For the blackbody Sun ( )

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

Energy from Physics, Ch The illuminated junction: generation, collection and the cell's characteristic

Problem

For the blackbody Sun (

T_\odot = 5772\,\mathrm{K}

), the photon flux above a threshold energy

E_g

falls in the Wien tail of the Planck spectrum once

x_g \equiv E_g/(k_BT_\odot) \gtrsim 2

, where it is well approximated by

\Phi(E_g)\propto e^{-x_g}(x_g^2+2x_g+2)

. Using this scaling, a silicon cell's photon ceiling is known to be

J_{\rm ceiling}=e\Phi(E_g)=53\,\mathrm{mA\,cm^{-2}}

for

E_g=1.12\,\mathrm{eV}

. ((a)) Using the Wien-tail scaling above, estimate the photon ceiling

e\Phi(E_g)

for a GaAs cell,

E_g=1.42\,\mathrm{eV}

, by scaling from the silicon value. ((b)) A record single-junction GaAs cell has a measured short-circuit current density of about

29.6\,\mathrm{mA\,cm^{-2}}

at one sun under the standard AM1.5G spectrum. What fraction of the blackbody photon ceiling from part (a) does it reach, and how does this compare with silicon's

41/53 = 77\%

, found the same way? Both fractions set a ground-level AM1.5G current against a blackbody count outside the atmosphere, so they compare the two cells with each other, not with their own AM1.5G ceilings.

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