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

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 < E < 4 × 10⁵V/cm can be expressed in the form $\text{α = α}{}_{\mathrm{\infty }}\text{exp}\text{(}\text{?b}{}_{\mathrm{n}}\text{E}\text{)}$ for electrons and $\text{β = β}{}_{\mathrm{\infty }}\text{exp}\text{(}\text{?b}{}_{\mathrm{p}}\text{E}\text{)}$ for holes, with α_∞ = 9·2 × 10⁵ cm^?1, β_∞ = 2·4 × 10⁵ cm^?1, b_n = 1·45 × 10⁶ V/cm and b_b = 1·64 × 10⁶ V/cm.     

Measurements of bandgap narrowing in Si bipolar transistors

Theory predicts appreciable bandgap narrowing in silicon for impurity concentrations greater than about 10¹⁷ cm^?3. This effect influences strongly the electrical behaviour of silicon devices, particularly the minority carrier charge storage and the minority carrier current flow in heavily doped regions. The few experimental data known are from optical absorption measurements on uniformly doped silicon samples. New experiments in order to determine the bandgap in silicon are described here. The bipolar transistor itself is used as the vehicle for measuring the bandgap in the base. Results giving the bandgap narrowing (ΔV_g0) as a function of the impurity concentration (N) in the base (in the range of 4.10¹⁵–2.5 10¹⁹ cm^?3) are discussed. The experimental values of ΔV_g0 as a function of N can be fitted by:

$\text{δV}{}_{\mathrm{g0}}\text{= V}{}_1\text{ln}\text{N}\text{N}{}_0\text{+}\text{ln}{}^2\text{N}\text{N}{}_0\text{+C}$

where V₁, N₀ and C are constants.It is also shown how the effective intrinsic carrier concentration (n_ie) is related with the bandgap narrowing (ΔV_g0).     

A simple static circuit model for low-high junctions

A simple circuit model for low-high junctions is developed by using basic charge-control concepts. The model is valid in the low-level injection regime. The junction current is expressed as a function of the quasi-Fermi level separation in the space-charge region, and contains linear and non-linear terms. It is shown that the linearity of the junction depends on which of the two terms dominates at a given applied voltage. Calculated static V-J characteristics are given for an n-n⁺ device with donor concentration, N_D, on n-side as a parameter and that on n⁺-side equal to 10¹⁹ cm^?3. For N_D ≦ 10¹³cm^?3, the device is non-linear, for N_D = 10¹⁴ and 10¹⁵ cm^?3, the device is linear in low-level injection regime, and for $\text{N}{}_{\mathrm{D}}\text{≧ 10}{}^{16}\text{cm}{}^{\mathrm{?3}}$, the device is linear over a practically realizable range of applied voltages. The proposed model is expected to be useful in integrated circuit modeling.     

Low density photoexcitation phenomena in semiconductors: Aspects of theory and experiment

The basic mechanisms related to the photoexcitation of electron-hole pairs in semiconductors under conditions of low excitation density, low temperature and high crystal purity are reviewed. The use of high-resolution emission spectroscopy of band-to-impurity optical transitions in GaAs to measure the energy distribution functions $\text{?(E)}$ of electrons and holes in optically excited carrier plasmas of well defined densities (10¹⁰ cm^?3≤n≤ 10¹³ cm^?3) is described. With this experimental method (i) the energy relaxation of initially hot carrier distributions after pulsed photoexcitation ($\text{h}\text{?}\text{ω ? E}{}_{\mathrm{g}}$), (ii) stationary non-equilibrium distributions of electrons in the conduction band under cw photoexcitation ($\text{h}\text{?}\text{ω ? E}{}_{\mathrm{g}}$) and (iii) the transport properties of resonantly excited carrier plasmas in low electric fields ($\text{0≤|}\text{F}\text{|≤20}\text{V/cm}$) are investigated. The observed distribution functions are compared with theoretical results on the basis of the known band structure data of GaAs, taking into account polar optic and acoustic phonon scattering, the interaction among the carriers, ionized impurity scattering, and using approximate solutions of the appropriate transport equation.     

A compensation law for reverse-biassed ZnSe Schottky diodes

Zinc selenide Schottky diodes fabricated by a variety of techniques obey the law $\text{I = I}{}_0\text{exp}\text{(}\text{V}\text{V}{}_0\text{)}$ in reverse bias, where V₀ is nearly independent of temperature. We report the experimental discovery of a correlation between I₀ and V₀ which may be represented approximately as a linear relation between ln I₀ and V₀^?1 over thirty orders of magnitude of I₀. Implications of the relation are discussed.     

