Showing papers in "Solid-state Electronics in 1969"

Normalized thermionic-field (T-F) emission in metal-semiconductor (Schottky) barriers

Abstract: Thermionic field (T-F) emission in uniformly doped metal-semiconductor (Schottky) barriers is analyzed to yield a normalized solution in closed form for the forward and reverse current (I)-voltage (V) relationship. A quasi one-dimensional approach and Maxwell-Boltzmann statistics are used. The formulation is expressed in terms of the ‘flat-band’ current density Im, the band bending Eb in the semiconductor depletion region, the materials constant E0 0 ( ln [ I I m ] = − E b E 0 0 at 0°K in the WKB approximation), and kT. The kinetic energy in units of Eb at which the maximum injection of carriers occurs in the semiconductor is shown to be cosh -2(kT/E0 0). Current flow in the temperature range between pure thermionic emission (kT/E0 0 ⪢ 1) and pure field emission (kT/E0 0 ⪡ 1) is analyzed and criteria for the transition of T-F emission to thermionic and to field emission are given. Computer solutions for the energy distribution of the injected carriers and for the normalized I-V characteristic are presented in graphical form. The results permit a straightforward calculation of the barrier height and the impurity concentration in the semiconductor from measurements of current density and differential resistance at a single applied bias. Application of these results explains a reported discrepancy between barrier heights deduced from photothreshold, C-V and I-V characteristics of WGaAs and AuGaAs Schottky barriers. A relatively constant excess temperature T0 (i.e., ln I ∝ (T + T0) when V ⪢ kT/q) is predicted in the case of large Eb/E0 0 in the higher kT/E0 0 range where thermionic emission is nearly predominant. I ∝ [exp(qV/kT) − 1] is shown to be a general expectation for all Schottky barriers near zero bias when the I-V characteristic is dominated by either thermionic or thermionic-field emission. The assumption of a Gaussian energy distribution of carriers leads to values for the slope of ln I vs. V in reasonable agreement with the results of the computer analysis, but the prediction of the absolute value of the current density deviates rapidly from the computed value when kT/E0 0 departs appreciably from unity. The Gaussian distribution also does not provide the smooth transition from T-F to thermionic emission characteristic of the computer solution.

General theory for pinched operation of the junction-gate FET

Abstract: A device oriented model is developed to describe the operation of the junction-gate field-effect transistor (FET) beyond pinch-off. The model is derived on the basis of a generalized structure with an arbitrary channel doping profile. It provides a qualitative and quantitative description of the current conduction mechanism, and is applicable over the entire dynamic range of device operation. Current conduction mechanisms in the vicinity of the source and the drain are examined separately. It is shown that the saturation of carrier drift velocities at high electric fields results in formation of a drain space-charge region of finite length. An approximate solution of the two-dimensional Poisson's equation is developed to describe the potential distribution within this region. A significant result of the device model is the prediction of a finite drain resistance in pinched operation, which shows a strong dependence on the device operation point.

Isolation of junction devices in GaAs using proton bombardment

Abstract: Proton bombardment has been used to convert both p- and n-type GaAs into high resistivity material. It will be shown that this technique is useful for isolating junction devices and fabricating arrays. The average carrier concentration in the bombarded layer is less than 1011/cm3, and the layer thickness is about one micron for every 100 keV of proton energy. These layers are apparently unaffected by a 16 hr anneal at 300°, and only slightly affected at 400°. Using this technique, we have isolated islands of n-type GaAs on a semi-insulating substrate, separated p-n junctions on an n-type substrate, and suppressed edge breakdown in Au-GaAs Schottky barrier diodes.

Expedient method of obtaining interface state properties from MIS conductance measurements

Abstract: In obtaining accurate values of interface state density and majority carrier capture cross section for SiSiO 2 interfaces from MIS capacitor admittance measurements, it has been necessary to analyze considerable data. The reason for this is a new effect described previously, namely the large dispersion of interface state time constant caused by fluctuations of surface potential. A computer program briefly outlined here has been developed which calculates interface state properties from a minimum of measured input data. The data required are: (i) low frequency capacitance vs. bias to get surface potential, (ii) admittance vs. frequency at fixed bias to get standard deviation of surface potential, and (iii) admittance vs. bias at two frequencies to get interface state density and majority carrier capture cross section vs. energy. A listing of the computer program and a description of how to use it can be obtained on request.

