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Showing papers in "Semiconductor Science and Technology in 1987"


Journal ArticleDOI
TL;DR: In this paper, a simple procedure for calculating the strengths of the more important absorption features and the concentrations of the corresponding defect centres as functions of the radiation dose and of the carbon and oxygen concentrations in the silicon was described.
Abstract: Room-temperature irradiation of silicon with 2 MeV electrons can create many defects that give rise to optical absorption lines. The authors describe a simple procedure for calculating the strengths of the more important absorption features and the concentrations of the corresponding defect centres as functions of the radiation dose and of the carbon and oxygen concentrations in the silicon. The following absorption features and centres are considered: the 969 meV line (two-carbon-atom centre), the 865 cm-1 line (C+O centre), the 1020 cm-1 line (C+O+self-interstitial), the 835 cm-1 line (vacancy+O'A centre'), the 1.7 mu m band (di-vacancy) and the 488 meV line (C+O+vacancy centre).

137 citations


Journal ArticleDOI
TL;DR: In this paper, a new model was proposed to predict the large values of the activation energies for capture and emission, using purely spectroscopic input data, and without introducing an unnaturally large lattice relaxation.
Abstract: Spectroscopic investigations of Si-doped AlxGa1-xAs reveal that the deep donor ('DX centre') exhibits an electron-phonon interaction of moderate strength. The Huang-Rhys factor turns out to be 0.5 and the dominant coupling is with the LO1 phonons. These data lead to the formulation of a new model for this class of centres, which unifies the basic concepts of two former models, due to Saxena (1980-2) and to Lang and Logan (1977-9), respectively. The charm of the new model is in its ability to predict the large values of the activation energies for capture and emission, using purely spectroscopic input data, and without introducing an unnaturally large lattice relaxation.

92 citations


Journal ArticleDOI
TL;DR: In this paper, the Frohlich electron-photon interaction and the Lyddane-Sachs-Teller (LST) splittings of the optic phonon modes in mixed crystals with two-mode behavior were discussed.
Abstract: The authors discuss the Frohlich electron-photon interaction and the Lyddane-Sachs-Teller (LST) splittings of the optic phonon modes in mixed crystals with 'two-mode' behaviour. The theoretical results for these properties within a two-mode model are described. For the alloy In0.53Ga0.47As they discuss the experimental evidence for the LST splittings and the electron-phonon coupling of the two longitudinal optic (LO) phonon branches, including their own studies of phonon satellites of exciton recombination in In0.53Ga0.47As/InP quantum wells. The electron-phonon coupling is much weaker for the 'InAs-like' modes than for the 'GaAs-like' modes. They show that the primary reason for this effect is coupling of the LO distortions of the alloy by the macroscopic electric field.

73 citations


Journal ArticleDOI
TL;DR: In this article, a soft threshold factor is introduced into the theory of lucky drift and the results are applied to some major semiconductors, such as Ge, Si, GaAs, InP and GaP.
Abstract: Arguments are presented for the existence of a soft threshold to impact ionisation in GaAs and other related semiconductors. A soft-threshold factor is introduced into the theory of lucky drift and the results are applied to some major semiconductors. Excellent fit of theory to experiment is obtained, which confirms that the thresholds are indeed soft. Soft-threshold factors and new mean free paths are obtained for Ge, Si, GaAs, InP and GaP. The mean free paths are shown to obey a simple law. The results for GaAs are applied to the case of multilayer APD. It is shown that excellent agreement with the results of Capasso et al. (1982) are obtained, even with a 60:40 division of band edge discontinuity.

70 citations


Journal ArticleDOI
TL;DR: In this paper, it is shown that the action of the Hamiltonian operator on the periodic functions also introduces coupling between envelope functions and that this coupling is non-local in general.
Abstract: In a recent letter (see ibid., vol.2, p.460 (1987)) the author outlined the first exact formulation of the envelope function method. In this paper the details of this new exact formulation are given. For clarity the discussion is carried out for the one-dimensional case. In previous approximate treatments coupling between envelope functions is mediated only by the action of the momentum operator on the periodic functions. It is shown that in the exact treatment, the action of the Hamiltonian operator on the periodic functions also introduces coupling between envelope functions and that this coupling is non-local in general. The nature of these new coupling terms is examined for an abrupt heterojunction. The relation between the new exact envelope function equations and previous work is discussed extensively. In particular, by making reasonable approximations to the new coupling terms, the author has managed to derive the effective mass equation for multilayer structures (particle in a box model in the quantum well case); the derivation sheds light on the vexed question of boundary conditions to be used in conjunction with this equation. The paradox of obtaining non-local envelope function equations from a local Schrodinger equation is also resolved.

