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Semiconductor Optics 1 pp 453–483Cite as

Excitons Under the Influence of External or Internal Fields

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Abstract

Application of external fields is a well suited strategy to reveal the properties of excitons in semiconductors. It further leads to new phenomena which are interesting for device applications. The external field can be applied temporally constant [79E1, 85H1] or as systematic perturbation in modulation techniques [69C1, 73S1, 04G1]. We will restrict our discussion here to the presentation of general features and of some selected topics and examples. We consider the influence of magnetic, electric and strain fields on the optical properties of excitons including their continuum states and we proceed again from bulk materials to structures of lower quasi-dimensionality. Mostly these fields are applied from outside, but there are also cases of internal fields, e.g., strain fields due to lattice misfit in epitaxy or piezo-electric fields resulting from such strain.

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Authors and Affiliations

  1. Institute of Applied Physics, Karlsruhe Institute of Technology, Karlsruhe, Baden-Württemberg, Germany

    Heinz Kalt & Claus F. Klingshirn

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Correspondence to Heinz Kalt .

Problems

Problems

24.1

Typical values of the deformation potential are around 10 eV. What is the shift of the band edges for \(\Delta a/a = 10^{-3}\)?

24.2

Do you expect the band-gap shifts due to the lattice deformation by acoustic and by optical phonons to be identical or not? Why?

24.3

Calculate the diamagnetic shift at \(\varvec{B}= 10\) T for excitons characterized by \(E^{\text {b}}_{\text {ex}} = 5\,\text {meV}\), \(\varepsilon = 15\) and by \(E^{\text {b}}_{\text {ex}} = 100\,\text {meV}\), \(\varepsilon = 6\), respectively.

24.4

Calculate the Zeeman splitting for a spin singlet and a triplet exciton for \(n_{\text {B}} = 1\), \(g_{\text {e}} = 1.6\) and \(g_{\text {h}} = 2.2\). What is the difference if at \({\varvec{B}} = 0\) the two states already show a finite energy splitting \(\delta \)?

24.5

Do you expect that the linear Stark effect can occur for \(n_{\text {B}} = 1\) and/or for \(n_{\text {B}} = 2\) excitons? Why?

24.6

Calculate in the simplest approximation the Stark shift for excitons with the data given in connection with Problem 3 and for an electric field strength E of 10\(^3\) Vm\(^{-1}\), 10\(^6\) Vm\(^{-1}\), and 10\(^{-2}\) \(E^{\text {b}}_{\text {ex}}(ea_{\text {B}})^{-1}\).

24.7

Calculate the quantum confined Stark effect by perturbation theory for a quantum well with infinitely high barriers and the other data as for the hh exciton in GaAs or InAs. Compare with experimental data.

24.8

Proof whether the two examples given in the introduction to this chapter are correct.

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Kalt, H., Klingshirn, C.F. (2019). Excitons Under the Influence of External or Internal Fields. In: Semiconductor Optics 1. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-24152-0_24

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