A comparison of simple and numerical two-dimensional models for the threshold voltage of short channel MOSTs

The threshold voltage for short channel MOSTs has been derived by two-dimensional numerical computation. The results can be expressed in normalised form with the reduced threshold voltage, V_T ? V_FB ? 2φ, given as a fraction of the reduced long-channel threshold voltage, V_T∞ ? V_FB ? 2φ, where V_FB and φ are the flat-band and bulk Fermi potentials respectively. An extremely good fit to the theoretical predictions is then given by

$\text{V}{}_{\mathrm{T}}\text{?V}{}_{\mathrm{FB}}\text{?2φ}\text{V}{}_{\mathrm{T\infty }}\text{?V}{}_{\mathrm{FB}}\text{?2φ}\text{=1?}\text{aW}{}_{\mathrm{sr}}\text{L}{}^{\mathrm{b}}$

where

$\text{a?0.94?0.17}\text{W}{}_{\mathrm{s}}\text{rj}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$

$\text{b?0.90?0.66}\text{log}{}_{10}\text{W}{}_{\mathrm{s}}\text{r}{}_{\mathrm{j}}\text{+0.37}\text{X}{}_{\mathrm{ox}}\text{W}{}_{\mathrm{s}}$

where the junction depth, r_j, and oxide thickness, x_ox, are expressed as fractions of the source depletion layer thickness, W_s, and where the channel length, L, is given as a fraction of the one-dimensional theoretical spread, W_sr, of a depletion region around a cylindrical step-junction.This empirical expression is valid over a wide range of normalised device geometries (0.4 < L/W_sr < 40, 0.1 < r_j/W_s < 10, 0.01 < x_ox/W_s < 0.2) and, except for very shallow junctions (r_j/W_s ? 1), differs only slightly from the simple model proposed by Yau. A comparison of the theory with experimental results shows good agreement for MOSTs fabricated with channel lengths between 2 and 5 μm using conventional photolithography.     

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).     

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).     

Equivalent temperature of hot electrons

The two extensions of the Einstein relation qD_par = kT_eμ_par and qD_par = kT′_eμ′_and define, in the case of hot electrons, two different electron temperatures T_e and T′_e. It is shown here that the two interpretations are fully equivalent in that they lead to the noise expressions $\text{S}{}_{\mathrm{I}}\text{(0)=4kT(}\text{I}\text{V}\text{and}\text{S}{}_{\mathrm{I}}\text{(0) = 4kT′}{}_{\mathrm{e}}\text{(}\text{d}\text{I}\text{d}\text{V}\text{)}$, respectively. The T′_e interpretation, however, is slightly favored, since it leads to the simple expression $\text{S}{}_{\mathrm{V}}\text{(0) = 4kT′}{}_{\mathrm{e}}\text{/}\text{d}\text{I}\text{d}\text{V}\text{)}$ for the open-circuit noise.     

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.     

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.     

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.     

On the influence of substrate doping on the input conductance and the induced gate noise in MOSFETs

The input conductance g_gs and its associate noise spectrum $\text{S}{}_{\mathrm{g}}\text{(?)}$ in MOSFETs is evaluated numerically and expressed in terms of a doping parameter φ. The results augment earlier calculations by Klaassen. For g_gs a function F₂(φ) is introduced that depends only slowly on φ and on the bias voltages V_g′ and V_b′. Expressing the noise in terms of the parameter $\text{β =}\text{S}{}_{\mathrm{g}}\text{(?)}\text{(4kTg}{}_{\mathrm{gs}}\text{)}$, it is found that β is practically independent of φ, V_g′ and V_b′.     

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.     

