setatS fo ytisneD
s
Bi p
Bi
-8
-6
-4
-2
0
Binding Energy w.r.t. VBM
Figure 3.8: Bi s and p partial density of states within the valence band. The
majority of the weight of the p states is at lower energy than the s states.
which the antibonding state contributes nearer to the top of the valence band.
Thus, we conclude that the Bi 6s – O 2p antibonding state causes an upward
shift of the valence band maximum as compared to LaCuOSe, resulting in a
reduction of the optical band gap.
The total electron yield (TEY) absorption spectra and DFT calculations of
the conduction band density of states are shown in Figures 3.10 and 3.11. The
DFT calculations show that the O 2p PDOS reflects the PDOS of the cations.
The low energy Bi 6p orbital contribution to the bottom of the conduction
band results in a lowering of the conduction band minimum in the bismuth
compound, again contributing to the smaller gap of BiCuOSe.
3.4.2
Ca-doped BiCuOSe and Mg-doped LaCuOSe
The effect of calcium doping on the electronic structure of BiCuOSe and magnesium doping on LaCuOSe was studied. XAS of the Ca L3,2 edge shows the
40
40 x
XES
O 2p
La 5p (1/3)
ytisnetnI
B
AB
510
515
520
525
530
535
540
545
Photon Energy (eV)
Figure 3.9: LaCuOSe emission spectrum and calculated density of states. Weak
bonding and antibonding states are observed between the La and O p states.
clear presence of calcium in nominally 6% doped samples. Some evidence of
weak calcium presence also appears in the undoped samples, possibly the result
of cross-contamination from the vacuum chamber. It is expected that the Cu
L3,2 edge shape will change when Ca2+ is substituted on the Bi3+ site, reflecting compensation of the reduced charge on the bismuth site by an increased
charge on the copper site. The Cu2+ absorption line is expected to increase
in intensity compared to the Cu1+ absorption. Similarly, the substitution of
doubly ionized magnesium onto the La3+ site is expected to be countered by
the same charge in the copper site charge.
Ca L3,2 absorption was measured in order to confirm the presence of Ca in
the BiCuOSe films. As shown in Figure 3.12, the Ca L3 and L2 absorption
41
TEY
O 2
p
p (1/4)
Bi 6
Cu 4s (1/4)
ytisnetnI
526
528
530
532
534
536
538
540
Photon Energy (eV)
Figure 3.10: Measured absorption spectrum and Gauss-broadened calculated
density of states for BiCuOSe, showing that the O 2p density of states reflects
the cation density of states.
peaks are clearly observed in BiCuOSe doped with 6% Ca. There is some Ca
detected in the nominally undoped films, possibly the result of contamination
in the vacuum chamber. The expected results of this substitution are twofold.
The peak in the oxygen emission spectrum corresponding to the Bi 6s – O
2p bonding state should be diminished, and the charge of the Cu ion should
change from 1+ to 2+. However, neither of these two was observed. The oxygen
emission spectrum looks essentially the same for both the doped and undoped
films, as shown in Figure 3.13. Additionally, Cu emission measurements did
not provide a consistent picture of the Cu charge state from measurement to
measurement.
42
TEY
p
La d (1/4)
Cu s (1/4)
O
ytisnetnI
526
528
530
532
534
536
538
540
Photon Energy (eV)
Figure 3.11: Measured absorption spectrum and Gauss-broadened calculated
density of states for LaCuOSe, showing that the O 2p density of states reflects
the cation density of states.
In LaCuOSe, we again expect a change in the copper charge state from 1+
to 2+, and indeed such behavior is observed in the Cu L3,2 emission spectrum,
as shown in Figure 3.14. The intensity of the Cu2+ peak clearly increases
relative to the Cu+ in the doped film, as compared to the undoped film [16],
indicating that doping with Mg2+ on the La
3+
site results in a change of the
copper charge.
The impact of calcium doping on the bismuth site remains an open question that warrants further investigation, especially given that in LaCuOSe, the
predicted behavior upon doping was observed. The comparatively light doping
of BiCuOSe (roughly 6%) compared to LaCuOSe (15-20%) may explain why
43
L2
L3
ytisnetnI
Nominally Undoped
6% Ca
340
342
344
346
348
350
352
354
Photon Energy (eV)
Figure 3.12: XAS scans of the Ca L3,2 edge in undoped and 6% Ca-doped
BiCuOSe
the expected behavior was observed in LaCuOSe, but not in BiCuOSe.
3.5 — Conclusions
Comparison of BiCuOSe to LaCuOSe reveals that the reduced band gap of
BiCuOSe arises from an anti-bonding state which raises the valence band maximum and the Bi 6p contribution to the conduction band minimum. Measured
band gaps are in agreement with optically determined values. The existence of
a Bi 6s - O 2p bonding state has been observed below the main valence band
region at 11 eV below the valence band maximum, which is consistent with
other Bi oxides. The results are consistent with the revised lone pairs model,
in which lone pairs are formed as a result mixing between the Bi 6p and Bi 6s
– O 2p antibonding states. The top of the valence band of BiCuOSe is similar
to that of LaCuOSe because there is little interaction between Bi 6s states and
the higher energy (relative to O 2p) Se 3p states. This similarity explains why
44
Undoped
6% Ca Doped
ytisnetnI
510
515
520
525
530
535
540
545
Photon Energy (eV)
Figure 3.13: O K edge x ray emission of doped and undoped BiCuOSe films.
both materials exhibit similar transport properties.
45
2+
Cu
ytisnetnI
+
Cu
Undoped
Mg doped
920
930
940
950
960
Photon Energy (eV)
Figure 3.14: Cu L3,2 emission spectra for undoped and Mg-doped LaCuOSe
thin films
46
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82(7):1048, 2003.
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Masahiro Hirano, and Hideo Hosono. Heteroepitaxial growth of a wide-gap
p-type semiconductor, LaCuOS. Applied Physics Letters, 81(4):598–600,
2002.
[12] H Ohta, K Nomura, M Orita, M Hirano, K Ueda, T Suzuki, Y Ikuhara,
and H Hosono. Single-Crystalline Films of the Homologous Series InGaO3(ZnO)m Grown by Reactive Solid-Phase Epitaxy. Advanced Functional Materials, 13(2):139–144, February 2003.
[13] P. Blaha, K. Schwarz, G.K.H. Madsen, D. Kvasnicka, and J. Luitz.
WIEN2k, An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties. September 2001.
[14] D J Payne, M D M Robinson, R G Egdell, A Walsh, J McNulty, K E
Smith, and L F J Piper. The nature of electron lone pairs in BiVO4 .
Applied Physics Letters, 98(21):212110, 2011.
[15] Aron Walsh, David J Payne, Russell G Egdell, and Graeme W Watson.
Stereochemistry of post-transition metal oxides: revision of the classical
lone pair model. Chemical Society Reviews, 40(9):4455–4463, 2011.
[16] T S Herng, D C Qi, T Berlijn, J B Yi, K S Yang, Y Dai, Y P Feng,
I Santoso, C Sánchez-Hanke, X Y Gao, Andrew T S Wee, W Ku, J Ding,
and A Rusydi. Room-Temperature Ferromagnetism of Cu-Doped ZnO
Films Probed by Soft X-Ray Magnetic Circular Dichroism. Physical review
letters, 105(20):207201, November 2010.
48
4 — Electronic and Optical Properties of SnS
Tin monosulfide is an indirect semiconductor made from earth-abundant, nontoxic elements, which may be suitable for use as an absorber layer in thin film
photovoltaics. In this work, we demonstrate the deposition of (010)-oriented
SnS thin films using pulsed laser deposition from a sulfur-rich target under
varying growth conditions. Films exhibit p-type conductivity and have carrier
densities of 1014 to mid-1015 cm−3 and mobilities of 7-15 cm2 2V−1 s−1 . We
observe an indirect gap of 1.16 eV and a direct absorption onset at 1.31 eV.
The films exhibit a rapid absorption onset, exceeding 105 cm-1 at 0.56 eV
above the band gap. The complex refractive index is reported for wavelengths
from 300 to 2000 nm. Comparison to defect and optical absorption calculations
confirms that p-type conductivity is the result of tin vacancies and that SnS is
an indirect material. Calculated carrier densities show that growth conditions
change from sulfur-rich at low temperature to tin-rich at high temperature.
4.1 — Introduction
Great progress has been made in thin film photovoltaic technology and commercially available CdTe and CuInGaSe2 (CIGS) cells offer conversion efficiencies
of around 9%. It is unlikely, however, that these materials will ever be costcompetitive with conventional energy sources. The cost of producing these
cells is driven by the requirement to handle hazardous materials in the case
49
of CdTe, and by the dependence on relatively scarce In and Ga in the case of
CIGS, as well as the relative difficulty of producing high quality CIGS with the
desired stoichiometry. [1][2][3] In order to lower the cost per Watt, high conversion efficiency, easily-made materials composed of earth-abundant elements
are essential.
