Current-voltage characteristics of GaAs p-i-n and n-i-n diodes

Using the same basic equations as Kazarinov et al.[2], but assuming that the product of the electron drift velocity and of the electron lifetime remains constant, we have derived a new formula for the forward d.c. current—voltage characteristic distinguished by the saturated voltage. We have shown that this formula can describe the measured characteristics of some GaAs p-i-n and n-i-n diodes.     

Temperature rise in microwave p-i-n diodes: A computer aided analysis

Results of a computer aided thermal analysis of microwave p-i-n diodes are presented in this paper. The nonlinear heat flow equations in one dimension are solved using the central finite difference method of Leibman's formulation taking into account the temperature dependence of thermal conductivity and specific heat. Results are presented showing the temperature profile inside the device as a function of microwave pulsewidth and power dissipation. The effect of a heat sink on the temperature rise is also shown. The main conclusion arrived at is that the nonlinear thermal properties lead to higher temperature rise in the device and larger thermal time constants than could be expected otherwise. The method used for calculation is applicable for other solid state devices like the TRAPATT, the fast recovery thyristor, and power transistors where similar orders of power levels are involved.     

An extension of the ideal diode analysis for the heavily doped p-n diode

In this paper, an extension of the ideal-diode analysis for the heavily-doped p-n junction diode is proposed. The heavy doping effects such as carrier degeneracy and band gap narrowing are accounted for by using a tractable empirical approximation for the reduced Fermi-energy given by[12] and employing effective intrinsic density. Under the assumption of low-level injection, it is found that the injected minority-carrier current, and the charge storage in the quasi-neutral regions should depend exponentially on values of F(Y), where F(Y) is a function of dopant dentisy at the depletion edge of the quasi-neutral emitter (or) base region of the p-n junction. Results of our calculations of excess hole current for the short base and the long-base diode show significant change from the values predictged by the conventional diode theory.     

Effect of a d.c. electric field parallel to the depletion layer on the microwave oscillations in a p-i-n IMPATT diode

High frequency properties of a p-i-n IMPATT diode have been analysed when an additional d.c. electric field parallel to the area of the junction and perpendicular to the high electric field caused by reverse biasing the device is established in the space charge layer. The transit time required by the carriers to cross the depletion layer is increased due to the increase in the path length caused by the change in the direction of the resultant field while the velocity of the carriers remain saturated. It is found that the frequency for maximum negative resistance decreases with the increase of the additional d.c. electric field.     

A contribution to the theory of the open-circuit photovoltage of an abrupt p-n junction

The theory for calculating the open-circuit photovoltage of an abrupt p-n junction, as originally given by Parrott [5], is generalized to include degeneracy and heavy doping effects. A useful approximation is given which simplifies the general theory considerably. Results are presented for silicon assuming rigid bands with parabolic density of states functions and assuming the free-carrier screening model for the bandgap narrowing.     

Boundary conditions at p-n junctions

A discussion is presented of the relationships between carrier densities at a p-n junction and the junction potential. The major purpose of the work is to discuss the relationship between the Fletcher and Misawa boundary conditions. In addition, a discussion is presented of an extension of the normal boundary conditions to account for current flow within the junction space charge region.     

Characterisation of linearly graded p-n junction

Electrostatic potential, carrier densities and space charge density distributions have been calculated using an iterative scheme for linearly graded p-n junction. It is found that the results obtained from this scheme are close to those given by rigorous numerical formulations, especially at applied forward bias. As an application of this scheme the charge-defined emitter space-charge-layer transit time has been calculated and results compared with those of numerical algorithms.     

Transition-capacitance calculations for double-diffused p-n junctions

A study of the depletion-layer characteristics of double-diffused p-n junctions, formed by successive diffusion of opposite type impurities into a semiconductor, is presented. The general form of the impurity profile is taken to be N(r) = N_SA e^?ar(ar+2k) where N_S, A, a and k are constants and r is the distance. This general form reduces to Gaussian, erfc and two-step diffusion profiles as particular cases. Results are shown graphically for typical values of these constants.It is shown that the double-diffused junctions can be well approximated by equivalent double-exponential profiles in the impurity range of practical interest and C-V relations are obtained analytically. The results obtained are convenient for ready engineering calculations. The accuracy and the range of validity of the approximation are discussed.A simple and accurate analytical method is outlined for the calculation of reverse-biased sidewall capacitance of double-diffused structures, with special reference to the emitter junction of a planar transistor. It is shown that by approximating the impurity profiles by Gaussian distributions, the metallurgical junction formed is given by an ellipse and this leads to a simple evaluation of the sidewall capacitance. An expression obtained for the impurity gradient along the sidewall enables the computation of forward-biased depletion-layer capacitance when the mobile carriers in the depletion region are to be considered.     