A new approach to the determination of MS-barrier heights from photoelectric data and/or an alternative way to determine the value of the Richardson constant

The short circuit current (I_sc) and the open-circuit voltage (V_oc) of MS-diodes were measured making use of internal photoemission.The Schottky barrier heights were then obtained by the usual extrapolation of Fowler plots [1] corrected according to the operational method presented before [2].Combining the equation for the short circuit current and open circuit voltage of an illuminated junction (from the equivalent circuit) with the equation relating saturation current to barrier height we then sum up alternative methods of using I_sc, V_oc data: (a) Fowler plots using either I_sc or V_oc to deduce φ_B; (b) using I_sc and V_oc (for any wavelength or average over a certain range) to deduce the barrier height φ_B, if the effective Richardson constant $\text{A}{}^7$ (and the tunneling transmission coefficient θ) are assumed known; (c) using I_sc and V_oc to deduce $\text{A}{}^7$ (and then $\text{m}{}^1$ or θ (in the product $\text{θA}{}^7$ if the φ_B values derived from Fowler plots or/and common IV-data (thermal current) are assumed correct. This approach could lead to the determination of several parameters ($\text{A}{}^7$, $\text{m}{}^1$, etc.) as a function of temperature, crystal orientation or for different semiconductors.The interrelation of the methods is shown in flow diagram form. Measurements on Rh-nSi diodes are taken as an example, and the agreement between φ_B values from the different methods is shown to be excellent, if a lower than usual $\text{A}{}^7$ value is used (which follows the published trend of $\text{A}{}^7$ with field strength).The Fowler method is based upon knowledge of the response per incident photon as a function of the wavelength. The importance of monitoring the light actually incident upon the metal interface is pointed out.     

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     

Characteristics of Cr-SiO2-nSi tunnel diodes

The admittance of Cr-SiO₂-nSi tunnel diodes was measured at 195 and 295 K, from which the surface potential ψ_s(V_a) and the energy distribution of the surface states N_ss which communicate with the silicon were determined. By employing these data, the I(V_a) characteristics measured at 77, 195 and 295 K are interpreted as tunneling current consisting of two components. The first is a net electron tunnel current from the Si-conduction band through the oxide into the metal which dominates at room temperature for forward bias V_a greater than 0.4 V. Introducing a simple model of a trapezoidal SiO₂ barrier allows us to calculate the band to band current, resulting in typical values of the barrier height η_o = 0.24 eV and barrier width $\text{d}{}_{\mathrm{o}}\text{= 24}\text{A}\text{?}$. The second component is a net recombination current of electrons from the Si-conduction band into surface states which then tunnel through the oxide into the metal; this component dominates for reverse bias and for small forward bias, especially at low temperatures. It is a current via surface states N_sm which are at the Si-SiO₂ interface but rapidly communicate with the metal, and it is therefore recombination controlled. Together, these components explain the measured bias and temperature dependence of the d.c. current.     

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.     

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%.     

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 $\text{V}{}_{\mathrm{J}}\text{?}\text{4kT}\text{e}$.     

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.     

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.     

The evaluation of interface parameters in MIS structures—I. Theory

The theory relative to the interaction of interface states with majority carriers is reconsidered in the high frequency limit. The admittance of an interface state continuum is examined as a function of surface state energy.It is shown that in the high frequency limit ωτ>1, the energy range of the interface states contributing to the parallel capacitance (C_pT) and the conductance (G_pT) is different. At fixed interface potential u_F, the contribution C_p(u) due to states at potential u is a sharply peaked function, and shifts with increasing frequency from the Fermi level towards the majority carrier band edge. At the same time G_p(u) broadens considerably. Both functions thus can not be used jointly to describe the surface density function if the condition ωτ<1 is not met.An alternative function $\text{(}\text{d}\text{du}{}_{\mathrm{F}}\text{)(}\text{G}{}_{\mathrm{p}}\text{n}{}_{\mathrm{s}}\text{)}$ that peaks near to the Fermi level, independently of the frequency range considered, is proposed. The properties of this function give rise to the extended conductance technique (E.C.T.), which enables one to obtain N_ss and σ_n from the experimental data.The main advantage of the E.C.T. is that the continuum of interface states is accurately probed at the Fermi level with a practically frequency independent resolution.     

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).