Showing papers in "Solid-state Electronics in 1973"

Electron and hole ionization rates in epitaxial silicon at high electric fields

Abstract: Ionization rates for electrons and holes are extracted from photomultiplication measurements on silicon p+n mesa diodes for electric fields of 2·0 × 105−7·7 × 105 V/cm at temperatures of 22, 50, 100 and 150°C. These results are particularly pertinent to the analysis of high-frequency (∼ 100 GHz) silicon IMPATT diodes. The rates obtained here are in reasonable agreement with previously published data of van Overstraeten and DeMan, although slightly larger in magnitude. Calculated curves of breakdown voltage vs background doping level are presented using the room temperature ionization rates. Also a comparison is made to previously reported rates. The new rates provide a closer agreement between predicted and measured breakdown voltages for breakdown voltages less than 70 V.

Use of a Schottky barrier to measure impact ionization coefficients in semiconductors

Abstract: The use of a Schottky barrier to determine the impact ionization coefficients of electrons and holes in semiconductors has been studied analytically and also evaluated experimentally by comparing the results for silicon with those already available in the literature. The Schottky barrier offers several advantages over a diffused p-n junction in such measurements. Pure electron initiation and pure hole initiation can be separately achieved. The abrupt barrier provides an accurately known electric field, and the linearity of the field distribution simplifies the problem of extracting the ionization coefficients from the multiplication data. We present a general solution of the charge multiplication equation and derive expressions for the ionization coefficients for the particularly simple conditions that can be achieved in a Schottky-barrier junction. Our results for silicon in the range 2 × 105 α = α ∞ exp ( −b n E ) for electrons and β = β ∞ exp ( −b p E ) for holes, with α∞ = 9·2 × 105 cm−1, β∞ = 2·4 × 105 cm−1, bn = 1·45 × 106 V/cm and bb = 1·64 × 106 V/cm.

Investigation of the MOST channel conductance in weak inversion

Abstract: The drain-source conductance of several MOS transistors has been studied as a function of the silicon surface-potential ψs in the weak and intermediate inversion region, under the condition of quasi-thermal equilibrium at room temperature. The silicon surface conductance per square ifG(in□ has been measured to vary exponentially with qψs/kT in weak inversion for excess minority carrier densities extending over the range 105-1011 cm−2. The exponential behaviour of G□ vs. qψs/kT appeared to be insensitive for the presence of interface states, when distributed around peak values as large (As) 6 × 1011/cm2 eV at ≈ 200 meV energy distance from midgap. Garrett and Brattain predicted theoretically that the excess minority carrier surface charge for weak inversion should also be an exponential function of qψs/kT, we conclude that the minority carrier mobility remains constant over the entire weak inversion region. A refined version of the low frequency CV method the so-called ‘split’ CV method has been introduced, which allows a simple determination of the charge trapped in interface states in weak and intermediate inversion as well as a determination of the bulk dope density.

Discharge of MNOS structures

Abstract: The discharge of MNOS memory devices at zero or low gate voltages is studied theoretically and experimentally. A theory based on direct tunneling of charge carriers from traps in the silicon nitride layer into the silicon describes the experiments quite well. The discharge process is found to be logarithmic in time, starting at a certain time, ift d , which is exponentially dependent on the oxide thickness, and ending at another time, extrapolated to much larger than 10 years. Some implications of the discharge model are discussed.

An analysis of the threshold voltage for short-channel IGFET's

Abstract: For short-channel insulated-gate field-effect transistors (IGFET) operating with source-to-substrate reverse bias, the threshold voltage is in general a function of channel length and drain-to-source voltage. It is shown in this analysis that these dependences can be attributed to the two-dimensional distribution of the depletion charges. Starting from two fundamental relations, the overall charge neutrality and the voltage relations based on the energy band diagram, a generalized threshold voltage equation in integral form is derived. A closed-form threshold equation is then obtained using a regional approximation with a simplified piecewise-linear depletion profile. The equation includes as new factors, the channel length, junction depth and drain voltage, and passes to the conventional form for increasing channel length. The theoretical threshold voltage expression is found to predict the correct tendencies and is shown to be in reasonable agreement with experimental measurements.