Richardson constant and tunneling effective mass for thermionic and thermionic-field emission in Schottky barrier diodes

Abstract: An appreciable difference is shown to be expected to exist between the experimentally measured Richardson constant and the ‘ideal’ Richardson constant associated with the flux of a Maxwellian distribution of carriers in a semiconductor. The equality which must exist between the Richardson constant for the forward and reverse characteristics is discussed. The semiconductor charge carrier energy—wave vector relationship rather than that of the metal is shown to be dominant because it controls the cone of acceptance for carriers incident on the barrier from the metal side. The effective mass in the ideal Richardson constant for T-F emission is shown to be the same as that for thermionic emission. This mass, which is associated with the E - k relationship transverse to the direction of current flow, can be considerably different from the tunneling effective mass which is the effective mass component in the direction of the current flow.

On the effective carrier lifetime in p-s-n rectifiers at high injection levels

Abstract: For a description of the recombination in p + - s - n + diodes at high injection levels an effective carrier lifetime τ eff is introduced, which includes the recombination in the p + and n + regions. From general equations, an explicit evaluation of τ eff for the conditions of lifetime determination from the stored charge and a discussion of the carrier decay after interrupting the current is given. Assuming a constant high-level lifetime in the base, the obtained dependence of the effective lifetime on the injected carrier density agrees with earlier experiments. Measurements of τ eff can be used for a determination of lifetime in the highly-doped layers.

Messung des übergangswiderstandes zwischen metall und diffusionsschicht in Si-planarelementen

Abstract: Zusammenfassung In der vorliegenden Arbeit wird eine Struktur beschrieben, die eine wirklichkeitsnahe Messung des Ubergangswiderstandes zwischen Metall und Diffusionsschicht im Halbleiter ermoglicht. Neben grundsatzlichen Uberlegungen werden die notwendigen mathematischen Beziehungen fur rechteckige und konzentrische Kontaktanordnungen bereitgestellt und die moglichen Unsicherheiten bei der Auswertung abgeschatzt. Das Ergebnis erster Messungen wird mitgeteilt.

Carrier mobility in silicon MOST's

Abstract: The mobility and density of free carriers in surface channels have been obtained from conductivity and Hall measurements performed on large experimental silicon MOST's. Uniform n- and p-type channels, with various crystallographic orientations have been studied over a range of temperatures, gate biases, and reverse biases between the channel and substrate. No trapping of induced carriers has been observed when the gate voltage is more than a few volts above threshold. The mobility of free carriers is very small at threshold. It increases rapidly with gate voltage and shows a maximum of about 1 3 or 1 2 of its bulk value, at gate voltages corresponding to free carrier densities of about 2–7 × 1011 carriers/cm2. At larger gate voltages the mobility shows a slow decrease. The mobility is also affected by bias between channel and substrate. A hysteresis in channel conductance is observed at room temperature. It is shown that a hysteresis in carrier mobility contributes appreciably to this effect. Finally, it is demonstrated by means of an example that the variations of mobility with gate and substrate bias have an appreciable influence on the drain characteristics of MOST's.

Minority carrier injection of metal-silicon contacts

Abstract: The minority carrier injection ratio from metal-silicon contacts has been measured using a metal-emitter transistor structure. Contacts of four different metals with barrier heights ranging from 0.65 to 0.85 eV on n -type silicon with doping level from 10 14 to 6 × 10 16 cm −3 were examined. This systematic investigation shows that the injection ratio at low current levels is a constant and is determined only by the barrier height of the contact and the doping of the semiconductor, while at high currents it increases with the total current. This result is in good agreement with theoretical predictions.

The electrical properties of dislocations in silicon—I: The effects on carrier lifetime

Abstract: Lifetime measurements were made on both n-type and p-type silicon which contained dislocation densities of the order of 107 per cm2. The dislocations were introduced by plastic deformation at 750°. A theory for transient recombination, based on R ead 's hypothesis of a potential barrier at the dislocation, is developed to explain the experimental data. The theory and the measurements show that the potential barrier inhibits the capture of majority carriers causing long lifetimes to be observed. Also, it is shown that for small excess carrier densities, the lifetime is independent of the dislocation density and only weakly dependent on the majority carrier density. An analysis of the data in n-type silicon reveals that the dislocation has an acceptor level which is approximately 0.52 eV below the conduction band, and which has a capture cross section for electrons of approximately 10−15 cm2. In p-type silicon the dislocation is found to have a donor level whose location is not as well defined. The donor state was measured at 0.50 eV, 0.42 eV and 0.38 eV above the valence band in 200 Ω-cm, 50 Ω-cm, and 10 Ω-cm material respectively. The donor state's capture cross section for holes is about 10−16 cm2 for all three resistivities. It is suggested that in p-type material the donor states lie in a band rather than at a discrete level.