Tin (II) sulfide is one such option. SnS is a layered orthorhombic semiconductor composed of weakly coupled layers stacked along the long axis (Figure
4.1), with an indirect gap of 1.16 and a direct transition at 1.31 eV, close to
the ideal gap for a photovoltaic absorber layer. An absorption coefficient of
104 - 105 cm−1 has been reported for SnS thin films. [4][5] The electronic and
optical properties of SnS make this material an attractive candidate for use in
thin film solar cells.
While SnS has attracted sporadic attention for decades, the literature is
lacking both quantity and consistency, with the gap being variously reported as
direct and indirect, and ranging from around 1 eV to 1.5 eV. [6][7][8][9] Recent
computational work reveals an indirect gap at 1.07 eV, with a direct absorption
edge located 0.4 eV above the gap, along with an absorption coefficient of mid
105 cm−1 . This result is in excellent agreement with the measured optical
properties of SnS thin films.[10]
This chapter demonstrates the growth of highly oriented, stoichiometric
SnS on fused silica substrates using pulsed laser deposition. Laser energy density, substrate temperature, and pulse rate are varied to modify the electrical
and structural characteristics of the films. As-grown films consistently display
p-type conductivity; however, it has been reported that low temperature annealing in air for short periods of time can lead to n-type SnS with conductivity
similar to that of the films reported here. [11] This provides a possible route
50
b
b
c
a
Figure 4.1: Layered orthorhombic structure of SnS
for the fabrication of bipolar junctions made entirely from SnS.
4.2 — Experimental Details
Thin films of tin sulfide were grown using pulsed laser deposition on fused
silica substrates cleaned in acetone and methanol for 15 minutes each in an
ultrasonic bath, then rinsed in deionized water and blown dry with nitrogen.
An SnSx (x > 1) target prepared in house from SnS2 powder pressed using a hot
isostatic press with a density of about 80% theoretical density was sanded and
polished prior to deposition. X ray analysis of powder removed from the target
surface show diffraction peaks consistent with Sn2 S3 and SnS2 phases (Figure
4.2). The target was ablated using a 248 nm KrF excimer laser pulse rates
of 3 to 7 Hz, producing a relatively narrow deep purple plume that extended
about one inch from the target surface. The target-substrate distance was kept
fixed at 5 cm, well outside the plasma plume. Energy density was varied from
0.5 to 1.5 J/cm2 . Five thousand pulses were used for all depositions used for
electrical measurements. Substrate temperature ranged from 300 to 500 ◦ C, as
51
SnS2
Sn2S3
stnuoC
10
20
30
2
q
40
50
60
Figure 4.2: Diffraction pattern of target used for SnS depositions
measured by a thermocouple near the back side of the platen and calibrated
using a pyrometer to measure the front side (substrate-facing) temperature.
Following deposition, films were cooled at 30 ◦ C/min in vacuum, and then
stored in air.
Structure characterization was carried out using a Bruker D8 Discover x-ray
diffractometer in the parallel beam geometry with Cu Kα radiation. Sample
orientation was confirm via χ scans. Film density was determined from the
critical angle of x-ray reflectivity measurements performed with a Rigaku Ultima IV diffractometer. Electrical transport properties were measured using
a LakeShore Cryotronics 7504 Hall effect measurement system at a magnetic
field of 2 Tesla, with pressed indium contacts in the van der Pauw geometry.
Film thickness was determined using an AlphaStep 500 profilometer and
confirmed by spectroscopy ellipsometry. Surface morphology was determined
using a Digital Instruments Multimode III atomic force microscope. All AFM
52
images were gathered in tapping mode using uncoated n-type silicon cantilevers.
Cross-sectional images were obtained using an FEI Tecnai G2 Spirit transmission electron microscope.
Stoichiometry analysis was performed using a Cameca SX50 electron microprobe at accelerating voltages of 12, 15, and 20 kV. Kα emission from sulfur,
oxygen, zinc, and silicon was measured, along with Lα emission from tin. All
samples were coated with a 20 nm conductive carbon layer.
Optical transmission and reflection spectra were collected using a doublegrating spectrometer with a tungsten lamp and InGaAs detector for nearinfrared measurements and a xenon lamp and silicon detector for ultraviolet
and visible measurements. The effect of thin film interference was removed by
calculating the absorption coefficient using T /(1 − R) = exp(−αd), where T is
transmission, R is reflection, α is the absorption coefficient, and d is the film
thickness. Optical constants were determined using a J.A. Woolam V-VASE
spectroscopic ellipsometer at incidence angles of 60◦ , 65◦ , and 70◦ , with use of
an auto-retarder to modify the incident beam polarization.
4.3 — Results and Discussion
Films were deposited over a range of temperatures, pulse rates, and energy
densities. All films appear metallic and uniform. The results detailed below
indicate that the electronic properties of SnS can be easily tuned by varying
deposition parameters. Stoichiometry analysis by EPMA shows that all films
are composed of 50 at. pct. tin and 50 at. pct. sulfur to within experimental
limits, indicating non-stoichiometric transfer of the target elements into the
films and demonstrate the need to use sulfur-rich targets to produce a desired
SnSx stoichiometry. There was no observable oxidation even when films were
53
Temperature (◦ C)
Pulse Rate (Hz)
Fluence (J/cm2 )
Zn
Sn
S
O
Total
500
3
1
0.001
0.494
0.504
0
0.999
500
5
1
0.001
0.494
0.503
0
0.998
500
7
1.5
0.001
0.498
0.500
0
0.999
500
7
1.5
0
0.497
0.501
0
0.998
500
7
0.7
0.001
0.49
0.506
0
0.997
300
7
1
0.001
0.495
0.503
0
0.999
400
7
1
0.001
0.494
0.503
0
0.998
Table 4.1: Stoichiometry analysis of SnS thin films grown under different conditions
left in air for several weeks, indicating that SnS films are stable in air. The
results of EPMA analysis are summarized in Table 4.1.
4.3.1
Structural Properties
X-ray diffraction measurements show that all films are orthorhombic (space
group P bnm) and strongly b-axis oriented, owing to the weak Van der Waals
coupling between layers that stack along the long axis. All peaks in the diffraction patterns can be attributed to (0k0) SnS peaks (Figure 4.3). The (020) peak
is forbidden, but does show up weakly in the x-ray diffraction patterns of some
films, indicating that there is some deviation from perfect crystallinity. The
(040) and (111) peaks of SnS are quite close, and published crystallographic
data is inconsistent about the exact positions of the peaks. In order to confirm
(010) orientation, θ − 2θ scans around the (131) peak were performed with
the film tilted assuming (010) (χ = 51.7◦ ) and (111) (χ = 23.5◦ ) orientations.
(Figure 4.4) The (131) peak is observed when the film is tilted for an assumed
(010) orientation, but not when the film surface is assumed to be (111), thus
confirmed the film orientation. φ scans did not indicate any preferred in-plane
orientation. The observed growth direction is consistent with the easy cleavage
plane identified by Hegde et al. [8]
54
(040)
ytisnetnI
(080)
10
20
30
40
50
60
70
2q
Figure 4.3: θ-2θ scan of SnS film deposited on fused silica. Only (0k0) peaks
are present
Counts
100
9
8
7
6
36
5
38
40
42
44
2θ
4
3
2
36
38
40
42
44
2θ
Figure 4.4: θ-2θ scans of SnS (131) peak, with sample tilted for (010) orientation and (111) orientation (inset).
55
Measured
Model
ytisnetnI
1
2
3
4
2θ
Figure 4.5: SnS x-ray reflectivity pattern
X-ray reflectivity measurements give an average film density of 5.2 g/cm3 ,
in excellent agreement with reported results [12]. Additionally, the uniform
oscillations (Figure 4.5) are an indication of phase purity and the roughness
is estimated to be 0.6 nm, in good agreement with atomic force microscopy
measurements. Cross-sectional TEM images confirms that the films are dense
and free of voids, as shown in Figure 4.6.
56
Figure 4.6: TEM cross section of SnS thin film deposited on fused silica
4.3.2
Transport Properties
The electronic properties of SnS are tunable over a rather narrow range by
adjustment of the deposition temperature, laser energy density, and pulse rate.
All films are p type, owing to the small formation enthalpy of Sn vacancies;
this will be explored further in this chapter, when the experimental results are
compared to calculation.
Deposition Temperature
Films were deposited at substrate temperatures from 200 to 500 ◦ C with a fixed
pulse rate of 7 Hz and energy density of 1 J/cm2 . These conditions resulted
in films that were approximately 100 nm thick, as did all other depositions
used for electrical characterization. Figure 4.7a summarizes the temperaturedependent transport measurements for films grown between 300 and 500 ◦ C.
