Showing papers on "Effective mass (solid-state physics) published in 1995"
TL;DR: In this article, the electronic properties of the wurtzite-type AlN and GaN were analyzed on the basis of the effective-mass Hamiltonian, where the hexagonal symmetry was considered.
Abstract: The electronic band structures of the wurtzite-type AlN and GaN are calculated by using a self-consistent full-potential linearized augmented plane-wave method within the local-density-functional approximation. In order to clarify the electronic properties near the Brillouin-zone (BZ) center and to give an important guideline on the material designs for short-wavelength optical devices, we link the first-principles band calculations with the effective-mass approximation. The electronic properties are analytically studied on the basis of the effective-mass Hamiltonian, where we consider the hexagonal symmetry of the wurtzite structure. The effective-mass parameters, such as electron effective mass, hole effective masses, or, equivalently, the Luttinger-like parameters, crystal-field splitting and spin-orbit splitting, are determined by reproducing the calculated band structures near the BZ center. The obtained results show that the cubic approximation is fairly successful in the analysis for the valence-band structures of the wurtzite-type nitrides. Further, the calculated parameters for GaN are consistent with the observed ones.
520 citations
TL;DR: Relativism and nonrelativistic empirical tight-binding theory is generalized to incorporate time-dependent electromagnetic fields in a gauge-invariant manner that does not introduce any extra adjustable parameters.
Abstract: Relativistic and nonrelativistic empirical tight-binding theory is generalized to incorporate time-dependent electromagnetic fields in a gauge-invariant manner that does not introduce any extra adjustable parameters. Based on this approach, it is shown that explicit expressions can be derived for the effective mass tensor, the effective Land\'e g factor, the current, the frequency-dependent transverse dielectric function, and the wave-vector- and frequency-dependent longitudinal dielectric function. A finite basis analogue of the optical f-sum rule is derived and shown to impose a condition on tight-binding parameters.
285 citations
TL;DR: In this article, the size dependence of the energy band gap for hydrogen saturated silicon clusters, wires and slabs is calculated using all electron density functional theory, and an effective mass model with finite barriers for both valence and conduction band is found to semiquantatively account for the numerical findings.
Abstract: The size dependence of the energy band gap for hydrogen saturated silicon clusters, wires and slabs are calculated using all electron density functional theory. The hydrogen saturation is considered as a model for a wider band gap insulator enclosing the silicon structures. With this perspective in mind, an effective mass model with finite barriers for both valence and conduction band is found to semiquantatively account for the numerical findings.
256 citations
TL;DR: In this article, the electron tunnelling in device grade ultra-thin 3-6 nm n + poly-Si/SiO 2 /n-Si structures has been analyzed.
Abstract: In this work the electron tunnelling in device grade ultra-thin 3–6 nm n + poly-Si/SiO 2 /n-Si structures has been analysed. The well known analytic expression for the Fowler-Nordheim tunnelling current was adapted to include the case of direct tunnelling of electrons, which becomes important for oxide layers thinner than 4.5 nm. For these ultra-thin oxide MOS structures it is necessary to take the band bending in the Si substrate and in the poly-Si layer into account to determine the oxide electrical field strength and to derive the tunnelling parameters of the measured current-voltage characteristic. A method is explained to derive the tunnel barrier height φ s and the effective mass of the tunnelling electron m ox from the experimental tunnel current characteristics. It is shown that both the direct tunnelling and the Fowler-Nordheim tunnelling current can be quantitatively explained by a WKB approximation using m ox as the single fitting parameter.
256 citations
TL;DR: Instantaneous Galilean invariance is used to derive from first principles the expression for the Hamiltonian of an electron with a position-dependent effective mass, as well as the adequate boundary conditions for the wave function in the case of abrupt heterojunctions.
Abstract: Instantaneous Galilean invariance is used to derive from first principles the expression for the Hamiltonian of an electron with a position-dependent effective mass, as well as the adequate boundary conditions for the wave function in the case of abrupt heterojunctions. A very elementary model sustaining these results in the envelope-function approximation is also proposed.
246 citations
TL;DR: In this paper, the axial and planar modes of 6H-SiC were measured by Raman scattering at room temperature and the plasmon frequency, carrier damping, and phonon damping were deduced.
