Impurity Gradient Research Articles

Transversal Effect in a Metal-to-Metal Interface

It is shown that a transversal potential appears when a current flows along a film with a transversal impurity gradient. The potential is evaluated in the relaxation time approximation for the Boltzmann-Bloch equation, being quadratic in the applied field. Semi-classical Monte Carlo simulations have verified those results.

Formation and characterization of porous silicon layers for application in multicrystalline silicon solar cells

The electrochemical formation of porous silicon (PS) layers in the n + emitter of silicon p–n + homojunctions for solar energy conversion has been investigated. During the electrochemical process under constant polarization, a variation of the current density occurs. This effect is explained by considering the doping impurity gradient in the emitter and by TEM characterization of the PS layer structure. Optical transmission measurements indicate that modifications of the refractive index and absorption coefficient of PS are mainly related to the porosity value. Reflectivity measurements, spectral response and I–V characteristics show that PS acts as an efficient antireflection coating layer. However, beyond a critical layer thickness, i.e. when PS reaches the p–n + interface, the junction properties are degraded.

Experimental verification of the physics and structure of the bipolar junction transistor

The authors present an electrical characterization of discrete bipolar junction transistor (BJT) devices, with nonuniform doped emitter and base zones. The measurement of the I-V and C-V characteristics of the emitter-base and the collector-base junctions and the common emitter current gain allows to determine relevant parameters of the device. These are the built-in voltage of both junctions, the impurity gradient profiles, the electrical area of both junctions, the base and the emitter Gummel numbers and the collector doping. The whole experiment can be conducted in a laboratory session of 3-4 hour length and it is specifically addressed to students taking lectures in semiconductor device physics. The results obtained give a deep insight into both the physical structure and the physical processes involved in the transistor behavior.

Electric breakdown in GaN p-n junctions

Electric breakdown in GaN p-n junctions was investigated. GaN p+-p-n+ structures were grown on 6H–SiC substrates by metalorganic chemical vapor deposition. Mg and Si were used as dopants. Mesa structures were fabricated by reactive ion etching. Capacitance–voltage measurements showed that the p-n junctions were linearly graded. The impurity gradient in the p-n junctions ranged from 2×1022 to 2×1023 cm−4. Reverse current–voltage characteristics of the p-n junctions were studied in the temperature range from 200 to 600 K. The diodes exhibited abrupt breakdown at a reverse voltage of 40–150 V. The breakdown had a microplasmic nature. The strength of the electric breakdown field in the p-n junctions depended on the impurity gradient and was measured to be from 1.5 to 3 MV/cm. It was found that the breakdown voltage increases with temperature. The temperature coefficient of the breakdown voltage was ∼2×10−2 V/K.

Stresses generated by impurities in diamond

Abstract Single dissolved nitrogen, boron or hydrogen atoms cause the diamond lattice around them to expand by 40%, 33.7% and 31%, respectively. Such large atomic strains generate short-range stresses around each dissolved impurity atom. If the impurity is dissolved uniformly in a diamond crystal, the atomic strains around each impurity atom will produce an overall uniform expansion that will not generate macro stresses in the diamond crystal. However, if the impurity is not dissolved uniformly, incompatible macrostrains will result that will generate large elastic stresses in the diamond crystal. These stresses may strengthen or weaken a diamond crystal depending on their magnitudes, signs (i.e. compression or tension) and spatial distributions in the crystal. An inhomogeneous distribution of impurities can be generated either by the appearance of higher order growth facets during crystal growth, which generate differential segregation of impurities between the high- and low-order crystal growth sectors or by temporal changes in growth conditions which generate radial impurity gradients. Since growth conditions control the distribution of impurities in the diamond, diamonds can be strengthened or weakened by different growth conditions.

Toroidal drift mode stability in a contaminated plasma

Toroidal drift mode features and stability are studied, using a fluid description, for a plasma with two ion species: impurity and main ions. Impurity and main ion temperature gradient (ITG) modes dominate for larger temperature gradients, ηi≳1, while dissipative trapped electron (DTE) and impurity-induced modes are present also for ηi<1. Simple analytical expressions for the stability thresholds are derived from conditions given by the impurity and main ion fluids.