70 citations


Journal ArticleDOI
TL;DR: In this paper, the Fourier transform photoluminescence spectroscopy (FTPS) was used to measure boron, phosphorus and aluminium concentrations in silicon by comparing the intensities of bound and free-exciton luminescence features.
Abstract: Calibrations are reported for measuring boron, phosphorus and aluminium concentrations in silicon by comparing the intensities of bound-exciton and free-exciton luminescence features. Particular attention has been directed towards investigating the effects of excitation density and instrumental resolution. The luminescence spectra have been corrected for the system response so that the calibrations are independent of the equipment used and are hence transferable. Fourier transform rather than dispersive spectroscopy has been employed to measure the luminescence spectra. Since Fourier transform photoluminescence spectroscopy is a relatively new technique, it is described in some detail.

65 citations


Journal ArticleDOI
TL;DR: In this article, the conduction bands in GaAs and In have been studied very accurately through the cyclotron resonance over a wide range of energies using the photoconductive detection technique.
Abstract: The conduction bands in GaAs and In have been studied very accurately through the cyclotron resonance over a wide range of energies using the photoconductive detection technique. Pronounced band non-parabolicity has been measured in GaAs. Values for the band-edge masses of 0.0660 m0 and 0.07927 m0 respectively have been determined. A five-level k.p model of the band structure in the presence of a magnetic field has been used to describe the data where resonant and non-resonant polaron contributions to electron energies are included in the theory. The non-parabolicity and spin-doublet splitting of the cyclotron resonance are well described by the employed formalism in both materials and the theory also gives a reasonable account of the anisotropy of the band in GaAs. The fit to experimental data allowed the authors to determine the matrix element of momentum Q between the higher conduction and valence bands in both materials.

61 citations


Journal ArticleDOI
TL;DR: In this article, the concentration of Cs traps was determined from infrared LVM absorption measurements, which together with previous EPR reorientation data give D=0.44 exp (-0.87 eV/kT) cm2s-1.
Abstract: FZ silicon has been irradiated at 140 K with 2 MeV electrons to displace substitutional carbon atoms Cs into interstitial sites Ci. The concentrations of the two species were determined from infrared LVM absorption measurements. Isothermal anneals in the range 297-331 K showed a loss of neutral Ci atoms with first-order kinetics and the formation of di-carbon centres. From the known concentration of Cs traps, values of the diffusion coefficient were determined, which together with previous EPR reorientation data give D=0.44 exp (-0.87 eV/kT) cm2s-1.

59 citations


Journal ArticleDOI
TL;DR: In this paper, the luminescence of bevelled AlxGa1-xAs structures at different temperatures as a function of the alloy composition was investigated using the electron microprobe analysis.
Abstract: Spatially resolved experiments have been performed on the luminescence of bevelled AlxGa1-xAs structures at different temperatures as a function of the alloy composition. The AlAs mole fraction (x) of the samples investigated ranges from 0.15 to 0.52. This was determined by measurements employing the electron microprobe analysis. At T=85 and 300 K the band-gap energy of direct-gap material Eg(x) has been evaluated from band-to-band optical transitions, whereas at lower temperatures (T=2 and 38 K) the peak position of the luminescence line originating from the radiative decay of excitons bound to neutral donors served as a measure for the composition dependence of the fundamental energy gap in the direct-gap as well as in the indirect-gap region. For AlAs contents lower than 40 mol.% the luminescence data show that Eg(x) varies linearly with the composition. Our observations at different temperatures suggest that the temperature coefficient of the direct band gap increases with rising x. In contrast to Dingle's results for the crossover parameters we find xc=0.374 and Ec=2.057 eV at T=38 K and xc=0.41 and Ec=1.98 eV at T=300 K.

