A cyclotron resonance experiment on silicon at a fixed microwave frequency of shows…

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Free electrons, energy bands and electronic structure · Semiconductor physics and devices

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

Problem

A cyclotron resonance experiment on silicon at a fixed microwave frequency of

35.0\,\mathrm{GHz}

shows two hole resonances at

B_1=0.200\,\mathrm{T}

and

B_2=0.613\,\mathrm{T}

. ((a)) Compute the cyclotron mass for each line and assign each to the heavy-hole or light-hole branch, given silicon's masses

m_{hh}=0.49\,m_e

and

m_{lh}=0.16\,m_e

. ((b)) A separate p-type silicon sample doped with

N_A=2.0\times10^{15}\,\mathrm{cm^{-3}}

of boron gives hole densities

p=1.8\times10^{14}\,\mathrm{cm^{-3}}

60\,\mathrm{K}

p=1.95\times10^{15}\,\mathrm{cm^{-3}}

150\,\mathrm{K}

, and

p=1.2\times10^{16}\,\mathrm{cm^{-3}}

650\,\mathrm{K}

. Identify the regime at each temperature, with your reasoning. ((c)) The hole mobility of the same sample is measured as

1.2\times10^{4}\,\mathrm{cm^2\,V^{-1}s^{-1}}

50\,\mathrm{K}

, a maximum of

1.6\times10^{4}\,\mathrm{cm^2\,V^{-1}s^{-1}}

100\,\mathrm{K}

, and

5.0\times10^{2}\,\mathrm{cm^2\,V^{-1}s^{-1}}

300\,\mathrm{K}

. State which scattering mechanism dominates on each side of the maximum.

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