Room-temperature ( ) photoluminescence measurements on GaAs/AlGaAs quantum wells give

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 Heterostructures, quantum wells and the two-dimensional electron gas

Problem

Room-temperature (

300\,\mathrm{K}

) photoluminescence measurements on GaAs/AlGaAs quantum wells give

E_g(\mathrm{GaAs})=1.424\,\mathrm{eV}

, and measured line energies of

1.464\,\mathrm{eV}

for a

10\,\mathrm{nm}

well and

1.508\,\mathrm{eV}

for a

6\,\mathrm{nm}

well. ((a)) Using the

10\,\mathrm{nm}

result to calibrate the total confinement energy

E_1+E_{hh1}

, and assuming an infinite-well scaling

(E_1+E_{hh1})\propto 1/L^2

, predict the photoluminescence energy for the

6\,\mathrm{nm}

well. ((b)) State the percentage difference between this prediction and the measured

6\,\mathrm{nm}

value. ((c)) Explain, in one sentence, the physical reason for the sign of the discrepancy.

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