Error analysis of surface state density determination using the MOS capacitance method

Abstract: A detailed theoretical and numerical analysis of the possible errors of this method due to experimental inaccuracies is made. Inaccuracies in oxide thickness, substrate impurity concentration, asymptotic capacitances at strong inversion and accumulation, stray capacitance, absolute capacitance and voltage readings are considered. In addition, errors due to neglecting recombination at interface surface states, bulk states, surface channels and to series resistances are considered. The errors in the total interface density of state calculation can be minimized so that the method is sensitive to densities to 2×10 9 states/cm 2 -V in a range of E − E i = ±14 kT in SiSiO 2 MOS diodes at 300°K. The main contribution to error in this range comes from assumed inaccuracy in the absolute capacitance reading (±0.002 pF), the stray capacitance error (±0.01 pF) and the asymptotic capacitance errors (±0.002 pF). Near the band edges, the error increases rapidly, to 10 13 states/cm 2 -V at the band edge for inverted surface and to 10 11 states/cm 2 -V at the band edge for accumulated surface. The main source of error at the band edge for surface accumulation comes from the absolute accuracy of capacitance reading. For the inverted surface, inaccuracies due to both the absolute accuracy of capacitance reading and asymptotic capacitance contribute. By using substrate materials of both conductivity types, this method is then sensitive to total (all time constants) interface state density of a few times 10 9 states/cm 2 -V over an energy range of 28 kT centered at the midgap and to density of 10 11 states/cm 2 -V at the band edge.

Theoretical effects of exponential band tails on the properties of the injection laser

Abstract: Calculations have been made of various GaAs injection laser properties, assuming the high doping levels present in these devices to be responsible for the formation of band tails with density of states varying as exp ( −E E 0 ) . Simple analytical expressions are obtained for carrier concentrations and emission rates, which are not possible for other forms of the band tail density of states. These expressions facilitate the solution of the laser kinetic equations and thus exact relations are derived for threshold currents, lasing frequencies, I–V characteristics, and light power outputs, both above and below threshold, within the scope of the initial approximation.

Exact analytical solution of high frequency lossless MOS capacitance-voltage characteristics and validity of charge analysis

Abstract: The small signal equivalent circuit model is employed to obtain the exact nonuniform transmission line for high frequency MOS capacitance calculations. The semiconductor capacitance, given by the open circuit input capacitance of the line, is described by a simplified Riccati equation which is valid for arbitrary impurity distribution in an extrinsic semiconductor. Numerical solutions are obtained using the fourth order Runge-Kutta method for the case of constant impurity concentration. The validity range (measured by the amount of surface band bending) and the accuracy of the various approximations of the capacitance calculations using charge analysis are established by comparing with the exact solution from the transmission line. It is shown that for doping greater than 1014/cm3, the complete minority carrier depletion model gives accuracy better than 10−6 C0 for carrier concentration ratio of (majority/minority) > 500 at the oxide-semiconductor interface, or UIS > 2UF−6. For stronger surface inversion, the high frequency charge analysis formula can be used with equal or better precision. It is noted that the exact transmission line model used here to verify the charge models is particularly valuable for substrates with spatially varying impurity concentration.

Non-equilibrium C-V and I-V characteristics of metal-insulator-semiconductor capacitors

Abstract: The C-V characteristics of metal-insulator-semiconductor (MIS) structures exhibit considerable departure from their quasi-equilibrium behavior under the application of large depleting voltages. The deviation is the result of d.c. current flowing through the insulator, so that steady state non-equilibrium conditions exist in the semiconductor. The primary effects are a lowering of the high frequency capacitance below its quasi-equilibrium minimum value C ∞ , a deviation of the I-V characteristics of the structure from those of the insulator and the development of a large voltage drop across the semiconductor. The low and high frequency capacitances coincide in this non-equilibrium range. The non-equilibrium properties have been observed for deposited films of Si 3 N 4 , SiO 2 , and Al 2 O 3 . Experimental data are presented for films of pyrolytically deposited Si 3 N 4 on p - and n -type silicon substrates, in the dark and for various levels of illumination. A model is developed in which current in the semiconductor occurs through the generation of carriers in the depletion region, and bulk diffusion of carriers in the case of illumination, and where the insulator current proceeds through the Poole-Frenkel mechanism. Agreement between theory and experiment is obtained, and the possible use of the non-equilibrium effect in determining the minority carrier lifetime of the substrate is indicated.

