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Studies of the response of excitonic transitions in quantum wells to external perturbations have proven useful in understanding the electronic properties of quantum wells. This paper discusses the use of two such perturbations, electric fields and uniaxial stress, in photocurrent and photoluminescence excitation spectroscopy measurements on GaAs/AlxGa1-xAs quantum wells. When an electric field is present in a square quantum well, forbidden excitonic transitions become visible. The excitons also exhibit a Stark shift to lower energies. Since the Stark shifts for different excitons are not the same, it is possible to tune the energy separations between the excitons. By applying electric fields to a 160 Å well, an anticrossing between the excited states of the first heavy hole exciton and the 1s ground state of the first light hole exciton has been observed. The effect of a uniaxial stress on a quantum well is found to depend strongly upon the axis along which the stress is applied. This is in contrast to bulk GaAs. The application of a uniaxial stress to a quantum well can help determine the valence band symmetry of a particular exciton, since heavy and light hole excitons exhibit different energy shifts in a stress. This fact has been used in conjunction with polarization and electric field dependent measurements to identify exciton peaks which arise from mixing between the second heavy and first light hole valence subbands.
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Recent advances in quantum well (QW) tunneling devices are discussed. These include resonant tunneling (RT) bipolar and field effect transistors; infrared lasers and detectors based on sequential RT and superlattice effective mass filters.
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Resonant tunneling in a variety of double barrier, single quantum well heterostructures has been investigated. Negative differential resistance has been observed by tunneling through both the ground and first excited quasistationary states of the quantum well. The peak positions agree well with a 65% conduction band offset. The tunnel barriers have been replaced by short period binary superlattices, where an anomalously low barrier height is observed. Resonant tunneling through a GaAs contact / double AlGaAs barrier / single InGaAs quantum well heterostructure has also been observed, where we have demonstrated tunneling through the first excited state above a ''hidden" ground state of the quantum well. Finally, we have observed resonant tunneling through a double barrier, single quantum well HgTe/Hg1-xCdxTe heterostructure where a peak-to-valley tunnel current ratio of 1.4:1 is observed at room temperature. This observation provides direct evidence for the existence of the proposed intrinsic interface state model.
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Recent progress in research on resonant tunneling diodes, and on lateral quantization effects in quantum wells renews hope for the development of active unipolar heterojunction devices which incorporate no depletion layers, and hence can be extremely compact in both vertical and lateral dimensions. If such devices meeting the fundamental requirements for ultrahigh density integrated circuits can be developed, and if revolutionary chip architectures which overcome current interconnection limitations can be devised, then a new generation of integrated circuits approaching the ultimate limits of functional density and functional throughput may eventually ensue. Although many of the most challenging problems in this scenario have not yet been addressed, progress is being made in the areas of fabrication and characterization of resonant tunneling devices, simulation of such devices using quantum transport theory, and simulation of nearest-neighbor connected (two-dimensional cellular automaton) architectures. This paper reviews the progress in these areas at Texas Instruments, and discusses the prospects for the future.
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A short, elementary introduction into the physics of n-i-p-i doping superlattices is presented. Their electrical and optical properties which result from the unique tunability of their bandstructures are discussed. Examples of GaAs based n-i-p-i and hetero-n-i-p-i superlattices illustrate the novel phenomena that have been predicted and experimentally observed. The device potential of these engineered semiconductor materials is also discussed.
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Tunability of the optical absorption spectrum with electrical bias in GaAs doping super-lattices (n-i-p-i crystals) is demonstrated by both photoconductivity and direct transmis-sion measurements. A linear change of transmission of up to 22% is achieved at 0.89 μm wavelength through a 2.1 μm thick n-i-p-i crystal by varying the p-n junction bias between -2.0 V and 0.6 V. Highly tunable and efficient electroluminescence is also observed in strongly doped n-i-p-i crystals at room temperature with peak energies shifted more than 600 meV below the bulk bandgap (λ > 1.55 μm).
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In this paper, we examine two features of acceptor states in GaAs doping superlattices. First, we consider how the finite size of acceptor state wavefunctions affects optical matrix elements and below-gap luminescence spectra. Next, we examine the finite width of the acceptor band caused by potential fluctuations associated with the random configuration of charged impurities in the system and discuss the impact of this width on luminescence.