-3
3
13
2
12
14
11
10
9
6
5
4
300
2
10
Mobility (cm /Vs)
Carrier Density (10 cm )
6
5
4
14
57
8
400
500
0.8
1.2
3
4
5
6
7
2
Temperature (˚C) Fluence (J/cm ) Pulse Rate (Hz)
(a)
(b)
(c)
Figure 4.7: Electrical transport properties of SnS thin films grown on fused
silica
Films grown at 200 ◦ C were insulating and their electrical properties could not
be measured. Above 500 ◦ C, films do not form. Conductivity ranges from 1.5
to 9 mS/cm and mobility varies from 7 to 15 cm2 /Vs, with both showing a
positive correlation with substrate temperature. Carrier density ranges from
3 × 1014 to 7 × 1015 cm−3 . It can be inferred from the transport data that
films grown at higher temperature are of better quality and have fewer defects,
consistent with increased surface mobility of the evaporants.[13]
Laser Energy Density
Laser energy density was varied from 0.5 to 1.5 J/cm2 with the substrate temperature and pulse rate fixed at 500 ◦ C and 7 Hz, respectively. Carrier concentration decreased approximately linearly with energy, from 1.4 × 1015 cm−3
at 0.5 J/cm2 to 3.5 × 1014 cm−3 at 1.5 J/cm2 . mobility increased from 10 to
14 cm2 /Vs, while conductivity decreased from 2.2 to 0.8 mS/cm, as shown in
58
Figure 4.7b. This indicates that higher energy growths result in higher quality
films, similar to the result obtained for temperature variation.
Pulse Rate
Laser pulse rate was varied from 3 to 7 Hz with the substrate temperature
fixed at 500 ◦ C and the laser energy density set to 1.0 J/cm2 . Despite the
mean diffusion time being much shorter than the time between pulses, pulse
rate has a rather significant impact on the electronic properties of the films.[13]
Mobility showed a marked increase from 8 cm2 /Vs at 3 Hz to 15 cm2 /Vs at 7
Hz. Conductivity ranged from 0.9 to 1.5 mS/cm. Carrier density held relatively
constant at approximately 7.5 × 1014 cm−3 from 3 to 5 Hz, and creased to
3.4 × 1014 cm−3 at 7 Hz, as shown in Figure 4.7c.
The electrical characteristics of SnS are in line with the photovoltaic absorber design principles outlined in 1.2. SnS thin films exhibit low intrinsic
carrier density and while the mobility is somewhat low compared to, for example, CdTe, it may still be possible to use SnS as an absorber layer.
4.3.3
Optical Properties
All films exhibit very similar optical properties. Plots of (αhν)1/2 and (αhν)2
vs hν were used to determine the optical band gap by finding the intercept
between the linear region near the absorption onset and the baseline sub-gap
absorption. Both indirect – (αhν)1/2 – and direct – (αhν)2 – appear linear
near the gap. Indirect and direct onsets of absorption at 1.16 eV and 1.31 eV,
respectively, were found. The absorption coefficient was measured for films with
thicknesses of 96, 135, 163, and 173 nm, in order to ensure that adequate signal
was obtained in both the low and high absorption regions of the spectrum. The
average absorption coefficient is shown in Figure 4.8, along with the range of
59
10
4
1
4
5
-1
α (10 cm )
2
2
0.1
4
2
0.01
1.5
2.0
2.5
3.0
3.5
4.0
Energy (eV)
Figure 4.8: Optical absorption spectrum for SnS thin films deposited on fused
silica
measured absorption at selected energies. An absorption coefficient of 3.6 5.9 ×104 cm−1 is measured at 1.5 eV, and the absorption reaches 2.8 - 4.5
×105 cm−1 at 2.5 eV, as shown in Figure 4.8. These results are in excellent
agreement with the calculation reported by Vidal etal. [10] The rapid onset of
strong absorption - faster than CuInSe2 - is necessary to achieve high efficiency.
[14] The optical properties are ideally suited for use in thin film photovoltaics,
with a moderate band gap that should allow for a high open circuit voltage
and large short circuit current, provided that carriers can be extracted which
may be possible due to the high absorption coefficient that allows the use of
very thin films.
The complex index of refraction was determined from spectroscopic reflection ellipsometry data fit to a Tauc-Lorentz oscillator model [15]. The refractive
index has a peak value of 4.8 at 580 nm. An index of refraction n of 3.83 is
60
5.0
2.5
4.5
2.0
4.0
n
3.5
1.0
3.0
0.5
2.5
0.0
400
k
1.5
800 1200 1600 2000
λ (nm)
Figure 4.9: Refractive index and extinction coefficient for SnS thin films on
fused silica.
obtained at 1500 nm, along with an extinction coefficient of 1.81 at 500 nm, as
shown in Figure 4.9. The measured index of refraction is notably higher than
previously reported results.[5][16][17] This may be the result of differences in
film density, phase purity and crystallinity. The films reported in this work are
well crystallized, highly oriented, and very dense (5.2 g/cm3 ). Other reports
of the refractive index do not report the film density and claim polycrystalline
orientation.
4.3.4
Comparison with Calculations
Experimental optical absorption and carrier concentrations are in excellent
agreement with defect DFT and GW calculations performed at NREL using
VASP [18]. Both LDA and GGA calculations were performed, with LDA reproducing the experimentally determined structure better than GGA. It has
been found that the defect formation enthalpies depend strongly on the lattice
parameter of the weakly coupled axis. Thus, the long axis was constrained to
the experimental value of b = 11.2 Å. Carrier densities were obtained using
61
thermodynamic calculation procedures detailed in the work of Persson et al
[19]. The carrier density is given by
p(EF , T ) =
q
X
D
q N exp[−∆HD,q (Ef , µi )/kT ]
|
{z
}
(4.1)
cD,q
where q is charge, D is the type of defect, and ∆H is the formation enthalpy,
given by
∆HD,q (Ef , µ) = ED,q − EH −
X
ni (∆µi + µsolid
) + q(Ev + EF )
i
(4.2)
i
where ED,q − EH is the total energy with and without the defect, ni is the
number of defect atoms (+1 if a defect atom is added, -1 if a defect atom is
removed), µi is the chemical potential of atom i, Ev is the VBM without defects
and EF is the Fermi level. The number of defects at room temperature is the
same as that at room temperature because the defects are not removed upon
cooling. Simulation of tin rich and sulfur rich growth conditions was accomplished by modifying the chemical potentials for tin and sulfur and formation
enthalpy of SnS following the method detailed by Lany [20].
The GW calculations show that SnS has an indirect gap at 1.07 eV. However, direct allowed optical transitions dominate the SnS absorption, leading
to strong absorption coefficient in excess of 105 cm−1 within 0.5 eV of the band
gap. The calculated absorption spectrum turns on at a notably higher value
than measured experimentally when excitonic absorption effects are neglected;
however, the calculated spectrum agrees well with the measured spectrum when
excitonic absorption effects are included, as shown in Figure 4.10.
Defect calculations performed at NREL indicate that under sulfur-rich con-
62
Figure 4.10: Experimental (solid, gray) and calculated absorption with (solid,
black) and without (dashed, black) excitonic effects included
Figure 4.11: Calculated formation enthalpies for SnS under tin-rich and sulfurrich growth conditions
ditions, tin vacancies are likely to form, resulting in p-type conduction in nominally undoped films, as shown in Figure 4.11 . Notably, no energetically favorable defects were found that would give rise to n-type conductivity. Even
under Sn-rich conditions, only the SnS anti-site defect is predicted to form, and
then only when Fermi level is position at the conduction band minimum.
The calculated hole concentration agrees well with the experimentally determined concentrations, as shown in Figure 4.12, and indicates a transition
from sulfur-rich to tin-rich growth as the deposition temperature is increased.
63
Figure 4.12: Experimental (squares) carrier densities for SnS thin films and
calculated (solid curves) carrier densities under tin and sulfur-rich growth conditions
This is the expected result, since sulfur has a much lower melting point (115.21
◦
C vs 231.93 ◦ C) and much higher vapor pressure than tin.
4.4 — Conclusions
The growth of strongly oriented SnS on fused silica substrates using pulsed
laser deposition has been demonstrated. Film growth occur by layering along
the weakly coupled b axis. Use of a sulfur-rich target results in films that are
stoichiometric tin monosulfide. The films show a band gap of 1.16 eV, with a
direct transition at 1.31 eV. Strong absorption in excess of 105 cm−1 is observed
above 1.6 eV. While these films display somewhat low mobility of 7-15 cm2 /Vs,
it may be possible to use such films as an absorber layer due to the strong absorption. Additionally, growth parameters have been identified which minimize
the hole concentration in the films. This could be used as a starting point for
the fabrication of n-type SnS thin films. Comparison with calculations reveals
that the the p-type conductivity is the result of energetically favorable tin vacancies. The calculated carrier densities agree well with experiment. There is
64
good agreement between calculated and experimental optical absorption when
excitonic effects are considered.
