Impurities and Excitons

Part of the Graduate Texts in Physics book series (GTP)

Selected impurities are frequently introduced into semiconductors to make them n–type or p–type. The introduction of impurities into a crystal lattice not only shifts the Fermi level, but also results in a perturbation to the periodic potential, giving rise to bound impurity levels which often occur in the band gap of the semiconductor.

Open image in new window This problem considers the density of Frenkel defects. By considering \(N'\) as the density of possible interstitial sites, show that the density of occupied interstitial sites is
$$\begin{aligned} n_i\simeq (NN')^{\frac{1}{2}} \; \exp \biggr [{-\frac{E_i}{2k_BT}} \biggr ] \end{aligned}$$
where \(E_i\) is the energy needed for removing an atom from a lattice site to form an interstitial defect site.

The band gaps of \(\mathrm{WSe}_2\) and \(\mathrm{MoSe}_2\) are 1.64 and 1.61 eV, respectively, and their conduction band offset is 228 meV with \(\mathrm{WSe}_2\) higher in energy than for \(\mathrm{MoSe}_2\).

The exciton binding energy of an exciton in monolayer \(\mathrm{MoS}_2\) is 400 meV. Assuming that this binding energy is dominated by the ground particle-in-a-box energy corresponding to the 3.0 Å layer thickness of this material, with an effective mass of \(m^*=0.6m_o\), estimate the binding energy of bilayer \(\mathrm{MoS}_2\) (thickness \(=\) 9.16 Å). (See Fig. 20.21)

Calculate the bound state energies of excitons in GaAs (with both heavy and light holes) for

Repeat Problem 20.4 for germanium.

Is the binding energy for an exciton in a semiconducting wire of 100 Å diameter increased or decreased relative to bulk values if the Bohr radius of the exciton for this material in the bulk is 30 Å? Under which conditions would the effect of confining the exciton within a small diameter wire be large? What is the reason for your answer?

Suggested Readings

© Springer-Verlag GmbH Germany, DE 2018

Dresselhaus M., Dresselhaus G., Cronin S.B., Gomes Souza Filho A. (2018) Impurities and Excitons. In: Solid State Properties. Graduate Texts in Physics. Springer, Berlin, Heidelberg
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