Showing papers on "Effective mass (solid-state physics) published in 1977"

Deep Level Impurities in Semiconductors

Abstract: Solids are usually divided into metals and nonmetals. In a simplified scheme we may say that nonmetals consist of insulators and semiconductors. Both can be described by energy bands separated by a forbidden energy gap Eg• Whether a nonmetal is considered to be an insulator or a semiconductor often depends on the temperature at which its properties are to be investigated or used. In this chapter we use "semi­ conductor" to mean a nonmetal with a band gap from at least a few tenths of an eV up to a maximum of 10 eV. The considerable interest in semiconductors since the 1930s has been stimulated by their technical significance. Unlikl� metals, the physical properties of semi­ conductors can be considerably modified by introducing small amounts of foreign atoms. In this manner the resistivity of a silicon crystal can be changed by about seven orders of magnitude when one-millionth of the atoms in the crystal are replaced by suitable foreign atoms. Note that impurity substitution of this magni­ tude does not affect the band gap or other basic characteristics of the host material. Moreover, depending on the kind of foreign atom, the electrical current through the crystal is carried by electrons or holes. Hence multilayer structures with different types of conductivity can be constructed by doping a semiconductor crystal in­ homogeneously, resulting in devices such as diodes, transistors, lasers, etc. Experimentally it is found that replacing an atom of the host lattice by a foreign atom results in lattice defects with physical properties depending considerably on the particular atom introduced. Good understanding of such impurity centers has been achieved at least for Si and Ge when the foreign atom belongs to the groups of the periodic table closest to that of the semiconductor. They introduce localized donor and acceptor levels in the otherwise forbidden energy gap and are often described by the effective mass theory of Kahn & Luttinger (KL-EMT) (1-3), giving a hydrogen-like spectrum of levels with binding energies En' which can be written as

Droplet Model of the Giant Dipole Resonance

Abstract: The nuclear giant dipole resonance is discussed using a macroscopic model with two new features. The motion is treated as a combination of the usual Goldhaber-Teller displacement mode and the Steinwedel-Jensen acoustic mode, and the restoring forces are all calculated using the droplet model. The A dependence of the resonance energies is well reproduced without any adjustable parameters, and the actual magnitude of the energies serves to fix the value of the effective mass m* used in the theory. The giant dipole resonance is found to contain a large component of the Goldhaber-Teller type of motion, with the Steinwedel-Jensen mode becoming comparable for heavy nuclei. The width GAMMA of the giant dipole resonance is estimated on the basis of an expression for one-body damping.

Theory of Valley Splitting in an N -Channel (100) Inversion Layer of Si I. Formulation by Extended Zone Effective Mass Theory

Abstract: The theories based upon the multi-valley effective mass equation proposed by Twose are criticized and it is concluded that they can not explain the observed valley splittings. In order to treat valley splittings correctly, a formulation based upon the extended zone scheme is presented with the main interest in the valley splitting in an n -channel (100) inversion layer of Si.

Gain-frequency-current relation for Pb 1-x Sn x Te double heterostructure lasers

Abstract: The active region gain expression for Pb 1-x Sn x Te lasers is obtained from the k \cdot p model of the conduction and valence band extrema. Curves of gain versus frequency with current, temperature, and majority carrier concentration as parameters are calculated using published values of the k \cdot p model parameters. In addition, threshold current versus temperature and threshold current versus majority carrier concentration curves are given. A simple expression is obtained for the conductivity effective mass for use in the equation for free-carrier absorption appropriate to the highly degenerate majority carrier concentrations typical of Pb 1-x Sn x Te laser material.

Effective mass and collision time of (100) Si surface electrons

Abstract: The effective mass of electrons in (100) Si inversion and accumulation layers was measured by the temperature broadening of oscillatory magnetoconductance technique for a wide range of substrate doping level, geometry, and interface charge as well as various field-strength and substrate biases. It is shown that the apparent effective mass values are very sensitive to these parameters. Measurements were made at constant magnetic field but for varying oxide charge so that for a given magnetic field the effect of oxide-charge scattering could be eliminated by extrapolating to zero oxide charge. The result was remarkably a carrier-concentration independent mass of about 0.21. Collision broadening of the oscillations was studied to determine the scattering time $\ensuremath{\tau}$. The values of $\ensuremath{\tau}$ were found to be sensitive to the preexponential damping factor in H. The results are in fair agreement with the zero-field conductivity and average magnetoconductance measurements.