57 citations


Journal ArticleDOI
TL;DR: In this paper, the four recombination mechanisms that are most important for p-type CdxHg1-xTe are discussed and compared to the experimental results, and an analysis of lifetime versus temperature variations suggests that the Auger-7 recombination mechanism is not important for P-type material grown by the Bridgman technique.
Abstract: Photoconductive lifetime measurements have been carried out on thick samples of both doped and undoped slices of p-type CdxHg1-xTe prepared by Bridgman and accelerated crucible rotation (ACBT) Bridgman techniques. Means of reducing and/or allowing for surface recombination from front and back surfaces are described. The four recombination mechanisms though to be the most important in p-type material are outlined and compared to the experimental results. An analysis of lifetime versus temperature variations suggests that the Auger-7 recombination mechanism is not important for p-type material grown by the Bridgman technique. Measurements of lifetime in material covering a wide range of carrier concentration values confirms this view. An investigation of ZnS passivation on both n- and p-type material suggests that it can be a useful passivation for photovoltaic n-on-p devices.

54 citations


Journal ArticleDOI
TL;DR: The Schottky barrier diodes were made by DC magnetron deposition and by thermal evaporation of Al on both n-and p-type GaAs substrates as discussed by the authors.
Abstract: Schottky barrier diodes were made by DC magnetron deposition and by thermal evaporation of Al on both n- and p-type GaAs substrates. Information about the electrical behaviour of these diodes was obtained from I-V, C-V and I-V-T measurements. It was found that for the diodes with a sputter-deposited metal contact a large density of donor-like defects is present in the near-surface region, together with a region of decreasing density deeper into the semiconductor. An out-annealing of these donor-type defects is observed at temperatures lower than 250 degrees C. The interaction between Al and GaAs, leading to the formation of AlxGa1-xAs, may be responsible for the observed changes in barrier heights and doping densities for the diodes annealed at temperatures higher than 250 degrees C.

Journal ArticleDOI
TL;DR: In this article, the infrared absorption lines observed at low temperatures in Zn-doped GaAs epilayers passivated with hydrogen and deuterium are ascribed to As-H and As-D stretching modes where the As atom involved is the first neighbour of the Zn acceptor.
Abstract: Infrared absorption lines observed at low temperatures in Zn-doped GaAs epilayers passivated with hydrogen and deuterium are ascribed to As-H and As-D stretching modes where the As atom involved is the first neighbour of the Zn acceptor. This attribution is shown to be consistent with a model for hydrogen passivation of acceptors on gallium sites in GaAs.

Journal ArticleDOI
TL;DR: In this paper, the authors showed that at higher temperature this defect anneals, with the formation of nearest-neighbour (B-donor) substitutional pairs, corresponding to a defect with axial symmetry.
Abstract: Compensated silicon containing boron and a group V donor has been irradiated with 2 MeV electrons at a temperature of 110 K. LVM lines at 730 and 757 cm-1 have been attributed to interstitial 11B and 10B atoms respectively. These defects anneal with second-order kinetics in the range 200-250 K leading to a diffusion coefficient D=0.04 exp(-0.58 eV/kT) cm2 s-1. Centres involving two equivalent boron atoms are formed and give LVM lines at 903, 912, 928 cm-1 ( omega /sub ///) and 599, 613, (624) cm-1 ( omega perpendicular to ) corresponding to a defect with axial symmetry. This centre anneals at a slightly higher temperature of 250-300 K to give the previously reported Q centre which shows one LVM line per isotope. At higher temperature this defect anneals, with the formation of nearest-neighbour (B-donor) substitutional pairs. A comparison is made with published results for Bi centres obtained by the EPR and DLTS techniques.

Journal ArticleDOI
TL;DR: In this paper, the same authors report measurements for two types of Schottky diodes with different bulk doping in the frequency range 0.01 Hz to 10 kHz, with the temperature and bias as variable parameters.
Abstract: Dielectric spectroscopy of semiconductors (DSS) reveals the frequency spectra of delayed electronic transitions in semi-insulating systems and it may be used to study the trapping/de-trapping processes in the space charge regions of Schottky diodes and at the metal-semiconductor interfaces. The authors report measurements for two types of diodes with different bulk doping, in the frequency range 0.01 Hz to 10 kHz, with the temperature and bias as variable parameters. The trapping processes in the space charge region are shown to have non-exponential time dependence, and the interfacial processes give strong deviations from the classically expected behaviour at very low frequencies and high temperatures, with a strong dependence on external bias. Certain phenomena appear to point to many-body interactions having a role in determining the rate processes in these Schottky diodes.

