Three separate measurements are made on doped silicon samples.

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

Solid State Physics, Ch Semiconductors: masses, statistics, defect levels and mobility

Problem

Three separate measurements are made on doped silicon samples. ((a)) A cyclotron resonance experiment at microwave frequency

f=35.0\,\mathrm{GHz}

on p-type silicon shows two hole resonances, at

B_1=0.200\,\mathrm{T}

and

B_2=0.610\,\mathrm{T}

. Using

m^*=eB/\omega

with

\omega=2\pi f

, calculate the two masses (in units of

m_e

) and state which line is the heavy-hole line and which is the light-hole line. ((b)) A Hall carrier density

n_H(T)

is measured on an n-type silicon sample with

N_D=2\times10^{15}\,\mathrm{cm^{-3}}

n_H=3\times10^{14}\,\mathrm{cm^{-3}}

60\,\mathrm{K}

n_H=2\times10^{15}\,\mathrm{cm^{-3}}

150\,\mathrm{K}

, and

n_H=1\times10^{16}\,\mathrm{cm^{-3}}

650\,\mathrm{K}

. Identify the regime (freeze-out, extrinsic or intrinsic) at each temperature, with a one-line reason for each. ((c)) An electron drift mobility

\mu_n(T)

is measured on a doped silicon sample:

\mu_n=800\,\mathrm{cm^2\,V^{-1}s^{-1}}

20\,\mathrm{K}

\mu_n=3160\,\mathrm{cm^2\,V^{-1}s^{-1}}

50\,\mathrm{K}

\mu_n=1450\,\mathrm{cm^2\,V^{-1}s^{-1}}

300\,\mathrm{K}

, and

\mu_n=670\,\mathrm{cm^2\,V^{-1}s^{-1}}

500\,\mathrm{K}

. Using pairs of points on either side of the peak, estimate the power-law exponent

n

\mu_n\propto T^n

below and above

50\,\mathrm{K}

, and name the scattering mechanism responsible for each.

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