Transport length variation due to dopant gradients in AlGaAs

The transport length of minority carriers has been determined by various EBIC methods on low-doped n-type (AlGa)As. Transport lengths of 12 mu m and 6 mu m were concluded from EBIC investigations as a function of primary energy of the electron beam at T=300 and 80 K, respectively. The hole diffusion length obtained by EBIC profiles using an electron beam scan along the surface is 3.8 mu m at room temperature. Based on an impurity gradient in the growth direction observed by capacitance-voltage measurements the authors explain the long transport length as being due to carrier acceleration in the electric field.

Asymptotic analysis of a non-linear model for substitutional diffusion in semiconductors

The simple non-Fickian model for the substitutional diffusion of an impurity in a III-V semiconductor proposed by Zahari and Tuck assumes that both the impurity and host atoms diffuse by a vacancy mechanism. Here we give an asymptotic analysis of the governing pair of coupled partial differential equations, obtaining analytical solutions for the impurity and vacancy distributions in systems for which the impurity diffusivity is much greater than that of the vacancies. Two problems are considered. The first is that in which the impurity concentration is initially zero and a prescribed concentration is given at the surface. The second problem models the diffusion of ion implanted impurity, for which initial impurity and vacancy distributions are specified and a condition of zero impurity flux is assumed at the surface. Both leading order and correction terms are obtained and in each case the solution predicts the anomalous ‘double profiles’ often observed in III-V systems. The ‘ion-implantation analysis’ also displays the observed phenomenon of ‘uphill’ diffusion against the impurity gradient close to the surface.

Textural transitions in titanium alloys during polymorphic transformations and recrystallization of the beta-phase

1. Analysis of the crystallographic texture of the α-phase in rolled sheets of titanium pseudo-α-alloys that had previously been subjected to short-term annealing at different temperatures makes it possible to determine the temperature of the polymorphic transformation of these alloys with high accuracy and investigate the recrystallization process of the high-temperature phase. The temperature Tpt=955±15 and 1018±17°C for alloys OT4 and VT20, respectively. 2. Use of x-ray photography with layer-by-layer removal of material from the surface of the specimen makes it possible to ascertain the variation in the temperature of the phase transition over a section of an article in the presence of an impurity gradient across the thickness. Thus, Tpt=1053±17°C on the surface of an alloy VT20 sheet; this is ∼35°C higher than that in the core.

Breakdown voltages of base-collector junctions of medium- and low-voltage graded collector transistors

Recent works on current mode second breakdown show that a substantial measure of protection against failure by avalanche injection can be built into a transistor by grading the impurity concentration of the collector. The breakdown voltage of the base-collector junction is an important parameter in designing the transistor. In this paper, the open emitter breakdown voltages of medium- and low-voltage epitaxial bipolar transistors with graded collectors are computed numerically. A general expression for the open emitter breakdown voltage as a function of initial collector doping (doping at the collector side of the base-collector interface) and collector impurity gradient has been obtained. Empirical expressions for collector parameters as a function of open base bulk breakdown voltage and common emitter current gain are also derived.

A new expression for breakdown voltage of practical linearly graded p-n junction

An analytical investigation of realistic linearly graded silicon p-n junctions, currently used in high-voltage device structures, is performed. Basic corrections to the fundamental theory of reverse-biased, linearly graded p-n junctions are analytically formulated. Closed-form relations for the breakdown voltage BV and peak space-charge region extension (at breakdown) in practical linearly graded junctions are presented. A thorough investigation of linearly graded junctions used in power devices is performed. Basic corrections to the fundamental theory of linearly graded junctions have been analytically formulated. It is shown that the departure from the classical linearly graded case is more obvious as the background impurity concentration drops below C/sub B/=10/sup 15/ cm/sup -3/ and the impurity gradient a increases above 5*10/sup 16/ cm/sup -4/. For C/sub B/ 10/sup 16/ cm/sup -4/, the linearly graded junction behaves like an abrupt one. For a>10/sup 19/ cm/sup -4/ and C/sub B/ >

Resistive electrostatic instabilities

The appropriate toroidal equations governing the stability properties of resistive electrostatic instabilities are derived and analyzed. These equations include the influence of impurity gradients and are valid for both strongly collisional and semicollisional regimes. Analytic and numerical solutions have been obtained in the sheared slab limit with toroidal curvature effects approximated with the familiar constant gravity model. The results indicate that for relevant experimental conditions, the resistivity-gradient-driven class of electrostatic modes is difficult to excite. Hence, with the possible exception of the very edge, these instabilities do not appear to be a likely candidate to account for the large thermal transport observed in the exterior region of most tokamak plasmas.

