Showing papers on "Band gap published in 1970"

Electrical and Optical Properties of Narrow-Band Materials

Abstract: The electrical and optical properties of materials which are characterized by narrow bands in the vicinity of the Fermi energy are discussed. For such materials, electronic correlations and the electron-phonon coupling must be considered explicitly. Correlations in $f$ bands and in extremely narrow $d$ bands can be handled in the ionic limit of the Hubbard Hamiltonian. It is shown that free carriers in such bands form small polarons which contribute to conduction only by means of thermally activated hopping. Wider bands may also exist near the Fermi energy. Carriers in these bands may form large polarons and give a bandlike contribution to conductivity. A model is proposed for determining the density of states of pure stoichiometric crystals, beginning with the free-ion energy levels, and taking into account the Madelung potential, screening and covalency effects, crystalline-field stabilizations, and overlap effects. Exciton states are considered explicitly. The Franck-Condon principle necessitates the construction of different densities of states for electrical conductivity and optical absorption. Because of the bulk of experimental data presently available, the model is applied primarily to NiO. The many-particle density of states of pure stoichiometric NiO is calculated and is shown to be in agreement with the available experimental data. When impurities are present or nonstoichiometry exists, additional transitions must be discussed from first principles. The case of Li-doped NiO is discussed in detail. The calculations are consistent with the large mass of experimental information on this material. It is concluded that the predominant mechanism for conduction between 200 and 1000 \ifmmode^\circ\else\textdegree\fi{}K is the transport of hole-like large polarons in the oxygen $2p$ band. A method for representing the many-particle density of states on an effective one-electron diagram is discussed. It is shown that if correlations are important, donor or acceptor levels cannot be drawn as localized levels in the energy gap when multiple conduction or valence bands are present. This result comes about because extrinsic ionization energies of two correlated bands differ by an energy which bears no simple relation to the difference in energies of the intrinsic excitations, which are conventionally used to determine the relative positions of the bands.

Amorphous versus Crystalline GeTe Films. III. Electrical Properties and Band Structure

Abstract: Various transport studies have been carried out on amorphous and crystalline GeTe films of 80 A to 10 μ thickness. Crystalline GeTe has a low resistivity (∼10−4 Ω·cm at 300°K) which increases with temperature slowly and nearly linearly at low temperatures (below ∼300°K) and rapidly at higher temperatures. The hole concentration (N∼1010−1021 cm−3) increases only slightly with temperature. Mobility varies as N−4/3. These results in conjunction with the tunnel‐spectroscopy and optical data show that crystalline GeTe is a degenerate (and thus metallic conduction), p‐type narrow band gap (∼0.1–0.2 eV) semiconductor with Fermi level ∼0.3–0.5 eV inside the valence band. The linear increase of the susceptibility mass with hole concentration, the constancy of the Hall coefficient up toωLτ=0.35 (ωL=Larmor frequency, τ=collision relaxation time), and the monotonic increase of thermopower with temperature indicate that conduction takes place only in a single valence band. Amorphous GeTe films exhibit activated conduction. The dc resistivity varies from 410° to 77°K as ρ0 exp (Eg/2kT), where Eg is about 0.8 eV and ρ0 is the resistivity of crystalline GeTe films. Ac resistivity decreases with frequency (ω) as ω−n, where n lies between 0.5 and 1.0, depending on the temperature. The activation energy for ac conduction decreases rapidly from the dc value to zero with decreasing temperature as well as increasing frequency. The capacitance of amorphous GeTe at 77°K varies as ω−0.2 while the loss factor is independent of the frequency. With increasing dc field, the linear dependence of current on voltage changes to a power relation Vn, where n varies rapidly from ∼3 to 6 or more in a small range of the applied field. At very high fields, I ∝expβF1/2 (β=constant) is observed. These results, together with the tunnel‐spectroscopy, and optical data suggest that amorphous GeTe may be represented as a p‐type semiconductor with band gap ∼0.8 eV with exponential tailing of the bands and a continum of localized states in the vicinity (both sides) of the band edges. Conduction takes place by two parallel processes of intrinsic excitation across the band gap, and thermally and/or field‐assisted hopping from one localized (trapping) state to another. Dc conduction by hopping at low fields is negligible. At higher fields, trap modified space‐charge‐limited current flow and Poole‐Frenkel effect determine the nonlinear field dependence of current.