65
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67
5 — (SnCa)S Alloys
Thin films of (SnCa)S have been prepared by pulsed laser deposition. The
rocksalt structure is adopted in films that have calcium cation fraction of 0.4
or larger, in agreement with calculations that show that the stable crystal
structure transitions from orthorhombic to rocksalt when the calcium cation
fraction is 0.17 or larger. Films exhibit a moderate gap of 1.1 - 1.3 eV, again in
agreement with the predicted gap of 1.5 eV for films with 50% calcium content.
Contraction of the lattice is observed as calcium content is increased, consistent
with reports of CaS and rocksalt SnS. DFT calculations overestimate the lattice
parameter by about 1%.
5.1 — Introduction
Orthorhombic SnS is a p-type semiconductor that has attracted considerable
attention in recent years as a potential absorber layer in thin film photovoltaics.
It possesses a suitable indirect band gap of 1.1 eV. The indirect gap does not
have a detrimental impact on the absorbing properties of SnS, which reaches
absorption in excess of 105 cm−1 within 0.5 eV of the band gap as a result of
direct transitions located close to the band gap. However, SnS-based solar cells
which use CdS as a buffer layer have only achieved conversion efficiencies of
1.3% or less [1, 2]. Two main factors limit the suitability of orthorhombic tin
sulfide for use in photovoltaics. The indirect gap is smaller than the ideal for a
68
photovoltaic absorber layer. Additionally, the transport properties are highly
anisotropic. While the in-plane hole effective masses (0.13me and 0.2me ) are
comparable to materials such as CuInGaSe2 , the effective mass along the weakly
coupled direction is unsuitably large (1.5me , leading to poor conduction along
this direction. The minority carriers also suffer from anisotropic transport
properties, although not as pronounced as the majority carriers. The in plane
effective masses for the electrons are 0.13me and 0.2me , slightly larger than
materials such as CdTe and CIGS, but possibly acceptable in an absorber
layer. The out of plane effective mass, however, is quite large at 0.5me [3].
While orthorhombic SnS (space group pnma) is the energetically favorable
phase, recent calculations reveal that the rock salt phase (space group f m3̄m)
has a formation enthalpy only 0.08 eV above that of the orthorhombic phase.
The high symmetry phase can be reached by alloying with a rocksalt material,
conferring with it isotropic transport properties. In this work, SnS has been
alloyed with CaS to form rocksalt Sn1−x Cax S thin films with a band gap of
about 1.1 - 1.3 eV, in between that of the wide gap CaS (EG = 4.5 eV) and
the zero gap predicted for rocksalt SnS [4].
5.2 — Predicted Properties
Formation enthalpy calculations indicate that at Ca fractions in excess of 0.17,
SnCaS thin films will undergo a structural phase transition from orthorhombic
(space group 62) to rocksalt (space group 225), as shown in Figure 5.1.
The resulting material is predicted to have a direct band gap of 0.6 eV for
x = 0.25 and 1.5 eV for x = 0.5, as shown in Figure 5.2. The absorption
turns on to 105 cm−1 at 1.75 eV for x = 0.25, 1.15 eV above the band gap.
For x = 0.5, the absorption reaches 105 cm−1 at 1 eV above the gap, before
69
Figure 5.1: Formation energy for Sn1−x Cax S for rocksalt (SG 225) and orthorhombic (SG 62) structures
dropping slightly and returning to 105 cm−1 at 1.3 eV above the gap.
5.3 — Experimental Details
Thin films of Sn1−x Cax S were prepared by pulsed laser deposition (PLD) on
amorphous SiO2 and h001i silicon with a 100 nm thermal oxide layer. Films
were deposited from targets made from tin, calcium, and sulfur, with tin to
calcium ratios of 4:1, 2.33:1, and 1:1 using a 248 eV KrF pulsed excimer laser.
4:1 and 1:1 targets were prepared from CaS and Sn metal, annealed under
flowing H2 S for four hours at 400 ◦ C. The resulting powder was ground, pressed,
and then annealed for a further two hours at 400 ◦ C for two hours. The
2.33:1 target had approximately 20% excess sulfur added prior to being pressed.
Notably, the targets were not rocksalt SnCaS, as confirmed by x-ray diffraction,
shown in Figure 5.3. The target-substrate separation was fixed at 5.4 cm.
Substrate temperature was varied from 300 to 600 ◦ C with a laser fluence of
1.0 J/cm2 and pulse rate of 7 Hz. All films were deposited in vacuum, with a
base pressure of 10−9 Torr. Following deposition, films were cooled rapidly in
70
Figure 5.2: Calculated absorption spectra for Sn1−x Cax S
vacuum.
Glancing incidence x-ray diffraction for phase identification purposes was
performed using a Rigaku RAPID diffractometer with an incidence angle of
10◦ . For lattice parameter measurements, θ – 2θ x-ray measurements were
collected using a Bruker D8 Discover x-ray diffractometer and a Rigaku Ultima
IV diffractometer in the parallel beam geometry with Cu Kα radiation.
Cross sectional imaging and electron diffraction data were collected using
an FEI Titan transmission electron microscope at accelerating voltages of 80
and 200 kV. Samples were rotated to alter the crystallographic direction being
measured. Diffraction from the silicon substrate was used to calibrate the
patterns.
Chemical composition of the films was determined by measured Kα emission
from sulfur, oxygen, silicon, and calcium, and Lα emission from tin using a
Cameca SX 50 electron microprobe at accelerating voltages of 10, 15, and 20 kV.
Energy dispersive x-ray spectroscopy was used for stoichiometry measurements
71
50/50 Sn/Ca
70/30 Sn/Ca
CaS
SnS
10
20
30
40
50
60
2θ
Figure 5.3: X ray diffraction patterns powder removed from (SnCa)S targets
of TEM samples.
Optical transmission and reflection data were collected using a custommade spectrometer with a double grating monochromator. Measurements in
the ultraviolet and visible regions were performed using a xenon lamp and
silicon detector. A tungsten lamp and InGaAs detector were used for near
infrared measurements.
The absorption coefficient α was calculated using
T /(1 − R) = exp(−αd), where T is transmission, R is reflection, and d is
the film thickness, which was determined using a J.A. Woolam V-VASE spectroscopic ellipsometer.
Resistivity and Hall measurements were performed using a LakeShore Cryotronics 7504 Hall Effect Measurement System at magnetic fields up to 2 T.
Contact was made using pressed indium. Room temperature Seebeck coefficients were obtained using a custom-built system with a maximum temperature
differential of 5 K.
72
5.4 — Experimental Results and Discussion
Film growth is characterized by two distinct regimes. At 300 and 400 ◦ C, films
closely preserve the cation ratio of the targets, with a slight (of order 5 - 10%)
preference for calcium. However, in films deposited at 500 and 600 ◦ C, tin is
lost almost entirely, as depicted in Figure 5.4. This agrees with the observation
noted for SnS thin films, in which films failed to deposit at temperatures above
500 ◦ C.
1.0
70/30 Sn/Ca Target
0.9
50/50 Sn/Ca Target
SxaCx-1nS ni
0.8
x
0.5
0.7
0.6
0.4
0.3
300
400
500
600
Deposition Temperature (¡C)
Figure 5.4: Calcium content of (SnCa)S films grown at different temperatures
X-ray and TEM diffraction reveal that films with calcium cation occupation
of 40% and above adopt the rocksalt structure. Glancing incidence measurements show that the films are rocksalt (SnCa)S, as seen in Figure 5.5. As can
be seen in the peak positions for Sn0.38 Ca0.62 S and orthorhombic SnS (with c
as the long axis) given in Table 5.1, expected reflections from the orthorhombic
phase are not present the measured spectra. Reflections from the film can all
73
*
*
Sn0.38Ca0.62S
ytisnetnI
(113)
*
*
*
(002)
(022)
(024)
20
(224)
(004)
(111)
40
60
2
80
q
Figure 5.5: Glancing incidence x ray diffraction of (SnCa)S deposited on thermal oxide silicon. Asterisks denote substrate reflections.
be indexed to the rocksalt phase, with the observed intensities indicating a
preferential (001) orientation.
In θ – 2θ measurements, the (002) and (022) peaks of rocksalt Sn1−x Cax S
are readily observed and were used to determine the lattice parameter of the
films. The diffraction patterns were shifted to align the silicon (002) reflection
to the accepted value of 2θ = 32.96◦ . The lattice contracts as calcium is added
to the system, shifting the (002) peak to higher 2θ, as shown in Figure 5.6.
