Mark Lundstrom (2011), "Solar Cells Lecture 1: Introduction to Photovoltaics," http://nanohub.org/resources/11875.

1. NCN Summer School: July 2011
Introduction to Photovoltaics
Prof. Mark Lundstrom
lundstro@purdue.edu
Electrical and Computer Engineering
Purdue University
West Lafayette, Indiana USA

2. copyright 2011
This material is copyrighted by Mark Lundstrom under
the following Creative Commons license:
Conditions for using these materials is described at
http://creativecommons.org/licenses/by-nc-sa/2.5/
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3. acknowledgement
Dionisis Berdebes, Jim Moore, and Xufeng Wang
played key roles in putting together this tutorial.
Their assistance is much appreciated.
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4. modern solar cell
Chapin, Pearson, and Fuller, Bell Labs. 1954
http://www.bell-labs.com/org/physicalsciences/timeline/span10.html#
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5. solar cell progress
5
5 http://en.wikipedia.org/wiki/File:PVeff(rev100921).jpg

6. solar cell industry
SunPower / Applied Materials
Mark Pinto, “Renewable Solar Energy: Has the Sun Finally Risen on Photovoltaics?”
https://nanohub.org/resources/6332
6

7. solar cell
A solar cell is a junction (usually a PN junction) with sunlight shining on it.
To understand how a solar cell works, we need to understand:
1) how a PN junction works (w/o the light)
2) how light is absorbed in a semiconductor (without a PN junction)
3) what happens when we put the two together.
7

8. outline
1) Introduction
2) PN junction fundamentals (dark)
3) Model solar cell: dark IV
4) Optical absorption / light-generated current
5) Model solar cell: illuminated
6) Discussion
7) Summary
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9. silicon energy bands

conduction empty states
“band” T=0K
EC
valence
EG = 1.1 eV
“band”
EV
filled states

“core levels”
9 Lundstrom 2011

10. intrinsic n-type p-type
−
+
n0 N ≈ ND p0 P ≈ NA
EC EC EC
EF
EF
EF
EV EV EV
“hole”
EV EV EV “holes”
filled states filled states filled states
10 Lundstrom 2011

11. Fermi level
+
n0 N ≈ ND −
p0 P ≈ NA
1
f0 (E ) =
EC 1 + e(E − EF ) kBT EC
1
EF
E = EF → f0 (E ) =
2
EF
EV E << EF → f0 (E ) = 1 EV
EV “holes”
EV
filled states
E >> EF → f0 (E ) = 0
filled states
11 Lundstrom 2011

12. intrinsic semiconductor
EC
n0 = ni
EF = EI p0 = ni
EV
n0 p0 = ni2
“hole”
EV
filled states
ni ∝ e− EG kBTL
ni (300 K ) ≈ 1010 cm -3
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13. n-type semiconductor
+
n0 N ≈ N D
EC +
n0 ≈ ND
EF
n0 p0 = ni2
+
EV p0 = ni2 ND
EV
filled states
n0 = ND ≈ 1017 cm -3
ni (300 K ) ≈ 1010 cm -3
13
p0 ≈ 10 3 cm -3
Lundstrom 2011

14. p-type semiconductor
EC −
p0 ≈ NA
n0 p0 = ni2
EF
−
EV n0 = ni2 NA
“holes”
EV
filled states
p0 = NA ≈ 1017 cm -3
ni (300 K ) ≈ 1010 cm -3
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n0 ≈ 10 3 cm -3
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15. PN junction
+
n0 N ≈ ND −
p0 P ≈ NA
EC EC
EF What happens if we
bring the p and n EF
regions together?
EV EV
EV “holes”
EV
filled states filled states
15

16. PN junction in equilibrium
n0 N ≈ N D n0 P ≈ ni2 NA
Fermi level
EC lower is constant!
EC = -qV qVbi
p-type
V = Vbi EF EF V=0
n-type
p0 P ≈ NA
p0 N ≈ ni2 ND
slope
Vbi ~ EG ID = 0 proportional to
qVbi =
kBT NA ND
ln
VA = 0 electric field
q ni2 16

17. PN junction in equilibrium
n0 P ≈ ni2 NA
P0 = ?
qVbi
EF EF P 0 = e− ∆E kBT
n0 N ≈ N D
p0 P ≈ NA
p0 N ≈ ni2 ND
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18. PN junction under forward bias
nP > ni2 NA
P = P 0 eqVA kBT
q (Vbi − VA ) P = e− q(Vbi −VA ) kBT
FN
n0 N ≈ N D FP
“excess carriers”
p0 P ≈ NA
A positive voltage on p-side
pulls the bands down.
p0 N ≈ ni2 ND
Energy barrier is lowered.
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19. PN junction under forward bias
Excess electron
concentration on the p-side.
∆nP (x)
q (Vbi − VA ) WP
Qn = q ∫ ∆nP (x)dx
FN
n0 N ≈ N D
0
FP
p0 P ≈ NA Qn Q p
ID = +
tn tp
The time, t n is the average time for an electron on the p-side to
“recombine” or to diffuse to the contact and recombine. Let’s see
why recombination leads to current. 19

20. recombination leads to current
minority carriers injected across junction
Fn qVA FP
ID
− VA +
Every time a minority electron recombines on the p-side, one
20 electron flows in the external current.