Abstract: LO‐phonon–plasmon–coupled modes in n‐type 4H– and 6H–SiC single crystals with free‐carrier concentrations of 1016–1018 cm−3 have been measured by Raman scattering at room temperature. The axial‐type mode for which plasma oscillation and atomic displacement are parallel to the c axis, and the planar‐type mode for which these oscillations lie in the c plane, have been individually observed. From a line‐shape analysis of the observed spectra, the plasmon frequency, carrier damping, and phonon damping have been deduced. These quantities have large differences between the axial‐ and planar‐type mode in 6H–SiC, indicating its large crystal anisotropy. On the contrary, 4H–SiC shows small anisotropy. The longitudinal and transverse effective mass components of the electron have been determined from the plasmon frequency using carrier densities derived from Hall measurements. The deduced values are m∥=1.4m0 and m⊥=0.35m0 for 6H–SiC, and m∥=0.48m0 and m⊥=0.30m0 for 4H–SiC. The carrier mobility obtained from the ana...
193 citations
TL;DR: In this paper, the electron effective mass in hexagonal GaN films grown by metal organic vapor phase epitaxy on sapphire substrates was determined by cyclotron resonance experiments.
Abstract: The electron effective mass in hexagonal GaN films grown by metal organic vapor phase epitaxy on sapphire substrates is determined by cyclotron resonance experiments. Its value is m p* = 0.22±0.005 m o. Taking polaron effects into account the band edge mass is m b* = 0.20±0.005 m o. From the resonance linewidth a mobility of 3500 cm2/Vs at 6 K is obtained.
142 citations
TL;DR: In this article, Fourier transform infrared absorption spectroscopy has been performed on a GaN epitaxial film grown by the hydride vapor phase epitaxy on sapphire substrate.
140 citations
TL;DR: In this paper, the optically detected cyclotron resonance (ODCR) studies of electron effective masses in 4H SiC were performed on high-purity n-type 4HSiC epitaxial layers grown by chemical vapor deposition at both X band (9.23 GHz) and Q band (35.05 GHz) microwave frequencies.
Abstract: Results from optically detected cyclotron resonance (ODCR) studies of electron effective masses in 4H SiC are reported. ODCR measurements were performed on high‐purity n‐type 4H SiC epitaxial layers grown by chemical vapor deposition at both X band (9.23 GHz) and Q band (35.05 GHz) microwave frequencies. Electron effective masses in 4H SiC were directly determined as m⊥*=0.42m0 and m∥*=0.29m0. A scattering time in the basal plane τ⊥≊4.3×10−11 s, and hence, the corresponding electron mobility μ⊥≊1.8×105 cm2/V s, was obtained from a fit of the ODCR line shape.
106 citations
TL;DR: In this paper, the thermopower η of Sr1−xLaxTiO3 ceramics was investigated up to x=0.5 and in the temperature range between 150 K and 1200 K.
Abstract: The thermopower η of Sr1−xLaxTiO3 ceramics was investigated up to x=0.5 and in the temperature range between 150 K and 1200 K. In addition, the carrier concentration n was determined by Hall measurements and by a chemical Ti3+‐analysis. For low temperatures and high n, η depends linearly on temperature and on n−2/3, as expected from a degenerate quasi free electron gas. In the case of high temperatures and low n, the absolute value of η rises with 1.5⋅ln10⋅k/e per decade of temperature and with ln10⋅k/e per decade of carrier concentration, as expected from a classical broad‐band semiconductor obeying the Boltzmann statistics. In the range of degeneration an effective mass meff of 4.2 electron masses can be deduced without the assumption of a transport factor Ae. In the classical range Ae=3 can be evaluated, requiring only a temperature and lanthanum independent meff. Thus, the thermopower of Sr1−xLaxTiO3 ceramics can be described by a constant effective mass and a constant transport factor within a wide range of temperature and lanthanum content. Furthermore, the transition from degeneration to classical behavior can be described as a function of temperature and electron density, e.g., at room temperature it takes place at about x≊0.2 (i.e., n≊3.4⋅1021/cm3).
102 citations
TL;DR: A comparative survey of known experimental and theoretical values of heavy-hole and electron effective mass in GaAs, InAs, and A1As is presented in this article, where room-temperature values of these parameters are given for the above binary solutions and for their ternary compounds.
Abstract: A comparative survey of known experimental and theoretical values of heavy-hole and electron effective mass in GaAs, InAs, and A1As is presented in this work. Recommended room-temperature values of these parameters are given for the above binary solutions and for their ternary compounds.