Similar growths of orthorhombic SnS on silicon result in highly oriented films
with only the (0k0) peaks present in the x ray diffraction pattern. The lattice
parameter contracts as calcium content is increased, from 5.75 Å for x = 0.4 to
5.69 Å for x = 0.92, as shown in Figure 5.7. The measured lattice parameters
of the Sn1−x Cax S films with x = (0.4, 0.93) closely match the trend determined
from reports of rocksalt SnS (a = 5.80 Å) and CaS (a = 5.689 Å) [5, 6]. DFT
74
(hkl)
(111)
(002)
(022)
(113)
(222)
(004)
(133)
(024)
(224)
(115)
Relative
2θ Intensity
26.9
0.60
31.2
1
44.7
0.71
52.9
0.29
55.5
0.25
65.0
0.11
71.7
0.12
73.9
0.31
82.3
0.23
88.6
0.09
Rocksalt
Relative
(hkl)
2θ Intensity
(011) 21.9
0.33
(012) 26.0
0.59
(102) 27.5
0.69
(110) 30.5
0.50
(111) 31.5
1
(004) 32.0
0.66
(113) 39.1
0.48
(114) 44.7
0.32
(200) 45.5
0.27
(121) 48.5
0.26
Orthorhombic
Table 5.1: Calculated peak positions and intensities for rocksalt Sn0.38 Ca0.62 S
and orthorhombic SnS
calculations overestimate the observed lattice parameter by 1% and 1.4% for x
= 0.4 and 0.92, respectively.
Electron diffraction of polycrystalline SnCaS confirms the formation of cubic
phase SnCaS, as shown in Figure 5.8, looking along the h100i zone axis and in
Figure 5.9 looking along the h011i zone axis. Rotation of the films shows no
evidence of an orthorhombic phase.
The films are highly insulating and mobility measurements could not be
obtained. However, Seebeck measurements do indicate that the films are p
type, with a Seebeck coefficient of 900 - 1900 µV/K, for films with 35% – 55 %
Ca cation content.
Optical measurements indicate that the band gap of films with moderate
calcium content (x = 0.35 – 0.55) varies from 1.1-1.3 eV, increasing with rising
Ca content. Films with approximately 95% calcium on the cation site exhibit
a very slow onset of absorption with no obvious band gap. At this level, tin
acts as an impurity in CaS and causes low absorption at all energies. The
absorption of films with turns on notably slower than tin sulfide, reaching 105
75
0.92
ytisnetnI
0.4
0.62
30.0
30.5
31.0
2
31.5
32.0
q
Figure 5.6: X ray diffraction of the (002) peak of Sn1−x Cax S thin films with
different compositions. The numbers on the plot indicate x.
5.84
5.82
)( retemaraP ecittaL
5.80
5.78
5.76
5.74
DFT
Literature
5.72
XRD
5.70
TEM
Fit
5.68
0.0
0.2
0.4
x in Sn
0.6
1-x
0.8
1.0
CaxS
Figure 5.7: Lattice parameter of Sn1−x Cax S films as a function of calcium
content
76
Figure 5.8: Electron diffraction pattern of SnCaS thin film looking along the
h100i zone axis
77
Figure 5.9: Electron diffraction pattern of SnCaS thin film looking along the
h011i zone axis
cm−1 at 0.7 eV above the gap, as shown in Figure 5.10.
5.5 — Conclusions
(SnCa)S alloys are predicted to transition from an orthorhombic structure to
a rocksalt structure when the calcium content is greater than x = 0.17. Thin
films of (SnCa)S with calcium content of 40% have been deposited on fused
silica and thermal oxide silicon by pulsed laser deposition. X ray diffraction
and electron diffraction confirm that the films adopt the rocksalt structure,
with no evidence of an orthorhombic phase. The contraction of the lattice as
calcium content is increased agrees well with reported values for the lattice
parameter of rocksalt SnS and CaS. The band gap is shifted to higher energy
as calcium content is increased from 35 - 55 % (1.1 - 1.3 eV), in good agreement
with calculations. The absorption turns on to 105 cm−1 within 0.7 eV of the
78
6
4
2
5
10
1-
)
6
mc(
4
2
a
x = 0
4
x = 0.35
10
6
x = 0.55
4
x = 0.95
2
3
10
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Energy (eV)
Figure 5.10: Absorption spectra of Sn1−x Cax S thin films deposited on fused
silica
band gap. Films with very high calcium content (greater than 90%) do not
show a clear band gap and exhibit a very slow onset of absorption.
79
Bibliography
[1] K T Ramakrishna Reddy, N Koteswara Reddy, and R W Miles. Photovoltaic properties of SnS based solar cells. Sol. Energ. Mat. Sol. Cells,
90:3041–3046, September 2006.
[2] S A Bashkirov, V F Gremenok, V A Ivanov, V V Lazenka, and K Bente.
Tin sulfide thin films and Mo/p-SnS/n-CdS/ZnO heterojunctions for photovoltaic applications. Thin Solid Films, 2012.
[3] Julien Vidal, Stephan Lany, Mayeul d’Avezac, Alex Zunger, Andriy Zakutayev, Jason Francis, and Janet Tate. Band-structure, optical properties,
and defect physics of the photovoltaic semiconductor SnS. Applied Physics
Letters, 100(3):032104–032104–4, January 2012.
[4] M Jin, N Kim, H Kim, and C Yoon. Optical Properties of Undoped and
Co2+ -Doped CaS, CaSe, BaS, and BaSe Single Crystals. 2001.
[5] Huan Luo, Raymond G Greene, Kouros Ghandehari, Ting Li, and Arthur L
Ruoff. Structural phase transformations and the equations of state of calcium chalcogenides at high pressure. Physical Review B, 50(22):16232, 1994.
[6] B F Bilenkii, A G Mikolaichuk, and D M Freik. Struktur und optische
Eigenschaften von epitaxialen SnTe-, SnSe-, und SnS-Schichten. 1968.
80
6 — Conclusions
6.1 — BiCuOSe
Thin films of the p-type BiCuOSe have been prepared by pulsed laser deposition
on single crystal MgO and SrTiO3 substrates. Films are strongly oriented with
large grain sizes in excess of 250 nm. Films exhibit a hole mobility of 1.5
cm2 V−1 s−1 . This mobility is unaffected by the introduction of calcium dopants
onto the bismuth site, because the transport takes place within the [Cu2 Se2 ]2−
layers, as is the case in other layered copper compounds such as LaCuOCh.
High hole concentrations in excess of 1018 cm−3 in undoped films are the result
of copper vacancies, as confirmed by EPMA. Copper vacancies are the dominant
producer of holes in other layered mixed anion materials including LaCuOCh
and BaCuChF. The carrier density rises to 5 × 1020 cm−3 in films with 10%
calcium substitution on the bismuth site. As a result, the conductivity of the
films increases upon doping by about two orders of magnitude from 1 to 100
S/cm.
Calcium transfer from the targets into the films depends on laser fluence,
with films grown from a 6% calcium-doped target having calcium content of 6
- 10% depending on fluence. The calcium content matches the stoichiometry
of the target when a fluence of 1 J/cm2 is used, but increases rapidly past 9%
at 1.25 J/cm2 .
81
Optical measurements reveal a band gap of about 1 eV in the thin films,
while measurements of single crystals exhibit a band gap of 0.84 eV. This
discrepancy may be explained by the very low transmission through the single
crystals, resulting in an underestimation of the band gap.
Soft x ray spectroscopy of the oxygen K edge and density functional theory
calculations of BiCuOSe and LaCuOSe have been employed to elucidate the
impact of the Bi 6s state on the optical and electronic properties of BiCuOSe.
The results show that Bi 6s mixes with O 2p to form bonding and antibonding states at 11 eV and 3 eV below the valence band maximum, respectively.
This is consistent with the revised lone pairs model. The fact that the Bi 6s
states contribute deep within the valence band as opposed to at the top of the
valence band explains why BiCuOSe exhibits similar hole transport properties
to LaCuOSe, despite the hybridization of the Bi 6s and O 2p states. A slight
raising of the valence band maximum is also observed in BiCuOSe as compared
to LaCuOSe. The conduction band minimum has considerable Bi 6p character,
which results in a shift of the CBM to lower energies, explaining the small gap
observed in BiCuOSe as compared to the transparent p-type semiconductor
LaCuOSe, which has a band gap of 3 eV. Analysis of the oxygen x-ray emission and absorption spectra together reveals band gaps of 1 eV and 3 eV for
BiCuOSe and LaCuOSe, respectively, in agreement with band gaps determined
from optical transmission and reflection measurements.
X ray absorption measurements of Ca-doped BiCuOSe and Mg-doped LaCuOSe reveal that the Cu charge changes from +1 to +2 as Mg is substituted
onto the La site. However, a clear picture of calcium doping did not emerge
in BiCuOSe. The predicted change in the Cu charge was not observed, nor
did the intensity of the Bi 6s - O 2p bonding state observed in the emission
82
spectrum diminish, as would be expected if there is less bismuth in the material. Nonetheless, examination of the Ca L3,2 absorption edge does reveal the
presence of calcium in the films. It is possible that the results in the case of
BiCuOSe did not reflect the prediction because the calcium concentration in
the films was too low to significantly impact either the Cu charge or the weight
of the bonding peak in the oxygen emission spectrum.
6.2 — Tin Sulfide and Alloys
Tin sulfide thin films have been grown on amorphous fused silica substrates.
