Conductivity Effective Mass Research Articles

Boltzmann-equation approach to the negative magnetoresistance of ferromagnetic-normal-metal multilayers.

The Boltzmann equation is solved for a system consisting of a ferromagnetic--normal-metal--ferromagnetic metallic trilayer. The in-plane conductance of the film is calculated for two configurations: the ferromagnetic layers aligned (i) parallel and (ii) antiparallel to each other. The results explain the giant negative magnetoresistance encountered in these systems when an initial antiparallel arrangement is changed into a parallel configuration by application of an external magnetic field. The calculation depends on (a) geometric parameters (the thicknesses of the layers), (b) intrinsic metal parameters (number of conduction electrons, magnetization, and effective masses in the layers), (c) bulk sample properties (conductivity relaxation times), (d) interface scattering properties (diffuse scattering versus potential scattering at the interfaces), and (e) outer surface scattering properties (specular versus diffuse surface scattering). For perfect specular scattering at the surfaces the problem becomes identical to an infinite multilayer, periodic system. It is found that a large negative magnetoresistance requires, in general, considerable asymmetry in the interface scattering for the two spin orientations. All qualitative features of the experiments are reproduced. Quantitative agreement can be achieved with sensible values of the parameters. The effect can be conceptually explained based on considerations of phase-space availability for an electron of a given spin orientation as it travels through the multilayer sample in the various configurations.

Mechanism of piezoresistance in p-type Ge

By conductivity calculations for the degenerate valence bands in Ge with and without stress, we show for the first time that the principal mechanism for piezoresistance in p-type Ge is the stress-proportional mobility change of holes, but the carrier redistribution is the second order effect. Energy dependent conductivity effective masses, which tend to ellipsoidal masses at the band edges from the heavy- and light-hole masses at high hole energy may be associated with the hole mobility change.

Electron effective mass in Pb 1− xGd xTe

Polycrystalline lead-telluride samples doped with gadolinium have been investigated. The thermoelectric power coefficient, Fermi level and the effective mass of the density of states are studied as a function of the temperature and impurity atoms concentration. From the reflection spectra of the samples we have calculated the conductivity effective mass m c ∗. The values obtained for m c ∗ are for different compositions of x (Pb 1− x Gd x Te). The experimental results show a good agreement between the data on the density of states efiective mass m do ∗ and the conductivity efiective mass m c ∗ for carrier concentration up to 10 19cm −3.

Optimal properties of semimagnetic compound Pb 1− xGd xTe with x=0.01 and 0.025

Reflectivity and transmission spectra of a new semimagnetic compound Pb 1− x Gd x Te with x=0.01 in the 300-77K temperature range are reported. From reflectivity data the high dielectric constant ϵ(∞) is deduced. Lyddane-Sachs-Teller relation gives the static dielectric constant ϵ(0). The conductivity effective mass m ∗ c measured from the plasma frequency agrees well with the one deduced from absorption measurements α vs the wavelength in the short wavelength range. The energy gap as well as its temperature dependence is given by absorption data. The introduction of low concentration magnetic ion Gd does not affect drastically the optical properties of the material comparatively to the optical PbTe ones.

Electronic structure and impurity-limited electron mobility of silicon superlattices.

With the utilization of a new complex-band-structure technique, the electronic structure of [100]-oriented model Si-${\mathrm{Si}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Ge}}_{\mathrm{x}}$ and metal-oxide-silicon superlattices have been obtained over a wide range of layer thickness l (11\ensuremath{\le}l\ensuremath{\le}110 A\r{}), complementing previous results obtained for very thin layer systems (l\ensuremath{\le}11 A\r{}). For l\ensuremath{\ge}44 A\r{}, it is found that these systems exhibit a direct fundamental band gap, produced in large part by the Brillouin-zone folding of the bulk conduction-band edges. In the same range, the transverse band-edge electron effective mass is reduced to a limiting value of 0.73 of the bulk conductivity effective mass, supporting our previous suggestion that a band-structure-driven enhancement in transverse electron mobility over bulk silicon may be possible. Simple effective-mass scaling yields an enhancement of about 1.2 in the (low-temperature) impurity-scattering limit and about 2.2 in the (high-temperature) phonon-scattering limit. Detailed consideration is made of the simpler of the two cases, impurity-scattering-limited electron mobility, with the result that enhanced mobility is indeed predicted for sufficiently high carrier concentrations.