21. recombination at a contact
minority carriers injected across junction
Fn qVA FP
ID
− VA +
Every time a minority electron recombines on the p-side, one
21
electron flows in the external current.

22. forward bias summary
∆nP (x)
I n1 ∝ e qVA kBT
1) Injected current produces a
population of “excess”
electrons in the P-type
q (Vbi − VA )
region...
2) Excess electrons in the P-
FN type region recombine…
n0 N ≈ N D FP
3) Every time an electron and
p0 P ≈ NA hole recombine, an
electron flows in the
p0 N ≈ ni2 ND external circuit.
0 < ID
22
VA > 0 Lundstrom 2011

23. ideal diode equation
Qn Q p
ID =
tn
+
tp Qn ∝
NA
(e
ni2 qVA kBT
− 1)
0 < ID I D = I 0 (eqVA kBT − 1)
− VA + “ideal diode equation”
I D = I 0 (eqVA nkBT − 1)
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n =1
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24. outline
1) Introduction
2) PN junction fundamentals (dark)
3) Model solar cell: dark IV
4) Optical absorption / light-generated current
5) Model solar cell: illuminated
6) Discussion
7) Summary
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25. generic crystalline Si solar cell
SF = 1000 cm/s key device
n+ “emitter” (0.3 μm) parameters
base doping: NA = 1016 /cm3
p-type “base”
emitter doping ND = 6x1019 /cm3
minority carrier lifetime τn = 34 μs
(198.9 μm) (base)
base thickness W = 198.9 μm
p+ “Back Surface Field” (BSF)
(0.8 μm) front junction depth xjf = 0.3 μm
back junction depth xjb = 0.8 μm
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R
Lundstrom 2011 s = 1 Ohm-cm2

26. equilibrium e-band diagram
EF EF
199.2 200
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27. dark I-V
J D = J 0 (eqVA nkBT − 1)
n >1
n =1
n≈2
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28. recombination: V = 0.7 V
entire device front surface region
~70%
~10%
~20% ~20%
x
∫ R(x′ )dx′
R(x) 0
L
28 ∫ R(x′ )dx′
0
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29. series resistance
− VA + RS
0 < ID
− VA +
I D = I 0 (eqVA kBT − 1) VD = VA + I D RS
( )
I D = I 0 eq(VD − I D RS ) kBT − 1
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30. dark I-V and series resistance
I D RS
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31. outline
1) Introduction
2) PN junction fundamentals (dark)
3) Model solar cell: dark IV
4) Optical absorption / light-generated current
5) Model solar cell: illuminated
6) Discussion
7) Summary
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32. absorption of light
EC
hc
λ< E = hf > EG EG
EG
EV
c hc
fλ = c f= E = hf =
λ λ
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33. solar spectrum (outer space)
space AM0 = “air mass 0”
AM 0
Earth
Integrated power = 136.6 mW/cm2
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34. solar spectrum (terrestrial)
atmosphere
1
θX AMX = AM1.5 : θ x = 48.2 deg
cos θ x
“G” = “global”
Earth
Integrated power = 100 mW/cm2)
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http://en.wikipedia.org/wiki/Air_mass_(solar_energy)

35. how many photons can be absorbed?
Example: Silicon Eg = 1.1eV. Only photons with a wavelength
smaller than 1.1 m will be absorbed.
solar
spectrum
(AM1.5G)
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36. wasted energy for E > EG
Energy is lost for photons with energy greater than the bandgap.
hf > EG
Electron is excited above However, extra energy is lost due to
the conduction band. thermalization as electron relaxes
back to the band edge.
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37. how many photons are absorbed in a finite
thickness?
Incident flux: Φ 0
Flux at position, x : Φ (x) = Φ 0 e−α (λ )x
optical absorption coefficient:
α (λ ) > 0 for E > EG (λ < hc EG )
Generation rate at position, x :
d Φ (x)
G (x) = − = Φ 0α (λ )e−α (λ )x
dx
L
 

