Intervalence Band Transitions Research Articles

Valence and Conduction Band Structure and Infrared Optical Properties of Tellurium in the Presence of Pressure

AbstractThe influence of pressure on the valence and conduction band structure and on the infrared optical properties of tellurium is investigated by means of group and perturbation theory. The first peak of the 11 μm‐band which corresponds to a direct intervalence band transition at the BZ corner H is shifted linearly by stress of any symmetry. At a certain critical value of hydrostatic pressure or uniaxial pressure parallel to the c‐axis it changes over into a second peak of the 11 μm‐band which is due to a transition on the symmetry line P. For hydrostatic pressure and uniaxial pressure parallel to the c‐axis the alteration of the fundamental edge results from a strain dependence of the energy gap being approximately linear. The deformation potential constants of the gap and of the first peak of the 11 μm‐band are determined by means of experimental data.

Intervalence band transitions in tellurium. II. Polarization E ⟂ c

AbstractFor the polarization E ⟂ c a weak absorption band dependent on hole concentration was found in tellurium in the spectral range 50 to 200 meV. This absorption is found at low temperatures and for hole concentrations > 1017 cm−3 It can be explained by intervalence band transitions H6‐H4 on the basis of the k·p perturbation treatment of part I. Further‐more the coupling between the valence bands H6, H4 and their energetic distance are determined. Other possible interpretations for the absorption band – the quadrupole and the forbidden transitions between the H5, H4 bands – are discussed.

Spectral photoconductivity of tellurium in the CO 2 laser wavelength range

Infrared photoconductivity measurements on tellurium single crystals and evaporated films at 90 K yielded a maximum response at 0.126 ± 0.002 eV using a low power CO 2 laser. The frequency dependence of the response was slow and could not be interpreted as vast intervalence band transitions.

Absorption from Neutral Acceptors in GaAs and GaP

We present a new calculation of the absorption due to transitions of holes between neutral acceptors and the various valence-band sublevels in GaAs and GaP. The acceptor wave function was approximated by a previously suggested expression for ground-state wave functions appropriate to complicated band extrema. Numerical calculations of the absorption from intervalence-band transitions of free holes and neutral acceptors have been performed. Good agreement with experimental results is obtained.

Intervalence Band Transitions in Tellurium. I. Polarization E ‖ c

AbstractHigh resolution measurements of the intervalence band transitions of electrons in tellurium (hole concentration p = 1014 to 1018 cm−3) were performed for polarization E ∥ c in the spectral range 60 to 200 meV a t low temperatures. The absorption spectra were calculated on the basis of a k · p perturbation method. The transition probabilities show a considerable variation ∼(ℏω)−2. A procedure is described for the determination of the valence band parameters from the optically measured data. With these parameters it is possible to determine the hole concentration of the samples from their absorption spectra.

Modulation of Intervalence Band Transitions Due to Acoustoelectric Domains

It is shown that intervalence band transitions are modulated by acoustoelectric domains. The investigations were carried out in tellurium which has an intervalence band transition at a wavelength of 11 μm. At the same wavelength a modulation of the free-carrier absorption by acoustoelectric domains was observed as well.

Infrared absorption by interband transition of holes in tellurium

The infrared absorption in tellurium single crystals due to the intervalence band transition of holes was investigated at liquid helium temperatures. A broad absorption band was newly found around 150 meV, besides the main absorption peaks at 126.0 and 128.6 meV. The results can be interpreted by using the model of the dumb bell shaped energy surface on the valence band of tellirium.

The infra-red Faraday effect in p-type semiconductors

The infra-red Faraday effect has been measured in p-type Si, GaSb and GaAs. These and previous measurements on p-type germanium are interpreted in terms of contributions due to light and heavy holes and intervalence band transitions. The contribution of the free holes to the total rotation is extracted for each material and combined with Hall effect data. These combined data are used to deduce the light and heavy hole masses in GaAs and GaSb. For GaAs the masses are found to be 0 089m0, 0 51m0 and for GaSb they are found to be 0 056m0, 0 33m0. In Ge and Si, where the masses are already known from cyclotron resonance experiments, the data are used to find the relative populations of the light and heavy hole states, giving 5 8% and about 7% respectively. The observed frequency dependences of the rotation due to intervalence band transitions in GaAs and Ge are compared with those deduced theoretically by summing the effects of the direct Landau transitions.

Infrared Absorption in P-Type Semiconductors with Zincblende Structure –Application to Zinc Telluride–

Infrared absorption in p -type semiconductors due to the transitions from split off valence bands to shallow acceptor states and to heavy and light hole bands was investigated in terms of k – π perturbation approach. Contrary to the case of germanium (diamond type), transitions from the split off valence bands to the top valence bands are allowed at \(\varGamma\) point in the zincblende structure. Although the contribution of the π matrix elements between \(\varGamma_{7v}\) and \(\varGamma_{8v}\) states to the absorption cross section is not large compared with that due to the k – π perturbed parts of wave functions in GaAs, they are of comparable magnitude in ZnTe. The radii of shallow acceptor states are determined to be 26 and 10 A respectively for Ge and ZnTe, by fitting the formulas derived here to experimental data. In the case of ZnTe, the change of absorption curve relative to photon energy with increasing temperature may be attributed to the increasing contributions of inter-valence band transitions.

