Donor quasi-hydrogenic

Table 5.10. Calculated EM transition energies (meV (cm-1 in parentheses)) from the Is state to the first np quasi-hydrogenic donor levels of five compounds with the sphalerite structure. Enp is. R ood/n2. For InSb, GaAs, and InP, es at low temperature is taken as 17, 12.4, and 12.2, respectively, and rnn/rne is taken from Table 3.6. Experimental Is — 2p transition energies are given in Table 6.37...

For the quasi-hydrogenic donors discussed in Sect. 5.2.3, the OS /ab between the two discrete levels a and b are assumed to be the same as those for the hydrogen atom, and the absorption cross section is scaled by the factor... 

The existence of metastable quasi-hydrogenic donor (QHD) states associated with Landau levels with N > 0 for large values of the magnetic field has been mentioned in Sect. 5.2.3. The absorption of a large number of such states has been observed on GaAs for relatively high doping levels, as shown in Fig. 6.43. 

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... 

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