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

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

24.0\,\mathrm{GHz}

, with the magnetic field along a crystal axis, shows two hole resonances as the field is swept, at

B_1=0.0369\,\mathrm{T}

and

B_2=0.283\,\mathrm{T}

. ((a)) Compute the cyclotron mass

m^*=eB/\omega

for each line and assign each to the heavy-hole or light-hole branch, given germanium's masses

m_{hh}=0.33\,m_e

and

m_{lh}=0.043\,m_e

. ((b)) A Hall measurement on a separate n-type germanium sample doped with

N_D=1.0\times10^{14}\,\mathrm{cm^{-3}}

of arsenic gives electron densities

n=3.0\times10^{12}\,\mathrm{cm^{-3}}

40\,\mathrm{K}

n=9.7\times10^{13}\,\mathrm{cm^{-3}}

120\,\mathrm{K}

, and

n=5.0\times10^{14}\,\mathrm{cm^{-3}}

450\,\mathrm{K}

. Identify the regime (freeze-out, extrinsic or intrinsic) at each temperature, with your reasoning. ((c)) The same sample's electron mobility is measured as

9.0\times10^{3}\,\mathrm{cm^2\,V^{-1}s^{-1}}

20\,\mathrm{K}

, rising to a maximum of

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

60\,\mathrm{K}

, then falling to

3.9\times10^{3}\,\mathrm{cm^2\,V^{-1}s^{-1}}

300\,\mathrm{K}

. State which scattering mechanism dominates on each side of the maximum and the power law expected for each.

Browse the problem library