A two-dimensional mathematical model of the insulated-gate field-effect transistor

Abstract: This paper is concerned with the mathematical details of a numerical model of the insulated-gate field-effect transistor; a computer-aided analysis of the device, based on this model, appears separately A finite-difference scheme is presented for obtaining an approximate solution of a system of nonlinear elliptic partial differential equations describing the carrier distribution in such a device model In particular, our scheme allows the device current, as a function of the applied bias voltages, to be reliably calculated The results of numerical experiments appraising the accuracy of the method are also included

The C-V characteristics of Schottky barriers on laboratory grown semiconducting diamonds

Abstract: Measurements of the differential capacitance of evaporated gold Schottky barriers on laboratory-grown, boron-doped semiconducting diamonds have been obtained for the first time as functions of reverse-bias voltage, frequency, and temperature The data are analyzed on the basis of a model which includes the effects of long time constants for hole capture from the deep (boron) level, as well as previously unobserved effects due to the series resistance of the bulk The barrier height at 300°K is found to be 1·73 ± 1·10 eV , in good agreement with the ‘one-third band gap’ value of Mead and Spitzer Excellent correlation is found between optical transmission measurements and the C-V analysis for the uncompensated boron concentration, indicating that all of the optically observable dopant is electrically active By fitting the model with two adjustable parameters at room temperature, good agreement is obtained between measured and calculated capacitance over two and a half decades as a function of temperature The analysis indicates that the activation energy of the acceptor level is 0·26–0·37 eV for the samples studied, while the associated capture cross-sections are 0·9–2·0 × 10 −17 cm 2

Minority carrier effects upon the small signal and steady-state properties of Schottky diodes

Abstract: Schottky diode theory is re-evaluated by applying the combined thermionic emission-diffusion theory to both the majority and minority carrier flows across the metal-semiconductor contact. Under both steady-state d.c. and small signal a.c. conditions, numerical solutions to the semiconductor transport equations subject to boundary conditions determined from the combined theory are used to investigate the effects of minority carriers upon the properties of uniformly doped Schottky diodes. High injection effects and contact limitations are shown to influence the minority carrier injection ratio and the total stored minority carrier charge. It is further shown that the small signal impedance of a large class of Schottky diodes becomes inductive under moderate forward bias.

Formation kinetics and structure of Pd2Si films on Si

Abstract: Backscattering and X-ray techniques have been used to study properties of palladium silicide (Pd2Si) formed by evaporating thin Pd layers on Si followed by heat treatment. The rate of formation of Pd2Si in the temperature range of 200–275°C has been measured by 2-MeV 4He+ ion backscattering. The Pd2Si layer is found to grow at a rate proportional to the square root of time for thicknesses ranging from approximately 200–4000 A. The rate of growth is found to be independent of Si substrate orientation or doping type and the rate constant is found to fit a single activation energy of Ea = 1·5±0·1 eV over the temperature range measured. X-ray diffraction indicates the structure to be Pd2Si with the basal plane roughly parallel to the substrate surface for films formed on 〈111〉, 〈110〉, 〈100〉 and evaporated (amorphous) silicon substrates. The degree of preferred orientation is markedly stronger on [111] Si. Ion channeling measurements confirm that in this case the c-direction of the Pd2Si is parallel with the [111] direction in the underlying Si.

Transport equations in heavily doped silicon, and the current gain of a bipolar transistor

Abstract: The Fermi level and effective density of states are calculated for heavily doped silicon, using methods similar to those of Kleppinger and Lindholm and Van Overstraeten et al. For the case in which Boltzmann statistics can be applied to both types of carriers, modified transport equations are obtained in terms of two “heavy doping parameters,” which measure the magnitude and skewness of the effective forbidden band. These results are applied to the calculation of the d.c. current gain of a diffused bipolar transistor. We obtain reasonable current gain values without employing short carrier lifetimes, and our numerically calculated dependence of the current gain on injection level is reasonable. However, the quantitative accuracy of our calculations is limited by several factors.