Analysis of electric field distributions in ultra-shallow silicon junctions under thermodynamic equilibrium conditions

A comprehensive analysis of electric field distributions in ultra-shallow, heavilydoped, strongly-asymmetric silicon n-p junctions is performed under thermodynamic equilibrium conditions. The physical deficiences of previous approaches to the built-in electric field computations in such very steep junctions are examined on the grounds of semiconductor fundamentals. It is shown that in the surface-controlled region of ultra-shallow silicon junctions the built-in field E calculations depart from the bulk-type computations precisely in view of the peculiar physical features of the semiconductor surface (discontinuities of impurities, surface states, etc.). The basic theoretical contention of this paper is that: (a) the electric field strength E should necessarily go to zero at a ‘free’ (air or vacuum) surface of such junctions, and (b) if the projected built-in field nears the surface on the heavily-doped side of an ultra-shallow junction, then it is compulsory to take into account the interaction between E and the prevailing surface charges. The results of this work suggest that all processes in the surface-controlled region of the heavily-doped layer in ultra-shallow silicon junctions are being shaped by the peculiar interplay of the bulk field E created by the impurity gradients with the field E surf originated in the surface states. Based upon the presented physical background, a computational model for built-in field distribution is detailed in this work. Several important implications of presented results and raised issues are also outlined in this work.

Role of impurity dynamics in resistivity-gradient-driven turbulence and tokamak edge plasma phenomena

The role of impurity dynamics in resistivity-gradient-driven turbulence is investigated in the context of modeling tokamak edge plasma phenomena. The effects of impurity concentration fluctuations and gradients on the linear behavior of rippling instabilities and on the nonlinear evolution and saturation of resistivity-gradient-driven turbulence are studied both analytically and computationally. At saturation, fluctuation levels and particle and thermal diffusivities are calculated. In particular, the mean-square turbulent radial velocity is given by 〈v̂2r〉 =(E0Ls/Bz)2 (L−1η+L−1z)2. Thus edged peaked impurity concentrations tend to enhance the turbulence, while axially peaked concentrations tend to quench it. The theoretical predictions are in semiquantitative agreement with experimental results from the TEXT [Bull. Am. Phys. Soc. 30, 1443 (1985)], Caltech [Phys. Fluids 29, 309 (1986)], and Tosca [in the Proceedings of the 12th European Conference on Controlled Fusion and Plasma Physics (European Physical Society, Budapest, 1985), Vol. I, p. 311] tokamaks. Finally, a theory of the density clamp observed during CO-NBI on the ISX-B tokamak [in Plasma Physics and Controlled Nuclear Fusion Research (IAEA, Vienna, 1981), Vol. I, p. 377] is proposed.

Fabrication of a new type of field-effect transistor using neutralisation of shallow donors by atomic hydrogen in n-GaAs (Si)

We describe a new process for the fabrication of GaAs field-effect transistors. This process is based on the neutralisation of shallow donors by atomic hydrogen diffused into a highly silicon-doped epilayer. This original process should be able to produce field-effect transistors with low access resistances. Better linearity and high breakdown voltage are expected owing to the active impurity gradient present in the hydrogenated layer. The first HFETs (hydrogenated FETs) show very encouraging characteristics. For a gate length of 1.2 ?m their typical transconductance is 330 mS/mm and the cutoff frequency is larger than 15 GHz.