Journal ArticleDOI
TL;DR: In this article, a sharp peak was observed in the absorption and luminescence spectra near the absorption edge of n-type modulation-doped GaAs-AlxGa1-xAs multiple quantum wells.
Abstract: A well defined sharp peak was observed in the absorption and luminescence spectra near the absorption edge of n-type modulation-doped GaAs-AlxGa1-xAs multiple quantum wells. The peak is assigned as the Fermi edge anomaly similar to the many-body effects in the soft X-ray spectra of metals. As the temperature was raised above 10 K, the peak disappeared, but it was restored by the application of magnetic field. The magnetic field dependence of the peak indicates that it has an excitonic character.

Journal ArticleDOI
TL;DR: In this paper, the interaction of atomic hydrogen with cleaved n-and p-type GaAs samples has been studied by photon-emission yield spectroscopy, Auger et al. showed that the interaction occurs in two steps: an adsorption which saturates with one H per surface atom, then a dissociation.
Abstract: The interaction of atomic hydrogen with cleaved n- and p-type GaAs samples has been studied by photon-emission yield spectroscopy, Auger electron spectroscopy, electron energy loss spectroscopy and low-energy electron diffraction. It is shown that the interaction occurs in two steps: first an adsorption which saturates with one H per surface atom, then a dissociation. During the adsorption stage: (i), keeping a 1*1 structure, a change in surface relaxation is very likely; (ii), H binds covalently to the substrate atoms with a sticking coefficient of 1 and (iii), a band of H-induced states about 0.22 eV wide grows at approximately 0.12 eV below the valence band edge.

Journal ArticleDOI
TL;DR: In this paper, the electrical properties of metal-CdTe contacts have been measured for a diverse group of 18 metals by using currentvoltage and capacitance-voltage techniques, and it has been found that the bulk thermodynamic data provide an approximate description of the interface reactivity for most of the systems studied.
Abstract: The electrical properties of metal-CdTe contacts have been measured for a diverse group of 18 metals by using current-voltage and capacitance-voltage techniques. The contacts were formed by metal evaporation onto chemically etched surfaces of n-CdTe single crystals. A large number of metals yield a barrier height of 0.72+or-0.03 V, independent of the work function of the metal. Mn, Cr and V were different, producing ohmic or very low barriers. The nature of the CdTe(110) surfaces produced by chemical etching using bromine in methanol was studied by an X-ray photo-emission technique. The authors have also carried out a detailed investigation into the microscopic interactions at selected interfaces by soft X-ray photo-emission using a synchrotron radiation source. Detailed comparisons of the microscopic interaction of Ag and Mn with the oxidised surfaces, using photo-emission are reported. In contrast to the behaviour of Ag, the Mn overlayer reduces completely the CdTe native oxide layer, leading to low-barrier contacts. It has been found that the bulk thermodynamic data provide an approximate description of the interface reactivity for most of the systems studied.

Journal ArticleDOI
TL;DR: In this paper, the photoluminescence wavelength of the quantum well and the superlattice increased after Zn diffusion, which can be attributed to the In-Ga interdiffusion at the heterointerfaces as a result of the interchange mechanism between the interstitials and substitutional zinc atoms.
Abstract: Data are presented showing for the first time that Zn diffusion into a GaxIn1-xAsyP1-y-InP quantum well and superlattice (of 100 ? thickness) completely disorders the quantum well and superlattice layers. The photoluminescence wavelength of the quantum well and the superlattice increased after Zn diffusion, which can be attributed to the In-Ga interdiffusion at the heterointerfaces as a result of the interchange mechanism between the interstitials and substitutional zinc atoms.

Journal ArticleDOI
TL;DR: In this paper, the effect of a magnetic field on the currentvoltage characteristics of semiconductor tunnel barriers in which superlattices are used to filter the initial and final states is described.
Abstract: The authors describe the effect of a magnetic field on the current-voltage characteristics of semiconductor tunnel barriers in which superlattices are used to filter the initial and final states. A field applied parallel to the layers was found to destroy the negative differential conductance intrinsic to such structures, with a zero-bias anomaly appearing in high fields. A qualitative explanation of this, which considers the effect of the field on the electron states in the superlattice and on the tunnelling process, is presented.

