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
Reference: William Shockley and Hans J.Queisser, J.Appl.Phys.32, 510 (1961); doi : 10.1063/1.1736034

Physical Model

◼
  • Single cut-off frequency: for E ≥ hν effect otherwise no effect
    • ◼
  • p-n junction solar cell is at
    T
    C
    = 0, surrounded by a blackbody at T =
    T
    s.
    • ◼
  • Introduce finite
    T
    C
    and replace surrounding body at
    T
    S
    by radiation coming from the sun at a small solid angle
    ω
    s
    .

    • Ultimate Efficiency Hypothesis

    Each photon with
    E>
    hν
    g
    produces 1
    q
    e
    at a voltage of
    V
    g
    =
    hν
    g
    q
    e
    .

    Formula Check for Incident Power

    In[]:=
    Remove[h,ν,Ts,κ,c]
    In[]:=
    (2πh)
    ∞
    ∫
    0
    3
    ν
    exp
    hν
    κTs
    -1
    ν
    2
    c
    Out[]=
    ConditionalExpression
    2
    5
    π
    4
    Ts
    4
    κ
    15
    2
    c
    3
    h
    ,Re
    h
    Tsκ
    >0

    Physical Constants

    Blackbody Radiation

    Useful Parameters for the Calculation

    Calculation and Result

    As a Function of
    xg

    As a Function of bandgap

    FURTHER EXPLORATIONS
    Calculation of
    η
    max
    with
    T
    C
    =300K
    Radiative recombination & lifetime consideration
    AUTHORSHIP INFORMATION
    Suman Banerjee
    6/23/17
    suman.banerjeee@gmail.com