Reference: William Shockley and Hans J.Queisser, J.Appl.Phys.32, 510 (1961); doi : 10.1063/1.1736034
Shockley–Queisser Limit
Shockley–Queisser Limit
The Shockley-Queisser limit is the upper theoretical limit for the efficiency of p-n junction solar cells. It plays an important role in estimating how far an experimental solar cell efficiency is from the maximum achievable theoretical efficiency.
June 23, 2017—Suman Banerjee
Physical Model
Physical Model
◼
Single cut-off frequency: for E ≥ hν effect otherwise no effect
◼
p-n junction solar cell is at = 0, surrounded by a blackbody at T =
T
C
T
s.
◼
Introduce finite and replace surrounding body at by radiation coming from the sun at a small solid angle .
T
C
T
S
ω
s
Ultimate Efficiency Hypothesis
Ultimate Efficiency Hypothesis
Each photon with produces 1 at a voltage of =.
E>
hν
g
q
e
V
g
hν
g
q
e
Formula Check for Incident Power
Formula Check for Incident Power
In[]:=
Remove[h,ν,Ts,κ,c]
In[]:=
(2πh)ν
∞
∫
0
3
ν
exp-1
hν
κTs
2
c
Out[]=
ConditionalExpression,Re>0
2
5
π
4
Ts
4
κ
15
2
c
3
h
h
Tsκ
Physical Constants
Physical Constants
Blackbody Radiation
Blackbody Radiation
Useful Parameters for the Calculation
Useful Parameters for the Calculation
Calculation and Result
Calculation and Result
As a Function of xg
As a Function of
xg
As a Function of bandgap
As a Function of bandgap
FURTHER EXPLORATIONS
Calculation of with =300K
η
max
T
C
Radiative recombination & lifetime consideration
AUTHORSHIP INFORMATION
Suman Banerjee
6/23/17