### Homework 3 - QMplus - Queen Mary University of London

```Queen Mary, University of London
School of Physics and Astronomy
Condensed Matter B
Homework Set 1
To be handed in by 4 p.m. on Wednesday, 4th February 2015
Problem 1: Exciton size (5 marks)
To appreciate the size of a system at which carrier confinement becomes significant calculate the value of the
exciton Bohr radius aB in silicon given that the dielectric constant of Si is ε = 11.9, m∗e = 0.26me and m∗h = 0.36me .
Problem 2: Diode I(V) curve (10 marks)
For the I(V ) curve in the figure below:
1. Explain the origin of the value of the residual current IR in the reverse bias. Explain how and why this value
will change if temperature is increased from T1 to T2 and sketch curves for both temperatures. (5 marks)
2. Explain the effect on the I(V ) curve of exposing the diode to light and sketch the curve corresponding to
an illuminated diode alongside the curve in the figure below. Explain the effect. (Can you suggest possible
applications by examining the curve for an illuminated diode?) (5 marks)
Problem 3: Schottky barrier (10 marks)
Find the height of the potential barrier (eVD , see lecture notes page 15) for a Au-Ge metal-semiconductor (Schottky)
contact at room temperature (T = 300 K) if ρ = 1 Ω cm for germanium, work function of gold ΦAu = 5.1 eV, and
electron affinity in germanium χGe = 4.0 eV. Electron mobility in Ge is 3900 cm2 V−1 s−1 , NC = 1.98×1015 ×T 3/2
cm−3 (see page 10 of the lecture notes for the definition of NC ), where T is the absolute temperature.
Problem 4: Quantum well (10 marks)
Calculate the lowest energy corresponding to absorption of a photon in a quantum well made of an intrinsic Ge
layer placed between two pure diamond layers. The width of the quantum well is L = 10 nm. The band gap of bulk
Ge is 0.7 eV, band gap of diamond is 5.5 eV. Effective masses of electrons and holes in Ge are 0.041me and 0.04me
respectively.
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