1
UNDERSTANDING SEMICONDUCTOR
DEVICES
D.L. Pulfrey
Department of Electrical and Computer Engineering
University of British Columbia
Vancouver, B.C. V6T1Z4, Canada
pulfrey@ece.ubc.ca
http://nano.ece.ubc.ca
Pisa, May 27-30, 2008
2
Schedule
Day 1: Solar Cells
Day 2: LEDs
Day 3A: HBTs
Day 3B: HEMTs
Day 4A: Si MOSFETs
Day 4B: Carbon nanotube FETs
3
PV: large and small
12 MW Arnstein,
Germany
Tabernas desert, Spain
Photos of solar cell installations
5kW Boston
Massachusetts
http://256.com/solar/
4
The Photovoltaic Effect
We need to consider:
1. Energy source
2. Absorption
3. Transport
4. Collection
UDEL
5
The sun as a resource
• Value for Hsun ?
• How is the energy
generated ?
• Value for H0 ?
• How much is lost in the
atmosphere ?
• What is Air Mass ?
UDEL
6
Irradiance standards
ASTM G173-03 Reference Spectra
2.00
Etr W*m-2*nm-1
Global tilt W*m-2*nm-1
Direct+circumsolar W*m-2*nm-1
1.50
-2
Spectral Irradiance W m nm
-1
1.75
1.25
1.00
0.75
0.50
What are the absorbers?
0.25
0.00
250
500
750
1000
1250
1500
1750
2000
2250
Wavelength nm
UDEL
2500
2750
3000
3250
3500
3750
4000
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• EHP generated.
• We need to know the
band structure.
Potential energy of electron
Absorption
Determining E-k
What is the wavelength of an
electron with v = 107 cm/s ?
What is the lattice
constant for Si ?
What are the boundary
conditions ?
8
9
Boundary conditions
PE
or
Bloch''s theorem
What is this k ?
What are these ?
Allowed values of E
What are the
implications for E ?
10
11
Bands and states
What is N in this
example ?
How many
electrons allowed in
each band ?
If this were Si,
how many
bands would be
filled at 0 K ?
Can k be identified with
momentum ?
12
Absorption in real materials
What is the momentum of
a photon ?
How does absorption
occur in Si ?
13
Phonons
AP near zone centre
Phonon dispersion
OP near zone edge
Note: magnitudes of phonon momenta
and energies
14
Phonon assistance
E
X
X
What's happening here ?
k
  E p  E g


 (  E  E ) 2 (  E  E ) 2 
g
p
g
p

 ( )  B 

Ep
 Ep 

1
1  exp
 exp

k
T
k BT 
B

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Absorption coefficient
UDEL
 ( ) 
4k r ( )