Silicon p−n insulator-metal (p-n-I-M) devices

Silicon p-n-I-M devices with thin insulating layers ($\text{thicknesses}\text{? 30}\text{A}\text{?}$), named MTIS devices, have been developed. The two terminal device shows an S-shaped negative resistance characteristics similar to a Schockley diode (or p-n-p-n diode). Typically the threshold and sustaining voltages are 10 ～ 15 and 1.3 ～ 2 volts, respectively. The former however can be controlled by optical illumination. Turn-on time including delay is less than 2 nsec and turn-off time ? 1 nsec or less. A thyristor-like device with its third terminal connected to the n-layer shows switching operation controllable by this terminal. A monolithic linear array of p-n-I-M diodes with 30 μm spacing operates as a shift register through coupling of adjacent diodes. Life of the two terminal devices recorded at present is over 1.5 × 10⁴ hr. These devices can be applied to low power and high-speed electrical switching and also to optical switching and integrated logic circuits.     

Theory of open circuit voltage decay in a p-n junction diode at high injection

A high injection theory of open circuit voltage decay in a p-n junction diode is given. The theory takes into account the saturation of junction voltage at high injections and coupling between emitter and base of the diode. The results are in qualitative agreement with the available experimental results. In particular the theory explains the plateau which has been observed in most experimental results on the open circuit voltage decay at high injections.     

The forward biased,Abrupt p-n junction

The abrupt, forward biased pn-junction is solved very accurately for its terminal characteristics and injection efficiency for all values of forward bias. This is accomplished by using a three-region approach and formulating the transport problem in terms of the local pn-product. Analytic solutions are derived for low, medium and high injection conditions.The low injection regime is characterized by negligible majority carrier density increases. However, in this injection region bulk width modulations due to decreasing transition layer widths modify the standard diffusion model results.The medium injection condition prevails if majority carrier density changes due to injection are significant on the lightly doped side of the junction. This as well as an inreasing bulk voltage drop are taken into account to establish new relationships for injection efficiency, which is decreasing with injection, and the terminal characteristics.The high injection regime involves significant majority carrier modulation in both bulk regions. The injection efficiency becomes a constant which is determined by mobility differences since diffusion currents are negligible. The transition region vanishes in width and its total voltage drop goes to zero. The current through the device is governed by a power law because it is a conductivity modulated resistor.     

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.     

C–V index of hyperabrupt p-n junctions

C–V index n for hyperabrupt p⁺-n junctions with exponentially retrograded n-region has been computed numerically for different values of parameters characterizing the impurity profile and the results have been plotted graphically. Although n is found to vary with the bias across the junction for any given impurity distribution, the maximum value nmax of n is determined only by the ratio of the background concentration to the crossover concentration in the retrograded region. By making this ratio R₀ smaller and smaller, values of n substantially larger than unity can be obtained. Practical considerations, however, limit the maximum value of n to about 10. An empirical relation expressing nmax as a function of the ratio R₀ has been obtained. Calculated results are compared with the values of n measured on hyperabrupt junctions fabricated by a double diffusion process.     

Harmonic distortion in a one-dimensional p-n-p transistor

A method to obtain nonlinear distortion of small a.c. signals in a one-dimensional bipolar transistor is described. The fundamental physical semiconductor equations are the basis from which the small-signal relations are derived. A finite difference scheme is employed to achieve space-discretization; temporal dependence of input-output relations is given in terms of Volterra functional series. The internal distribution of quasi-Fermilevels, potential and excess carrier densities is discussed and some computational results are produced. The influence of frequency, bias point, and external circuit elements on distortion properties is illustrated. Throughout, a common-emitter p-n-p transistor structure is assumed. The theory of Volterra series analysis is briefly summarized.     

A difficulty in the theory of p+-n junction diode noise

It is shown that the usual theory of p⁺-n junction diode noise leads to the following difficulty. The spectrum of the open-circuit noise voltage of the diode does not go to zero fast enough at sufficiently high frequencies, so that the spectrum cannot be integrated from 0 to ∞. The difficulty is removed when the effect of the capacitance C_j of the junction space charge region is taken into account. This is a particular example of a more general result.     