The effect of an interfacial layer on minority carrier injection in forward-biased silicon Schottky diodes

Abstract: It is shown that the degree of minority carrier injection in Au-Si junctions can be substantially increased by the inclusion of a thin interfacial layer between the metal and the semiconductor. When a forward voltage is applied to the junction, a part of this voltage is developed across the interfacial layer. This favours the reduction of the barrier height to minority carriers, which tunnel from the metal into the semiconductor. The minority carrier injection current increases at the expense of the majority carrier current. For a given oxide thickness, γ(= Jminority/Jtot) increases with forward bias, approaching a saturation value for a few volts applied to the junction. For a given voltage, γ also shows a variation with interfacial layer thickness, δ, and the present results indicate that an oxide thickness can be chosen to optimise γ. In the case of a gold-silicon junction with an insulating layer of thermally-grown oxide, as δ is increased to 40 A, the saturation value of γ increased from 10 −4 for δ = 10 A through a maximum of 2 × 10−1 for δ ⋍ 30 A. For oxides prepared by r.f. sputtering, the maximum value of γ is 10−1 and occurs for δ ⋍ 80 A. These results are of considerable importance in the improvement of injection luminescence in metal-semiconductor diodes.

Schottky-barrier capacitance measurements for deep level impurity determination

Abstract: The time dependence of a Schottky-barrier capacitance due to thermal excitation of trapping centres has been studied. An expression for the junction capacitance is derived which is not restricted to any special range of reverse bias nor to a special relation between shallow and deep impurity concentration. The concentration ratio of shallow to deep centres is calculated from the values of the capacitance at zero and infinite time. From a capacitance vs. time plot the trap emission rate for electrons e n is obtained. Their energetic level within the forbidden band-gap is determined from the temperature dependence of e n as well as from the capacitance-time variation. Experimental studies which do confirm the calculations were carried out on gold contacts on oxygen-doped n -type GaAs. Representative results of the investigated samples were: shallow donor density 3 × 10 15 cm −3 , trap density 9·8 × 10 15 cm −3 , electron emission rate 6 × 10 −2 sec −1 , energetic level 0·68 eV and capture cross section 7 × 10 −16 cm 2 .

Bestimmung von parts per billion sauerstoff in silizium durch eichung der IR-absorption bei 77°K

Abstract: Zusammenfassung Fur die IR-Absorption von Sauerstoff in Silizium wurden mit Hilfe des Schmelzextraktionsverfahrens neue Eichkurven bei Raumtemperature und 77°K ermittelt. Die experimentellen Methoden werden beschrieben und deren Fehlerquellen diskutiert. Als neue Werte zur Berechnung der Sauerstoffkonzentration aus den gemessenen Absorptionskoeffizienten ergaben sich 4,9 ± 0,2 ppm A/cm−1 bei Raumtemperatur und 1,9 ± 0,1 ppm A/cm−1 bei 77°K. Diese Werte sind bis zum Faktor 2,5 niedriger als bisher veroffentlichte Werte. Dadurch erniedrigt sich die Nachweisgrenze der IR-Absorptionsmethode bei 77°K auf 20 ppb. A, womit die meisten in Si-Kristallen vorkommenden Sauerstoffkonzentrationen bestimmt werden konnen.

Measurement of low densities of surface states at the SiSiO2-interface

Abstract: By a careful process SiSiO2-interfaces can be made with a low oxide charge Qox and with a low surface states density Nss. For dry oxides on (100) Nss-values as low as a few 109 cm−2 eV−1 are found on samples with an oxide charge density of 3·0 × 1010 cm−2. Only the Nicollian-Goetzberger conductance method is proved to give reasonable results on these structures. The quasi-static low frequency C-V-technique is in good agreement with the conductance technique for samples with Nss-values higher than 1·0 × 1010 cm−2 eV−1. The spatial fluctuation of surface potential, mainly caused by oxide charge fluctuations, is an important parameter when studying the high or low frequency C-V-characteristics. Some irregularities in the experimental Nss-φs-curves are explained.

Electrical properties of CuInSe2 single crystals

Abstract: Various bulk electrical properties and device characteristics have been measured. It has been shown that the majority carrier type is dependent on crystal stoichiometry. Mobilities of 660 cm2/V sec and 30 cm2/V sec have been measured for n-and p-type samples, respectively. Rectifying contacts and p-n junctions have been investigated by small signal analysis and the associated doping levels and equilibrium band diagrams have been determined. Photovoltage measurements on rectifying contacts have shown that the band-gap has a value of 0.95 ± 0.01eV.