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A new class of superlattices consisting of alternate layers of quasi-one-dimensional (Q1D) conducting polymers is theoretically considered. Although both compositional and doping superlattices are possible, only the doping superlattices are considered in detail. In particular, expressions for the two-dimensional density of electrons and holes in a solitonic as well as a polaronic doping superlattice are obtained. Next, these quantities are used to discuss the optical absorption coefficient, a(w), and the photoconductive response of these Q1D superlattices. Due to the presence of nonlinear excitations such as solitons and polarons in doped conducting polymers, the optical absorption arises not only from the usual interband transition but also from the transitions involving localized levels in the Peierls energy gap. The absorption coefficient is a tunable quantity for the Q1D superlattices since the effective band gap can be tailored to suit the radiation wavelength of interest. In addition, for a certain range of doping levels these superlattices exhibit a new kind of solitonic and polaronic "semimetallic" behavior. Finally, certain means of experimentally measuring a(w) for photon energies smaller than the Peierls gap are described and novel features including the device applications of Q1D superlattices and related modulated structures are discussed.
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Under pressure, covalent semiconductors transform to more closely packed metallic (or small band gap) structures, with large reductions in volume ~15-20%. Recent experiments on AlAs/GaAs epitaxial multilayers have revealed that the analogous phase changes in superlattices exhibit several remarkable properties. Depending on layer width, transitions may occur: a) discretely within individual AlAs or GaAs layers, b) collectively within many similarly composed layers, or c) within the entire superlattice as a whole. Furthermore, the zincblende phase of AlAs can be superpressed far above its bulk transition threshold; this superpressing is greater in thinner layers and is limited by the stability of GaAs. These properties reflect the importance of the epitaxial interface for the total energy of a superlattice. A model is presented that considers the energy competition between destroying the interface by producing misfit defects, or preserving it by forming strained layers (in the high pressure phase.) Recent total energy calculations by Martin suggest that, for sufficiently thin layers, one of several novel strained-layer metal/semiconductor structures could be stable at high pressure. Conditions for creating such structures in various materials systems, and for retrieving them metastably at 1 atm., are discussed.
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Growth and properties of Si/Ge and Si/SixGe1-x strained layer superlattices are reviewed. The critical thickness of single layers and asymmetrically strained superlattices are determined by LEED and Raman spectroscopy. The importance of strain symmetrization is discussed. Built-in strains are determined by phonon Raman scattering. The effects of strain on the band structure are analysed theoretically. Transport measurements in selectively doped samples lead, in connection with self-consistent subband calculations, to a consistent picture of band ordering. In short period superlattices a quasi-direct band gap semiconductor can be achieved. Zone-folding effects are also observed in the phonon properties of such superlattices. They are discussed both for the acoustical and optical branches.
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We have carried out full-scale pseudopotential calculations of the effect of zone-fol-ding on band structure, optical absorption and non-linear response function of semiconductor superlattices. To provide a complete picture of this phenomenon we chose to study GaAs-Gal-xAlxAs, Si-Si1-xGe and HgTe-CdTe superlattices which represent examples of the breakdown of the simple particle-in-a-box model because of Γ - X mixing, strain and relativistic effects, respectively.
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An investigation of the effect of an in-plane electric field on the photocurrent and photoluminescence characteristics of (Zn,Mn)Se multiple quantum well structures and ZnSe epilayers has been carried out. Measurements were performed on an epilayer and a multiple quantum well sample with well widths of 29Å and having a single 68Å. well interposed into the structure. The data observed clearly show evidence of photo-luminescence quenching and increase in photoconductivity due to ionization of excitons.
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The presence of lattice mismatch in CdTe/CdMnTe superlattices, grown on Cd MnTe buffer layers, can give rise to strain in the CdTe layers, lifting the degeneracy of the valence band edge, resulting in ellipsoidal bands. We calculate, within an effective mass framework, the effect of the superlattice modulating potential on spin exchange in this system and derive conditions for the stability of a magnetic polaron in this system for (001) and (111) strained layer superlattices.
