A heavily doped n-type GaAs epilayer has interband background permittivity and…

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Semiconductor physics and devices · Dielectric and optical properties of solids

Solid State Physics, Ch Collective and coupled excitations: plasmons, polaritons and polarons

Problem

A heavily doped n-type GaAs epilayer has interband background permittivity ε∞=10.9\varepsilon_\infty=10.9 and conduction-band effective mass m∗=0.067 mem^*=0.067\,m_e. A Drude fit to its infrared reflectivity places the plasma edge, the zero of ε1\varepsilon_1, at ℏωp/ε∞=0.150 eV\hbar\omega_p/\sqrt{\varepsilon_\infty}=0.150\,\mathrm{eV}; the reflectivity minimum itself sits a little higher, where ε1=1\varepsilon_1=1. ((a)) Find the unscreened plasma energy ℏωp\hbar\omega_p. ((b)) Find the free-electron density nn in cm−3\mathrm{cm^{-3}}.

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