The resulting films are all strongly oriented along the long, van der Waal’s
coupled axis. As expected, however, no preferentially in plane orientation was
observed. The film orientation was confirmed by tilting the films to angles
appropriate to detect the (131) peak in θ − 2θ scans if the films are either (010)
(long axis) or (111) (most intense peak, located near the (010) peak) oriented.
The (131) peak was clearly observed when the film orientation was assumed
to be (010), but not when the films were taken to be (111) oriented, thus
confirmed that stacking along the weakly coupled axis is the preferred growth
method. This clears up an important discrepancy in the literature, in which
there are many reports of (111) oriented tin sulfide thin films. The observed
growth direction matches the easy cleavage plane identified in single crystal
work.
Film growth conditions were varied to optimize the carrier density and
mobility. All films are p-type and have mobilities of 7 - 15 cm2 /Vs, along
with hole concentrations of 1014 − 1016 cm−3 . More energetic growths at higher
temperatures and fluence result in a transition from a sulfur-rich growth regime
to tin-rich, resulting in improved hole mobilities and decreased carrier densities.
83
Optical absorption measurements give a band gap of 1.2 eV and show that
absorption of 105 cm−1 is observed 0.5 eV above the band gap. The absorption
ultimately reaches 4.5 × 105 cm−1 . Spectroscopic ellipsometry measurements
were used to determine n and k. The absorption coefficient and band gap
determined from ellipsometry measurements closely matches that determined
from optical transmission and reflection measurements. The measured optical
constants are slightly larger than those reported in the literature. This is likely
because the films are very dense (5.2 g/cm3 ) as determined by x ray reflectivity,
matching the density determined from the reported structure of SnS.
Defect and absorption calculations performed at NREL confirm that SnS
is a p-type semiconductor with an indirect band gap just above 1 eV. The
source of the holes is energetically favorable tin vacancies. The predicted carrier
density for growths at various temperatures under tin and sulfur rich conditions
closely matches the measured carrier concentrations and indicate a transition
from sulfur-rich to tin-rich growth conditions as the temperature is increased.
Calculated optical absorption spectra agree very closely with experimentally
observed absorption when excitonic absorption effects are considered.
Calculations performed at NREL indicate that SnS should form a rocksalt
phase when alloyed with CaS to form Sn1−x Cax S. The predicted changeover
from an orthorhombic stable phase to a rocksalt stable phase occurs at x = 0.17.
Thin films of Sn1−x Cax S with x from 0.4 to 0.95 are rocksalt, while those prepared from a nominally x = 0.2 target appear as polycrystalline orthorhombic
SnS. X ray diffraction and TEM confirm the rocksalt phase and show a contraction of the lattice from 5.75 Å when x = 0.4 to 5.7 Å when x = 0.03.
This trend is in nearly exact agreement with that predicted from reports of the
structure of CaS (a = 5.69 Å) and rocksalt SnS deposited on NaCl (a = 5.8Å).
84
According to calculations, the band gap should be 0.6 eV in films with
x = 0.25 and 1.5 eV in films with x = 0.5. Experimental measurements indicate
a band gap of about 1.1-1.3 eV for films with calcium content of x = 0.35 and
x = 0.55 and reaches 105 cm−1 just above 2 eV. In more calcium-rich films
(x = 0.95), the absorption turns on very slowly and there is no clear band gap.
The absorption fails to reach 105 cm−1 until 4 eV.
Both orthorhombic SnS and the (SnCa)S rocksalt alloys show promise as
photovoltaic absorbers. They are made from earth abundant materials and exhibit absorption coefficients that are suitable for use in thin film photovoltaics.
The somewhat low mobility of SnS may prove detrimental, but can likely be
improved with more well-developed growth procedures. The formation of rocksalt (SnCa)S alloys as predicted by calculations lends credence to the idea of
predicting materials that may have suitable properties, then choosing the best
candidates for growth.
85
APPENDICES
86
A — Pulsed Laser Deposition
A.1 — Introduction
Pulsed laser deposition is a common physical vapor deposition method for thin
film growth, primarily in research applications. Interest in thin film growth by
laser ablation started in the 1960s and continued to be used for thin film growth
throughout the proceeding decades to grow many different materials. However,
PLD gained little traction until high quality films of the high temperature
superconductor YBa2 Cu3 O7−δ deposited on SrTiO3 and Al2O3 by PLD were
reported in the late 1980s [1, 2].
In PLD, a high energy laser beam is focused onto a target, resulting in
ablation of the surface and the formation of a highly directional plasma plume
that expands largely upward away from the surface of the target and deposits
onto the substrate. PLD is particularly useful for the growth of complex materials such as the quaternary high temperature superconductors because of
its good stoichiometry preservation. Particularly, cation ratios in the target
are transferred faithfully into the film. Additionally, in PLD, highly energetic
particles with temperatures well in excess of the melting point are ejected from
the target and kinetic effects must be considered. This can make it possible to
stabilize phases at lower substrate temperatures than would be required in, for
example, a sealed tube reaction. SnCaS is predicted to form in excess of 1000
87
◦
C. However, polycrystalline films of SnCaS can be made at as low as 300 ◦ C
by PLD.
PLD has seen very limited use in industrial-scale production. The plume
distribution typically follows a cosn θ dependence, where n > 4, giving a
strongly forward-directed (away from the target surface) plume that falls off
rapidly with θ, resulting in films that have non-uniform thickness and limiting
the film diameter to about 1”. This highly directional plume also introduces
difficulties in monitoring the deposition rate via conventional quartz crystal
monitors because the deposition rate depends so strongly on position. The
limitation on substrate size can be relaxed somewhat by rastering the laser
beam over a large diameter target or by moving the substrate. Large diameter
targets are required because of the formation of secondary phases at the target
surface as a result of ablation [3]. Using a rotating substrate and target in
combination with a rastering mirror, yttria films with less than 5% thickness
variation and nearly uniform stoichiometry have been grown on 200 mm silicon
wafers [4]. Reel to reel processing has been employed to make tapes of tens
of meters [5]. The complexity of both depositing large area films and of monitoring growth from a highly localized plume hamper PLD’s use in industrial
settings.
A.2 — Growth Parameters
Film properties such as roughness, density, crystallinity, and stoichiometry can
be controlled by varying parameters during growth. The most frequent parameters that are modified are temperature, pulse rate, laser energy density,
and process gas. Others that can be modified include cooling rate and targetsubstrate separation distance. The former of these may be useful when making
88
thin films of one compound by depositing layers of other compounds and then
annealing after deposition. The latter may prove useful in cases where the
stoichiometry of the plume varies with distance from the target.
A.2.1
Temperature
Substrate temperature during growth largely determines the crystallinity of
the films. Low temperature growths generally result in amorphous films that
can be crystallized by post-growth annealing. As the temperature is increased,
the crystallinity of the films improves, resulting in polycrystalline films when
grown on amorphous substrates and epitaxial films when grown on single crystal
substrates. Temperature also can have a dramatic impact on stoichiometry. For
example, in the SnCaS system discussed in Chapter 5, the stoichiometry is fairly
constant at 300 and 400 ◦ C substrate temperature, but changes radically to a
mostly CaS phase in the films grown at 500 and 600 ◦ C substrate temperature.
In this system, tin, with its melting point of 232 ◦ C, is lost preferentially over
calcium, which has a much higher melting point of 839 ◦ C.
A.2.2
Fluence
Laser fluence affects film quality, deposition rate, and stoichiometry. While
one of the main arguments for using pulsed laser deposition is its preservation
of the stoichiometry during deposition, in fact that stoichiometry of the film
and target can differ quite radically. In the case of BiCuOSe doped with Ca,
the calcium doping of the target is not reflected in the films. Stoichiometry
deviations can be partly eliminated by increasing the laser fluence above some
material-specific value. In materials such as SrTiO3 , this trick is insufficient
and films still have considerable cation stoichiometry deviations that give rise
89
to radical variations in the electrical properties of the films, with the resistivity
ranging over seven orders of magnitude in the case of SrTiO3 [6].
Below some threshold value, typically about 0.5 J/cm2 for group VI compounds, the deposition rate is very low and results in little to no film formation
as the evaporation of material from the substrate is enough to cancel out any
deposition from the PLD process. Pure metals are notoriously difficult to deposit by PLD and even long depositions (in excess of 50,000 pulses) result in
films that are only tens of nanometers thick. For comparison, 5000 pulses at
1 J/cm2 typically results in chalcogenide films that are of order 100 nm thick.
Above some value, typically around 1.5 - 2 J/cm2 for chalcogenides, large,
micron-sized pieces of the target are ejected and may be incorporated into the
film, resulting in very rough surfaces. This generally occurs when the laser
penetrates well into the target. This problem can be largely eliminated by using high density targets and choosing laser energies that are strongly absorbed.
