An abrupt silicon - junction has its side doped to

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

An abrupt silicon

p

n

junction has its

p

side doped to

N_A=3.0\times10^{16}\,\mathrm{cm^{-3}}

, known from the growth. The

n

-side doping

N_D

is unknown but of the same order, so neither side's share of the depletion width can be neglected. Measured at

T=300\,\mathrm{K}

, the depletion capacitance per unit area

C

at two reverse biases

V

(with

V<0

for reverse bias) gives:

V=-1.0\,\mathrm{V}

1/C^2 = 2.11\times10^{15}\,\mathrm{cm^4\,F^{-2}}

V=-3.0\,\mathrm{V}

1/C^2 = 4.52\times10^{15}\,\mathrm{cm^4\,F^{-2}}

. Use

\varepsilon_s=11.7

for silicon,

\varepsilon_0=8.854\times10^{-14}\,\mathrm{F\,cm^{-1}}

e=1.602\times10^{-19}\,\mathrm{C}

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

and

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

. ((a)) Show that

1/C^2 = \dfrac{2(V_{bi}-V)}{e\varepsilon_s\varepsilon_0 N_{\rm eff}}

with

N_{\rm eff}=N_AN_D/(N_A+N_D)

, use the two data points to extract

N_{\rm eff}

, and from it find

N_D

. ((b)) Extract the built-in voltage

V_{bi}

from the data, and compare it with

(k_BT/e)\ln(N_AN_D/n_i^2)

for the dopings you now have.

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