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In order to obtain both p- and n-type conduction in a wide-bandgap II-VI compound semiconductor, we have prepared ZnSe-ZnTe strained-layer superlattices (SLS) by MBE with a modulation doping technique. Modulation-doped superlattices were analyzed by photoluminescence (PL) and the van der Pauw method. The effect of strain on the film quality induced in the SLS structure by lattice mismatch was investigated. Furthermore, the SLS structure has been directly observed by Transmission Electron Microscopy (TEM).
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The hydrostatic-pressure coefficients of the bandgap energies for four different types of semiconductor heterojunction structures were obtained from photoluminescence measurements at 4K and pressures up to 4 kbar. The structures studied were n-type and p-type InxGa1-xAs/GaAs and n-type GaAs/GaPx As1-x strained-layer superlattices, n-type InxGa1-xAs/GaAs single strained quantum wells and an undoped GaAs/AlAs superlattice. The bandgap energies ranged from 1800 meV for the GaAs/ALAS structure to 1280 meV for the InxGa1-xAs/GaAs single strained quantum wells. Pressure coefficients for the InxGa1- As/GaAs and GaAs/GaPxAs1-x structures were found to be in the range of 10 to 12 meV/bar. However, the pressure coefficient of the luminescence energy from the GaAs/AlAs superlattice was found to be -2 meV/kbar. This negative pressure coefficient is consistent with the interpretation that the luminescence is due to a transition between the conduction-band X-point in the AlAs layers and the valence-band r-point in the GaAs layers.
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The photoluminescence intensity of InGaAs/GaAs strained layer single quantum wells with p-type doping was measured as a function of magnetic field. Two different experimental techniques were used, and both show a reduction of intensity with complete suppression occurring at B=35T. Self-consistent potential and energy level calculations indicate complete migration of charge out of the well back to the dopants as a consequence of applied magnetic field.
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Optical nonlinearities of bulk and multiple-quantum-well GaAs are discussed. Logic devices using GaAs etalons are exclusively introduced.
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Nonlinear optical properties of semiconductor superlattices are examined theoretically. We have studied the third-order nonlinear susceptibility of semiconductor superlattices due to the band nonparabolicity, intervalence-hand transitions, and photo-excited plasma effects. We found that x(3) of semiconductor superlattices are in general (up to two orders of magnitude) larger than that of the corresponding hulk semiconductors.
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The low temperature exciton scattering rate in a structure consisting of a series of undoped single GaAs quantum wells of widths 5,10,20 and 80 nm separated by undoped 34 nm A10.3Ga0.7As barriers has been investigated in the frequency domain as a function of electric field. The low temperature n=1 heavy hole homogeneous exciton linewidth studied using a combination of resonant Rayleigh scattering and photoluminescence excitation spectroscopy is found to show dramatic increases, to values in excess of the inhomogeneous width, for certain values of electric field which depend on the particular well being studied. The change in exciton scattering rate is interpreted as being due to resonant tunnelling of carriers between neighbouring wells of different widths as bound states are brought into alignment by the external electric field.
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Envelope function calculations indicate that the GaAs-AlAs band edge configuration changes from a straddled, type-I line-up to a staggered, type-II arrangement when the GaAs width is below about 32Å. The binding energy of the ground state exciton is calculated variationally for this heterojunction arrangement. Anisotropy in both electron and hole effective masses is considered and calculations performed assuming perfect confinement of both sorts of carriers. Calculated binding energies are of a similar magnitude to those of the is heavy hole exciton for this materials system when its band edge configuration is the more familiar type-I.
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The interaction between two closely spaced quantum well (QW) structures has been studied by observing the change in photoluminescence (PL) energy as a function of the barrier thickness between the wells. Theoretical model and experimental results agree to within a few meV for these structures. The strongest coupling is for the narrowest wells and the thinnest barrier. Only the symmetric <----> symmetric transition between the n=1 states of the confined electron and heavy hole states was observed.
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Intersubband absorption has been measured in a 50 period superlattice composed 71 Å GaAs wells separated by 30 Å barriers of AlAs. The peak absorption was observed at 1224 cm-1 corresponding to 8.2 μm. The absorbed oscillation strength was extremely large in agree-ment with theory. Using a different superlattice having AlxGal-xAs barriers, we fabricated a detector sensitive to 10 μm infrared radiation. It had a responsivity of R= 0.52 A/W, and a narrow band spectral response of Δλ/λ = 10%.
