A GaAs quantum well of width is grown between barriers

PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Condensed Matter, Materials & Soft Matter · Wave mechanics in one dimension

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

Problem

A GaAs quantum well of width

L=8\,\mathrm{nm}

is grown between

\mathrm{Al_{0.3}Ga_{0.7}As}

barriers. For a

10\,\mathrm{nm}

well with a

243\,\mathrm{meV}

barrier, the finite barrier was found to lower the ground subband energy by about 40 per cent from the infinite-barrier value. Take the GaAs conduction-band effective mass as

m^*=0.067\,m_e

. ((a)) Compute the infinite-barrier ground subband energy

E_1

for this

8\,\mathrm{nm}

well. ((b)) Using the 40 per cent reduction as a rough estimate appropriate to a barrier of comparable height, estimate the finite-barrier

E_1

for this well.

Related theory

Quantum Mechanics

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