Gtot = ∫  ∫ G (x, λ )dx  dλ

0 
 37

38. what determines alpha?
E E
conduction conduction
band band
p2
EG E= EG need
2m phonon
p p
valence valence
band band
Direct gap: strong absorption Indirect gap: weaker absorption
(high alpha) lower alpha) 38

39. light absorption vs. semiconductor thickness
The direct bandgap of CIGS allows it to absorb light much faster than Silicon.
A layer of silicon must be 104 microns thick to absorb ~100% of the light,
while CIGS need only be about 2 microns thick.
CIGS (direct) Si (indirect)
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40. maximizing light absorption / generation
1) Maximize the number of phonons anti-reflection (AR) coating
that get into the solar cell (AR
coating, texturizing).
2) Maximize the “effective” thickness of
the absorber. solar cell
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41. light-trapping in high-efficiency Si solar cells
370 − 400 µm
24.5% at 1 sun
Martin Green Group UNSW – Zhao, et al, 1998
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42. collection of e-h pairs
1) Light generates electron-hole pairs
EC
E = hf > EG
EV 2) PN junction collects e-h pairs
n-region collects the minority carrier EF
electrons
p-region collects the minority carrier
holes
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43. collection efficiency
Photo-generated carriers should diffuse But some may
to the junction and be collected. recombine in the
base.
“base”
EF (absorbing layer)
“emitter”
And some may diffuse
to the contact and
JL recombine.
CE ≡
J L max
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“collection efficiency” Lundstrom 2011

44. voltage-dependence of collection
Vbi − VA “base”
EF (absorbing layer)
“emitter”
As long as VA < Vbi, the applied bias should affect the collection of carriers.
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45. current collection
The generated carriers are only useful to us if they are able to
be collected.
Electron diffusion length: Distance e will travel before recombining
n+ p
t < Ln = Dnτ n
Generated e-
For Si: μn~1200 cm2/V-s; n~34s
Ln~320 m
0 t
Therefore we cannot make the absorbing layer arbitrarily thick.
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46. real thickness vs. optical thickness
24.5% at 1 sun
Martin Green Group UNSW – Zhao, et al, 1998
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47. outline
1) Introduction
2) PN junction fundamentals (dark)
3) Model solar cell: dark IV
4) Optical absorption / light-generated current
5) Model solar cell: illuminated
6) Discussion
7) Summary
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48. diode current under illumination
1) Light generates e-h pairs
EF
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49. diode current under illumination
2) PN junction collects e-h pairs 3) Current flows through load
IL < 0
EF
ID > 0
RL
− VL +
forward bias across PN junction
IL < 0 develops
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50. net current
4) Forward bias reduces current 5) IV characteristic is a superposition
ID
I 0 (eqVD nkBT
−1 )
Fn qVD Fp
VD
IL < 0
I D = I 0 (eqVD nkBT
)
− 1 − IL
50 dark current - light-generated
Lundstrom 2011 current

51. IV characteristic
6) Maximum power point
I D = I 0 (eqVD nkBT
)
− 1 − IL
ID
Pout I SCVOC FF
η= =
Pin Pin
VOC
VD
Pout = I DVOC = 0
− I SC
IL < 0
Pout = I SCVD = 0
PD = I DVD < 0
51
Pout = I mpVmp = I SCVOC FF

52. “superposition”
IL < 0 IL > 0
+
RL VL > 0
−
light-generated current dark current
I D = I 0 (eqVD )
(bias independent) nkBT
−1
52

53. effect of series and shunt resistors
http://upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Solar_cell_equivalent_circuit.svg/60
1px-Solar_cell_equivalent_circuit.svg.png 53

54. series and shunt resistors
Effect of series resistance Effect of shunt resistance
FF FF
0.84 0.84
0.79 0.71
0.74 0.58
I = I L − I0  eq (V + IRS )/ k B T − 1 − V + IRS
Modified Diode Equation:   R
SH
54 Lundstrom 2011

55. model solar cell simulation
ADEPT 2.0 nanoHUB.org
Results:
VOC = 616 mV
J SC = 39.4 mA/cm 2
FF = 0.83
η = 20.1%
(See slide 26 for parameters)
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56. outline
1) Introduction
2) PN junction fundamentals (dark)
3) Model solar cell: dark IV
4) Optical absorption / light-generated current
5) Model solar cell: illuminated
6) Discussion
i) superposition
ii) efficiency limits
iii) costs
7) Summary
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57. i) principle of superposition
I D (VD ) > 0 I TOT
+
IL < 0 RL V = VD > 0
VD
−
Photo-generated current collected by
the junction. Generally assumed to I DARK = I 0 (eqVD nkBT
)
−1
be independent of the junction
voltage.
determined by recombination
Superposition says that we can processes in the dark
add the two solutions to get the
57
total response of the solar cells.

