Electrical conduction in semiconductors at low temperatures

This thesis is concerned with the study of the magnetophonon effect in a wide range of semiconductors. The five materials investigated are n-InP, n-CdSe, n-Ge, p-Ge and p-GaAs. The effect which was first predicted in a theoretical paper by Gurevich and Firaov (1951) arises from the resonant coupling of optical phonons with conduction electrons in an applied magnetic field. Extrema occur in the magnetoresistance when the phonon energy approaches an integral number of Landau level spacings. The resonance condition is
Nωc = NeB⁄m* = ωe ; N = 1,2,3 ... (1)
where ωe is the phonon frequency, ωc the cyclotron frequency, m* the carrier effective mass and B the applied magnetic field.
There are three main applications of the magnetophonon experiments to the study of the properties of conduction electrons. Firstly, equation (1) may be used to determine a precise value of the band edge effective mass provided that small corrections for band non-parabolicity and polaron effects are taken into account, secondly, the data are a test of recent theories concerning the problem of electrical conduction in an applied magnetic field. Thirdly, the magnetophonon structure which appears in the non-ohmic magnetoresistance at low temperatures can reveal new mechanisms for the energy relaxation of warm electrons.
The first application of magnetophonon resonance is of particular relevance to the study of n-InP and n-CdSe since previously the conduction band effective masses had not been known precisely. In n-InP (Eaves et al., 1971) up to eleven extrema have been observed in the transverse orientation over the temperature range from 77 K to 300 K. The low frequency cyclotron effective mass deduced from the field positions of the peaks is 0.082 m0 ± 0.001 m0 at 77 K and 0.078 m0 ± 0.001 m0 at 300 K. The dependence of the peak amplitudes in InP on magnetic field and ionised impurity concentration are in agreement with the theoretical treatment of the transverse magnetophonon effect by Barker (1972), The magnetophonon structure in n-CdSe (Eaves et al., 1972) is considerably weaker in amplitude and can only be observed in a limited temperature range around 80 K. After corrections are applied for band non-parabolicity and the polaron effect, the low frequency cyclotron masses are deduced to be 0.122 m0 for B ⊥ c-axis and 0.127 m0 for B ∥ c-axis. The relatively polar nature of both InP and CdSe provides a test of two recent theoretical studies of the magnetophonon effect. First, a comparison of the value of m* derived directly from equation (1) with that obtained from recent cyclotron resonance experiments shows that the optical polaron correction factor by which m* must be multiplied to obtain the low frequency cyclotron mass is (1 + 0.73 α/3)-1, in excellent agreement with the predictions of Meare et al., (1968) and the theoretical estimate by Palmer (1970). Second, the displacement of the magnetic field positions of the minima in the longitudinal magnetoresistance ρzz away from the resonance fields given by equation (1) is in qualitative agreement with the damping theory of Barker (1972a).
The magnetophonon structure which has been observed in n- and p-Ge (Eaves et al., 1970) is the most extensive yet reported. In both materials the anisotropy of the peaks has been studied for orientations of B in the (110) crystal plane and accurate values are deduced for the cyclotron effective masses of both the electrons and holes over the temperature range from 55 K to 260 K. In n-Ge, the structure can be interpreted solely in terms of intravalley scattering by optical phonons at the centre of the Brillouin zone. No peaks can be identified as arising from intervalley transitions and such processes are estimated to be at least an order of magnitude weaker than intravalley scattering processes. This result is in opposition to that of Sokolov and Tsidil'kovskii (1967) who attributed some of the minima which they observed in the longitudinal magnetoresistance of n-Ge to intervalley optical phonon scattering. The striking series of peaks in p-Ge are the first definitive observation of the magnetophonon effect due to optical phonon transitions in the valence band of a semiconductor. The complex splitting of the harmonics at fields above 50 kG is rather difficult to interpret precisely but appears to reflect the complex dependence of the heavy hole Landau level energies on kB, the hole wavevector in the direction of the applied field. A series of magnetophonon peaks has also been observed in the transverse magnet ore sistance of p-GaAs at a temperature of about 100 K. The magnetic field positions of the five light hole peaks provide an estimate of the band-edge light hole effective mass of 0.091 m0.
In the ohmic electric field regime, the structure in the magnetoresistance disappears as the temperature is lowered below about 50 K due to the decreasing importance of optical phonon scattering in limiting the electron mobility. However, fay applying electric fields of sufficient strength to heat the electron temperature above that of the lattice, extrema can be made to reappear in the magnetoresistance. The phonons responsible for the structure are those which dominate the energy relaxation of the electrons and the reappearance of the peaks arises from the oscillatory variation with magnetic field of the energy relaxation time of the electrons. In InP, at a temperature of about 10 K f the most prominent series of peaks is caused by electron capture at a shallow ionised donor site accompanied by the emission of a single L.O. phonon. At electric fields below about 5 V/cm a second series of five extrema, accurately periodic in 1/B, appears in the magnetoresistance. This structure is attributed to energy relaxation of electrons by the simultaneous emission of a pair of band-edge transverse acoustic phonons. The field positions of the peaks satisfy the condition
Nℏeb⁄m* = 2ℏω (T.A.X) (2)
where ℏω (T.A.X) is the T.A. phonon energy at the X-point of the Brillouin zone. In addition to the structure arising from phonon emission processes, additional peaks appear in the magnetoresistance of all the n-InP samples studied. The field positions of these extrema appear to correspond to an energy relaxation mechanism in which the electrons inelastically scatter from neutral donor sites which are thereby excited from the ground state to the lowest energy Landau state.
The energies of the donor states which are required for the interpretation of the warm electron magnetophonon data are deduced from a series of photoconductivity experiments on n-InP (Stradling et al., 1972). This work involved the use of two cryostats designed for infra-red measurements at temperatures down to 1.2 K. The spectra reveal the presence of two shallow donor species whose ground states are separated in energy by an amount equivalent to 0.7 cm-1. The mean ionisation energy of the two impurities is 61.0 cm-1. The photoconductive response also shows an additional peak at 33.8 cm-1 which appears to have an intensity directly related to the width of the shallow donor lines.