A germanium p-n junction ( at

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

Solid State Physics, Ch Junctions and devices, finished

Problem

A germanium p-n junction (

n_i\approx2\times10^{13}\,\mathrm{cm^{-3}}

300\,\mathrm{K}

, far larger than silicon's

1.0\times10^{10}\,\mathrm{cm^{-3}}

) is measured from

0.10

0.22\,\mathrm{V}

and shows a single straight line on

\log_{10}J

against

V

down to the lowest measured current, with no low-bias upturn:

V=0.100\,\mathrm{V}

J=1.00\times10^{-4}\,\mathrm{A\,cm^{-2}}

V=0.220\,\mathrm{V}

J=1.00\times10^{-2}\,\mathrm{A\,cm^{-2}}

. Take

k_BT/e=25.85\,\mathrm{mV}

300\,\mathrm{K}

. ((a)) Find the ideality factor from the data and extrapolate to

V=0

to get

J_0

. ((b)) Explain, using the ratio

J_{\rm gen}/J_0\propto W_dN/(n_iL)

, why this diode shows only the

n_{\rm id}=1

diffusion line over this range while a silicon diode of the same doping shows a visible

n_{\rm id}=2

recombination line at low forward bias, and what the clean line down to

0.10\,\mathrm{V}

says about this diode's minority-carrier lifetimes.

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