Dielectric relaxation contribution to dispersion of junction admittance

Significant frequency dispersion is observed in capacitance vs voltage measurements on solar cell structures prepared on high resistivity semiconductors such as a-Si and CdS. An equivalent circuit analysis of both Schottky barrier and Mott barrier devices shows that the equivalent parallel plate capacitance measured in an experiment corresponds to the distance from the interface to a position in the semiconductor bulk where the dielectric relaxation time is $\text{τ(x}{}_1\text{) =}\text{1}\text{ω}$ with ω the angular frequency. Comparison of measured C - V - f curves with reported for junctions in the dark and under $\text{～}\text{1}\text{3}$ AM1 illumination.     

The ƒT Characteristics of epitaxial NPN Transistors in upward operation

The gain-bandwidth products $\text{?}{}_{\mathrm{T}}$ of specially designed planar npn transistors were measured in upward operation at different operating current levels. It was found that the increase of $\text{?}{}_{\mathrm{T}}$ at high current levels cannot be accounted for by the variation of the factor (kT/qI_cxC_je. In fact, a plot of the delay time $\text{τ}{}_{\mathrm{T}}\text{( =}\text{1}\text{2}\text{π?}{}_{\mathrm{T}}$ against (1/√I_c) gives a straingth line at high current levels. Such observations can be explained by assuming that the lightly doped epi-emitter is operating at high injection levels. The high current limit of $\text{?}{}_{\mathrm{T}}\text{or}\text{τ}{}_{\mathrm{T}}$ depends on the epi-thickness w_epi and on the ratio between the volume of the parasitic region in the epi-emitter V_Ep and the collector area A_c     

Effect of injection efficiency and dimensions on the performance of a forward biased P+−I alloyed junction

P⁺?I junction has a high carrier injection, when forward biased. The bias voltage is dropped across the junction and the intrinsic region. The injection efficiency γ at the junction has been found to depend upon the voltage drop V_J across the barrier and the thickness of the intrinsic layer expressed as $\text{d}\text{L}$ where d is the thickness of the intrinsic layer and L is a measure of the diffusion length of the carriers in the intrinsic region. As V_J is varied the injection efficiency remains close to unity for low values of V_J but decreases for larger values of V_J, the decrease being more for larger values of $\text{d}\text{L}$. The ratio of the voltage drop across the intrinsic layer V_I to the voltage drop V_J across the junction depends upon the injection efficiency at the junction γ and the ratio $\text{d}\text{L}$. As γ decreases $\text{V}{}_{\mathrm{I}}\text{V}{}_{\mathrm{J}}$ increases, the increase being more for larger values of $\text{d}\text{L}$. The forward J?V characteristic is found to depend upon $\text{d}\text{L}$. As $\text{d}\text{L}$ decreases a lower resistance is offered by the diode. Modifications arising out of carrier-carrier scattering have also been considered. For a given V_J and $\text{d}\text{L}$, carrier-carrier scattering reduces γ. A reduced value of γ increases $\text{V}{}_{\mathrm{I}}\text{V}{}_{\mathrm{J}}$ and makes J?V curve less steep. The analysis has been carried out for $\text{V}{}_{\mathrm{J}}\text{?}\text{4kT}\text{e}$.     

Ohmic contacts to Si-implanted InP

Ohmic contacts to Si-implanted, n⁺ layers on semi-insulating InP are investigated on the basis of the transmission line model. It is found that Au/Ni/AuGeNi/InP system shows a good ohmic behaviour with the specific contact resistance $\text{ρ}{}_{\mathrm{c}}\text{of}\text{2 × 10}{}^{\mathrm{?5}}\text{Ω}\text{cm}{}^2$ and the minimum contact resistance $\text{Z}{}_{\mathrm{c}}\text{of}\text{～ 2 × 10}{}^{\mathrm{?3}}\text{Ω}\text{cm}$ for a Si-dose higher than 2 × 10¹⁴ cm^?2 at 100 or 200 keV. The results indicate that, in the FET fabrication, at least 120 μm in length is necessary in order to obtain source and drain electrodes with the minimized resistance.     

Electron temperature dependences of nonradiative multiphonon hot-electron capture coefficients of deep traps in semiconductors—I: Small lattice relaxation

Generalizing the theory of nonradiative multiphonon capture of thermal electrons for cases where the effective temperature T_e of conduction electrons differs from lattice temperature T_L, we develop a corresponding theory of hot electron capture. Its principal novelty is due to an exponential decrease ∝ exp(?E/k_Bτ) of the efficiency of this energy loss mechanism, at increasing electron energy E, for the usual regime of small lattice relaxation characterized by a corresponding “capture extinction temperature” τ. The resulting T_e-dependences of hot electron capture coefficients at sufficiently low T_e (

τ, i.e. in the “Sommerfeld factor regime”) are controlled by the net charge of the centre which means C(T_e) ∝ C(T_e) ∝ $\text{T}{}_{\mathrm{e}}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$, ∝ T_e⁰, or ∝ $\text{T}{}_{\mathrm{e}}{}^{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}$ exp$\text{[?3·(θ/T}{}_{\mathrm{e}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{]}$ in cases of attraction, neutrality, and repulsion, respectively. At high T_e