Band Structure of Transition Metals Studied by ESCA

Abstract: The position and shape of the energy bands of the following transition metals have been studied by ESCA: Fe, Co, Ni, Cu, Ru, Rh, Pd, Ag, Os, Ir, Pt, Au. The Fermi levels of the metals with unfilled d-bands are found in the high-energy flanks of the valence band spectra. For the noble metals the Fermi level is shifted toward higher energies. These observations are in general accordance with the overlap of d- and sp-bands in transition metals. An increase in band width is noted between corresponding elements in each series of transition metals. A comparison is drawn between band widths obtained in the present study and those deduced from cohesive energy data. An observed splitting in some of the bands seems to be much too large to be attributable to spin-orbit interaction. Core electron lines are recorded for the purpose of obtaining an energy calibration, estimating the contribution to the observed band spectra from inelastically scattered electrons, and checking the chemical state of the sample. The photoexcitation process and the energy losses of the electrons due to single-particle and plasmon excitations are discussed.

Random phase model of amorphous semiconductors I. Transport and optical properties

Abstract: A model is studied which assumes that, in the conduting states of an amorphous semiconductor, the phase of the probability amplitude for finding an electron on a particular atomic site varies randomly from atom to atom. This “random phase model” is used to calculate the conductivity, thermopower, and optical absorption. Experimental data on conductivity and thermopower are analyzed for three chalcogenide compositions. There is an upper limit on the mobility of about 20 cm 2 /V sec. The matrix element for an optical transition from conducting states to conducting states is shown to be equal to that from conducting states to localized states. Therefore an upper limit of the order of 10 17 eV −1 cm −3 can be put on the density of states in the middle of the energy gap, for some bulk semiconducting glasses. Measurement of optical absorption of low magnitude in the infrared would make it possible to deduce the density of states as a function of energy in the gap.

The metal-nonmetal transition

Abstract: An account is given of some of the mechanisms which can lead to a transition from a metallic to a nonmetallic state, when a parameter such as the interatomic distance or temperature is varied. The simplest of these is the band overlap or Wilson transition, which occurs when a conduction band overlaps a valence band; this is discussed in § 2 and for noncrystalline systems in § 15. These transitions can be described in the Hartree-Fock approximation. If the insulating property is due essentially to the repulsion between electrons (e2/r12), then the nonmetallic state is normally antiferromagnetic. The possibility of describing it by normal band theory with a spin-dependent potential is discussed in § 5. It is emphasized that antiferromagnetism can exist in the metallic state, and that the conditions for the appearance of conductivity and the disappearance of antiferromagnetism are not always the same. The nonmetallic behaviour, that is the existence of a Hubbard gap, normally persists above the Neel temperature (as in NiO), as does the gap in some metals, but not in chromium. Disordered systems, such as doped semiconductors, are discussed; here in the metallic state we suggest that the two Hubbard bands overlap, and that the metal-nonmetal transition can be described as an Anderson transition (§ 16). This model gives a simple explanation of the negative magnetoresistance. In some materials a transition occurs which does not involve magnetic moments or structural change, and for d bands, following Halperin and Rice, and Weger, we introduce the concept of an `orbital orientation wave' in degenerate d bands (§§ 5, 19.3, 19.4). A number of specific materials are discussed.

Interband Effects on Magnetic Susceptibility. : II. Diamagnetism of Bismuth

Abstract: The magnetic susceptibility of conduction electrons in the presence of spin-orbit interaction is calculated. The model is that due to Wolff which assumes two bands separated by a small energy gap. Our calculation shows that due to the interband effect of the magnetic field the susceptibility has a large contribution to diamagnetism when the Fermi energy lies in the band gap region. This result is applied to bismuth, and possible interpretations are proposed for the dependence of its magnetic property on the effective valence number and the cause of the anisotropy.

Properties of glow-discharge deposited amorphous germanium and silicon

Abstract: Films of silicon and germanium are deposited on glass using the radio-frequency glow-discharge decomposition of silane and germane gases respectively. When grown on a substrate at room temperature the films are amorphous, with a short range order of about 20 A. The resistivities of these films, as deposited, are typically 108Ω cm for silicon and 7 × 103 Ω cm for germanium, measured at 294°K. Thermal activation energies for conduction decrease continuously below the deposition temperature, and at low temperatures germanium follows the relation log ’ = A/T 1 4 , where A is a constant. This would seem to indicate that a hopping process in an impurity band is responsible for conduction at low temperatures. Photoconductivity has been observed in silicon but not in germanium. The threshold energy for this effect decreases with increasing deposition or annealing temperatures. This is also true of the high temperature thermal activation energy. It is suggested that this is due to the de-localisation of states in the valence and conduction bands as the short range order increases. The optical absorption coefficients of germanium and silicon have an exponential dependence on photon energy and the considerable absorption below the fundamental absorption edge of the crystalline form may indicate the presence of localised states in the band gap.