For metals, higher fluence is generally required, in part due to the significant
reflection of the laser from the surface. This issue can be reduced by operating
at frequencies above the plasma frequency. An ablation threshold of around 5
J/cm2 has been identified for metallic alloys. Below this, heating of the target
results in an evaporative growth process.[7]
A.2.3
Pulse Rate
Pulse rate can play an important role in PLD and have a rather noticeable
impact on the electrical properties of a film. In the case on tin sulfide, an
increase from 3 Hz to 7 Hz results in an improvement of the mobility by a
factor of five. Diffusion of atoms within the film and growth of crystallites
may play an important role. Additionally, the dead time between pulses can
90
allow the incorporation of elements from the background gas into the film. [8]
Operating at very low base pressure can alleviate this latter problem, although
the pressure rises considerably during deposition.
A.2.4
Process Gas
A process gas can be used to dramatically alter the films. A reactive process
gas such as oxygen can be flowed into the chamber during deposition in order
to correct for anion deficiencies. A notable example of this is ITO, in which
high vacuum growth results in very dark, oxygen deficient films, while growth
in 1 mTorr O2 results in transparent films.
Inert process gases can also have an impact on the films. The presence of
an inert gas causes the plume to remain more tightly focused and can improve
stoichiometric transfer while operating in the molecular flow regime. However,
at higher pressures when one is in the viscous flow regime as opposed to the
molecular flow regime, interaction of the plume with the gas can result in
broadening of the plume. The growth rate is also dramatically decreased when
growing at high pressures. This can be somewhat alleviated by moving the
substrate into the plume, but this has a tendency to result in re-sputtering of
the film and poor stoichiometry control.
91
Bibliography
[1] D Dijkkamp, T Venkatesan, X D Wu, S A Shaheen, N Jisrawi, Y H Min-Lee,
W L McLean, and M Croft. Preparation of Y-Ba-Cu oxide superconductor thin films using pulsed laser evaporation from high Tc bulk material.
Applied Physics Letters, 51(8):619–621, 1987.
[2] A Inam, M S Hegde, X D Wu, T Venkatesan, P England, P F Miceli, E W
Chase, C C Chang, J M Tarascon, and J B Wachtman. As-deposited high
Tc and Jc superconducting thin films made at low temperatures. Applied
Physics Letters, 53(10):908–910, 1988.
[3] B Dam, J H Rector, J Johansson, S Kars, and R Griessen. Stoichiometric transfer of complex oxides by pulsed laser deposition. Applied Surface
Science, 96-98:679–684, April 1996.
[4] J A Greer and M D Tabat. Large-area pulsed laser deposition: Techniques
and applications. Journal of Vacuum Science & Technology A: Vacuum,
Surfaces, and Films, 13(3):1175–1181, May 1995.
[5] V Matias, B J Gibbons, A T Findikoglu, P C Dowden, J Sullard, and J Y
Coulter. Continuous Fabrication of IBAD-MgO Based Coated Conductors.
IEEE Transactions on Appiled Superconductivity, 15(2):2735–2738, June
2005.
[6] Tsuyoshi Ohnishi, Keisuke Shibuya, Takahisa Yamamoto, and Mikk Lippmaa. Defects and transport in complex oxide thin films. Journal of Applied
Physics, 103(10):103703, 2008.
[7] Hans-Ulrich Krebs and Olaf Bremert. Pulsed laser deposition of thin metallic alloys. Applied Physics Letters, 62(19):2341, 1993.
[8] Michael NR Ashfold, Frederik Claeyssens, Gareth M Fuge, and Simon J
Henley. Pulsed laser ablation and deposition of thin films. Chemical Society
Reviews, 33(1):23–31, 2004.
92
B — X Ray Spectroscopy
X-ray spectroscopy is a powerful method for characterizing the electronic structure of materials. In the mid-20th century, synchrotron radiation sources became available and made it possible to generate x-rays across a broad range of
energies, making x-ray spectroscopy a practical tool.
Synchrotron sources are necessary because measurements require that the
x ray wavelength be varied over a broad range, particularly for absorption
measurements when one wishes to excite core electrons into the conduction
band to map out the partial density of states. For emission measurements, the
requirement is merely that the incident x ray energy be sufficient to eject a core
hole electron. Synchrotrons provide a broad spectrum of “white” light up to
some critical energy EC governed by the specifics of the synchrotron design,, as
shown in Figure B.1. A much more detailed discussion of synchrotron sources
can be found in the references [1].
X-ray spectroscopy can be broken down into three categories: emission,
absorption, and photoemission spectroscopy. These are sketched in Figure B.2.
In XES, a core electron is ejected by an incident x-ray. A valence electron
then decays to fill the core hole, resulting in the emission of a photon. In
XAS, a core electron is excited into an unoccupied level. The decay products
(either an Auger electron or a photon) are then measured. In XPS, a core
electron is ejected and its kinetic energy measured. Selection rules combined
93
1.00
Intensity
0.50
0.20
0.10
0.05
0.01
0.05 0.10
0.50 1.00
5.00
EEC
Figure B.1: Energy spectrum of x-rays emitted from a synchrotron
with monochromatic x-ray sources allows for the experimental determination
of the partial density of states.
B.1 — Transition Rates and Selection Rules
The discussion that follows closely mirrors that found in [2]. To understand
how this site and orbital selectivity comes about, we start with the Hamiltonian
H = Hγ + Hatom + Hint
(B.1)
where Hγ and Hatom are the photon and atomic Hamiltonians, respectively.
We are interested in the transition rate resulting from the photon-electron
interaction, and thus can ignore these two terms. The interaction Hamiltonian
Hint describes the interaction between the atom and the incident photon. The
interaction Hamiltonian is
Hint =
X
e X
~ ri ) + e
~ × A(~
~ ri )
p~i · A(~
~σi · ∇
mc i
2mc i
(B.2)
94
(a)
(b)
(c)
Empty
Valence
Core
Figure B.2: Schematic of three basic x-ray spectroscopy techniques. (a) XES,
(b) XAS, (c) XPS. In XAS and XES, a core hole is created and the decay
products measured. In XPS, the ejected core electron itself is measured.
where the sum is taken over the electrons in the atom. The first term describes
the interaction between the electron momenta and electric field, while the second describes the interaction between the electron spin and magnetic field. The
~ is
vector potential A
~=
A
X
~k,λ
~
~
Ao ε̂~k,λ b~k,λ eik·~r + b~†k,λ e−ik·~r
(B.3)
where b and b† are the boson annihilation and creation operators, respectively.
Hence, the first term describes photon absorption, while the second describes
emission. ǫ̂ is the polarization, and the sum is taken over wave number k and
polarization λ.
The spin term in the interaction Hamiltonian is a relativistic effect that
contributes minimally to x-ray spectroscopy, so it will be disregarded.
The transition rate is given by Fermi’s Golden Rule
Wi→f =
2π
|hψf |Hint |ψi i|2 δ(Ef − Ei ± Eγ )
~
(B.4)
95
where − is for photon absorption and + is for emission.
~
We can expand the exponential term in the vector potential as eik·~r ≈
1+i~k ·~r. Taking only the first term, we can obtain the electric dipole transition
rate
Wi→f = α
4ω 3
n| hψf |~r|ψi i |2 δ(Ef − Ei ± Eγ)
3c2
(B.5)
The Heisenberg equation of motion
˙ = 1 [~r, H ]
~r
i~
(B.6)
has been used to express the momentum in terms of position and frequency.
If one expresses ~r in spherical harmonics, it is found that the electric dipole
operator connects states of opposite parity, leading to the selection rules
∆l = ±1
∆m = 0, ±1
(B.7)
∆s = 0
The quadrupole term follows similarly, leading to the selection rules
∆l = 0, ±2
∆m = 0, ±1, ±2
∆s = 0
(li = 0 → li = 0 is forbidden)
(B.8)
96
B.2 — Decay Processes
In x-ray emission spectroscopy, a constant incident x-ray energy is used to eject
an electron and the resulting photon emission from the refilling of the core hole
is measured. In x-ray absorption spectroscopy, there are two possible decay
products. Refilling of the core hole by a higher energy electron results in the
emission of either a photon or an electron via Auger emission. A 1s2p2p Auger
process (as in oxygen K edge spectroscopy) is illustrated in Figure B.3.
b
b
bc
b
b
bc
b
b
b
b
bc
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
Figure B.3: 1s2p2p Auger decay process
Auger decay is the dominant mechanism for elements with Z < 30 and
binding energies less than about 1 keV, as shown in Figure B.4 [3]. For oxygen,
with Z = 8 and a 1s binding energy of 543.1 eV, the decay products are almost
entirely Auger electrons.[4]
97
Figure B.4: Percentage of decay via x ray fluorescence as a function of binding
energy. Figure taken from [3]
98
Bibliography
[1] G Bunker. Introduction to XAFS. Cambridge, 2010.
[2] B H Bransden and C J Joachain. Physics of Atoms and Molecules. Prentice
Hall, 2 edition, 2003.
[3] F de Groot and A Kotani. Core Level Spectroscopy. CRC Press, 2008.