TL;DR: In this paper, specular reflectance spectroscopy and four-point resistivity and Hall measurements were used to determine the optical and electrical properties of thin n-type semiconductors.
Abstract: Thallium oxide is a degenerate n-type semiconductor which can be electrodeposited from aqueous solution at room temperature. Thin films were characterized by transmission and specular reflectance spectroscopy and by four-point resistivity and Hall measurements. Optical parameters were determined by fitting the observed specular reflectance to the Drude equation. Due to the high free carrier concentration, the material reflects strongly in the near-infrared, and the band-to-band optical transitions are shifted by up to 1.1 eV by the Moss-Burstein effect. The optical and electrical properties of the films were a function of the deposition overpotential. Films grown at 44 mV had an intrinsic bandgap of 0.66 eV, resistivity of 2.8 x 10{sup -4} ohm-cm, mobility of 27 cm{sup 2}Vs, and conduction band effective mass of 0.43m{sub o}. Films grown at 300 mV had an intrinsic band gap of 0.51 eV, resistivity of 7.8 x 10{sup -5} ohm cm, mobility of 93 cm{sup 2}V s, and conduction band effective mass of 0.29m{sub o}. Mobilities measured by contact and optical methods are similar, which shows the optical technique may be used for conditions in which contact methods might fail. 20 refs., 11 figs., 2 tabs.
TL;DR: In this paper, it was shown that off-mass-shell meson-nucleon scattering amplitudes obtained using the PCAC choice of pion field must not be viewed as fundamental constraints on the dynamics, the determination of the effective meson mass in nuclear matter or the possible existence of meson condensates in the ground state of nuclear matter.
TL;DR: In this article, the Fowler-Nordheim tunneling currents were used to measure the thickness of thin silicon dioxide (SiO2) films and the average effective electron mass in the conduction band of SiO2.
Abstract: A novel method is presented for measuring the thicknesses of thin (<60 A) silicon dioxide (SiO2) films using the oscillations in the Fowler‐Nordheim tunneling currents. An important feature of the proposed method is that the accuracy of this method increases with decreasing oxide thickness and thicknesses changes of ∼1 A can be detected. The oscillations are also used for measuring the average effective electron mass in the conduction band of SiO2.
TL;DR: In this paper, Monte Carlo simulation results for the field and temperature-dependent electronic mobilities, drift velocities, and diffusion coefficients in 4H-SiC were presented, including crystal anisotropy.
Abstract: Monte Carlo simulation results for the field‐ and temperature‐dependent electronic mobilities, drift velocities, and diffusion coefficients in 4H‐SiC are presented. The calculations include crystal anisotropy, and values are obtained for field orientations both parallel and transverse to the c axis of the hexagonal structures. The simulations are based on electron effective mass data that has only recently become available. Our theoretical predictions of the electron mobilities and their anisotropy ratios compare very well with available experimental data at 300 K. A room‐temperature velocity of 2.7×107 cm/s was obtained in 4H‐SiC for transport parallel to the c axis. This value is found to be larger than both 6H and 3C material. Finally, our calculations for the longitudinal and transverse diffusion coefficients at 300 K indicate that both have appreciable field dependences and exhibit a ‘‘soft’’ threshold.
TL;DR: In this article, the acceptor ionization energy of GaN epitaxial films has been investigated in terms of acceptor acceptor dielectric constant (to phonon energy).
Abstract: The recent achievement of p-type doping in GaN epitaxial films emphasizes the importance of the acceptor ionization energy with relevance to the application of group III nitrides in visible-light-emitting devices. Measured values of approximately 200 meV suggest that doping efficiencies at room temperature may be no more than 1%, resulting in undesirable series resistance in LEDs and lasers. Consideration of the effective mass hydrogen model of the acceptor ground state in GaAs, GaP and GaN suggests that this large value of GaN results from the strong electronegativity of the nitrogen atom and the corresponding reduction in dielectric constant, compared with the other compounds. This is further emphasized by the need to use the high-frequency dielectric constant rather than the static value when the ionization energy is greater than the TO phonon energy. Using in ( infinity )=5.35 and an effective mass of 0.4 m provides good agreement with the measured ionization energy of GaN, this value of mn being consistent with estimates based on recent hole mobility measurements. It is also consistent with smoothly increasing hole mass in the sequence GaAs (0.33 m), GaP (0.37 m), GaN (0.40 m). Finally, the opportunity is taken to speculate about likely values of acceptor ionization energies in AlGaN and AlGaAsN alloys.