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We report on detailed photoluminescence (PL) and photoluminescence excitation (PLE) studies of GaAs/A1GaAs single quantum wells (SQW) with differing well widths measured over temperatures ranging from 5K to 300K. A new trapping phenomenon was observed at low temperatures, which affects the linewidth and PL intensities (radiation lifetimes) of free excitons in the SQWs and which is related to the formation of bound excitons. At higher temperatures, excitonic linewidths were primarily broadened by optical phonon scattering. The temperature dependencies of the excitonic energies of SQWs were similar to that of bulk material and were independent of the quantum well width.
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We present strong experimental evidence of interactions between light-hole and heavy-hole valence subbands in a GaAs/A1GaAs quantum well subjected to compressive uniaxial stress. The energies of higher order exciton states were determined as a function of stress using low temperature photoluminescence excitation spectra. Level repulsions, which are signatures of valence subband mixing, were observed between a number of light-hole and heavy-hole exciton states. A theoretical model, based on the Luttinger-Kohn and strain Hamiltonians, yielded results in substantial agreement with the experimental data. The cause of the main discrepancy, an anomalously strong level repulsion between the lowest energy light-hole exciton and a parity-allowed "forbidden" exciton, is not yet clear but possible explanations are discussed.
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Electroabsorption near the optical absorption edge of quantum well materials is interesting both for physics and applications. We briefly summarize the physical mechanisms involved (e.g. the quantum-confined Stark effect) and the applications to optical modulators and switching devices.
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A new class of single-crystal, semiconductor optical interference devices is described. The basic physics governing their operation and materials and growth methods to implement them are summarized. Recent experimental results for epitaxial optical filters, monolithic integration, and tunability are discussed.
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We present the design of an electro-optic modulator which is based on the quantum-confined Stark effect (QCSE) in GaAs quantum wells contained within the central layer of a Fabry-Perot etalon. The etalon mirrors are quarter wave stacks of Ga0.7A10.3As and AlAs, eliminating the need for the application of anti-reflection coatings. p-i-n-doping is employed with the undoped Or stack sandwiched between doped mirrors, enabling electric fields of the order of 105Vcm-1 to be readily developed across the quantum wells. Placing a multiple quantum well structure within an etalon resonant cavity gives flexibility of design in terms of operating wavelength and mode: Light incident perpendicular to the QW stack is modulated through the operation of the QCSE on the QW excitons, either electro-refractively by a change in the real part of the QW refractive index producing a wavelength modulation of the narrow-band Fabry-Perot transmission resonance or in electro-absorptive mode. The semi-empirical theory uses conventional multilayer optical matrix methods together with a recent theory of the QCSE which has been tested against the results of electro-reflectance experiments. In electro-absorption mode we find a ratio of 19:1 on:off at 857.5nm for 8 quantum wells. In electro-refractive mode, using 32 wells, we predict modulation from 10% to 76% reflection at 883nm. These figures exclude substrate effects. Extension of the theory to other materials systems is readily accomplished. We present the reflectivity spectrum of a high quality etalon in In0.53Ga0.47As/InP and find good agreement with the predictions of the optical matrix model.
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In this paper recent theoretical and experimental work in the area of multiple quantum well modulators is presented. The theoretical work includes the application of the effective mass approximation to compositional MQW structures and the use of a two-band tight-binding approximation to doping modulated Nipi structures. The theoretical calculations are used to obtain electric-field-dependent absorption and refractive index in the above MQW structures. Experimental electroabsorption in compositional MQW structures is described, as well as preliminary optical characterization of Nipi structures. Concepts of photoactivated and electrically addressed MQW-spatial light modulators are presented. Finally, theoretical evaluation of quantum dot arrays and their potential use in spatial light modulators is discussed.