Where does this come from ?
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Generation rate
UDEL
( x)   t exp( x)
d
 Gop  0
dx
How does this curve tell you
what the doping profile and
thickness of the solar cell
must be ?
17
Internal quantum efficiency
This completes the opening section on ABSORPTION.
We hope that each absorbed photon leads to one EHP,
which means that we do not want any INTRABAND
absorption,
AND, that the electron and hole can be separated,
which means that we don't want any EXCITONs.
Now we move on to the TRANSPORT phase.
18
Classical Transport
What does Heisenberg
"say" about this ?
19
NP-junction basics
P
P
Identify:
P
P
B
B
B
chemical potential energy, electrostatic potential, built-in voltage,
electrochemical potential energy.
What is the Depletion Region Approximation?
Can Vbi be measured ?
20
Full- and hemi-Maxwellians
/1E20
21
NP-junction at equilibrium
22
Quasi-Fermi Levels
Origina
l EF
EFn
EFi
EFp
23
The classical semiconductor-device equations
where the LOW-LEVEL APPROXIMATION has been used for U
24
Generation rate revisited
UDEL
Before using the "Complete
Set", recall the earlier slide on
generation rate.
Now that you know the solar
cell is a diode, can you
answer the previously posed
question?
How does this curve tell you
what the doping profile and
thickness of the solar cell
must be ?
25
Jphoto in Depletion Region
xj
xj+W
J eD (, x j )  q t exp( x j )[1  exp( W )]
Make the emitter thin, and DR wide
Jphoto in base region
How do we solve Poisson?
xj
xj+W
B
Why the BSF ?
There is competition for the
collection of electrons
J (, x j W )  ..................
B
e
What is the surface
recombination velocity ?
Should the base material be nor p-type? Heavily or lightly
doped?
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27
Recombination possibilities
Pierret
What is the value for n in the base?
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Minority carrier diffusion length
L  D
What are the values in the
emitter and in the base?
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Jphoto in emitter region
xj
W+xj
What are the boundary conditions?
J hE ( , x j )  ..................
J photo ( )  J hE (  , x j )  J eD (  , x j )  J eB (  , x j  W )
Is this
OK ?
Jphoto in the emitter and base regions
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Computation of Jphoto
y-axis units?
3
Which response (1, 2, or 3)
corresponds to which
region (E, D, or B)?
2
1
200
400
600
800
1000
 (nm)
Magnitude of Jphoto ?
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Maximizing Jphoto
Why pyramids?
What thickness and nr of AR coating?
Why rear oxide?
UDEL
Lambertian reflector?
33
Photovoltage
+
RLoad
-
Iphoto
• Connect load
• Voltage across the load forward biases the diode
• Dark current opposes Iphoto
+
RLoad
Iphoto
-
IL < Iphoto
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Superposition
I
Voc
V
Iphoto
What is the expression for Voc ?
35
The dark current
ln I
3
1 + 2
0.3 - 0.4
V
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Fill factor
Include parasitic R and
IDR(dark) in equivalent
circuit.
UDEL
What is the effect of
the R's and the extra
diode on Isc, Voc, FF ?
37
Iph=40e-3*A: A=0.9*pi*100/4
3
2.5
1.5
I
load
(A)
2
1
0.5
0
0
0.1
0.2
0.3
0.4
0.5
Vload (V)
0.6
0.7
0.8
0.9
1
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Effect of temperature and insolation
Day4, UDEL
39
Efficiency
World record for Si:
• Jsc = 42.2 mA/cm2
• Voc = 0.706 V
• FF = 0.828
•  = 24.7%
Give record values for Si
+
Show circuit again,
max power transfer
UDEL
RLoad
-
Match load to RCH
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Silicon purity
X
X
X
X
X
Metallurgical grade Si
Semiconductor grade Si
UDEL
Si + 3HCl
SiHCl3 + H2
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mc-Si solar cell
cost analysis
Rohatgi et al., IWPSD,
20-28, 2005
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mc-Si solar cells
UDEL
Single crystal
sc-Si
>10cm
Czochralski (CZ) float zone (FZ)
Multicrystalline
mc-Si
1mm-10cm Cast, sheet, ribbon
Polycrystalline
pc-Si
1µm-1mm
Chemical-vapour deposition
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Multicrystalline Si cells cells
UDEL
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Thin sc-Si solar cells
K.J. Weber et al., IEEE Photovoltaic Specialists Conf., 991-994, 2005.
10X reduction in Si
use claimed
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Optimum bandgap
Under AM1.5 conditions:
Max Theoretical Efficiency
~28%
The current best (in Lab)
Si
= 24.7%
GaAs = 26%
CIGS = 19.9%
http://photochemistry.epfl.ch/EDEY/NREL.pdf
What are the reasons for these
trends?
46
CIGS cells: a lower cost alternative (?)
Noufi, Rommel; Ken Zweibel. HIGH-EFFICIENCY CDTE
AND CIGS THIN-FILM SOLAR CELLS: HIGHLIGHTS AND
CHALLENGES. National Renewable Energy Laboratory.
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Properties of CuIn1-xGaxSe2
• Chalcopyrite structure, tetragonal bonding
• Vacancy doping*
• Direct bandgap
• Eg(x) 1.04 - 1.7 eV
• High absorption coefficient
• Can be printed onto glass and metal
• Needs heteroface cell structure
• Google has invested $$$$$ in it.
*
VCu0  VCu  h 
:
E a  0.03 eV
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Heterojunction advantages and problems
E
EC
Wide bandgap window, but
what happens at the
interfaces?
EV
And why is CdS needed?
x
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Multijunction cells: concept and practice
http://www1.eere.energy.gov/solar/solar_cell_structures.html#multijunction
http://www.emcore.com/assets/photovoltaics/Emcore_Manuscript_Fatemi_3P-B5-03_WCPEC-3.pdf
50
Matching the materials
J. M. Román, “State-of-theart of III-V Solar Cell
Fabrication Technologies,
Device Designs and
Applications,” Advanced
Photovoltaic Cell Design,
2004.
http://photochemistry
.epfl.ch/EDEY/NREL.
pdf
51
The world-record holder
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Efficiency comparison: materials and modules
UDEL
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Modules
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Module construction and operating temperature
UDEL
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Modules: bypass and blocking diodes
It's the same problem as
in mis-matched multijunction solar cells
UDEL
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Diurnal variation and seasonability
UDEL
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Battery storage
UDEL
58
$/Wpk estimates for power plants
Scrubbed
coal
1.290
IGCC coal 1.491
"Clean"
coal
2.134
Si PV
5
Nanosolar 2
CIGS PV
59
Fusion and Fission
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Nuclear in a "green" country
Mrs Merkel’s dramatic
change of heart surfaced
at an energy summit
attended by government
and industry heads in
Berlin last week, when it
became clear that her
ruling grand coalition’s
aim of closing Germany’s
17 nuclear power plants
by the early 2020s were
at odds with targets for
the reduction of CO2
emissions.
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Ferrari beware !
UDEL
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References
• UDEL http://www.udel.edu/igert/pvcdrom/index.html
• Pierret, R.F., "Advanced Semiconductor Fundamentals",
Addison-Wesley, 1987
• Day4
http://www.day4energy.com/