Electrical properties ofp-type GaSe

Abstract: Systematic resistivity and Hall-mobility measurements have been carried out over the temperature range (77÷850) K onp-type GaSe single crystals, grown from the melt in different conditions by the Bridgman-Stockbarger method. The correlation between electrical properties and growth conditions has been investigated for various crystal ingots. From the analysis of the experimental results the energies and the concentrations of the dominant acceptor levels have been obtained together with an estimate of the density-of-state effective mass of conduction and valence bands. Five acceptor levels have been observed at energiesE1=31 meV,E2=(50÷70) meV,E3=(140÷160) meV,E4=(180÷210) meV,E5=(280÷310) meV; some of these have been attributed to chemical interaction between GaSe and silica ampoules during growth. Density-of-state effective masses have been evaluated to bemh=0.5m0 andme=m0. Finally, Hall-mobility data have been analysed according to a theoretical model proposed by Schmid. From this analysis it has been found an optical-phonon energy ℏω = 12 meV, a coupling constant valueg2=0.24 and a deformation potential for the valence band e=5.2 eV/A.

Optical constants of lithium deposits as determined from the Kramers-Kronig analysis

Abstract: Optical constants of Li have been determined between 0 and 10.7 eV, using Kramers-Kronig analysis of the reflectance data. The dielectric constant ∊ = ∊1 + i∊2 and the optical conductivity are deduced and compared with theoretical calculations. The plasma energy as determined from the condition ∊1(ω) = 0 is near 6.73 eV and the energy loss function peaks at 6.90 eV. The effective mass m* deduced from the analysis of ∊1 in terms of a nearly-free-electron model is found equal to 1.80m. The optical conductivity exhibits important differences from the theoretical calculations. These discrepancies have been attributed to properties of the metal surfaces measured, particularly roughness and granularity.

Final-state interactions in the high-energy proton-deuteron charge exchange reaction

Abstract: The charge exchange channel of the proton-deuteron break-up reaction pd to npp at 1 GeV is studied in impulse approximation. The final-state interaction in the 1S0 state of the pp subsystem induces a slight asymmetry in the spectator proton angle and a threshold enhancement in the pp effective mass. The 20% of the observed events which have large effective mass may be explained quantitatively by the production of a Delta resonance which is de-excited through a final-state interaction with the spectator nucleon. It is concluded that almost all of the small-angle np charge exchange cross section at this energy involves nucleon spin-flip.

The complex form of donor energy levels in gallium phosphide

Abstract: The conduction band minima of GaP are now recognised to be exceptionally non-parabolic because of the existence of a 'camel's back' form This has a most serious effect on donor bound states of binding energy 10-20 meV, just the range of the p-states available for a fit by effective mass theory (EMT) for spheroidal conduction band extrema In the absence of a detailed EMT for such a complicated band structure the authors argue the approximate applicability of a variable gamma model This model is applied to the present knowledge of donor excited states obtained from electronic Raman scattering, bound exciton 'two-electron' luminescence satellites and direct photoexcitation spectra The parentage of the excited states observed in these different experimental techniques is critically reviewed It is shown that the variable gamma model has some merit; in particular gamma is seen to increase with the binding energy of the donor state described especially for the deep 1s state, the expected trend The first Zeeman data is presented for the donors SiGa, SP and TeP Several of the SiGa donor p-excited states split as expected although a weak transition to a state unanticipated on the EMT splits lika a p+or- state and magnetic splittings of the p+or- levels are unexpectedly state-dependent

Resonant Tunneling through Si/SiO2Double Barriers

Abstract: Evidence of resonant tunneling of electrons at room temperature has been found in nSi/SiO2/poly Si/SiO2/metal double-barriers. The observed singularities in the dc conductance curves have been explained as the tunneling through the quasistationary states of the potential well. The effective mass of tunneling electron and the Fermi level of polycrystalline Si have been determined from the measured resonant energies.