Current-voltage characteristics and capacitance of single grain boundaries in semiconducting BaTiO3 ceramics

Abstract: Specimens were prepared of doped ceramic barium titanate in the form of bars which, between their metallized ends, contained only one high-resistance grain boundary running across the entire cross-section. The measurements covered the differential capacitance of these individual grain boundaries, under bias, and their d.c. current-voltage characteristics. The results can be described quite well by a model in which a layer of a second phase present between the barium titanate grains is assumed to possess, firstly, acceptor character and, secondly, a dependence of its permittivity on the temperature and the electric field strength.

A study of SiO layers on Si using cathodoluminescence spectra

Abstract: Cathodoluminescence spectra were used to study centers in thin layers of thermally grown SiO2 on Si. The purpose was to learn more about the centers responsible for the radiation induced space-charge build-up observed in oxide-passivated, planar devices. The spectra were observed to contain three broad peaks; peak A at ∼2900A, peak B at ∼ 3700A and peak C at ∼ 4500A. These spectra were not affected by the conductivity-type, resistivity or crystalline orientation of the silicon, and were little affected by the oxide thickness or growth temperature. Ionizing radiation, destroyed the B peak, greatly enhanced the C peak but had little effect on the A peak. Wet-oxygen-grown oxides were less affected by ionizing radiation than were dry-oxygen-grown oxides. Baking wet-oxygen-grown oxides in dry nitrogen at ∼ 1100°C enhanced the B and C peaks. An etch-back experiment was used to determine the distribution of the three luminescence centers. The A center was distributed approximately uniformly throughout the bulk of the oxide. The B center was concentrated near the outer surface of the oxide layer and was undetectable close to the Si/SiO2 interface. The C center was located principally within < 200 A of the Si/SiO2 interface. The A center is believed due to the presence of Na. The B center is associated with the presence of H and may be due to interstitial H. The C center is believed to be the center responsible for the radiation induced space-charge buildup near the Si/SiO2 interface and to be due to trivalent Si. The C center is apparently the same center which produces the C absorption band (2150A) in fused silica.

Mathematical analysis of a heterojunction, applied to the copper sulphide-cadmium sulphide solar cell

Abstract: The mathematical analysis of the photoelectric effects in the heterojunction of CdSCu 2 S combines the excitation-recombination-diffusion process in the copper sulfide, the interface recombination and the electron transport across the barrier in the cadmium sulphide. This leads to a current-voltage characteristic in which the parameters include, among other things, the height of the barrier or the discontinuity in the conduction band edge. The conductances of barrier, interface and semiconductor which are important parameters of the current-voltage characteristic, depend exponentially on this discontinuity. Problems bearing on the collecting and the inverse injecting of minority charge carriers are mentioned. The after-heat treatment, an essential step in the production of solar cells, is given a possible interpretation. According to this, the oxygen at the interface of cadmium sulphide is absorbed during the heat treatment and determines the band bending in the adjacent CdS. The optimum after-heat treatment of the cell, according to the theory, is that which leads to a transition from the conduction band of the CdS to that of the Cu 2 S with practically no discontinuity.

Frequency dependence of C and ΔV/Δ(C−2) of Schottky barriers containing deep impurities

Abstract: The frequency dependence of ΔV/Δ(C −2 ) of Schottky barriers with deep impurities has been discussed on the basis of the depletion approximation. Systematic treatment has been developed of Schottky barriers having spatially distributed deep centers and useful expressions have been derived for ΔV/Δ(C −2 ) . It is shown that the impurity profile, the energy level and the electron emission rate of deep impurities can be determined by making measurements of the frequency dependence of ΔV/Δ(C −2 ) . The method of measuring ΔV/Δ(C −2 ) has also been briefly described.

