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Table of contents

Volume 3

Number 8, August 1988

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PAPERS

729

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A preparatory technique for Cs1-xZnxSe films is described. The results of investigations on the composition, surface features and photocorrosion of the Zn-ion-treated CdSe films have also been reported. It is shown that the annealing of these films at 100 degrees C for 30 minutes causes diffusion of Zn deep within the bulk. The resulting Cd1-xZnxSe films have also been examined by a scanning electron microscope. It is shown that the Zn adsorption and diffusion is mediated mainly via the grain boundaries. Short-term stability tests indicate that the S to or from Se exchange as a result of photocorrosion in the sulphide/polysulphide electrolyte is considerably reduced in Cd1-xZnxSe films compared to the CdSe films.

733

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For pt.I see ibid., p.729-32. Electrochemical photovoltaic cells, with open-circuit voltage=530 mV, short-circuit current=9 mA cm-2, fill factor=0.55 and efficiency=5% have been fabricated from chemically formed Cd1-xZnxSe layers. The results of the measurements on donor concentration, minority carrier diffusion length, band bending and traps have also been reported. The performance of Cd1-xZnxSe-film-based solar cells has been compared with the CdSe-film-based cells and the possible reasons for the improved performance of the former cells have been discussed.

739

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.

754

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The electron transport in submicrometre GaAs n+-n-n+ structures is simulated by a charge-sheet method. It is shown that the lag of inter-valley scattering between the Gamma , L and X valleys is of great importance in structures of submicrometre length. A good agreement between the experimentally measured and calculated I-V characteristic is obtained.

758

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Energy transport models of carrier behaviour in semiconductors are based on equations of carrier momentum and carrier energy conservation. Some terms of the modelling equations describe momentum and energy transfers between carriers and the lattice during scattering. The authors demonstrate how empirical parameters can quantify the inter-band scattering components of energy transport models for the Shockley-Hall-Read, band-to-band, impact ionisation and optical recombination and generation mechanisms. An evaluation of the empirical parameters is presented for Shockley-Hall-Read recombination and generation. Further, energy transfer is considered from the point of view of the lattice, and it is shown that a lattice energy conservation equation, which describes thermal effects in semiconductors, can easily be appended to the energy transport modelling equations. The explicit consideration, in energy transport models, of carrier energy gain from the electric field and carrier energy loss due to scattering leads to a more accurate thermal model than is possible with drift-diffusion transport models appended with a lattice heat flow equation incorporating a Joule-type heating term.

766

A self-consistent model for describing carrier transport in heavily doped semiconductor devices has been developed. The proposed model allows convenient treatment of non-uniform semiconductors in a manner that is both thermodynamically consistent and consistent with the transport equations, the steady-state continuity equations and the electrostatic potential with explicit boundary conditions at the contacts. The complex problems are reduced to determining two types of quantities: the reference electrostatic potential and the activity coefficient of the carriers. In order to find the simple working equations for the model, two choices of reference for the electrostatic potential are discussed. The presented transport equations are written in a simple Shockley-like form, in which the effects associated with the non-uniform band structure and the influence of Fermi-Dirac statistics are described by a thermodynamic property, the activity coefficient of the carriers, which is expressed in terms of two band model parameters, the effective band-gap shrinkage, Delta Eg, and the effective asymmetry factor, A. In this form they are convenient for use in computer-aided analysis and the design of heavily doped semiconductor devices.

773

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High-field Hall and Shubnikov-de Haas (SDH) measurements on modulation-doped GaAs/(Al,Ga)As quantum well (QW) structures have been interpreted on a model in which an asymmetric potential distribution across the QW causes a well-width-dependent spatial separation of the probability densities of electrons in different sub-bands. In narrow wells, <150 AA, this effect is small, and the electron distribution can be considered as a single two-dimensional electron gas (2DEG) extending throughout the well, with a low mobility characteristic of the inverted (GaAs on (Al,Ga)As) interface. In the wide well samples, >or approximately=450 AA, the electron density in the lowest sub-band is spatially concentrated near to the inverted interface, while the second sub-band has a peak density close to the normal, high mobility, interface; the electrons in these sub-bands thus have different mobilities, and magnetoresistance effects characteristic of parallel conduction in two distinct 2DEG channels are observed. For intermediate thickness wells, approximately=250-300 AA, the two sub-band populations are close to those in the corresponding wide well samples, but because of the increased spatial overlap of the wavefunctions, the mobilities in the two subbands are similar. This results in a characteristic 'beating' phenomenon in the SDH curves. This model is shown to accord with published self-consistent calculations for modulation-doped quantum wells.

781

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Studies of the capacitance of all sputtered CuxS/CdS heterojunctions are presented. C-F characteristics are measured in the range 100 Hz to 10 MHz and at temperatures ranging between 220 and 340 K. A deep donor level in the CdS is identified 0.25 eV below the conduction band edge. A relative distribution of interface states is deduced from C-V measurements at forward bias and low frequencies. Two types of heterojunctions are examined: (i) with a low density of interface states and (ii) with a higher density of these. Both types of heterojunction were obtained by controlling the parameters of the sputtering process at the junction formation.