Theory of ion-temperature-gradient-driven turbulence in tokamaks

An analytic theory of ion-temperature-gradient-driven turbulence in tokamaks is presented. Energy-conserving, renormalized spectrum equations are derived and solved in order to obtain the spectra of stationary ion-temperature-gradient-driven turbulence. Corrections to mixing-length estimates are calculated explicitly. The resulting anomalous ion thermal diffusivity χi=0.4[(π/2)ln(1+ηi)]2[(1+ηi)/τ]2 ρ2pcs/Ls is derived and is found to be consistent with experimentally deduced thermal diffusivities. The associated electron thermal and particle diffusivity, and particle and heat-pinch velocities are also calculated. The effect of impurity gradients on saturated ion-temperature-gradient-driven turbulence is discussed and a related explanation of density profile steepening during Z-mode operation is proposed.

On approaches to the built-in electric-field calculations in shallow silicon n+-p junctions

A critical appraisal of recent approaches to the built-in electric-field E calculations in shallow heavily doped strongly asymmetric silicon n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> -p junctions is performed. The existence of a large (≃ 1 - V/µm), positive field E of built-in nature on the surface of the n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> -layer-reported previously through the computation of E as a gradient of erfc impurity profile in very steep n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> -p junctions-is refuted on the grounds of semiconductor fundamentals. Alternatively, it is shown that: 1) under thermal equilibrium conditions and a "free" (air or vacuum) silicon surface, the built-in field should necessarily go to zero at the semiconductor surface; 2) if the projected built-in field E nears the surface on the heavily doped side of a junction, then it is compulsory to take into account the interaction between E and the prevailing surface charges. The results of this work suggest that all processes in the surface-controlled region of the heavily doped layer are being shaped by the interplay of the bulk field E created by the impurity gradients with the field E <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">surf</inf> originated in the surface states.

Redistribution phenomenon of residual impurities in undoped GaAs epitaxial layers grown by MOCVD as a function of growth time

It is experimentally demonstrated that under certain growth conditions, the deposition time of intentionally doped single-crystal GaAs mono-epitaxial layers grown by Metallic-Organo-Chemical Vapor Deposition (MOCVD) on (100) GaAs substrates strongly influences the residual impurities content. Five samples, each grown with a different deposition period but under the same growth conditions and sequence were investigated. The residual impurities in the upper part of the epilayer (0.4μm to 1μm below the layer surface) were determined using C-V measurements. The results show that in this range of depth: (1) the residual impurity concentration is lower in layers deposited during longer periods, and higher in layers deposited during shorter periods; (2) the distribution profile of these impurities can be approximated as linear; (3) the impurity gradient is larger for layers deposited during shorter periods than in layers deposited during longer periods. The above relations between residual impurities and growth time may be important in developing procedures for GaAs devices fabricated by the MOCVD method.

On the majority carrier collection in p +-p-n + and n +-p-p + silicon solar cells

The spectral responses of a few bifacial n +-p-p + silicon solar cells, 220 – 330 μm thick, were measured to investigate the possibility of majority carrier collection in n +-p-p + back-surface field and p +-p-n + front-surface field silicon solar cells. It was found that, under low level conditions, any appreciable collection of photogenerated majority carriers has to be field aided. Therefore, under low level conditions hole collection may contribute substantially to the photocurrent density of a p +-p-n + or n +-p-p + cell and this may come from the p + or p region provided that not only is the concentration of photogenerated holes in that region substantially large but also there exists a built-in electric field due to the impurity gradient to aid the process. For high level conditions, however, holes can be collected from the uniformly doped p base region with or without the aid of an electric field.

Theory and experiments on open circuit voltage decay of p-n junction diodes with arbitrary base width, including the effects of built-in drift field in the base and recombinations in the emitter

An expression for the forward current induced open circuit voltage decay of a p-n junction diode with a finite base width is derived. The expression includes the effects of recombination in the emitter and the built-in drift field in the base which may arise due to a nonuniform impurity profile. The voltage decay rate is dependent on the base thickness, base drift field, emitter dark saturation current, the effective surface recombination velocity at the back contact, and the minority carrier lifetime in the base. The effects of the drift field in the emitter, emitter lifetime, and surface recombination velocity at the emitter surface are completely taken into account by the emitter saturation current. Experimentally observed voltage decay plots for thin base hyperabrupt varactor diodes with retrograded impurity gradients in the base are reported. It is shown that the experimental results can be interpreted satisfactorily using the above theory. The values of the minority-carrier lifetime in the base are determined from the experimental results.