A p-type silicon wafer with acceptor density is illuminated at normal incidence by…

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Earth, Climate & Energy Physics · Semiconductor physics and devices

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

Problem

A p-type silicon wafer with acceptor density

N_A = 1\times10^{15}\,\mathrm{cm^{-3}}

is illuminated at normal incidence by monochromatic

800\,\mathrm{nm}

light with photon flux

\Phi_0 = 2\times10^{17}\,\mathrm{cm^{-2}\,s^{-1}}

just inside the front surface (reflection already excluded). At

800\,\mathrm{nm}

the absorption length in silicon is

1/\alpha = 12\,\mu\mathrm{m}

. The radiative and Auger coefficients of silicon are

B = 4.7\times10^{-15}\,\mathrm{cm^3\,s^{-1}}

and

C_p = 9.9\times10^{-32}\,\mathrm{cm^6\,s^{-1}}

, and a defect level in this wafer independently limits the lifetime to

\tau_{\rm defect} = 100\,\mu\mathrm{s}

. A finished cell made from similar material is measured at

300\,\mathrm{K}

under

1000\,\mathrm{W\,m^{-2}}

to have

J_{sc} = 32\,\mathrm{mA\,cm^{-2}}

and

J_0 = 2\times10^{-13}\,\mathrm{A\,cm^{-2}}

. ((a)) Find the optical generation rate

G

at the front surface and at a depth of one absorption length. ((b)) Find the combined minority-carrier lifetime, including the radiative, Auger and defect routes. ((c)) Find the cell's open-circuit voltage, fill factor and efficiency.

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