Theory of dynamic charge current and capacitance characteristics in MIS systems containing distributed surface traps

Abstract: Theoretical studies have been made on the dynamic characteristics of the metal-insulator-semiconductor (MIS) capacitor containing distributed surface traps. It has been shown that when the surface traps are in dynamic equilibrium with the voltage ramp, the device exhibits steady-state charge, current and capacitance characteristics. When the surface traps are out of equilibrium with the voltage ramp, then the emission of trapped charge is a function of time only and not of voltage. Under such conditions, the characteristics are considered to be non-steady-state in nature. In the steady state, the emission of electrons from a continuum of surface traps accounts for the reduction in the slopes of the C–V curves from the ideal ones. Kinks are manifested when the traps just empty the last of their electrons. In the non-steady state, electron emission can be described by the non-steady-state (time-dependent) occupancy function derived herein, which is shown to be similar in shape to the Fermi function. This means that electron emission takes place from a narrow band of energy positioned near the uppermost-filled traps. Hysteresis effects are manifested in the C–V characteristics due to the non-steady-state emission of trapped charge. At the transition from the steady state to the non-steady state and vice versa, kinks are exhibited in the charge and capacitance characteristics, while step changes in current components are also predicted. The physical processes involved have been stressed and closed-form expressions have been obtained for the charge, current and capacitance in terms of the trapping parameters, sweep-rate and temperature.

Surface charge and stress in the Si/SiO2 system

Abstract: A model for the stress distribution in thermally oxidised silicon slices has been developed using beam theory and bimetallic strip theory. The stresses have been confirmed by making lattice parameter measurements on oxidised silicon using the APEX X-ray diffraction technique. The often suggested relationship between the surface charge density at the Si/SiO2 interface and the stress in the silicon surface has been investigated and shown to be inconsistent. Finally, analysis of the variation of surface charge density with oxide thickness has caused us to postulate the presence of both positively and negatively charged centres at the interface.

MOS threshold shifting by ion implantation

Abstract: In this paper, the theoretical description of threshold shifting of MOS devices by implantation of an impurity beneath the control electrode is presented. Experimental measurements are presented which verify the theoretical predictions. In particular, MOS capacitors and transistors were used to experimentally verify the theory ( n -type Si substrates to verify the case of p -channel devices). Implanted layers sufficient to compensate the background substrate doping were used. This layer creates a buried conducting channel beneath the gate that is isolated from the substrate by the p-n junction. Modulation of this conduction region by the surface depletion region was found to be responsible for the transistor action. For n -type substrates ( p -channel devices) ion energies of 33 and 53 keV were selected for use with gate oxides of ≈ 0·1 μm. Boron doses ranged from 5×10 10 to 2×10 12 atoms/cm 2 . Threshold shifts from 0·2 to 5 V were observed. Device performance was not degraded by the implantation. Annealing temperatures as low as 500°C were found to be sufficient to anneal the damage caused by the implantation. Changes in the characteristic C vs V curves of the devices were predicted and experimentally observed. A method of picking the approximate turn-off voltage of the devices from the C vs V curves is pointed out.

Properties of silicon implanted with boron ions through thermal silicon dioxide.

Abstract: The properties of silicon implanted with boron ions through thermal SiO2 films were studied using sheet resistivity measurements (corroborated by Hall data). Electrical properties for implants through 0.1 μm of SiO2, as compared to bare silicon, showed no unusual behavior as a function of anneal temperature. Sheet resistivity measurements as a function of SiO2 thickness for fixed ion energy, and as a function of energy for fixed oxide thickness were made after 525 and 925°C anneals, for boron doses of 1013, 1014 and 1015 ions/cm2. The profile of boron ions in SiO2 is near Gaussian for the energy range investigated and the stopping power is 0 to 20% lower than the theoretical value currently in the literature. Considerations for device manufacture are discussed in light of the results.

Metal-germanium Schottky barriers

Abstract: A systematic study has been made of the electrical characteristics of Schottky barriers fabricated by evaporating various metal films on n -type chemically cleaned germanium substrates. The diodes, with the exception of AlGe contacts, exhibit near-ideal electrical characteristics and age only slightly towards lower barrier height values. AlGe contacts exhibit very pronounced ageing towards higher barrier height values, due to formation of an extra aluminium oxide interfacial layer. Because of this, the barrier height values of aged AlGe contacts derived from I - V and C - V characteristics differ significantly. The dependence of the barrier height, ( φ b ) on the metal work function, φ m , for different metal-germanium contacts shows that surface states play an important role in the formation of the barrier. The density of germanium surface states is estimated to be D s = 2 × 10 13 eV −1 cm −2 .