[4] A Thompson, D Attwood, E Gullikson, M Howells, K J Kim, J Kirz, J Kortright, I Lindau, Y Liu, P Pianetta, A Robinson, J Scofield, J Underwood,
G Williams, and H Winick. X-Ray Data Booklet. Lawrence Berkeley National Laboratory, Berkeley, Ca, October 2009.
99
C — Spectroscopic Ellipsometry
Spectroscopic ellipsometry is a powerful technique for the characterization of
semiconducting thin films. Here, a brief overview of the physics behind ellipsometric measurements is given, along with an overview of how measurements are
performed and how modeling is carried out in order to extract optical constants
and other film properties such as thickness and roughness. Only spectroscopic
ellipsometry carried out in reflection mode will be considered here. In an effort
to make this as clear as possible, I will use script for complex quantities and
italics for real quantities. The discussion here closely follows that given in the
Handbook of Ellipsometry [1].
Ellipsometry uses polarized light to determine the optical properties of
solids. The change in polarization upon reflection, Ψ, and the phase change ∆
are measured and can be used to extract the thickness and optical constants.
Starting with the wave equation in a material
~−
∇2 E
∂
∂t
~
~ + µε ∂ E
µσ E
∂t
!
=0
(C.1)
where µ and ǫ are the permeability and permittivity, respectively, and σ is
the conductivity. If the material is non-conducting (e.g. a semiconductor for
frequencies below the band gap), then the conductivity term can be dropped
and we arrive at the wave equation for an electromagnetic wave in a linear,
100
isotropic dielectric:
~ − µε
∇2 E
~
∂ 2E
=0
∂t2
(C.2)
~ can be obtained by taking the
An identical expression for the magnetic field H
~ = J~ + ∂ D~ . This leads to the
curl of the curl equation for magnetic field ∇ × H
∂t
plane wave solutions
n
o
~ = ℜ E~0 ei(~k·~r−ωt)
E
n
o
~ =ℜ H
~ 0 ei(~k·~r−ωt)
H
(C.3)
We can drop the magnetic field term because the magnetic moments cannot
respond to oscillations in the field that are of order optical frequency.
Let’s assume the light is propagating along ẑ and thus the electric field is
confined to the xy plane. The interesting part comes in connecting this to
the relative phase ∆ between x̂ and ŷ oriented electric fields and the relative
amplitude of the fields along x̂ and ŷ. The complex vector E~ can be rewritten
in terms of the phase difference ∆ and the real field amplitudes Ex and Ey :


E~ = 


E~x   Ex e
=
E~y
Ey
i∆



(C.4)
The relative amplitude can be related to the polarization change Ψ by
tan Ψ =
Ex
Ey
(C.5)
where Ψ is defined with respect to the s polarization axis, as indicated in Figure
101
p
Ψ
s
Figure C.1: Polarization ellipse. The position on the ellipse gives the s and p
components of the electric field
C.1. The angle ∆ defines the difference between the maximum s polarization
and the maximum p polarization. For a given frequency ω, it takes ∆/ω time
to go from the maximum s polarization to the maximum p polarization.
The ratio of reflected intensities for s and p polarization is given by
ρ=
rp
= tan Ψei∆
rs
(C.6)
To relate this to the refractive index, we use the Fresnel equations
p
n2 − sin2 θ
p
rs =
cos θ + n2 − sin2 θ
p
n2 cos θ − n2 − sin2 θ
p
rp =
n2 cos θ + n2 − sin2 θ
cos θ −
(C.7)
Hence, a measurement of Ψ and ∆ can be used to obtain the refractive index
n.
102
Source
Monochromator
Polarizer
Retarder
Detector
Analyzer
θ
Film
Substrate
Figure C.2: Schematic of spectroscopic ellipsometry experimental setup
C.1 — Ellipsometry Measurements
A typical ellipsometer configuration is depicted in Figure C.2. The setup consists of a light source, followed by a monochromator to select a specific wavelength. The polarizer and optionally a retarder made of a birefringent material
are used to prepare a well-defined polarization state for the incident beam.
Upon reflection, the light passes through a rotating analyzer (another polarizing filter) and into the detector, allowing measurement of the reflected polarizaQ
tion state. The final state is given by Sf = j Mj Si where Mj are the Mueller
matrices describing each optical element, including the film. The matrices for
the polarizers and retarders can be found in Hecht (section 8.13.3 in the fourth
edition or 8.12.3 in the third edition) [2].
C.2 — Dielectric Modeling
As we have seen, a measurement is of Ψ and ∆ provides a measure of the
dielectric constant. However, the system is not uniquely determined and we
cannot simply extract n and k directly from Ψ and ∆. To extract the optical
103
constants, we need to use a model to describe the behavior of the material
and we must know something about the material in advance (for example,
knowledge of the approximate thickness). There is a wide choice of models
for the dielectric function that are appropriate for different situations. For
transparent regions where ε2 is zero, the empirical Cauchy model
n = A + B/λ2 + C/λ4
(C.8)
k = α exp(β(E − γ))
(C.9)
can be used. The Drude model can be used to describe strongly absorbing
regions. In the case of semiconductors, we’re interested in regions where neither
of these models provides a satisfactory result. Typically one uses a slightly more
physical Lorentz model, or a model derived from the Lorentz oscillator model
such as the Tauc-Lorentz model which has been used to describe amorphous
semiconductors [3].
The Lorentz model treats atoms as fixed, heavy nuclei with light electrons
bound by springs. The electric field of the incident light induces a dipole
moment and causes the electrons to oscillate.
For displacement along the x direction, we have
mẍ = −mγ ẋ − mω02 x − eE0 eiωt
(C.10)
Assuming a solution of the form x(t) = A exp(iωt), we find
A=−
eE0
1
2
m ω0 − ω 2 + iγω
(C.11)
104
Now, we express the dielectric function as
P
ε0 E 0
eN A
=1−
ε0 E 0
ε=1+
ωp2
=1+ 2
ω0 − ω 2 + iγω
(C.12)
where ωp2 = e2 N/ε0 m.
The complex refractive index can then be obtained from
ε r = n2 − k 2
εi = 2nk
(C.13)
The absorption coefficient α = 4πk/λ vanishes below the band gap because
k is small and λ is large. At ω0 , the imaginary part of the dielectric constant
peaks and the absorption turns on.
In general, one starts from the oscillator model and generates Ψ and ∆,
varying the parameters of the model until the modeled ellipsometry parameters
match the measured values, as extracting n and k from the measured Ψ and
∆ is not possible except in the special case of isotropic samples. Least squares
fitting of the modeled Ψ and ∆ to the experimentally determined values yields
the optical constants of the material. Collection over a broad wavelength range
is necessary to extract both the optical constants and thickness of the film
under examination.
105
Bibliography
[1] H G Tompkins and E A Irene, editors. Handbook of Ellipsometry. William
Andrew and Springer-Verlag, 2005.
[2] E Hecht. Optics. Addison Wesley, 4 edition, 2002.
[3] G E Jellison, Jr., V I Merkulov, A A Puretzky, D B Geohegan, G Eres, D H
Lowndes, and J B Caughman. Characterization of thin-film amorphous
semiconductors using spectroscopic ellipsometry. Thin Solid Films, 377378:68–73, December 2000.
106
D — Calculated Electron Diffraction Patterns
Electron diffraction was employed in Chapter 5 to determine the crystal structure of the (SnCa)S alloy films and check for the existence of an orthorhombic
phase. Here, calculated diffraction patterns for both orthorhombic and rocksalt
structures are given.
D.1 — Orthorhombic SnS
Diffraction patterns along various zone axes for orthorhomic SnS (space group
pmcn) with lattice parameters a = 3.98 Å, b = 4.33 Å, and c = 11.18 Å are
given below.
Figure D.1: Electron diffraction pattern of orthorhombic SnS viewed along the
h001i zone axis
107
Figure D.2: Electron diffraction pattern of orthorhombic SnS viewed along the
h010i zone axis
Figure D.3: Electron diffraction pattern of orthorhombic SnS viewed along the
h100i zone axis
108
Figure D.4: Electron diffraction pattern of orthorhombic SnS viewed along the
h111i zone axis
Figure D.5: Electron diffraction pattern of orthorhombic SnS viewed along the
h011i zone axis
109
Figure D.6: Electron diffraction pattern of orthorhombic SnS viewed along the
h101i zone axis
Figure D.7: Electron diffraction pattern of orthorhombic SnS viewed along the
h110i zone axis
110
D.2 — Rocksalt (SnCa)S
Diffraction patterns for Sn1−x Cax S in the rocksalt structure (space group fm3m)
are given below.
Figure D.8: Electron diffraction pattern of rocksalt (SnCa)S viewed along the
h001i zone axis
111
Figure D.9: Electron diffraction pattern of rocksalt (SnCa)S viewed along the
h011i zone axis
Figure D.10: Electron diffraction pattern of rocksalt (SnCa)S viewed along the
h111i zone axis