Journal ArticleDOI
TL;DR: In this paper, the authors used infrared absorption measurements of the 19.5 mu band to determine the number density of the precipitates and their spherical radii, and fitted the results to theoretical models described by Ham (1958) for the diffusion limited growth of randomly distributed particles.
Abstract: Oxygen precipitation in silicon has been studied in the temperature range 500 to 600 degrees C using infrared absorption measurements of the 19.5 mu band. The data have been fitted to theoretical models described by Ham (1958) for the diffusion limited growth of randomly distributed particles. Values of cs, the equilibrium concentration of oxygen, were obtained directly, and assuming the normal diffusion coefficient for interstitial oxygen the authors determined the number density of the precipitates and their spherical radii. These results are linked to previous data obtained at higher and lower temperatures, yielding a self-consistent model. The value of cs decreases to a value of 8*1015 cm-3 at 650 degrees C, but then increases again to 2*1017 cm-3 at 450 degrees C. This behavior, not previously reported, is attributed to the importance of the surface energy for very small agglomerates. The results imply that if the thermal donors and cosite precipitates which are observed at low temperatures arise from oxygen aggregation, they could not form unless an oxygen complex, such as a di-oxygen species, has a much larger diffusion coefficient than an isolated interstitial oxygen atom.

Journal ArticleDOI
TL;DR: In this article, a theoretical framework for the transport of charge carriers in semiconductor multiple-quantum-well structures for motion perpendicular to the layers is presented, and the transport equations and transition rates are derived and discussed in relation to experimental results.
Abstract: The authors present a theoretical framework for the transport of charge carriers in semiconductor multiple-quantum-well structures for motion perpendicular to the layers. The formalism is derived on the basis of strong electric fields but they allow the possibility of describing the low-field ohmic region by using a simple scaling argument. Stark localisation in narrow energy bands implies that the transport phenomena are a superposition of phonon-assisted hopping and intra-band tunnelling. The transport equations and transition rates are derived and discussed in relation to experimental results. In addition they also consider the influence of an external magnetic field both parallel and perpendicular to the layers. The influence of disorder is considered and it is found that it can considerably modify the nature of the physical effects predicted on the basis of the 'pure' eigenstates. Recent experiments on magneto-transport perpendicular to the layers are discussed in the light of this theoretical formalism.

Journal ArticleDOI
TL;DR: In this article, the authors used magneto-transport measurements with the magnetic field aligned perpendicular to, and then parallel to, the interface of a number of (Al, Ga)As/GaAs two-dimensional electron-gas samples, to determine the populations of the first and second sub-bands in the interface potential well.
Abstract: The authors have used magneto-transport measurements with the magnetic field aligned perpendicular to, and then parallel to, the interface of a number of (Al, Ga)As/GaAs two-dimensional electron-gas samples, to determine the populations of the first and second sub-bands in the interface potential well. The total carrier density in the samples has been gradually increased by pulsed illumination either with a red (hv=1.95 eV) or infrared (hv=1.43 eV) LED, and it has been found that the carrier density at which the second sub-band is first occupied is lower when the red LED is used. This difference is ascribed to the effect of electron-hole pairs generated in the GaAs altering the depletion charge, and hence the sub-band spacing; such a mechanism does not operate when the infrared LED is used. Supporting evidence has been obtained from spectroscopic studies of the persistent photoconduction effect, and from mobility measurements.

Journal ArticleDOI
TL;DR: In this article, float-zone silicon doped with carbon (1.6*1017Cm-3) has been irradiated with 2 MeV electrons below 220 K up to a dose of 1.9*1018 electrons cm-2 leading to a monotonic decrease in the concentration of the substitutional impurity.
Abstract: Float-zone silicon doped with carbon (1.6*1017Cm-3) has been irradiated with 2 MeV electrons below 220 K up to a dose of 1.9*1018 electrons cm-2 leading to a monotonic decrease in the concentration of the substitutional impurity. Interstitial carbon is produced but its concentration saturates and then falls because the defects trap mobile self interstitials. New infrared absorption lines at 966 and 959 cm-1 (77 K) are ascribed to a C1-Sii pair defect which also acts as a nucleation site for agglomeration of Si1 atoms. The latter reactions appear to occur during irradiations at 300 K.