Cyclotron resonance and carrier scattering processes in anthracene crystals

Abstract: Cyclotron resonance experiments on holes orbiting in the ab plane of an anthracene crystal are described in detail. We were unable to reduce the cyclotron resonance experiment to a routine procedure and consequently are able to report useful cyclotron resonance measurements on only a few (six) anthracene crystals. Nevertheless we have been able to obtain useful information on the valence band structure and hole scattering properties in anthracene from these measurements. The measured effective mass of 11 me, where me is the free electron mass, is shown to be in qualitative agreement with calculations of the effective mass tensor. From the shape of the cyclotron resonance line at 2 K, we have obtained experimental hole scattering times ranging from 4×10−10 sec down to 10−12 sec and below depending on sample quality. By a detailed examination of the possible low temperature scattering mechanisms, we have concluded that, at 2 K, holes in anthracene are most efficiently scattered by charges trapped at point d...

High‐field drift velocity of silicon inversion layers—a Monte Carlo calculation

Abstract: This paper presents an accurate Monte Carlo calculation of the high‐field drift velocity of carriers in the p‐ and n‐channel inversion layers of silicon. The results are then compared with the results obtained by Hess and Sah by assuming a Maxwellian distribution of carriers. The models used in both these calculations are, however, the same as used by Hess and Sah. For the (100) surface of the n‐channel device, the electric subband expected to have the largest population at high fields is considered. For the p channel, only the lowest subband is taken and scalar effective mass is assumed. Lattice scattering mechanism alone is assumed to exist. It is found that the Monte Carlo calculation differs from the Maxwellian calculation. Also, the agreement between the former and the experiment of Fang and Fowler and of Sato et al. is not satisfactory. Possible origin of this discrepancy with the experiment is discussed.

Anisotropic quasiparticle properties in aluminum

Abstract: The electron-phonon interaction in aluminum was studied using Fermi-surface-fitted 4-OPW electron states, a realistic phonon spectrum, and integration mesh-density varying with local Fermi surface curvature. The resulting electron mass enhancement lambda and thermal scattering rate tau/sup -1/ are evaluated as functions of position on the Fermi surface. It was found that the agreement between observed and calculated cyclotron masses is improved by the use of an anisotropic effective mass enhancement (lambda) rather than the average one. The anisotropy of lambda is determined predominantly by mixing coefficient variations, rather than by phonon anisotropy. The scattering rate tau/sup -1/ exhibits order-of-magnitude variations over the Fermi surface at low temperatures. Its values at 5/sup 0/K are within 50% of the experimentally observed ones everywhere, with better agreement in free-electron regions. In free-electron regions, umklapp processes cause a more rapid increase than T/sup 3/ for temperatures above 15 to 25/sup 0/K. On ridges, where the initial T/sup 3/-coefficient is very large, a slower increase is found. There results a washingout of anisotropy with increasing temperature. The results on lambda are in good agreement with those of a recent similar calculation; the tau/sup -1/ results agree qualitatively but not quantitatively.

Electroabsorption in laminatedGaSe x S1−x semiconductors in the fundamental-absorption edge region

Abstract: Electroabsorption spectra at 300 K and 77K and under fields of 2·103V/cm and 4·104V/cm have been studied in the fundamental-absorption edge region of single-crystal solid solutions GaSexS1−x obtained by the Bridgman method. The characteristic of GaSexS1−x electroabsorption spectra at 300 K and 77 K is the presence of a strong negative peak associated with the ground state of the exciton, the amplitude of which grows with the field according to a power law (Δα∼Em, wherem>1). Exciton ground-state lines have been observed for the first time in GaSexS1−x (1≥x≥0.4) at 300 K. The exciton groud-state line in GaSexS1−x was analysed, due regard being given to its broadening in the electric field as a result of phonon-exciton interaction. The parameters of the band structure have been determined in GaSexS1−x (energy of allowed interband transitions Γ4−→Γ3+, exciton binding energy, reduced effective mass of an electron-hole pair, exciton Bohr radius, etc.). With GaSe0.5S0.5 a jump of 50 meV, which is attributed to a phase transition, is observed in the dependences ofEx andEgon composition. The compounds of GaSexS1−x (0.6≤x≤1) crystallize mainly in the e-modification, whereas those of GaSexS1−x (0≤x≤0.4) crystallize primarily in the β-modification.