58. superposition
We can superimpose two solutions when the differential
equations describing the problem are linear.
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59. solar cell physics
“semiconductor equations”
Conservation Laws: Relations:
  

κε −κε
D = 0 E = 0 ∇V
∇• D =ρ
ρ q( p − n + N D − N A )
= + −
  
 J= nq µn E + qDn∇n
(
∇ • J n −q=) (G − R ) 
n
 
J= pq µ p E − qD p ∇p
p
 R = f (n, p )
(
∇• Jp )
q= (G − R )
G = optical generation rate
(steady-state) etc.
59 Lundstrom 2011

60. when does superposition apply?
1) the junction space-charge region may contribute importantly to
either the photocurrent or the dark current, but not to both;
2) the carrier concentrations in the quasi-neutral regions must stay
within low-injection levels;
3) the series resistance (and shunt resistance) must contribute
negligilbly to the cell current-voltage characteristics;
4) the material parameters, such as the minority-carrier lifetime, must
be essentially independent of the illumination level;
5) the volume of the regions that contribute appreciably to the
photocurrent must stay essentially constant as the cell is loaded.
F. A. Lindholm, J.G. Fossum, and E.L. Burgess, “Application of the Superposition
Principle to Solar-Cell Analysis,” IEEE Trans. Electron Devices, 26, 165-171, 1979
60 Lundstrom 2011

61. ii) solar cell efficiency limits
1) Fill factor:
Determined by diode characteristic
and series resistances.
2) Short-circuit current:
Pout I SCVoc FF
η= = Increases as the bandgap decreases.
Pin Pin
For a given bandgap, determined by
reflection, absorption, recombination.
3) Open-circuit voltage:
Increases as the bandgap increases.
For a given bandgap, determined by
61
recombination.

62. Shockley-Queisser Limit
1) Smaller bandgaps give higher
short circuit current
2) Larger bandgaps give higher
open-circuit voltage
3) For the given solar spectrum, an
optimum bandgap exists.
W. Shockley, and H. J. Queisser, “Detailed Balance Limit of Efficiency of p‐n
Junction Solar Cells”, J. Appl. Phys., 32, 510, 1961.
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63. iii) costs: three approaches
1) High-efficiency , but high-cost solar cells
(high-quality crystalline materials)
2) Acceptable efficiency, but very low costs
(thin-film, amorphous/polycrystalline materials)
3) Concentration
(high efficiency cells with optical concentration)
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64. “grid parity”
For a photovoltaic power generation system to be economically
competitive the total costs of an installed PV system must be ~ $1/W,
which translates to 5-6 cents per kilowatt-hour.
A system includes:
1) Module costs
2) Power conditioning electronics
3) Installation and balance of systems.
Current costs are $3.40/W (2011).
Projected to decrease to $2.20/W by 2016
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65. the dollar per Watt goal
The U.S. Department of Energy is calling for research to meet the $1/W
goal. This requires modules at $0.50/W, with ~20% modules with 20-30
system lifetimes.
http://www1.eere.energy.gov/solar/
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66. outline
1) Introduction
2) PN junction fundamentals (dark)
3) Model solar cell: dark IV
4) Optical absorption / light-generated current
5) Model solar cell: illuminated
6) Discussion
7) Summary
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67. solar cell summary
1) Light is absorbed and produces e-h pairs
2) PN junctions separate e-h pairs and collect the carriers.
3) Current flow in external circuit produces a FB voltage and
the FB diode current reduces the total current.
4) Power out is ISCVOC FF.
5) Unlike integrated circuit chips, where the value added
comes from the design/system, manufacturing costs are
critical in PV.
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68. references
Textbooks:
Martin Green, Solar Cells: Operating Principles, Technology, and System
Applications, Prentice-Hall, 1981.
Jenny Nelson, Physics of Solar Cells, Imperial Collage Press, 2003
Antonio Lugue and Steven Hegedus, Handbook of Photovoltaic Science and
Engineering, John Wiley and Sons, 2003.
Compilation of current cell efficiencies:
Martin Green, et al., “Solar cell efficiency tables (version 37)”, 19, Prog. in
Photovoltaics, 2011
Survey of 3rd generation PV concepts:
Martin Green, Third generation photovoltaics: advanced solar energy
conversion, Springer, 2006.
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69. questions
1) Introduction
2) PN junction fundamentals (dark)
3) Model solar cell: dark IV
4) Optical absorption / light-generated current
5) Model solar cell: illuminated
6) Discussion
7) Summary
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