Journal ArticleDOI
TL;DR: In this paper, the variation of the AlGaAs energy gap (Eg) versus the aluminium concentration x was determined by precise X-ray measurements and the values of Eg were deduced from photoluminescence experiments.
Abstract: The authors have determined the variation of the AlGaAs energy gap (Eg) versus the aluminium concentration x. The x-values are determined by precise X-ray measurements and the values of Eg are deduced from photoluminescence experiments. They find the law, Eg(x)=Eg(O)+1.34x eV, for x<0.45 at T=2 K.

Journal ArticleDOI
TL;DR: In this article, a comprehensive carrier dynamical transport model for semiconductor device simulation is presented, which consists of carrier, carrier momentum and carrier energy conservation relations derived using a perturbation solution for the carrier distribution function.
Abstract: In this paper a comprehensive carrier dynamical transport model for semiconductor device simulation is presented. The model consists of carrier, carrier momentum and carrier energy conservation relations derived using a perturbation solution for the carrier distribution function. Carrier degeneracy, multiple conduction sub-bands and ellipsoidal constant energy surfaces are accounted for, and the effective masses and band edges are assumed to be spatially inhomogeneous. The new formulation overcomes modelling inaccuracies of previous energy transport models based on a drifted Maxwellian distribution function, and for spatially homogeneous, non-degenerate semiconductors offers several computational advantages.

Journal ArticleDOI
TL;DR: In this article, the band gap levels introduced by gold in germanium have been investigated using DLTS and three acceptor levels at Ec-0.056 eV, Ec- 0.215 eV and Ev+0.044 eV are observed, in agreement with published data obtained from Hall effect studies.
Abstract: The band-gap levels introduced by gold in germanium have been investigated using DLTS. The samples were taken from well characterised n- and p-type germanium crystals and were doped with gold by diffusion at 700 degrees C followed by a quench to room temperature. Three acceptor levels at Ec-0.056 eV, Ec-0.215 eV and Ev+0.135 eV and one donor level at Ev+0.044 eV are observed, in agreement with published data obtained from Hall effect studies. All four levels are attributed to one amphoteric defect, i.e. the gold substitutional.

Journal ArticleDOI
TL;DR: In this paper, the forward-degenerate four-wave mixing in three semiconductor-doped CdSxSe1-x glasses has been studied and the effective third-order nonlinear susceptibility increases with increasing absorption.
Abstract: Wavelength-dependent studies of forward-degenerate four-wave mixing in three semiconductor-doped CdSxSe1-x glasses have been conducted. The effective third-order nonlinear susceptibility increases with increasing absorption. No evidence for room-temperature excitonic structures was found.

Journal ArticleDOI
TL;DR: In this article, the IR and Raman scattering measurements of SIMOX structures implanted at various temperatures yield information on the structure and the strain in both the top silicon and the buried oxide layers.
Abstract: Infrared absorption and Raman scattering measurements of SIMOX structures implanted at various temperatures yield information on the structure and the strain in both the top silicon and the buried oxide layers. Both techniques can also be used to monitor the implant temperature after the implantation.

Journal ArticleDOI
TL;DR: In this paper, the structure and binding properties of excitons near GaAs-(AlGa)As hetero-interfaces are studied theoretically, and the two-dimensional exciton is found to be stable with an ionisation or desorption energy of the order 1 meV.
Abstract: The structure and binding properties of excitons near GaAs-(AlGa)As hetero-interfaces are studied theoretically. For certain doping levels and Al fractional contents, the two-dimensional excitons are found to be stable with an ionisation or desorption energy of the order 1 meV. The findings are compared with the trends in recent photoluminescence experiments.

Journal ArticleDOI
TL;DR: In this paper, the transition rate of a single quantum well is investigated using fully quantum mechanical methods and its variation with the width of the well is explored, and it is found that besides the familiar increase with increasing width of a well, the rate exhibits periodic peaks.
Abstract: Inter-sub-band transitions between electronic states of a single quantum well are considered. In such a double heterostructure a longitudinal polar optical mode emitted or absorbed in any transition can belong to one of a finite number of distinct branches. The transition rate is calculated here using fully quantum mechanical methods and its variation with the width of the well is explored. It is found that besides the familiar increase with increasing width of the well, the rate exhibits periodic peaks. These constitute a resonance effect which arises whenever the conditions of incorporating a new polar branch are satisfied. Illustrations are given specifically for GaAs/Ga0.7Al0.3As single quantum wells.