Doping effects on the band structure in n-type silicon at 300 K

Based on two screened donor potential models and taking into account the electron-electron interaction effect in the electron-donor interaction, the band-gap narrowing (BGN) in n-type doped silicon at 300 K is investigated. The BGN effect is expressed in terms of physical BGN (ΔE_g), a change in density of conduction-band states (Γ_n) and the change in effective electron (hole) mass (γ_n (γ_p)). In fact, electrical BGN is found to be given by $\text{ΔE}{}_{\mathrm{<mtext>g,\; elec.</mtext>}}{}^1\text{= ΔE}{}_{\mathrm{<mtext>g</mtext>}}\text{+ Γ}{}_{\mathrm{n}}\text{γ}{}_{\mathrm{n}}\text{+ Γ}{}_{\mathrm{p}}\text{+ ΔE}{}_{\mathrm{<mtext>g</mtext><mtext>,\; fd</mtext>}}\text{? ΔE}{}_{\mathrm{<mtext>g</mtext>}}\text{+ Γ}{}_{\mathrm{n}}$, where ΔE_g,fd represents the Fermi-Dirac statistics effect. Our results of $\text{ΔE}{}_{\mathrm{g}}\text{and}\text{ΔE}{}_{\mathrm{tg}}\text{,}\text{elec.}{}^1$ agree fairly with corresponding observed results, and the large values of $\text{Γ}{}_{\mathrm{n}}\text{? ΔtE}{}_{\mathrm{g}}\text{,}\text{elec.}{}^1\text{? ΔE}{}_{\mathrm{g}}$ obtained at high donor concentration are in good agreement with a qualitative discussion given by Marshak and Van Vliet. Finally, the present results for the effective intrinsic-carrier concentration n_ie are compared with corresponding results observed by Tang.     

Excess capacitance and non-ideal Schottky barriers on GaAs

Non-ideal $\text{1}\text{C}{}^2$ vs V plots showing curvature concave downwards can be transformed into linear $\text{1}\text{(C ? C}{}_0\text{)}{}^2$ vs V plots by determining the excess capacitance, C₀, as the intercept of a C vs $\text{(V + V}{}_{\mathrm{d}}\text{)}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$ plot, where V_d is the diffusion potential. The corrected curves indicate a uniform doping profile in agreement with independent Van der Pauw measurements. An analysis of the possible significance of C₀ indicates that its value can be used as an approximate quality index for materials fabricated by different methods.     

Thermal emission rates and capture cross-section of majority carriers at titanium levels in silicon

The thermal emission rates and capture cross-sections of majority carriers on the titanium associated levels in the depletion region of reverse biased silicon p⁺n and n⁺n junctions have been investigated using the admittance spectroscopy technique and the dark capacitance transient method. We have found three levels associated with titanium in silicon. Its thermal activation energies are E_c ?238 ± meV, E_c ?512 ± 5 meV and E_v + 320 ± 5 meV.For the E_c ?238 meV and E_v + 320 meV levels, the thermal capture cross-sections are independent of the temperature: σ_n = 1.01 × 10^?4 cm² and σ_p = 1.55 × 10^?15 cm². The electron capture cross-section on the E_c ? 512 meV levels shows a slight dependence with the temperature, $\text{σ}{}_{\mathrm{n}}\text{= 2.01 × 10}{}^{\mathrm{?16}}\text{(}\text{T}\text{300}\text{)}{}^{\mathrm{?(0.35\pm 0.1)}}\text{cm}{}^2$ in the [120–240 K] range, which can account for the nonradiative multiphonon emission process.     

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).     

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.     

The effect of built-in drift field and emitter recombinations on FCVD of a p-n junction diode

This paper discusses the Forward Current induced open circuit Voltage Decay (FCVD) of a p-n junction diode including the effects of recombinations in the emitter as well as the built-in drift fields in the base and in the emitter. The analysis is based on the quasi-static approximation (QSA) of the carrier profiles in the emitter. It is shown that the emitter effects on FCVD is completely determined by J_EO, the dark saturation current in the emitter. The value of J_EO in general, depends on the heavy doping effects in the emitter, the drift field in the emitter, emitter thickness and surface recombination velocity at the emitter surface. It is shown that for a diode with retarding drift field in the base, emitter recombinations play a very significant role in FCVD. The decay time constant for large values of time in this case is given by $\text{τ}{}_{\mathrm{<mtext>eff</mtext>}}\text{= τ}{}_{\mathrm{B}}\text{/[1 + ?}{}_{\mathrm{B}}{}^2\text{? (a ? ?}{}_{\mathrm{B}}\text{)}{}^2\text{],}\text{where}\text{a = J}{}_{\mathrm{EO}}\text{/J}{}_{\mathrm{BO}}\text{, ?}{}_{\mathrm{B}}$ is the drift field parameter in the base. The higher value of a, the faster is the voltage decay. For accelerating fields in the base, the time constant for large values of time is independent of emitter recombinations and is given by $\text{τ}{}_{\mathrm{<mtext>eff</mtext>}}\text{= τ}{}_{\mathrm{B}}\text{/(1 + ?}{}_{\mathrm{B}}{}^2\text{)}$. However, the decay rate for small values of time is strongly affected by emitter recombinations for both types of the field; the higher the emitter recombinations, the faster is the initial rate of the voltage decay. For extremely strong drift fields in the base, QSA in the emitter is not valid. The coupled continuity equations are solved with the conditions $\text{?}{}_{\mathrm{B}}{}^2\text{? τ}{}_{\mathrm{B}}\text{/τ}{}_{\mathrm{E}}$ and an analytic expression for FCVD is derived. It is seen that FCVD for strong base fields is determined solely by emitter lifetime τ_E except for small values of time of the order of a few τ_E.     