τ, i.e. in the “energy-loss factor regime”) these relations reduce to the form C(T_e) ∝ $\text{T}{}_{\mathrm{e}}{}^{\mathrm{<mtext>?</mtext><mtext>3</mtext><mtext>2</mtext>}}$ which is simply due to an increasing depopulation of the relevant region of low-lying band states. This theory is applied to electron capture by a singly charged repulsive gold centre and a doubly charged repulsive copper centre in germanium. The corresponding theoretical maximum values C_max.^(?1) = 5.2 · 10^?11 cm³ s^?1 and ifC_(rnmax.)^(?2) = 2.4 · 10^?12 cm³ s^?1 of hot electron capture coefficients are in good agreement with experimen observations.     

A simplified technique for measuring fast surface states

A technique is presented which measures the number of fast states (/cm²) between (flat band) φ_s = 0 and φ_s = 2φ_B using a high frequency C ? V and d.c. ramp I ? V tracing of any MIS capacitor. For cases where fast state densities near flat band are insignificant, the true flat band point V(φ_s = 0) is obtained from the high frequency C ? V curve. Then from the (I ? V) curve the V(φ_s = 2φ_B) point is obtained by graphically measuring off an area = I_max (2kT/q) ln (N_B/ni) between V = V_FB, V = V₁, I = Imax, and I ? V curve. Then the fast state density (N_FS(/cm²)), is obtained from the expression: $\text{Vφ}{}_{\mathrm{<mtext>s</mtext>}}\text{= 2φ}{}_{\mathrm{B}}\text{? Vφ}{}_{\mathrm{<mtext>s</mtext>}}\text{= 0 = 2φ}{}_{\mathrm{B}}\text{+}\text{q}\text{C}{}_{\mathrm{<mtext>ins</mtext>}}\text{[N}{}_{\mathrm{si}}\text{+ N}{}_{\mathrm{FS}}\text{]}$ where all values are known. For cases where significant fast states exist near flat band, the true flat band point can be obtained graphically from the I ? V tracing using any value of surface potential near mid gap calculated from the high frequency capacitance.     

Thermal emission rates and activation energies of electrons at tantalum centers in silicon

The thermal emission rates and activation energies of electrons trapped at the two Ta donor centers in n-type silicon are determined from transient capacitance measurements on Schottky barrier diodes made on phosphorus and tantalum doubly doped silicon crystals. The thermal activation energies are 232 and 472 meV for the two donor levels below the conduction band edge and the pre-exponential factors, A, are both 1.5 × 10¹⁰ sec^?1 in the Ahrrenius equation for the emission rate, $\text{A (}\text{T}\text{300)}{}^2\text{exp}\text{(}\text{> ?ΔE}\text{k}{}_{\mathrm{B}}\text{T}\text{)}$.     

The self-consistent analysis of the on-set of strong inversion in an MOS transistor with double-layer substrate impurity profile

A unique criterion of the surface potential at the onset strong inversion case is obtained from the extension of the single layer case. The criterion is clearly defined by setting of the increasing rate of the total minority carrier concentration Q_n equal to the increasing rate of the total depletion impurity charge Q_B. The same criterion then applies to analyze the on-set strong inversion case for the double layer profile. The expression for the surface potential ψ_s has the form of $\text{(}\text{kT}\text{q}\text{) {l}{}_{\mathrm{n}}\text{(}\text{N}{}_1\text{N}{}_2\text{n}{}_{\mathrm{i}}{}^2$3 ? l_n[1 ? (q(N₁ ? n₂)$\text{W}\text{Q}{}_{\mathrm{B}}\text{)]}}$. The first term is the same as 3 the conventional expression; however, the second term is new. The expression is a continuous function of the width W of first N₁ layer, and gives a consistent prediction in the limiting case for a single N₁ layer. Therefore, the inconsistent prediction of a discontinuity in $\text{ψ}{}_{\mathrm{s}}\text{[=(}\text{kT}\text{q}\text{)l}{}_{\mathrm{n}}\text{(}\text{N}{}_1\text{N}{}_2$)] from the 3 conventional expression in the single layer limit is then removed. The corrected magnitude to the conventional expression increases with the product of N₁N₂, the ratio of ($\text{N}{}_1\text{N}{}_2$) and ($\text{W}\text{x}{}_{\mathrm{<mtext>d</mtext><mtext>1</mtext><mtext>max</mtext>}}$), and the correction will give a positive M (negative) value as N₁ > N₂(N₂ > N₁).     