786

and

The authors have theoretically treated the effect of conduction band non-parabolicity on inter-sub-band absorption in doped semiconductor quantum wells. The authors have derived an analytical expression for the absorption at zero temperature. The absorption peak is shifted to lower energies and the peak height is reduced by non-parabolicity. These effects are small for GaAs-based quantum wells, but may be detrimental to InGaAs quantum wells.

791

and

The authors present the results on the band-structure effects in single-barrier tunnelling, calculated using a new scattering matrix method. Their results show that the transmission amplitude may be divided into two regions. The first is for electron energies in the band gap of the barrier material, where the transmission is found to be a single state property, with the Gamma state dominant. The appropriate barrier height, regardless of the direct/indirect nature of the barrier band gap, is the Gamma - Gamma band offset. The tunnelling behaviour is therefore single state like. The other regime is for electrons with energies above the barrier material's conduction band edge where, for indirect band-gap barriers, a sharp transition to an X dominated behaviour is observed. Coupling between the barrier Gamma and the X states are found in thin barriers and X well resonances are obtained. The single barrier transmission in this regime is therefore a multistate property.

797

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The authors report on the infrared excitation of sub-band levels in doped InGaAs/InP quantum wells. Periodic multi-quantum-well structures and a single well have been studied. Strong resonance transitions are observed when both sub-band wavefunctions are confined to the quantum well. The experimental transition energies are compared with the results of a self-consistent potential calculation. By scanning the infrared excitation across the sample, inhomogeneities are studied with a spatial resolution of approximately=1 mm2.

802

and

Thin layer semiconductor materials are analysed, by raster scanning the sample surface under a focused Q-switched Nd-YAG laser beam, in the source chamber of a high resolution MS702 mass spectrometer. The positive ions produced by the laser plasma erosion give a complete impurity survey of the layer down to detection limits of approximately 0.001 ppm atomic. Results have shown that surface impurities are effectively removed in the first scan and subsequent scans over the same area have given true measurements of impurities in typical layers. The method gives automatic erosion of sample surface areas from 0.1-130 mm2 with ionisation and mass analysis of the sample material removed. The depth of penetration is dependent on the material being analysed and the laser beam power at the sample surface. In general it is variable between 0.2 and 4 mu m for each scan. Any material, including insulators, can be analysed by this method providing it is not completely transparent to the laser light.

808

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The authors consider the capacitance-voltage relation for a metal-insulator-semiconductor structure on p-type Hg0.8Cd0.2Te to show how the quantisation of the surface carriers changes the conditions for band bending. The existence of a distinct ground state, with energy E0 comparable to the gap Eg, delays the onset of inversion until the bending exceeds Eg+E0. The capacitance for inversion shows the effect of both the finite extent of the wavefunction and the small density of states. By fitting to the measured capacitance several quantum parameters of the surface electrons have been determined.

LETTERS TO THE EDITOR

813

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The gettering efficiency for Au induced by Ne+ implantation in the n- and p-type silicon has been studied. The experiment shows that for gettering temperature 900 degrees C and annealing time 30 minutes the maximum efficiency of gettering in both types of Si occurs at the Ne+ dose of 1016 ions cm-2.

816

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Thin films of ZnS1-xOx and ZnS1-xSex have been deposited on to p-Si by radio-frequency sputtering either a solid target of ZnS in Ar/O2 mixtures or solid targets of ZnS and ZnSe. Both types of ternary compound are more conducting than pure ZnS, and thus potentially useful for DC electroluminescence. The ZnS1-xOx films prepared in O2/Ar mixtures greater than 2% O2 are too conducting for electroluminescent devices; gas mixtures containing only fractional percentages of O2 will yield appropriate conductivities. For ZnS1-xSex films the ideal value of x lies between 0.01 and 0.05.

819

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The authors present their studies of asymmetric resonant tunnelling structures. Results obtained from both analytical evaluations of matrix elements and numerical I-V calculations suggest that the resonance effect and the negative differential resistance characteristics can be substantially improved in the resonant tunnelling diodes with a high-low asymmetric barrier configuration. As an example, the authors show that the peak-to-valley current ratio can be increased from a typical value 3.5 to 11 utilising a high-low barrier configuration in, otherwise, a typical resonant tunnelling diode. Moreover, a novel rectifying associated with the asymmetric structure is predicted. This rectifying effect opens up a unique opportunity for new applications in high-speed electronics.

823

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Formation and gate control of sub- mu m size wires confined by depletion regions in a layered n-n+-n GaAs structure are analysed classically by applying Poisson's equation in two dimensions. The cross sectional area of the conducting semiconductor wire has been calculated as a function of layer dimensions and gate bias and is shown to be consistent with conductance measurements on an actual wire made by molecular beam epitaxy and electron beam lithography.