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It is now commonly accepted that the fractional valence band offset in the GaAs/ AlxGal-xAs material system lies in the region 0.3-0.4. This has important consequences for quantum well structures in which the bar Kier material is indirect (x > 0.45). If the GaAs width L is sufficiently small (Lz < 30Å) then for GaAs/AlAs quantum wells the lowest confined electron state of the system is at the X minima of the AlAs. This leads to so-called type II recombination involving electrons in the AlAs and holes in the GaAs. We have performed an extensive investigation of such phenomena on a number of GaAs/AlAs multiple quantum well structures where Lz < 30Å, using the techniques of photoluminescence (PL) and photoluminescence excitation spectroscopy (PLE). In the PL spectrum we observe both type I recombination; that is recombination of electrons and holes confined in the GaAs, and also a series of lines associated with the type II process. Using PLE we have identified the lowest confined exciton state of the type II system and combining this information with the temperature dependence of the type II PL spectra we ascribe the highest energy emission at 6K as due to the recombination of localised excitons. Further-more, absorption edges associated with higher lying (n>1) electron states confined at the X minima in the AlAs are observed in the PLE spectrum. These have relative strength and position which are in good agreement with theoretical predictions. Combining these results with a calculation of the type II exciton binding energy has led us to determine the fractional valence band offset to lie in the range 0.33-0.34.
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Calculations of free-carrier absorption in p-type semiconductor quantum wells as a function of carrier density, temperature and light intensity are reported. Valence band dispersions used in the calculation are obtained by a multi-band effective mass method which includes the effects of warping and heavy-light hole mixing. Carrier lifetimes are taken into account within the deformation potential approximation. Deviation of hole distribution from thermal equilibrium due to optical pumping is included in the calculation, and the saturation behavior is studied.
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A strain-induced ordered phase has been observed recently in the alloy layers fo a GeSi/ Si strained-layer superlattice, in which the ordered unit cell is non-centrosymmetric. Using the bond-charge model of Jha and Bloembergen, the second-order susceptibility and the linear electro-optic (Pockels) coefficient of the GeSi layers are calculated and are found to be comparable in magnitude to those of GaAs. The calculation has also been extended to artificial crystals consisting of alternating bilayers of Si and Ge on (001) Si substrates recently reported. For the indicated structure, the Pockels coefficient vanishes in this case for E [001].
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Novel and interesting effects in semiconductors that arise from the quantization of the energy levels of charge carriers (electrons and positive holes) confined to potential wells of very small dimensions are under intense investigation. Three regimes can be considered depending on whether the potential wells are small in one, two, or three dimensions. For the latter, the systems under study consist primarily of colloidal semiconductor particles suspended in a liquid matrix. Two-dimensional systems have also been prepared and are called quantum wires. However, the vast majority of work on quantum size effects has been done on one-dimensional systems in the form of multiple quantum wells (MQW) and superlattices (SL). We repogrzt results on superlattices used as photoelectrodes in photoelectrochemical (PEC) cells and on small quantized semiconductor particles in the form of colloids.
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The Einstein relation for the diffusivity-mobility ratio of the carriers in semiconductors (hereeafter referred to as DMR) is a very important one, since by being a thermo-dynamic relation this is independent of any scattering mechanisms and also since one can determine the diffusivity from this relation by knowing the mobility and vice-versa. besides, the simplest method of analyzing semiconductor devices taking into account the degeneracy of the bands is to use the DMR to express the performance at the device terminals and the switching speed in terms of carrier concentration.
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We have prepared amorphous Si/SiOx thin multilayer structures by evaporation onto substrates at room temperature. A detaied study of the optical absorption coefficient for individual layer thicknesses in the range 1.5 to 10 nm has been undertaken. We find evidence for bandgap widening in the thinnest layer superlattices. Our results show, however, that the position of the absorption edge is sensitive to sample quality. Extensive modelling on this system demonstrates that the apparent edge is particularly sensitive to layer thickness variations, i.e. to aperiodicity in the superlattice structure.
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Das Sarma and more recently Sigg et al., have examined the effect of electronic screen-ing on the mass and ground state energy of the polaron in a GaAs-GaA1As heterostructure. These authors calculate the self-energy of the electron using the Frohlich Hamiltonian which is suitably modified to account for the screening of the electron-phonon interaction. This method for calculating the self energy is somewhat difficult being based on concepts in many body theory. An alternate method based on semiclassical theory is presented in this paper and is used to calculate the electron self-energy. This method is physically easy to interpret and is far less complex than the earlier method. In addition the method provides some improvement over the earlier calculations. Using our method we have calculated the polaron mass and ground state energy. These results are compared with the corresponding results of the earlier authors.