Electronic structure of metals. V. Density of states effective masses of the alkali metals

Abstract: For pt.IV see ibid., vol.7, p.1439 (1977). The authors have applied the previously published results of an energy independent model pseudopotential calculation to evaluate the density of states effective masses, m*, at the Fermi level for the alkali metals in both solid and liquid phases. The results thus obtained are used to reduce the range of the uncertainties (i) in the existing theoretical values for m* and the electron-phonon coupling parameters and (ii) in the existing experimental values for the electronic specific-heat coefficients and the paramagnetic spin susceptibilities for the heavy solid alkali metals. Also, these results show that the change in the Fermi level density of states effective mass on melting is larger for the heavy alkali metals than for the lighter alkali metals.

Theory of strongly correlated charged-particle systems: Plasma turbulence and high-density electron liquids

Abstract: A unified theory is developed for describing dynamic and static properties of strongly correlated charged-particle systems, such as a high-density electron liquid and a strongly turbulent plasma, for which the correlation (or fluctuation) energy is comparable in magnitude to the kinetic energy. Based on the microscopic Klimontovich formalism, a systematic renormalization of the single-particle propagators is carried out and vertex corrections arising from strong correlations are taken account of. The resulting theory is examined, and found to be satisfactory, in the light of a number of rigorous criteria, such as explicit inclusion of statistical modification effects in the single-particle orbits, dynamic modification of effective particle interactions brought about by strong correlations, frequency-moment sum rules of the dielectric response function, and reproduction of exact results known in the static properties of the electron liquid; the theory is thus valid for all wave numbers and frequencies. With the aid of a velocity-average approximation, we show that the result can be expressed in a simplified form which still satisfies those criteria. Its relation with the polarization potential model in the theory of condensed matter is thereby noted; explicit expressions for the scalar and vector polarization potentials, the wave-number-dependent effective mass, and the collisional contribution to the response function are obtained.

Free excitons in InP in high magnetic fields

Abstract: The energy levels of free excitons were investigated in several III-V compounds in magnetic fields up to 20 T. The results of reflectance experiments in InP are presented here as an excellent example of the power of a recently developed adiabatic theory to describe the energy states of excitons in the high field limit. A best fit to this theory yields an accurate and complete set of band structure parameters. These are γ1 = 4.95, γ2 = 1.65, γ3 = 2.35, gc = 1.31, ϰ = 0.97 , and q ≅ 0. The exciton binding energy, the band gap, and the effective mass acceptor binding energy are calculated from the new band parameters. Differences in energetic position and relative intensity of the components in the Faraday and Voigt configurations are observed. They are possibly related to the effects of long-range exchange interaction.

Melting of the Phase Locking of Linear Charge Density Waves in TTF–TCNQ

Abstract: The method of self-consistent phonons is applied to the melting of the interchain phase locking of linear CDWs. The melting point is obtained as T c =0.11( m * / m ) 1/2 θ t , where m * is the effective mass of the phase mode phonon and θ t is its transverse Debye temperature essentially equal to the phase locking energy of Lee, Rice and Anderson.

de Haas-van Alphen measurements of the Fermi surfaces of rubidium and cesium

Abstract: We present the results of a detailed investigation of the geometry of the Fermi surfaces of rubidium and cesium by means of the de Haas-van Alphen (dHvA) effect. By using samples of random orientation, mounted with the least constraints possible, we have obtained extensive coverage of the entire Fermi surface. An in situ NMR sample enabled the infinite-field phase of the signal, as well as absolute areas, to be determined. The spin-splitting factor cos (πgm*/2m 0 ), was found to be positive for both metals. The data, taken in magnetic fields up to 52 kG and at temperatures down to 1.1 K, was fitted by a 10- and 12-term cubic harmonic model expansion for rubidium and cesium, respectively. These models indicate that the Fermi surfaces are somewhat more distorted than those derived from previous investigations. A large change in the signal amplitude of cesium with crystal orientation suggests a variation in the productgms* over the Fermi surface. Effective mass measurements in cesium show a significant discrepancy between the measured dHvA and specific heat masses.