Hole transport in gallium antimonide

The Hall coefficients R, Seebeck coefficients S, and electrical resistivities ρ of two undoped samples of p-type GaSb were measured over the temperature ranges 20–300 K for R and ρ and 40–300 K for S. The theoretical transport coefficients R, S, and ρ were fitted in a self-consistent way to the experimental data by adjusting the material parameters. The temperature range of the analysis (80–300 K) was found to be in the transition region between a multiellipsoidal valence band structure at low temperatures and a warped sphere structure at higher temperatures. The value deduced for the heavy hole conductivity effective mass was found to be about one third of the heavy hole density-of-states effective mass md1≊0.9 m0 which was used from the theory of Kolodziejczak.

Theory of silicon superlattices: Electronic structure and enhanced mobility

A realistic tight-binding band-structure model of silicon superlattices is formulated and used to study systems of potential applied interest, including periodic layered Si-Si1−xGex heterostructures. The results suggest a possible new mechanism for achieving enhanced transverse carrier mobility in such structures: reduced transverse conductivity effective masses associated with the superlattice band structure. For electrons in [100]-oriented superlattices, a reduced conductivity mass arises intrinsically from the lower symmetry of the superlattice and its unique effect on the indirect bulk silicon band gap. An order of magnitude estimate of the range of mobility enhancement expected from ths mechanism appears to be consistent with preliminary experimental results on Si-Si1−xGex superlattices.

IR absorption in p-type pb 0.97Sn 0.03Se

IR absorption in p-type melt grown Pb 0.97Sn 0.03Se crystals is reported. The results for the room temperature absorption coefficient (α) in the wavelength region 2–15 μm are analysed. The indirect absorption edge is found to be at 0.26 eV for this ternary alloy. In the longwavelength region α is found to be proportional to λ 2, in agreement with the classical free carrier absorption expression. The conductivity effective mass of holes is found to be 0.067 m 0 at 300°K.

The electron effective mass in heavily doped GaAs

A resolution to the order k6 of the three-level equation of Kane allows the authors to obtain a new expression for the conduction band energy and so new analytical expressions for the electron effective masses in the range of carrier concentration 1016-1019 cm-3. The calculated values of the conduction effective mass as a function of carrier density agree well, for the first time, with experimental values, which were obtained from Shubnikov-de Haas experiments by using a new expression for the oscillation amplitude. In this expression the authors take into account the effect of medium-range potential fluctuations induced by crystal inhomogeneities.

Transport phenomena in low and high magnetic field (Shubnikov-de haas effect) in n-type Ga 1− xAl xSb alloys

Galvanomagnetic measurements have been performed on n-type Ga 1− x Al x Sb with x ⪕ 0.3. For the first time the Shubnikov-de Haas oscillations have been observed. The Г band contribution to the conductivity for x < 0.15 was clearly pointed out from the measurements of the periods of oscillations and Hall effect. The conduction effective mass at the Fermi level was deduced for several samples.

Gain-frequency-current relation for Pb&amp;lt;inf&amp;gt;1-x&amp;lt;/inf&amp;gt;Sn&amp;lt;inf&amp;gt;x&amp;lt;/inf&amp;gt;Te double heterostructure lasers

The active region gain expression for Pb <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</inf> Sn <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf> Te lasers is obtained from the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k \cdot p</tex> 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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k \cdot p</tex> 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 <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</inf> Sn <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf> Te laser material.

Some physical properties of Ternary germanium bismuth telluride (GeBi 4Te 7) semiconducting crystals

High purity crystals of GeBi 4Te 7 have been prepared, and values of the electrical conductivity, thermoelectric power, Hall constant and of the i.r. reflectivity in the plasma oscillation region have been obtained. To interpret the results a simple three-valley model of the constant energy surfaces is proposed. Values of the dielectric constant ( ϵ g = 35), high frequency index of refraction ( n λ→0 = 5.9), the character of scattering of the free carriers, the Fermi level ( E F = 0.16 eV), the mean relaxation time of the free carriers (〈 τ〉) = 5.79 × 10 −15 sec), the free electron concentration ( N = 1.63 × 10 20 cm −3), the conductivity effective mass (m ∗ c = 0.27) and m 1 = m 3 = 0.51 m 3, m 2 = 0.18 m 0 have been calculated.

