A silicon cell at the detailed-balance limit delivers

PHYSICS · Multi-part · Fermi University Physics · Earth, Climate & Energy Physics · Energy resources and conversion · Energy resources and conversion

Energy from Physics, Ch How efficient a solar cell can be: detailed balance, tandems and the field

Problem

A silicon cell at the detailed-balance limit delivers, at one sun under the blackbody Sun (

S_0 = 1361\,\mathrm{W\,m^{-2}}

J_{sc} = 53\,\mathrm{mA\,cm^{-2}}

and

V_{oc} = 0.882\,\mathrm{V}

with fill factor

0.870

, at

T_c = 300\,\mathrm K

. It is placed under a concentrator of geometric concentration

C

and actively cooled so that

T_c

stays at

300\,\mathrm K

. Its contacts and grid add a specific series resistance

R_s = 1.0\times10^{-3}\,\Omega\,\mathrm{cm^2}

. Model the output power per unit cell area as

P(C) = \mathrm{FF}\,CJ_{sc}\,V_{oc}(C) - (CJ_{sc})^2R_s

, with the fill factor held at

0.870

and the current at maximum power taken as

CJ_{sc}

. ((a)) Find

V_{oc}

C = 100

. ((b)) Show that the efficiency

\eta = P/(CS_0)

is greatest at

C^* = \mathrm{FF}\,(k_BT_c/e)/(J_{sc}R_s)

, and evaluate

C^*

. ((c)) Find the efficiency at

C^*

and compare it with this model's value at one sun.