Spreading resistance correction factors

Abstract: The solution for the potential distribution from a circular flat contact current source on a semi-infinite medium composed of N layers of finite thickness and different resistivities is given. This is applied to the three-point spreading resistance probe system in the form of correction factors. Examples are given which indicate when a single layer approximation may not be used. A general scheme for correcting any type of profile is proposed and compared with other correction techniques.

An electron imaging system for the fabrication of integrated circuits

Abstract: An ultrahigh resolution electron image projection tube has been investigated as a means for fabricating large arrays of micron size transistors. Electrons are derived from an air stable photocathode whose surface contains an image of the desired array of diffusion or contact windows. Coaxial electromagnetic fields focus the electron image onto the silicon wafer targets. The observed resolution (∼ 1 μ), useful area (∼ 1 in. dia.), and depth of focus (∼ 25 μ) exceed that of any known light optics fabrication system. Also, the image tube approach is more efficient than the use of a single scanned beam, since large arrays can be exposed in a single operation. A method has been demonstrated for performing alignments.

Determination of deep centers in silicon by thermally stimulated conductivity measurements

Abstract: The technique of measuring thermally stimulated conductivity in reverse-biased junctions has been applied to silicon. It is shown that this provides a simple and effective method to determine energies as well as concentrations of deep centers directly in a junction device. In several n+-n-p+ Si high voltage rectifiers, four different trapping centers were detected in the 20Ω-cm n-region of the junctions. These centers have energies from 0.2 to 0.4 eV, and concentrations between 4×1011 and 3×1012cm−3.

Physical limitations of MOS structures

Abstract: The physical model of the MOS structure is re-assessed with particular reference to its usefulness in the understanding of the behaviour of MOSTs near the threshold or transition region and under high surface field and channel field conditions of operation. The properties of the surface inversion layer are examined in detail involving the analysis of the MOST channel conductance under arbitrary inversion and current flow conditions. Application of Schrieffer's theory of surface mobility to the analysis has resulted in a simple expression for the surface field dependent channel conductance which well explains the behaviour of practical transistors and easily lends itself to a method of determining the effective carrier thermal velocity vth, or the related effective mass in the inversion layer. Practical results on silicon MOSTs suggest that vth ⋍ (1·3 − 3) × 107 cm/sec for holes and (3–6) × 107 cm/sec for electrons depending on the surface conditions and resistivity. Extrapolated zero-field mobility near the surface has been found to vary between 50 and 70 per cent of the bulk mobility. The characteristics of MOSTs under high field saturation current flow conditions of operation bear little resemblance with the zero-current channel conductance behaviour. The former are determined by the hot-carrier limiting velocity, vlimit, which in the inverted surface has been found to be about half its bulk value.

Theory of gunn-effect logic

Abstract: A range of important aspects of Gunn-effect pulse-processing devices has been studied. Appreciable pulse gain can be obtained for correctly chosen diode parameters. Equally, the pulse coincidence does not have to be unreasonably large for high-grain diodes. A fan-out of more than 7 should be obtainable for diode resistivities larger than 10 Ω-cm. The power dissipation can easily be kept below 100 mW for gains up to more than 50 db. The three-terminal Gunn-effect comparator has been treated and the conditions for successful operation are given. Finally, a new comparator circuit has been proposed consisting of two two-electrode devices operating on one common load resistor.

Observations on a method of determining the carrier lifetime in p+-ν-n+ diodes

Abstract: In two recent papers, one by D avies (1) and the other by W ilson , (2) results have been given of measurements made by the forward pulsed diode method on silicon p + -ν- n + diodes. In this paper it is pointed out that the interpretation of the results by W ilson (2) may be in error and an alternative explanation for the “low level lifetime” observed is offered. A simple analysis of the alternative model is given and results which support the view that the new model is in fact the one operating in practice are also quoted.

Properties of GaP Schottky barrier diodes at elevated temperatures.

Abstract: Gallium phosphide Schottky barrier diodes, discussing construction and metals used, barrier height relationships to impurity concentration and temperature, rectifying characteristics and internal quantum efficiency

Characterization of burst noise in silicon devices

Abstract: Burst noise has been investigated in forward-biased silicon diodes and transistors. To separate surface effects from bulk effects, measurements were performed on gate-controlled devices. Both gate-voltage-dependent and gate-voltage-independent burst noise were observed. Burst noise under forward bias conditions has been characterized in terms of the bias across the p-n junction. From this characterization simple equivalent circuits are presented for diodes and bipolar transistors which model the main features of burst noise in these devices. Analytical expressions for the burst noise spectral distributions are developed and compared with experiment.

