Semiconductors donor states

Tin oxide is a semiconductor with a wide band gap of Eg 3.7 eV, which can easily be doped with oxygen vacancies and chlorine acting as donor states. It is stable in aqueous solutions and hence a suitable material for n-type semiconducting electrodes. 

In semiconductor phosphors the energy band structure of the host crystal plays a central role. Some semiconductor luminescence arises from decay of exciton states, other emission arises from decay of donor states generated by impurity or defect centers. It is not the magnitude of the band gap itself that separates insulator from semiconductor phosphors it is a question of whether the spectrum is characteristic of impurity energy levels as perturbed by the local crystal structure or whether the spectrum is characteristic of the band structure as modified by impurities. 

Apart from fundamental transitions in direct-gap semiconductors, other processes may be responsible for radiative decay of the semiconductor excited states. The most common are processes associated with electron-hole annihilation involving donor and acceptor sites (Figure 7.10) [33],... 

Several semiconductors have been studied using this technique the results from p-Zn3P2 are shown in Fig. 87 in which two localised and two VB -> trap transitions (which increase C for a p-type semiconductor) can clearly be seen. Results for n-CdSe in acetonitrile show something of the power of the technique acceptor states have been located at 1.40 and 1.57 eV above the VB edge these have been ascribed, respectively, to elemental Se and reconstructed polycrystalline CdSe domains. Two donor states, at 1.04 and 1.21 eV below the CB edge were also located in this study and appeared to be associated with an oxide film. It is in non-aqueous solvent, where faradaic reactions are often extremely slow, that this technique may have its best applications. 

The Coulomb interaction between the electron and the donor core is, of course, present in an amorphous semiconductor and binds an electron in much the same way, so the shallow donor state is preserved. The effective mass theory for dopants cannot be applied directly to amorphous semiconductors, because it is formulated in terms of the momentum-space wavefunctions of the crystal. It is not immediately obvious that the effective mass has any meaning in an amorphous... 

The simplest model of electron transfer across a semiconductor/metal interface assumes that the current depends linearly on the concentration of electrons at the semiconductor surface, s. It also assumes that the concentrations of acceptor and donor states in a metal are extremely large thus, these variables can be assumed to be constant and can be incorporated as time-independent quantities into the appropriate rate equations. This assumption is extremely reasonable for the moderate current densities that flow through typical semiconductor/metal interfaces. ... 

Various other electronic transitions are possible upon light excitation. Besides the band-band transitions, an excitation of an electron from a donor state or an impurity level into the conduction band is feasible (transition 2 in Fig. 1.9). However, since the impurity concentration is very small, the absorption cross-section and therefore the corresponding absorption coefficient will be smaller by many orders of magnitude than that for a band-band transition. At lower photon energies, i.e. at ph < g, an absorption increase with decreasing ph has frequently been observed for heavily doped semiconductors. This absorption has been related to an intraband transition (transition 4 in Fig. 1.9), and is approximately described by the Drude theory [4]. This free carrier absorption increases with the carrier density. It is negligible for carrier densities below about 10 cm ... 

Density of states at the lower edge of the conduction band Density of states at the upper edge of the valence band Density of donor states in the semiconductor Density of acceptor states Density of surface states... 

Since the first energy level calculations of the EM centres in silicon and germanium [28,34], many calculations have been undertaken to explain quantitatively the absorption and photoluminescence (PL) spectra associated with these centres in many semiconductors. The first part of this chapter is devoted to the presentation of the energy level calculations of EM donors and it is followed by the results of the calculations for EM acceptors. The modification to EMA, which is independent of the chemical nature of the centres, is also discussed. The chapter concludes with results of calculations of the oscillator strength (OS) for transitions between the ground states and the acceptor or donor states. 

The symmetry of an isolated atom is that of the full rotation group R+ (3), whose irreducible representations (IRs) are D where j is an integer or half an odd integer. An application of the fundamental matrix element theorem [22] tells that the matrix element (5.1) is non-zero only if the IR DW of Wi is included in the direct product x of the IRs of ra and < f. The components of the electric dipole transform like the components of a polar vector, under the IR l)(V) of R+(3). Thus, when the initial and final atomic states are characterized by angular momenta Ji and J2, respectively, the electric dipole matrix element (5.1) is non-zero only if D(Jl) is contained in Dx D(j 2 ) = D(J2+1) + T)(J2) + )(J2-i) for j2 > 1 This condition is met for = J2 + 1, J2, or J2 — 1. However, it can be seen that a transition between two states with the same value of J is allowed only for J 0 as DW x D= D( D(°) is the unit IR of R+(3)). For a hydrogen-like centre, when an atomic state is defined by an orbital quantum number , this can be reduced to the Laporte selection rule A = 1. This is of course formal, as it will be shown that an impurity state is the weighted sum of different atomic-like states with different values of but with the same parity P = ( —1) These states are represented by an atomic spectroscopy notation, with lower case letters for the values of (0, 1, 2, 3, 4, 5, etc. correspond to s, p, d, f, g, h, etc.). The impurity states with P = 1 and -1 are called even- and odd-parity states, respectively. For the one-valley EM donor states, this quasi-atomic selection rule determines that the parity-allowed transitions from Is states are towards np (n > 2), n/ (n > 4), nh (n > 6), or nj (n > 8) states. For the acceptor states in cubic semiconductors, the even- and odd-parity states labelled by the double IRs T of Oh or Td are indexed by + or respectively, and the parity-allowed transition take place between Ti+ and... 

In group-IV semiconductors, donors like P and As and acceptors like Al are monoisotopic, but others show an isotopic distribution (see appendix D). Beyond EMT, calculations of the isotopic splitting of the ground state of... 

Under stress, a one-valley EM donor state follows the energy shift of the valley it belongs to. A study of the effect of a uniaxial stress on the donor spectra in a multi-valley semiconductor (silicon) has been undertaken by Tekippe et al. [140]. The treatment given below follows this presentation closely, with minor changes in the notations. Following the deformation potential analysis of [60], the shift in energy Aof valley j of the CB of silicon or germanium with respect to the zero-stress conditions is ... 

Figure 7.12 (a) Intrinsic and (b) n-type semiconductor. New electron states (donor states) are created close to the conduction band. 

There is a significant difference between the defects (vacancies and interstitials) in semiconductors and those in metals that is, defects in a semiconductor can be charged electrically, whereas defects in a metal are considered neutral. Since they can be charged (or ionized), the concentration of these defects becomes a function of the Fermi level position in the semiconductor. Consider the charged states of vacancies in Si as an example. It is generally accepted that the single vacancy in Si can have fom charge states (Van Vechten 1980) V, F, and F , where + refers to a donor state, x a neutral species,... 

---