Theory of the High Density Exciton. I

Abstract: The boson creation and annihilation operators of excitons are introduced and the fermion Hamiltonian of high density electrons and holes is expanded in terms of these boson operators. Then a nonlinear integral equation for the high density excitons is derived and it is solved in two ways: 1) by the perturbational method and 2) exactly for a simple model of the Coulomb interaction in the random phase approximation and the effective mass approximation for the two band model of a conduction band and a valence band. As a result, the cutting down effects of both the band edges due to formation of high density excitons are shown to overcome the exchange self-energy of the electrons and the holes composing the high density excitons.

Photoemission from Organic Crystal in Vacuum Ultraviolet Region. IV

Abstract: The quantum yield and the energy distribution of photoelectrons were measured for organic crystals in the vacuum ultraviolet region. A model was presented for the photoemission from organic crystals with a narrow valence band, and a semiempirical power law was derived for the yield near the threshold. The ionization potentials found from the spectral distribution of the quantum yield using this model were as follows: anthracene–5.68 eV, naphthacene—5.43, pentacene—5.04, perylene—5.33, indanthrone—5.17, and tetrathionaphthacene—4.42. The effect of electrons which escape after one inelastic scattering was observed. It was shown how the contribution of once-scattered electrons can be separated in the energy distribution. The threshold for “pair production” was estimated to be nearly equal to the band gap for perylene and a little higher than the band gap for quaterrylene. The fine structures observed both in the yield spectra and in the energy distribution can be accounted for by assuming the existence of ad...

Liquid‐Phase Epitaxy of In × GA 1 − × As

Abstract: layers grown by liquid‐phase epitaxy were obtained in the range of , when grown on the (111 Ga) plane of GaAs. Attempts to grow alloys on the (110), (111 As), (100), and (112 As) planes resulted in polycrystalline layers. The alloy composition was determined by x‐ray fluorescence and the band gap by infrared transmission. The ternary‐phase diagram was calculated using Darken's quadratic formalism to describe the ternary liquid and assuming the solid solution in equilibrium with the liquid to be regular. It was found that the experimental results were in good agreement with the calculated phase diagrams. A number of liquidus isotherms were calculated in the temperature range of 700°–1200°C. Gallium arsenide isoconcentration curves are shown for 0.95, 0.90, 0.80, 0.50, and 0.30 mole fraction.

Conduction Bands in In1−xAlxP

Abstract: Cathodoluminescence (CL) and x‐ray emission excited by an electron microprobe in In1−xAlxP at ∼300°K have been monitored simultaneously to yield conduction band structure and alloy composition, respectively Efficient single‐line CL, characteristic of direct bandgap recombination, is observed for x between 00 and almost 05 Elsewhere, the CL, characteristic of recombination in indirect bandgap semiconductors, is weak The direct bandgap CL peak has a composition dependence given by hv=134+223x (eV) The bandgap in the alloy is direct for 000≤x<044 with a maximum gap of 233 eV

Temperature Coefficient of the Refractive Index of Diamond- and Zinc-Blende-Type Semiconductors

Abstract: We have calculated the temperature coefficient of the long-wavelength refractive index of several group-IV and III-V semiconductors, using the Penn model for the electronic contribution to the dielectric constant. The isotropic band gap of this model is identified with the band gap at the $X$ point of the Brillouin zone, which can be simply expressed in terms of pseudopotential coefficients. The explicit temperature dependence of this gap is calculated by applying to these pseudopotential coefficients the appropriate Debye-Waller factors. The thermal expansion effect is obtained in the manner suggested recently by Van Vechten. Good agreement between the calculated and the observed temperature dependence of the long-wavelength refractive index is found.