On the high frequency excess noise and equivalent circuit representation of the MOS-FET with n-type channel

Abstract: The noise in MOS-FET's is here represented by four parameters: the equivalent noise resistance Rn (measuring the drain noise), the equivalent noise conductance gn (measuring the uncorrelated part of the gate noise) and the correlation admittance Yz = gzj ωCz (measuring the correlated part of the gate noise). For some large geometry units we compared the experimental values of these parameters with the ones calculated under the assumption that the noise in the channel was thermal noise. Serious discrepancies between the theoretical and the experimental values were noted, indicating that white noise of non-thermal origin must be present in the channel. The observed data are explained with the help of local “mobility fluctuations” in the channel. By making reasonable assumptions about this noise source, the observed data can be explained in a qualitative manner.

The effect of strain on MOS transistors

Abstract: The effect of mechanical strain on the characteristics of MOS transistor structures has been measured. A strip of silicon cut from an array of MOS transistors on a slice was made into a cantilever and vibrated at about 60 Hz. The change in the device characteristics could be due to a variation in mobility or turn on voltage, but by careful investigation around the threshold of conduction it was concluded that the chief cause is due to mobility variation. This change in the mobility and hence the β of the transistor is consistent with a piezoresistive effect in the channel, the overall change in conductivity being some 50 times greater than that expected by simple geometric distortion. The piezoresistive effect in MOS structures can give rise to a change in the device characteristics due to strain built in during fabrication. This could lead to an undesirable situation in large scale arrays. Alternatively it is possible to propose using the strain sensitivity for a strain gauge and novel circuits for this purpose might be devised.

A new MNOS charge storage effect

Abstract: This paper describes a new charge storage effect occurring in MNOS tetrodes. The physical phenomenon used for charge storage is direct carrier injection over the Schottky barrier between silicon and gate insulator rather than tunnelling. This mechanism avoids the problem of high electrical fields and slow operating speeds inherent in previous MNOS structures. The basic memory cell is an n -channel MOS stacked gate tetrode which has the additional advantage of a built-in three dimensional bit selection. A simple physical model for the injection effect and the experimental results which characterize it are presented. The application of this effect to an electrically alterable read-only memory is described in detail.

Recoverable neuristor propagation on superconductive tunnel junction strip lines

Abstract: Superconductive tunnel junction strip transmission lines, both those utilizing normal electron tunneling and those utilizing Josephson tunneling, can support recoverable neuristor pulse propagation. Detailed analysis of the normal electron line, including studies with a lumped circuit analog, gives the pulse amplitude, velocity and bias threshold for neuristor propagation and indicates instability for some values of bias current. Experiments on tin-tin oxide-lead normal electron lines agree with the analysis, showing pulse amplitudes of 0.2–0.5 mV, propagation velocities of about 1.5×109 cm/sec and stability only over a narrow range of bias current values. A crude analysis predicts similar behavior for the Josephson junction line. Experiments on a single tin/aluminum-oxide-lead Josephson junction line show only partial, qualitative agreement with this analysis; the observed behavior also bears some resemblance to the predictions of previously reported approximate theories. Considerations of fabrication technology and power dissipation indicate that superconductive tunnel junction strip lines are perhaps the first practical neuristor realization for use in large systems.

On the potential barrier shape in Al–Al2O3–Al tunnel junctions

Abstract: In the conventional theoretical model for the tunnel current through thin Al2O3-layers sandwiched between metal electrodes a potential barrier of convex curvature is assumed. The convex curvature of the barrier is caused by the image potential. However, in this paper it will be shown, by means of the logarithmic derivative of the tunnel current, that a potential barrier of concave curvature leads to noticeably better agreement with experimental data than the convex barrier. It is suggested that a large positive ionic space-charge in the Al2O3-layer causes the concave curvature of the potential barrier.

Die metall-halbleiter-kontaktbarrieren der metalle aus der nebengruppe I und VIII auf silizium und germanium☆

Abstract: Zusammenfassung Die Barrierenenergien der sperrenden Metall-Halbleiterkontakte (Schottky-Kontakte) wurden fur folgende Kombinationen ermittelt: Si und Ge je als Halbleiter und die Metalle der 1. und 8. Nebengruppe des Periodischen Systems, namlich Cu, Ag, Au; Fe, Co, Ni; Ru, Rh, Pd; Os, Ir, Pt. Die Ergebnisse werden diskutiert. Dabei wird gezeigt, dass fur diese Metalle, die im wesentlichen als die Edelmetalle bezeichnet werden konnen, ein recht gut erfullter linearer Zusammenhang zwischen ihrer Ordnungszahl Z und ihrer Barrierenhohe ΘB besteht.