TL;DR: In this paper, a semianalytical analysis of the valence subband structure of cubic semiconductors was performed in the Kohn-Luttinger formalism, and analytic expressions for the effective mass tensor and full subband dispersion for GaAs and InAs were derived.
Abstract: We present semianalytical calculations of the valence subband structure for 〈011〉‐oriented quantum wells of cubic semiconductors. Working in the Kohn–Luttinger formalism [Phys. Rev. 97, 869 (1955)], we present analytic expressions for the effective mass tensor and show the full subband dispersion for GaAs and InAs. In addition to the usual extremum at k∥=0, 〈011〉‐oriented wells support saddle point spectra. In this case, the effective mass changes sign as a function of in‐plane crystallographic direction.
TL;DR: In this article, a novel semiconductor switching device is proposed based on unique control over the two-dimensional band structure of an AlSb−GaSb•InAs•AlSb heterostructure.
Abstract: A novel semiconductor switching device is proposed. It is based on unique control over the two‐dimensional band structure of an AlSb‐GaSb‐InAs‐AlSb heterostructure. By applying small electric fields, virtually any value can be achieved for such parameters as the energy gaps, effective masses, and carrier types and densities in the material. The proposed heterostructure can be readily fabricated with existing epitaxial techniques.
TL;DR: In this article, the transport properties of holes in Si1 − xGex channels were studied with a Monte Carlo technique, showing that the hole velocity is much larger than that of compressive or unstrained cases, especially at low fields.
Abstract: The transport properties of holes in Si1 − xGex are studied with a Monte Carlo technique. If the strain is applied to the Si1 − xGex channel, it raises the degeneracy of the heavy-hole and light-hole bands: for compressive strain, the heavy-hole band lies at a higher energy than the light-hole band, while for tensile strain, the order reverses, although it is technologically uncertain how to realize the tensile case at this stage. The transport properties are essentially the same for the unstrained and compressive cases, since most holes are in the heavy-hole band over the entire field range of interest. Although the overshot is negligible, the hole velocity is still higher than that of Si, reflecting the excellent hole transport properties in Ge. In the tensile case, we have observed a negative differential resistance region for 5 × 102–5 × 103V/cm, due to the hole transfer from the light-hole band to the heavy-hole band. The velocity is much larger than that of compressive or unstrained cases, especially at low fields. Because of the small effective mass in the light-hole band, the velocity overshoot is significant in the tensile strain case. These results provide motivation to try to realize the tensile strain case technologically.
TL;DR: In this paper, the effect of excitons in GaInAs-InP coupled asymmetric quantum wells on the refractive index modulation was analyzed numerically using a model based on the effective mass approximation.
Abstract: The effect of excitons in GaInAs-InP coupled asymmetric quantum wells on the refractive index modulation, is analyzed numerically using a model based on the effective mass approximation. It is shown that two coupled quantum wells brought in resonance by an applied electric field will, due to the reduction in the exciton oscillator strengths, have a modulation of the refractive index which is more than one order of magnitude larger than in a similar quantum well structure based on the quantum confined Stark effect, but with no coupling between the quantum wells. Calculations show that combining this strong electrorefractive effect with self-photo-induced modulation in a biased-pin-diode modulator configuration, results in an optical nonlinearity with a figure of merit of 20 cm/sup 3//J at a wavelength of 1.55 /spl mu/m. This value is large compared to optical nonlinearities originating from band edge resonance effects in III-V semiconductor materials. >
TL;DR: The collagen spectra provide the first high resolution neutron views of the proton-dominated modes of a protein over a wide energy range from the low frequency phonon region to the rich spectrum of localized high frequency modes.
TL;DR: Analysis of the amplitude of the quantum oscillations within the framework of a two-dimensional Lifshitz-Kosevich model reveals that this material appears to be only fully transformed into the high-field state at fields above similar to 27 T, where the quasiparticle scattering rate is observed to be low.