On phosphorus diffusion in silicon under oxidizing atmospheres

Abstract: Phosphorus diffusion in silicon has been carried out in both inert (nitrogen) and oxidizing (90% nitrogen plus 10% oxygen, dry oxygen, steam) atmospheres, over a wide temperature range (1000–1200°C) and for doping concentrations usually encountered in the silicon planar technology. The experimental data, interpreted on the basis of the Kato and Nishi theoretical model taking into account the redistribution phenomena at the moving oxide-silicon interface, show that the phosphorous diffusion coefficient is strongly influenced by the nature of the ambient atmosphere in which the diffusion is carried out. Two different values for the activation energy of the diffusion process, Ei = 3·5 eV for the inert and E0 = 2·5 eV for the oxidizing conditions, have been found. These values seem to confirm the phosphorous diffusion mechanism based on E-centers for the inert case, while for the oxidizing case a different diffusion mechanism should be considered.

Capacitive effects of Au and Cu impurity levels in Pt-N type Si Schottky barriers

Abstract: Au and Cu impurity effects on the capacitance-voltage ( C – V ) relationship of Pt- n type Si Schottky barrier diodes have been investigated over the frequency range of 100 Hz to 500 kHz at 200°K and 300°K. The barrier height of the Pt-Si system measured by C – V , I – V , and photothreshold techniques was 0.83±0.01 eV. Deep level C – V effects previously predicted by Roberts and Crowell were observed. Diodes on phosphorus-doped Si nearly compensated with Au clearly exhibited a non-monotonic low frequency C – V relationship. An inflection point in the C −2 - V curve attributable to the Au donor level 0.77 eV from the conduction band edge was observed. The experimental data show that the presence of deep levels makes barrier height measurements appreciably ambiguous and that impurity profiles determined from a C – V relationship using a model which neglects their presence can be shifted appreciably both in apparent magnitude and apparent position.

Theory of dynamic charge and capacitance characteristics in MIS systems containing discrete surface traps

Abstract: Theoretical studies have been made on the dynamic characteristics of the metal-insulator-semiconductor (MIS) capacitor containing discrete surface traps. It has been shown that when the surface traps are in dynamic equilibrium with the voltage ramp, the device exhibits steady-state charge and capacitance characteristics. When the surface traps are out of equilibrium with the voltage ramp, then the emission of trapped charge is a function of time only and not of voltage. Under such conditions, the characteristics are considered to be non-steady-state in nature. The emission of trapped charge in the non-steady state gives rise to a plateau or ledge in the C – V characteristics, while characteristics. The transition from the steady state to the non-steady state results in kinks in the characteristics. The physical processes involved have been stressed and simple expressions have been obtained for the charge and capacitance in terms of the trapping parameters, sweep-rate and temperature.

Effects of time dependence of multiplication process on avalanche noise

Abstract: Theoretical and experimental studies of noise generated due to the randomness of the multiplication process in the avalanche region of a uniform diode are presented. The theory extends the results of McIntyre to include the time dependence of the multiplication process. It also shows the correspondence between the results of McIntyre, Gummel and Blue, Hines and Tager. The space-charge feedback and transit-time effects have been neglected in this analysis. The theoretical and the experimental results described have shown that even at frequencies well below transit-time frequency, the importance of the factor resulting from consideration of the time dependence of the multiplication process cannot be ignored. The measurements of the avalanche noise on uniform p+-n-n+ silicon diodes are found to be in good agreement with the theory presented here.

Electroluminescence in forward-biased zinc selenide Schottky diodes

Abstract: Schottky diodes consisting of a metal contact on n -type ZnSe emit light when biased in the forward direction if there is a layer of insulating or semi-insulating material between the metal and the semiconductor. The electroluminescence spectrum is characteristic of luminescent centres in the ZnSe. There is a threshold voltage for electroluminescence which corresponds to the difference between the metal Fermi level and the top of the valence band of the semiconductor. For gold on ZnSe the threshold voltage is 1·3 V. Characteristics of the device differ from those of similar MIS systems because the oxide used here has appreciable conductivity.