Space-charge-limited currents in insulators containing traps distributed in energy

The transition from the ohmic current to space-charge-limited current (SCLC) strongly depends on the presence of traps in insulators. Generally these traps are not localized at a single energy, rather they are distributed in energy. To account for the effect of the distribution of traps around a single energy, say E_t, on SCLC, we propose a new distribution which broadly encompasses all the characteristics of the Gaussian distribution and at the same time is amenable to usual methods of analysis. The proposed distribution function is

$\text{N}{}^{\mathrm{E}}\text{= N}{}^0\text{exp}\text{[(E?E}{}^{\mathrm{t}}\text{)/kT}{}^{\mathrm{t}}\text{]}\text{{exp[(E?E}{}^{\mathrm{t}}\text{)/kT}{}^{\mathrm{t}}\text{+1}}{}_2$

where T_t is the characteristic temperature of the distribution. Applying the Regional Approximation Method the current-voltage characteristics for shallow as well as deep traps are obtained with the proposed distribution.     

Energy levels and concentrations for platinum in silicon

The energy levels and electrically active concentrations of platinum in silicon have been measured by Hall techniques. Analysis shows platinum to have two electrically active sites. The usual site N_PtI (assumed to be substitutional) predominates (>80%) and has two levels, a donor at E_v+0·28 eV, degeneracy γ_I⁺=2 in p-type material and an acceptor at E_c ?0·20 eV, $\text{γ}{}_{\mathrm{<mtext>I</mtext>}}{}^{\mathrm{?}}\text{=}\text{1}\text{6}$, in n-type material. However a second platinum site exists, and is present to a concentration N_PtII of about 10 per cent with an acceptor level at $\text{E}{}_{\mathrm{<mtext>v</mtext>}}\text{+ 0·42}\text{eV}\text{(γ}{}_{\mathrm{<mtext>II</mtext>}}\text{=}\text{1}\text{8}\text{)}$. The physical nature of this Pt associated site is unknown.Neutron activation analysis has been used to determine total atomic platinum concentrations for diffusions from 800 to 1250°C. These results, in conjunction with Hall measurements, show the electrical activity to be very high. Previous studies on platinum are reviewed and compared to the result of this work.     

Current transport mechanisms of electrochemically deposited CdS/CdTe heterojunction

The dark current transport mechanism in electrochemically deposited n-CdS/p-CdTe thin film heterojunctions is investigated. The forward current measured in the temperature range between 200° and 305°K can be expressed as J_f = J₀(T) exp (AV) and the reverse current can be expressed as $\text{J}{}_{\mathrm{r}}\text{= ?CV exp ?CV[?λ(V}{}_{\mathrm{d}}\text{?V)}{}^{\mathrm{<mtext>?(</mtext><mtext>1</mtext><mtext>2</mtext><mtext>)</mtext>}}\text{]}$. The current mechanisms are consistent with a multi step recombination-tunneling model.     

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.     

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.     

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).     

Energy levels and degeneracy ratios for magnesium in n-type silicon

The energy levels and degeneracy ratios of magnesium in n-type silicon have been determined by Hall effect measurements with the least square method. Magnesium ions appear to occupy two different sites and show different electrical properties. The first is amphoteric and exhibits an acceptor level at E_c ? 0.115 eV (±0.002 eV), degeneracy ratio γ_I^? = 2.5 as well as a donor level at E_c ? 0.40 eV (±0.01 eV), γ_III⁺ = 1. The second exhibits a donor level at E_c ? 0.227 eV (±0.004 eV), degeneracy ratio $\text{γ}{}_{\mathrm{II}}{}^{\mathrm{+}}\text{=}\text{1}\text{2.5}$. The physical nature of these Mg associated site is unknown.     

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     

Hot electron noise in n-channel JFETs between 150 and 300°K

The noise parameter $\text{α}{}_{\mathrm{T}}\text{=}\text{S}{}_{\mathrm{I}}\text{(?)}\text{(4kTg}{}_{\mathrm{m}}\text{)}$ of n-channel JFETs was measured as a function of the voltage V_GS?V_P with the temperature T as a parameter between 150 and 300°K. It was found that α_T could be approximated by the formula $\text{α}{}_{\mathrm{T}}\text{? (}\text{300}\text{T}\text{)α}{}_{300}$, indicating the presence of hot electron effects.     

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.     

Thermal noise measurements on space-charge-limited hole current in silicon

Silicon pvp devices were manufactured whose d.c. and a.c. properties conform closely to the simple model of trap-free space-charge-limited current (sclc) of holes. Room temperature measurements of the spectral density of the noise from 10 kHz to 10 MHz at various operating points reveal a white noise component whose value is given by $\text{S}{}_{\mathrm{v}}\text{ 〈Δν}{}^2\text{〉 Δ? = β · 4kT (V/I),}\text{where}\text{β = 1.0±6\%}$, and V/I is the d.c. resistance of the device at the operating point. At high operating points, where the d.c. characteristic agrees quantitatively with the dependence $\text{J = (}\text{9}\text{8}\text{)??}{}_0\text{μV}{}^2\text{/W}{}^3$ of pure sclc, the results reduce to S_i = α · 4kT (?I/?V), with α = 2.0±7%.     

Thermal noise in inversion layers

Experiments on uniform channel (V_DS ≈ 0) MOSEFTs with resistance R_DS show that the thermal noise is given by the normal Nyquist formula $\text{v}{}_{\mathrm{n}}{}^2\text{= 4}\text{kT}\text{R}{}_{\mathrm{DS}}\text{Δf}$. The modification to this formula which has been proposed is thus not necessary. The discrepancies are discussed.     

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.