Abstract: The de Haas-van Alphen effect has been measured in the organic conductor alpha-(BEDT-TTF)(2)KHg(SCN)(4) in pulsed magnetic fields of up to 54 T, temperatures down to 350 mK, and at three different angles. Analysis of the amplitude of the quantum oscillations within the framework of a two-dimensional Lifshitz-Kosevich model reveals that this material appears to be only fully transformed into the high-field state at fields above similar to 27 T, where the quasiparticle scattering rate is observed to be low. On entering the low-field state, the scattering rate is observed to increase dramatically. We also observe an apparent increase in the effective mass from similar to 1.5m(e) in the low-field state to similar to 2.7m(e) in the high-field state. The data at low fields are in accord with previous studies, but the nature of the higher harmonics of the de Haas-van Alphen oscillations at high fields appears to signify a departure from conventional Lifshitz-Kosevich behavior.
TL;DR: The band structures of 6H SiC and 4HSiC calculated by means of the full-potential linear-muffin-tin-orbital method are used to determine the effective mass tensors for their conduction-band minima and, contrary to previous suggestions, appreciable anisotropies in the c plane are found.
Abstract: The band structures of 6H SiC and 4H SiC calculated by means of the full-potential linear-muffin-tin-orbital method are used to determine the effective mass tensors for their conduction-band minima. The results are shown to be consistent with recent optically detected cyclotron resonance measurements, which find the ratio of cyclotron masses for B\ensuremath{\perp}c to B\ensuremath{\parallel}c to be larger (smaller) than unity for the 6H (4H) polytype. However, contrary to previous suggestions, appreciable anisotropies in the c plane are found. For 6H SiC, a strong dependency on band filling is predicted because of the occurrence of a double-well minimum along the ML axis. The calculated mass tensors for 3C and 2H are also reported.
TL;DR: In this article, the fast Fourier transform was applied on the photoreflectance (PR) spectra to separate the contributions from the heavy and light holes, respectively, and the electric fields in the undoped layer can be calculated from the frequencies of heavy or light holes. And the result of the heavy hole agrees well with that from the conventional FKOs fittings if the reduced mass is used in the conventional fittings.
Abstract: The photoreflectance (PR) spectroscopy of δ‐doped or similar structured sample has been observed to exhibit many Franz–Keldysh oscillations (FKOs). The beats are shown in the FKOs and they are attributed to the different frequencies of the FKOs of the transitions from the heavy and light holes. We have applied the fast Fourier transform on the PR spectra to separate the contributions from the heavy and light holes. The electric fields in the undoped layer can be calculated from the frequencies of heavy and light holes, respectively. The result of the heavy hole agrees well with that from the conventional FKOs fittings if the reduced mass=0.055 m0 is used in the conventional fittings.
TL;DR: It is found that at an even denominator filling fraction the fermion's effective mass diverges logarithmically at the Fermi level, and it is argued that this divergence allows for an exact calculation of the energy gaps of the fractional quantized Hall states asymptotically approaching these filling fractions.
Abstract: We consider a two-dimensional electron system in an external magnetic field at and near an even denominator Landau level filling fraction. Using a fermionic Chern-Simons approach, we study the description of the system's low energy excitations within an extension of Landau's Fermi-liquid theory. We calculate perturbatively the effective mass and the quasiparticle interaction function characterizing this description. We find that at an even denominator filling fraction the fermion's effective mass diverges logarithmically at the Fermi level, and argue that this divergence allows for an exact calculation of the energy gaps of the fractional quantized Hall states asymptotically approaching these filling fractions. We find that the quasiparticle interaction function approaches a \ensuremath{\delta} function. This singular behavior leads to a cancellation of the diverging effective mass from the long-wavelength low-frequency linear response functions at even denominator filling fractions.
TL;DR: In this article, the dependence of optical properties on crystal orientation was analyzed for long wavelength strained quantum-well (QW) GaAsP-InGaAsP lasers, and it was shown that the optical gain increases as the crystal orientation is inclined from [001] toward [110].
Abstract: The dependence of optical properties on crystal orientation is analyzed for long wavelength strained quantum-well (QW) GaAsP-InGaAsP lasers. The calculation is based on the multiband effective mass theory which enables us to consider the anisotropy and the nonparabolicity of the valence-band dispersions. It is found that the optical gain increases as the crystal orientation is inclined from [001] toward [110]. This is due to the reduced valence-band density of states. The differential gain is about 1.6 times larger for the [110]-oriented 1.55-/spl mu/m strained QW's than for equivalent [001]-oriented QW's. It is also shown that the threshold current density in 1.3-/spl mu/m strained QW lasers decreases to two-thirds of that in the [001]-oriented laser as the orientation is inclined away from [001] by 40/spl deg/-90. >
TL;DR: The Raman electronic continuum is calculated in an antiferromagnetic spin-fluctuation model of the superconducting state using a tight-binding model with, up to second nearest neighbors is used and in one case with effective mass anisotropy.