Lead telluride-lead tin telluride heterojunction diode array

PbTePb_0·80Sn_0·20Te heterojunction diode arrays have been fabricated from layers grown by the liquid phase epitaxy technique on Pb_0·80Sn_0·20Te substrates. The quality of grown surfaces was found to be dependent upon crystal orientation and substrate surface treatment. Constitutional supercooling has not been identified as a contributing factor. From the capacitance data, an inversion layer is believed to exist at the PbTePbSnTe interface. The diodes exhibit external quantum efficiencies ranging from 15 to 35 per cent without an anti-reflection coating. Junction zero bias impedances vary from 3 to 7 kΩ for a diode are of 6 × 10^?4 cm², yielding R₀A products from 1·8 to 4·2 Ω-cm². The average for an 18-element array is $\text{2·3 × 10}{}^{10}\text{cm Hz}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{/W}$ for 180°FOV a 300°K background.     

Avalanche injection into the oxide in silicon gate-controlled devices—II. Experimental results

An experimental investigation of the avalanche-injection phenomenon is presented in comparison with the theoretical analysis developed in the preceding paper. Experiments are performed on special highly-perfect gate-controlled p⁺-n diodes of different background impurity concentrations (5 × 10¹⁴–5 × 10¹⁵ cm^?3) and gate-oxide thicknesses (0.2–1.0 μm), biased as to obtain electron injection. A good order-of-magnitude (e.g. 2.2 × 10^?3 experimental vs 4.7 × 10^?3 theoretical) agreement is found between theory and experiment for the hot-carrier (electron) injection ratio η_i when experimentally determined maximum interface electric fields $\text{E}{}_{\mathrm{s}}\text{(0)}$ are used and the fitting parameters of the basic theory of Bartelink et al. are maintained. The gate-voltage and the oxide-thickness dependencies of $\text{E}{}_{\mathrm{s}}\text{(0)}$ are consistent with the corresponding observed values of η_i. The “electron-transparency” property of the oxide is defined and investigated finding that it is enhanced by, (i) removing the boron-doped mask oxide and growing a new (clean) oxide and, (ii) decreasing the oxide thickness. Avalanche-stress experiments are also presented and discussed.     

A simple method to test the existence of 2-D partial fraction decomposition

In this paper we give a simple method to test the existence of the decomposition of the form

$\text{A(Z}{}_1\text{, Z}{}_2\text{) A(Z}{}_1{}^{\mathrm{?1}}\text{, Z}{}_2{}^{\mathrm{?1}}\text{B(Z}{}_1\text{, Z}{}_2\text{B(Z}{}_1{}^{\mathrm{?1}}\text{, Z}{}_2{}^{\mathrm{?1}}\text{=}\text{(Z}{}_1\text{, Z}{}_2\text{)}\text{B(Z}{}_1\text{, Z}{}_2\text{+}\text{P(Z}{}_1{}^{\mathrm{?1}}\text{, Z}{}_2{}^{\mathrm{?1}}\text{)}\text{B(Z}{}_1{}^{\mathrm{?1}}\text{, Z}{}_1{}^{\mathrm{?1}}\text{)}$

for a stable two-dimensional transfer function of a recursive filter H(Z₁, Z₂) = A(Z₁, Z₂)/B(Z₁, Z₂).     

Low-frequency noise in Gallium Arsenide MESFETs

We observed the noise spectrum of GaAs MESFETs from $\text{1/?}$ noise through diffusion noise ($\text{1/?}{}^{1.5}$ spectrum) to thermal noise in the frequency range from 20 Hz to 2 MHz. At negative gate bias and floating drain the drain shows thermal noise, but when the gate is biased positively so that it draws gate current it will contribute excess noise to the floating drain. The current noise spectrum $\text{S}{}_{\mathrm{I}}\text{(?)}$ at both the gate and the floating drain shows an relationship, which is common for the Schottky barrier diodes.     

Reverse characteristics of rectifying TeSeCd structures

Current density j, measured as a function of reverse voltage V_R in rectifying TeSeCd structures, is found to be much lower under pulsed than steady voltage conditions. For pulsed voltages, it is observed that lnj is proportional to $\text{(V}{}_0\text{+ V}{}_{\mathrm{R}}\text{)}{}^{\mathrm{<mtext>l</mtext><mtext>n</mtext>}}$, with n between 2 and 3 and V₀ = 0.5 V. This form of dependence is consistent with reduction of the barrier potential by the electric field in the depletion layer. As the applied frequency is increased from 20 to 10⁶ Hz, the measured parallel junction capacitance is found to show an approximate 4 to 1 decrease, with the frequency-dependent portion varying as $\text{(}\text{frequency}\text{)}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}$ at higher frequencies. This is in accordance with theory in the literature for deep acceptors, which are thus considered to be dominant in the selenium of the structures. Trap release times, determined within the depletion layer, are found to decrease with increase in the total concentration of deep acceptors.