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A large number of devices based upon man-made structures (multiple quantum wells and superlattices) derive their unique transport properties as a result of the physical structure of the device and the resulting energy levels of the structure. At present, the properties of these structures are generally analyzed using "single-well" energy levels and ignore the strong coupling between che wells. Whereas this yields qualitative understanding of the physics involved, the properties of these devices are derived from the strong coupling between the wells such as in resonant tunneling. In order to quantitatively understand and design new devices, an efficient algorithm for determining the bound and resonant spectra is required. We show that an algorithm based upon R-matrix propagation techniques is capable of determining the required spectra and is numerically stable. The adaptation of the R-matrix algorithm to one-dimensional potentials is discussed and the expressions that determine the bound and virtual energy spectra for single quantum wells are obtained to illustrate the method. Results for the bound and virtual energy spectra of various structures in the presence of an applied bias are then presented. In general, the new algorithm has several advantages in that it is fast, numerically stable, efficient, incorporates the boundary condition on the wave function and its derivative, and can be adapted to any one-dimensional potential.
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he optical gain and quality of the light emitted in a quantum well structure are analysed in the presence of (a) optical, electrical and thermal couplings between adjacent wells, (b) tunnel leakage, (c) non-radiative and radiative interface recombinations, (d) lattice mismatch, (e) inhomogenity of the layers, (f) ratio of the width of the well to that of the barrier and (g) number of wells. It is felt that the thermalisation of the carriers through collisions with phonons is not necessarily an advantageous feature. Instead several alternatives like (i) mixed electrical and optical pumping mode techniques, (ii) creation of some metastable levels in the wells, (iii) longitudinal magnetic focussing or transverse magnetic deflection and (iv) several other junction pairs starting from GaAs/AlGaAs are discussed for illustrative purposes. Upconversion and mixing frequency techniques can be developed by impregnating barrier/well materials with slight additions of luminiphors as impurities.
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An explanation for the extra longitudinal strain in strained-layer superlattices is suggested, starting from a general theory of the dependence of strain on crystal size for cubic materials.
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The results for tower energy-Level splittings and Fermi energy are given for (100),(110),(111) oriented Si-nipi material. Under the assumption of dn < (=dp) < d1 and dn (=dp) < d1 the paper has generally studied the dependence of subband energies of electron and hole in this material on dopant concentration, dopant layer thickness and free carrier concentration. The results in the two cases are compared with each other.
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We report the observation, in the low temperature photoluminescence excitation spectra of high quality GaAs/AlGaAs single quantum wells, of distinctive peaks arising from the first excited level (2s) in addition to the ground state (1s) of heavy- and light-hole excitons. We utilize the accurate determination of the 2s-1s splitting energy, made possible by this observation, to derive the binding energies of the heavy- and light-hole excitons as a function of well width and find good agreement with other similar determinations and with recent theoretical calculations based on models of quantum wells with valence band coupling. The agreement with exciton binding energies derived from magneto-optical spectroscopic experiments is unsatisfactory and suggests that further work in the interpretation of the magneto-optical experimental spectra is required.
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The critical thickness hc of strained InxGa1-x As/GaAs layers grown by molecular beam epitaxy (MBE) on GaAs (100) substrates is determined by double crystal x-ray diffraction and low-temperature photoluminescence measurements for 0.07 < x < 0.25. The x-ray rocking curves exhibit peaks from the InxGa1-xAs layer that are easily detectable at thicknesses as low as 100 Å. The intensity of the photoluminescence peak is found to persist well beyond the experimentally determined critical thickness. Both techniques give essentially the same values of hc. The experimental results are compared with theoretical values of hc that are calculated from mechanical equilibrium and energy balance models. Good agreement is obtained between the results from the energy balance model and the experimental data.
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The effect of band mixing and non-parabolicity on quantum well gain and spontaneous emission is studied using k.p theory. Spectra of gain and spontaneous emission are strongly modified but the relation of maximum gain versus nominal current density is not strongly affected.
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Instabilities in solid state plasmas can potentially be used in a solid state analogue of the travelling wave amplifier. In this device, a direct transfer of energy from a constant current into plasma oscillations takes place. An experimental test will be proposed to determine whether or not this effect is possible in a modulation-doped superlattice. This test is based on calculations of the Raman spectrum of a layered electron gas in the presence of a constant current.
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