A thin, pseudomorphic layer of n-type ( , band gap at ) is grown, below its critical…

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

Solid State Physics, Ch Heterostructures, quantum wells and the two-dimensional electron gas

Problem

A thin, pseudomorphic layer of n-type

\mathrm{In_{0.15}Ga_{0.85}As}

(

N_d=2.0\times10^{17}\,\mathrm{cm^{-3}}

, band gap

E_g=1.24\,\mathrm{eV}

300\,\mathrm{K}

) is grown, below its critical thickness, on a p-type GaAs substrate (

N_a=1.0\times10^{17}\,\mathrm{cm^{-3}}

E_g=1.424\,\mathrm{eV}

). The measured conduction-to-valence offset split for this pair is

\Delta E_C:\Delta E_V=70:30

. ((a)) Find

\Delta E_C

and

\Delta E_V

at this interface. ((b)) State, with a reason, whether this is a type-I or type-II alignment, and describe qualitatively how

E_C

E_V

and

E_F

run across the structure (which side depletes, and what happens to each band edge at the interface itself, over and above the depletion-region bending set by the doping as in an ordinary p-n diode). ((c)) Because the InGaAs layer has a larger relaxed lattice constant than GaAs, growing it pseudomorphically on GaAs puts it under biaxial compression (a misfit-strain effect). Using the picture of the degenerate heavy- and light-hole bands at

\mathbf{k}=0

in an unstrained cubic semiconductor, explain what this strain does to the two bands and which one becomes the valence-band edge.

Browse the problem library