Bulk Trapping States in β‐Phthalocyanine Single Crystals

Abstract: From temperature dependence measurements of the SCLC and Ohmic current densities, the electron trapping levels in metal‐free phthalocyanine have been determined in several ambients. In vacuum, traps with a density 5 × 1019 cm−3 located 0.38 eV below the conduction band have been observed. Associated with this level are donor sites with a density 2 × 1012 cm−3. In oxygen and hydrogen, trapping sites near the middle of the bandgap are observed. Thickness dependence measurements prove that the trapping sites are located at discrete energy levels. The results are extended to comment upon traps in copper phthalocyanine. The measurements indicate that the electron mobility is not temperature dependent up to 373°K.

The temperature dependence of the band-edge effective masses of InSb, InAs and GaAs as deduced from magnetophonon magnetoresistance measurements

Abstract: Magnetophonon peaks are observed in the second derivative of the magnetoresistance of high purity samples of n-type InSb, InAs and GaAs over a wide range of temperatures. The temperature dependence of the band-edge effective mass in each material is deduced and compared with that predicted from the dilatational component of the change in band gap with temperature. In the case of InSb, the agreement is excellent but, with InAs and GaAs, the observed change is greater than that predicted although still less than that obtained by substitution of the change of optical energy gap with temperature.

On the theory of surface states in nearly free electron systems

Abstract: The existence of surface states in band gaps of a nearly free electron band structure is investigated. While in gaps at the Brillouin zone boundary one finds such a state only for positive potential matrix element, there a surface state always exists for band gaps inside the Brillouin zone.

An electron tunneling investigation of quench-condensed superconductors

Abstract: An electron tunneling investigation has been carried out on quench-condensed Bi, Ga, Pb, Pb∙75Bi∙25, Pb∙50Bi∙50, and Pb∙25Bi∙75. The energy gap and transition temperature have been measured for each sample. The tunneling derivative data have been analyzed in terms of the strong-coupling theory of superconductivity by means of a computer program of W. L. McMillan. The effective phonon spectrum, the Coulomb pseudopotential, the complex energy gap function, the pairing self-energy function, and the electron renormalization function have been determined for each sample. Certain parameters based on integrals over the phonon spectrum have also been calculated for each sample.

Debye-Waller Factors and the PbTe Band-Gap Temperature Dependence

Abstract: Measurements of the temperature variation of x-ray diffraction peak intensities have been used to show that the mean-square thermal displacement of Pb in PbTe is approximately twice that of Te. This phenomenon is explained, using a calculation of the mean-square displacements from vibrational eigenvalues and eigenvectors, in terms of the heavy thermal weighting of the acoustic modes relative to the optical. The Pb motion dominates in the acoustic modes, whereas the Te motion dominates in the optic modes. Debye-Waller factors obtained from the calculated mean-square displacements have been associated with a modified Lin-Kleinman pseudopotential to obtain a theoretical estimate of the temperature dependence of the band gap. The modifications are necessary because of errors associated with their treatment of spin-orbit interaction. The calculated band-gap increase of 0.008 Ry between 100 and 300 \ifmmode^\circ\else\textdegree\fi{}K is in fair agreement with an experimental estimate of the explicit increase. It is shown that the magnitude of the shift is quite sensitive to adjustable parameters in the gap calculation as well as to the Debye-Waller factors. The sign of the shift is dependent on the relative ordering of levels and the relative mean-square displacements of the ions but not, otherwise, on the details of the calculation.

Threshold Requirements and Carrier Interaction Effects in GaAs Platelet Lasers (77°K)

Abstract: The experimentally observed thresholds for laser operation of optically pumped GaAs platelets are presented. The measurements were performed on uniformly doped samples of p‐type, n‐type, and compensated crystal (doping range 1014/cm3≤n, p≤1020/cm3). The observed thresholds are considerably lower than previously measured or predicted and exhibit no essential dependence upon impurity concentration. The 16‐meV shift of laser photon energy from bandgap in lightly doped GaAs is ascribed, as before, to electron‐hole‐lattice (EHL) interactions. Based upon the results of platelet laser threshold data and photon energy data, a comparison is made of the relative strength of the various EHL interaction mechanisms. If Coulomb interaction and dielectric screening can be ignored, over a certain doping range a remarkable fit of the photon energy data is afforded by the electron‐electron interaction mechanism.