Optical Effective Mass of Holes in p‐Type AIIIBV Compounds

AbstractA comparative study is made of the concentration dependences of the optical effective masses of holes in a series of p‐type AIIIBV compounds. It is shown that in all compounds studied the optical effective mass of holes begins to increase under high concentrations of carriers. A qualitative explanation is given of such increase. The comparison of the concentration dependences of mp for various compounds shows that the valence bands are similar in various AIIIBV compounds. The structure of the valence bands in AIIIBV compounds is substantially different from the structure of the conductivity bands. Therefore in theoretical calculations of different effects it is necessary to distinguish quite distinctly the dependences on the density‐of‐states effective mass and on the conductivity effective mass, i.e. to be very cautions in the use of the quasiisotropic band approximation.

Preparation and some physical properties of semiconducting GeSb 2Te 4 crystals

High purity single crystals of GeSb 2Te 3 were prepared. Values of the electrical conductivity, thermoelectric power, Hall constant, Nernst-Ettingshausen coefficient and of the IR reflectivity in the plasma oscillation region were obtained. Analysis of the results yielded the dielectric constant ( ϵ g = 39), index of refraction n λ→0 = 6.15, the character of scattering of the free carriers, the Fermi level (E F = 0.31 eV) the relaxation time of the free carriers (〈 τ〉= 0.86×10 −14s) and the value of N p m c . To interpret the results, three-valley model of the energy band was proposed and values of the Hall structure factor ( β = 0.67), the Hall scattering factor (M 1 = 0.7), the free-hole concentration (N p = 4.8 ×10 20 cm −3) and of the conductivity effective mass m∗ = 0.55 and m 1 = m 3 = 1.34 m 0, m 2 = 0.36 m 0 were calculated.

Donor-Electron Transitions between States Associated with theX1candX3cConduction-Band Minima in GaP

Transitions from the ground states of Si, Te, and S donors associated with the lowest $X$ conduction band have been observed to excited donor states associated with the next-higher $X$ conduction band as well as transitions into the higher band. The ${X}_{3c}\ensuremath{-}{X}_{1c}$ interband energy is found to be 355 \ifmmode\pm\else\textpm\fi{} 3 meV with the conductivity effective mass in the higher band being $(0.14\ifmmode\pm\else\textpm\fi{}0.02){m}_{0}$.

Electron Effective Mass in PbS Single Crystals by Infrared Reflectivity Measurements

Infrared reflectivity measurements have been performed on a series of PbS single crystals. The temperature dependence of conductivity effective mass ms has been evaluated and used to compute the free-carrier mobilities. Results show how ms decreases as the crystal temperature decreases. Further results show how ms decreases as the carrier concentration decreases. The influence of crystal preparation on reflectivity properties has been studied. It has been determined that lead precipitates up to 1019 atoms/cm3 do not affect the minimum of the reflectivity curve but the homogeneity of the crystals does have a significant effect. Our determinations of conductivity effective mass of free carriers at each temperature have been used to compute the mobilities according to the two alternative theories of thermal vibration scattering, namely by acoustical and optical modes. Results show that the acoustical theory may not be used to predict temperature dependence of the mobilities, but that the optical polaron theory does give good predictions.