Abstract: The Raman electronic continuum is calculated in an antiferromagnetic spin-fluctuation model of the superconducting state. The dependence of the Raman cross section on temperature and on band structure is investigated. A tight-binding model with, up to second nearest neighbors is used and in one case with effective mass anisotropy. The gap is determined from numerical solution of the BCS equations using fast Fourier transforms, with pairing through the phenomenological spin susceptibility of Millis, Monien, and Pines.
Book•
01 Feb 1995
TL;DR: In this paper, the authors present an advanced textbook on semiconductor physics for graduate students in physics and electrical engineering departments, which can be used as a research reference for solid state scientists and semiconductor device engineers.
Abstract: Modern Semiconductor Quantum Physics has the following constituents: (1) energy band theory: pseudopotential method (empirical and ab initio); density functional theory; quasi-particles; LCAO method; k.p method; spin-orbit splitting; effect mass and Luttinger parameters; strain effects and deformation potentials; temperature effects. (2) Optical properties: absorption and exciton effect; modulation spectroscopy; photo luminescence and photo luminescence excitation; Raman scattering and polaritons; photoionization. (3) Defects and Impurities: effective mass theory and shallow impurity states; deep state cluster method, super cell method, Green's function method; carrier recombination kinetics; trapping transient measurements; electron spin resonance; electron lattice interaction and lattice relaxation effects; multi-phonon nonradiative recombination; negative U center, DX center and EL2 Defects. (4) Semiconductor surfaces: two dimensional periodicity and surface reconstruction; surface electronic states; photo-electron spectroscopy; LEED, STM and other experimental methods. (5) Low-dimensional structures: Heterojunctions, quantum wells; superlattices, quantum-confined Stark effect and Wannier-Stark ladder effects; resonant tunneling, quantum Hall effect, quantum wires and quantum dots.This book can be used as an advanced textbook on semiconductor physics for graduate students in physics and electrical engineering departments. It is also useful as a research reference for solid state scientists and semiconductor device engineers.
TL;DR: It is found that, in general, an increase of the initial electronic energy decreases the ability of the system to form localized states, but a large effective mass favors localized polaron formation for initially localized electrons, but this is not always the case for initially extended electronic states.
Abstract: We present results for the time evolution of a one-dimensional system consisting of an electron, described by a tight-binding Hamiltonian and a harmonic latttice, coupled by a deformation-type potential. We solve numerically the nonlinear system of equations of motion for this model in order to study the effects of varying the electronic effective mass for several initial conditions and coupling strengths. Different types of localized and extended states are formed with features that are absent from the traditional polaronic states and depend very strongly on the initial electronic configuration and effective mass in a very often unexpected manner. We find that, in general, an increase of the initial electronic energy decreases the ability of the system to form localized states. However, a large effective mass favors localized polaron formation for initially localized electrons, but this is not always the case for initially extended electronic states. In the latter case, increasing the effective mass of an electron initially close to the bottom of the band makes localization more difficult, while for an initially highly excited electron, localized polaron formation is possible only when the electronic effective mass and the atomic masses of the lattice become of the same order. Finally, for a small parameter range, we find an impressive recurrence, a periodic and a complete exchange between the electronic and vibrational degrees of freedom of a small part of the initial electronic energy.
TL;DR: In this article, an exact effective mass differential equation for electrons in heterostructures is derived by applying a k-space transformation of variables to the Burt envelope-function theory in which the Brillouin zone is mapped onto the infinite real axis.
Abstract: An exact effective-mass differential equation is derived for electrons in heterostructures. This equation is exactly equivalent to the Schr\"odinger equation, and is obtained by applying a k-space transformation of variables to the Burt envelope-function theory in which the Brillouin zone is mapped onto the infinite real axis. The mapping eliminates all nonlocal effects and long-range Gibbs oscillations in the Burt theory, producing an infinite-order differential equation in which interface effects are strongly localized to the immediate vicinity of the interface. A general procedure is given for obtaining finite-order boundary conditions from the infinite-order equation; the second-order theory reduces to the BenDaniel-Duke model with a \ensuremath{\delta}-function potential at the interface. The derivation is presented for a simple one-dimensional crystal but can easily be generalized for more complex situations.