Some Optical Properties of Layer-Type Semiconductor GaTe

Abstract: Some optical properties of GaTe single crystals, such as absorption coefficient, photoconductivity and reflectivity, have been measured. The crystal is usually p -type with carrier density 10 16 cm -3 , mobility 15 cm 2 /volt·sec and resistivity 20\(\varOmega\)·cm at room temperature. In the measurement of the photoconductivity, a minimum of the photoresponse corresponding to the strong line structure of absorption is observed and therefore the line structure is interpreted to be due to the formation of excitons. The energy gap and exciton binding energy are deduced from the shape of the absorption curve near the edge. The energy gap is 1.797 eV at 77°K and 1.700 eV at 300°K and the temperature coefficient ∂ E g /∂ T is found to be -4.35×10 -4 eV/°K. The exciton binding energy and the reduced effective mass associated with conduction and valence band are 0.025 eV and 0.089 m 0 , respectively. The reflectivity is found to change rapidly at the photon energy corresponding to the exciton absorption.

Electrical and Optical Properties of Si-SnO 2 Heterojunctions

Abstract: Electrical and optical properties have been investigated on Si–SnO2 heterojunctions. Semiconducting SnO2 film has been grown by a successive oxidation of the evaporated tin on the (111) surface of silicon single crystal. The SnO2 film shows the properties of a degenerate n-type semiconductor having the band gap energy of 3.5 eV. The current-voltage characteristics of Si–SnO2n–n heterojunction represent a good rectification. The photovoltage measurements demonstrate that the Si–SnO2n–n heterojunction has the photoresponse in the wide wavelength region from 400 to 1200 mµ at room temperature. The energy band diagram of Si–SnO2n–n heterojunction is determined from the results of these electrical and optical measurements.

Experimental Evidence for Trapped Exciton States in Liquid Rare Gases

Abstract: In connexion with studies of the electronic structure of disordered systems, we enquire whether there exist exciton states in simple liquids. We report the results of a vacuum ultraviolet spectroscopic study of liquid argon and of liquid krypton doped with xenon. Experimental evidence was obtained for Wannier-Mott type impurity states in liquids which have no parentage in the excited states of the isolated atoms constituting the dense fluid. The absorption spectra of the doped liquid rare gases were monitored in the region 160 to 120 nm. The following experimental results are reported: (a) In the Xe/Ar liquid two absorption bands corresponding to the $^{1}$S$\_{0}$ $\rightarrow $ $^{3}$P$\_{1}$ and to the $^{1}$S$\_{0}$ $\rightarrow $ $^{1}$P$\_{1}$ transitions (or alternatively to the n = 1 Wannier states) were identified at 141 nm (8.80 eV) dagger and at 123 nm (10.1 eV). An additional line was observed at 127 nm (9.76 eV). (b) In the Xe/Kr liquid three absorption bands were observed at 144.5 nm (8.59 eV), 125.5 nm (9.89 eV) and 129 nm (9.6 eV). (c) The absorption spectra of the doped liquids were compared with the spectra of 1 cm thick doped solid rare-gas crystals. From these results we conclude that: (a) The 127 nm (9.76 eV) band in the Xe/Ar liquid system and the 129 nm (9.61 eV) band in the Xe/Kr liquid system cannot be attributed to a perturbed 'atomic' state and are assigned to the n = 2 Wannier state in the liquid. (b) Line broadening of exciton states in the liquid can be accounted for by a simple scattering model. (c) Preliminary information on band gaps in liquid rare gases were obtained from the spectroscopic data. (d) The effect of liquid-solid phase transition on the line broadening of exciton states is consistent with electron mobility data in these systems.

Non-ohmic properties of some amorphous semiconductors

Abstract: The electrical conductivity of amorphous thin films of As 2 Te 3 and AsTeGeSi at low and high electric fields has been studied between 77°K and 350°K. Both semiconductors have the same energy gap width (0.9 eV) obtained from field measurements, but show different behaviour at high fields. In As 2 Te 3 there is a space charge limit current with a trap level located at 0.28 eV and in AsTeGeSi an exponential dependence of the current on the square root of the field appears. In AsTeGeSi the switching threshold voltage is practically identical with the thermal turnover voltage, so that internal Joule heating is probably the cause which gives rise to the Ovonic threshold switch. This supposition is supported by calculations which are based on filamentary constriction of the current in the on state of conduction. A quite good agreement between the theoretical and experimental I – V characteristics was obtained. The condition of reversibility of the switching is that the local temperature increase should not change the structure along the filament.