Quantum Effects in Cyclotron Resonance inp-Type Tellurium

Abstract

Quantum effects of cyclotron resonance of holes have been observed in tellurium by using high-resolution HCN and D 2 0 submillimeter laser spectrometers. The multiplicity of resonance absorption lines in both parallel and perpendicular directions with respect to the principal axis suggests complex energy surfaces with highly warped bands. In addition, cyclotron resonance of electrons thermally excited across the gap was obtained.We have observed cyclotron resonance of holes and electrons in tellurium using steady magneticfield intensities up to 165 kOe and an HCN laser source operating at a wavelength of 337 jum. A large number of absorption lines have been resolved as shown in Fig. 1. Since the quantum conditions are satisfied in the present experiments, namely, the laser photon energy Hco is larger than the Fermi energy and also %w> kT, we shall interpret the multiplicity of these absorption lines as the first observation of quantum effects in tellurium. In previous cyclotron resonance experiments 1-3 at millimeter wavelengths, the dual conditions cor» 1 and ho)>kT were only marginally satisfied and quantum effects were not resolved. The cyclotron-resonance nature of the present absorption lines was confirmed by observing the main features at a higher frequency using a continuous-wave D 2 0 laser.There have been indications from Shubnikovde Haas experiments 4 in heavily doped tellurium that the shape of the Fermi surface is complicated. The quantum effects in submillimeter cyclotron-resonance experiments due to warping are consistent with these studies. The first indication of structure in cyclotron-resonance observations was seen at a wavelength of 700 (im by Picard and Carter 2 in the form of a second harmonic but they observed no structure when the magnetic field was oriented parallel to the principal axis. Nevertheless, in view of the various experimental data accumulated over the past few years, a consensus has been developing that the surfaces of constant energy appear to consist of four ellipsoids of revolution at low energy close to the point H at the edge of the Brillouin zone, which then merge into two dumbbells as the energy is increased to a few millielectron volts. The axis of revolution of the dumbbells coincides with the hexagonal edges of the zone. Although we have not yet completed the detailed theory for these quantum effects in cyclotron resonance, we believe that the structure shown in the spectra of Fig. 1 indicates that this particular model of the Fermi surface is inadequate.Our experiments were performed with a continuous-wave HCN molecular gas-laser spectrometer described previously. 5 The magnetic field was furnished by a water-cooled copper so-14

Inter‐valence band magneto‐absorption in tellurium

“…But the influence of the trigonal warping is seen on the intensity of the absorption. Similar features were also reported by Button et al [6] for cyclotron resonance transition in the upper valence band. Thus if the terms of trigonal warping and the other higher order terms are neglected, the effective masses for both bands can be derived from (3).…”

Electronic impurity levels in semiconductors

“…Experimental evidence of magnetic field splittings of impurity level transitions has been obtained over a number of years (Burstein and Picus 1957, Boyle and Howard 1961, Horii and Nisida 1970, but the use of far infrared lasers has provided a powerful tool for detailed analyses in cases like donor levels in GaAs, InP, CdTe and CdSe, where the conduction band is simple and a comparison with theory is easier (Button et al 1969, Chamberlain et al 1971, 1972a,b, Narita and Miyao 1971. I n these cases a field-dependent central cell correction with related chemical shift was detected in the ground state (Xassau et al 1970, Fetterman et al 1971 and weaker transitions originating from the 2p-1 = (0, -1 , O ) level of formula (8.21) were also found (Chamberlain et al 1972a,b, Stradling et al 1972) in addition to the stronger transition 1s+2pn.…”