The small signal admittance of carbon implanted p-n diodes

In this paper we consider, in detail, how the introduction of radiation damage centres, produced by the implanation of carbon ions, affects the small signal admittance of silicon p-n diodes. Thermally stimulated capacitance measurements are used to obtain the charge states and activation energies of the damage centres. For carbon doses between 1 × 10¹¹ cm^?2 and 1 × 10¹² cm^?2 two trapping levels are observed with activation energies of E_t?E_v=0·31 eV and E_c?E_t=0·37 eV, and for doses between 5 × 10¹² cm^?2 and 5 × 10¹³ cm^?2 an extra level appears with an energy of E_c?E_t=0·25 eV. A study is made of the effects of these damage centres on the small signal capacitance and conductance of the diodes under forward bias. The results are interpreted in terms of a conductivity modulation effect, and it is proposed that this technique yields valuable information on the profile of the damage centres.     

Shot noise in back biased p-n silicon diodes

An earlier calculation of the noise due to generation of carriers in the space charge region in a p-n silicon diode by Lauritzen and by Scott and Strutt is corrected for the fact that the field distribution in the space charge region of a p-n junction is linear instead of uniform. If the noise is expressed as S_I(f) = 2eIΓ², we find $\text{Γ}{}^2\text{=}\text{11}\text{15}$ in a p⁺n or n⁺p junction, instead of $\text{Γ}{}^2\text{=}\text{10}\text{15}$ found previously.     

Crystal damage and the properties of implanted p-n junctions in silicon

The influence of crystal damage on the properties of implanted p-n junctions has been studied by variation of the amount of initial damage, variation of the recovery process, and variation of the residual damage. This was done by carrying out implantations at - 196, 25 and 700°C with 10¹⁵ B⁺/cm² at an energy of 50 keV, and at 25°C with 10¹⁵ BF₂⁺ at an energy of 250 keV and 10¹⁵ Ga⁺/cm² at an energy of 70 keV. Substrate orientations of both 〈111〉 and 〈100〉 were used, and annealing was done in a temperature range between 400 and 1100°C. Gettered as well as non-gettered slices were used for 〈111〉 oriented substrates. The diode properties were analyzed with the aid of Shockley-Read-Hall recombination statistics. Depending upon crystal history and processing, different traps are found to dominate the reverse current. Traps caused by the gettering of contamination as well as those caused by the damage itself play a role. The number of traps is found to be smaller than 10¹²/cm³ for well annealed diodes, resulting in a reverse current density of 0.2 nA/cm² at 1 V reverse bias.     

Hot photo-carrier and hot electron effects in p-n junctions

When a p-n junction of semiconductor (with bandgap energy E_g) is illuminated by light beam (with photon energy hv) in the condition of E_g>hv, such as in Ge p-n junction illuminated by CO₂ laser beam, an electromotive force (emf) was induced between the terminals of the p-n junction, which indicated the opposite polarity to the ordinary photovoltaic effect like a solar cell. Such an anomalous photovoltaic phenomenon was explained by an optically excited hot carrier effect, through the following experiment with electrical excitation. Using a rod of n- or p-type Ge with a p-n junction at the surface of its center and an ohmic contact at each terminal of the rod, the same kind of phenomena was observed when electric field is applied along the length of the rod. The perpendicularly induced voltage or current had the same polarity instead of the reverse change of the applied electric field, and increases with increasing the applied field strength. The perpendicularly induced emf was caused by warm or hot carriers crossing the potential barrier of the p-n junction, which is very sensitive to the departure from thermally equilibrium velocity distribution of carriers.     

Semiempirical determination of avalanche breakdown temperature parameters in p-n junctions

A method is proposed which permits the determination of the electric field dependence of the ionization coefficient at any temperature. Relative simple semiempirical expressions for the ionization coefficients α_n and α_p for electrons and holes as a function of electric field and temperature are derived. This is applied to express the avalanche breakdown voltage (U_B) and its temperature coefficient (β) as a function of impurity density or concentration gradient for abrupt and linearly graded p-n junctions, and of temperature. The results for U_B and β obtained from these expressions compare satisfactorily with exact numerical results. It is confirmed (both theoretically and experimentally) that β(T) exhibits a maximum at a definite temperature and that U_B (T) deviates significantly from a linear temperature dependence.