Valence band structure of germanium

The absorption produced by direct inter-valence band transitions provides a sensitive test for the calculated valence band shapes. A calculation by Kane of the valence band shapes of p-type germanium near k = 0 using second-order degenerate k. p perturbation theory and of the resulting absorption spectrum indicated that the mass of the split-off valence band had not been determined accurately. This inadequacy was shown up even more when the Kane model was used to predict the change in absorption produced by a small change in lattice temperature and a comparison made with recent experimental results. The availability of these accurate absorption data has stimulated a more accurate calculation of the valence band structure. Here the interactions between the valence bands and the two neighbouring conduction bands are calculated exactly rather than by perturbation theory. The next nearest conduction band is included as a perturbation. It is then found that the mass of the split-off band is substantially heavier than calculated by Kane, a requirement that better agreement with the observed spectrum be obtained. An expression for the conduction band energy is also presented. The coefficients of k2 and k4 in this expression are calculated and compared with the results of magneto-absorption experiments. Agreement within experimental error is achieved.

Magneto-Optical Studies of the Band Structure of PbS

By a combination of interband and free-carrier experiments performed on epitaxial and bulk $n$- and $p$-type crystals, the energy-band parameters of PbS in the vicinity of the band edge have been determined at 77\ifmmode^\circ\else\textdegree\fi{}K. Interband magneto-absorption measurements have established that the valence and conduction bands are nondegenerate (except for spin), approximately spherical and parabolic, and have extrema at essentially the same point in k space, probably the $L$ points. Analysis of the data yields values for the energy gap, the reduced effective mass and also the effective $g$ factors for both the valence and conduction bands. Measurements of the Burstein-Moss effect in the zero-field absorption edge indicate multiple bands, most likely at the $〈111〉$ zone boundaries. The individual valence- and conduction-band effective masses were determined from free-carrier Faraday rotation measurements at a temperature slightly above 77\ifmmode^\circ\else\textdegree\fi{}K. Additional structure in the rotation for $p$-type material indicates possible intervalence band transitions. The reversal of the interband Faraday rotation with carrier concentration and temperature is explained on the basis of the band structure determined here. The effects of strain and carrier concentration on the band parameters were also investigated and the effective deformation potential for dilation was determined.

The valence band structure of the III–V compounds

Absorption bands due to intervalence band transitions have been observed in p-type AISb and GaAs. In GaAs, three bands at 0·42 eV, 0·31 eV, and 0·15 eV are identified as transitions between : the split off valence band and the heavy-hole band, the split off valence band and the light hole band, and the light- and heavy-hole bands respectively; the spin-orbit splitting of GaAs is 0·33 eV at k = 0. In AISb, the bands at 0·75 eV and 0·15 eV are identified with transitions between the split off valence band and the heavy-hole band, and the light- and heavy-hole bands respectively; the AISb spin-orbit splitting at k = 0 is 0·75 eV. The spin-orbit splittings of all the III–V compounds are estimated using a simple model which employs the free atom spin-orbit splittings of the constituent atoms of the compounds. The observed splittings of GaAs, AISb, and other III–V compounds are in agreement with this model. The conduction and valence band effective masses at k = 0 of the III –V compounds derived from k.p. theory for the band structure of the zincblende semiconductors are shown to be consistent with available experimental data.

The Infra-red Faraday Effect in Germanium

Measurements of the infra-red Faraday effect have been made in n-type, p-type and intrinsic germanium. The Faraday rotations observed are interpreted as being due to free electrons in n-type germanium, valence to conduction band transitions in intrinsic germanium, and light and heavy holes and intervalence band transitions in p-type germanium. The rotations obtained for variously doped n-type specimens are used in conjunction with Hall effect measurements on the same specimens to evaluate the Hall scattering constant as a function of the impurity content. In p-type material the rotations obtained are used to estimate the relative population of the light and heavy hole states.

Infrared Absorption and Valence Band in Indium Antimonide

Infrared absorption is studied at near liquid helium temperature for $n$- and $p$-type degenerate samples of various carrier concentrations. The absorption in $p$-type samples, at photon energies larger than the energy gap, depends on the hole concentration. The results show that the valence band is warped and that the energy at $k=0$ is very close to the maximum energy of the band. A step in the absorption of $n$-type samples is observed which gives an estimate of $\ensuremath{\sim}0.012m$ for the effective mass of light holes. The long wavelength absorption in $p$-type samples is characteristic of intervalence band transitions.