Temperature-dependence of the combined effective mass of holes in silicon

The complex structure of the silicon valence band leads to great difficulties in studying the transport properties of holes in this material. On the basis of experimental and theoretical data we have calculated in this paper a low-field combined conduct ivi ty effective mass and combined density-of-states effective mass of holes which are temperature-dependent. The model we propose is valid for Ohmic problems in the temperature range from 40 °K to 400 °K. Theoretical calculations (1) of the hole energy band in silicon by the k . p method have established the following features. The valence b~ald can be obtained by overlapping individual atomic p-functions and exibits the max imum at k = 0. In the absence of spin-orbit splitt ing this maximum would be sixfold degenerate corresponding to the product of three p-functions with two spin-up and spin-down functions. Away from k : 0 there are three separate bands (E 1, E 2 and Ea) ~hich are doubly degenerate due to spin. I t is customary to label the bands by their spectroscopic character t)~ and by the magnetic quantum number ± M~ (degenerate in absence of magnetic field). Accordingly the first band E 1 is characterized by P~ and 3I~1⁄2, the second E 2 by P1⁄2 and M~_], the third E a by P1⁄2 and M~1⁄2. Spin-orbit splitting part ial ly removes the above degeneracy at k : 0 by lowering the two (E3) P1⁄2 bands with respect to the four P t bands (E 1 and E~). The coupling of the first two bands (E 1 and E2) leads to equienergetie surfaces of warped structure. For k ~ 0, E 1 is proport ional to k ~, keeping the same warped character as at k _~ 0. /E 2 does not mantain a parabolic character away from k ~ 0, its curvature changing with k 2, and tends to assume the same curvature of E 1. The curvature of E a changes with k 2 in the opposite way. From the above features the following conclusions can be summarized in the effectivemass approximation. The first band E 1 is characterized by holes having an energy* which is directiomdependent. The second band E~ is independent effective mass m 1 characterized by holes with effective mass m* which is increasing with energy and is direction-dependent. Calculations shows that at /¢ ~ 0 m * ~ m ~ , and that at kv~0 m~* approximates m~* for energies above about 0.02 eV from the minimum. The split-off

Hole Effective Masses in Highly Doped CdSb Determined from Infrared‐Plasma‐Reflectivity Measurements

AbstractThe infrared plasma reflectivity is measured on heavily Ag‐doped CdSb with hole concentrations of p = (0.7 to 3.0) × 1019 cm−3 in the spectral region λ = 3 to 30 μm at T = 85 and 300 °K. Conductivity effective masses and relaxation times of holes are determined from the plasma frequencies obtained by fitting experimental and theoretical reflectivity spectra. The masses are strongly anisotropic and weakly temperature dependent. The relaxation times for optical frequencies are slightly greater than those according to Hall mobilities. Scattering of holes on ionized impurities is concluded to be predominate in the relaxation mechanism.

Split-off valence band parameters for GaSb from stress-modulated magnetoreflectivity

Abstract We obtain the following results from interband magnetoreflectivity in p -type GaSb at 30°K: Δ = (0.749 ± 0.002) eV , ( m / m c + m / m so ) = 29.8 ±0.3, and ( g c + g so ) = -12 ± 6, where Δ is the spin-orbit splitting, m c and m so are the conduction and split-off band effective masses, and g c and g so their effective g -factors. From these results we deduce m so / m = 0.15 ± 0.03, g so = -6 ± 7, and K L = 3.0 ± 1.5, where K L is the valence band parameter introduced by Luttinger.

Electronic Properties of VO2near the Semiconductor-Metal Transition

Optical, thermal, magnetic, and transport properties of V${\mathrm{O}}_{2}$ in the vicinity of the semiconductor-metal transition temperature of 68\ifmmode^\circ\else\textdegree\fi{}C are discussed in terms of a simple one-electron band picture. Particular emphasis is placed on the variation in these properties from sample to sample. It is shown that all of the available experimental data can be qualitatively explained in terms of such a model. In the metallic state, there are at least two overlapping and partially occupied bands, resulting in a complex Fermi surface characterized by a conductivity effective mass near unity and carrier mobilities in the range between 1 and 10 ${\mathrm{cm}}^{2}$/V sec. There is no consistent evidence of a very narrow high-mass band near the Fermi level. In the semiconductor state, it is probable that the band overlap described above is removed by the lattice distortion, resulting in an energy gap of approximately 0.6 to 0.7 eV. This energy gap is filled to a density of typically ${10}^{19}$ to ${10}^{20}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ with donorlike and acceptorlike states, the energy distribution and density depending on the sample, so that it is impossible to obtain an accurate measure of the energy gap. The charge density associated with these donorlike and acceptorlike states is normally larger than that associated with the carriers in the band, resulting in electronic properties characteristic of heavily compensated semiconductors. The conduction-band effective mass and the electron mobility are both near unity in the semiconducting phase of V${\mathrm{O}}_{2}$. Some implications of these experimental results with respect to the application to V${\mathrm{O}}_{2}$ of several of the published theories on semiconductor-metal transitions in solids are pointed out.