Abstract
Shallow defect centers play a dominant role as donors and acceptors in nearly all semiconducting devices. The major features of their spectrum can be described by a quasi-hydrogen model, modified only by the dielectric constant and the effective mass of the host semiconductor. This relation yields very good results for higher excited states of a large variety of such defects, while the ground state shows substantial deviations according to the chemical individuality of the defect center. Such an individuality can be explained by considering the core potential and the deformation of the lattice after incorporating the defect.
Band anisotropies and the interaction between bands such as conduction-band valleys cause the lifting of some of the degeneracies of the quasi-hydrogen spectrum. Local stress and electric fields cause additional splitting. The dependence of levels on hydrostatic pressure can be used to identify shallow-level defects which are connected to one band only. The influence of externally applied uniaxial stress and electric or magnetic fields can be used for further identification.
Donors and acceptors can bind excitons. The binding energy sensitively depends on the effective mass ratio of electron and hole and the charge state of the impurity. For exciton binding at neutral donors and acceptors, a linear dependence from the ionization energy is found. Isoelectronic impurities can also bind excitons by attracting the electron at the core potential.
K. W. Böer: deceased
Notes
- 1.
This can easily be seen at the Γ point for k0 = 0: here, we have ψ(k = 0,r) = u(0,r) exp(i0 · r) = u(0,r).
- 2.
In semiconductors with several equivalent minima (Si, Ge), the wavefunction becomes a sum of contributions from each of the minima: \( {\sum}_j{\alpha}_j{F}_{j\;\mathrm{c}}\left(\mathbf{r}\right)\, {u}_{j\;\mathrm{c}}\left({\mathbf{k}}_{j\;0},\mathbf{r}\right) \).
- 3.
n is the principal quantum number, describing the entire energy spectrum for a simple hydrogen atom. All other states are degenerate. Therefore, in a pure Coulomb potential, this quantum number is the only one that determines the energy of a hydrogen level. When deviations from this spherical potential appear in a crystal, the D = Σl(l + 1) = n2 degeneracy of each of these levels is removed, and the energy of the s, p, d, … states is shifted according to R∞/(n + l)2. The importance of these transitions is discussed in Sect. 1.2. To further lift the remaining degeneracies of the magnetic quantum number, a magnetic field must act (see Sect. 3.4).
- 4.
For instance, when aqH ≅ 50 Å for the 1s state, it is 200 Å for the 2s and 450 Å for the 3s states, making the hydrogenic effective mass approximation a much improved approximation. In addition, in semiconductors where ε/m* is already very large, e.g., in GaAs with εstatm0/mn = 192.5, resulting in aqH = 101.9 Å ≅ 18a, this approximation is quite good for the 1s state. In GaAs, it results in EqH = 5.83 meV, while the experimental values vary from 5.81 to 6.1 meV for GaAs/Si and GaAs/Ge. For more comparisons between theory and experiment, see Bassani et al. (1974).
- 5.
Such a local pseudopotential is used near an impurity as opposed to the nonlocal pseudopotential used for band structure analysis (see Sect. 1.3 of chapter “Quantum Mechanics of Electrons in Crystals”).
- 6.
- 7.
The concentration of the A center and the NN centers is proportional to their absorption strengths.
- 8.
Electron spin resonance (ESR) is also referred to as electron paramagnetic resonance (EPR).
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Böer, K.W., Pohl, U.W. (2020). Shallow-Level Centers. In: Semiconductor Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-06540-3_18-3
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