Drift of the breakdown voltage in p-n junctions in silicon (walk-out)

A quantitative model for the time behaviour of the walk-out phenomenon in planar p-n junctions is given. The injection of hot carriers into SiO₂ and subsequent trapping of part of them is assumed to be the origin of the walk-out. The model is found to be in reasonable agreement with the experimental results on both p⁺?n and n⁺?p junctions. The parameters in the model are discussed in relation with the experiments.     

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.     

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.     

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.     

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.     

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.     

The effect of photogenerated carriers on the mean time delay for avalanche breakdown in p-n junctions

Avalanche breakdown in p-n junctions is preceded by a delay time between application of an overvoltage and the actual initiation of an avalanche discharge. The mean of this delay time has been studied as a function of photogeneration in p-n junction devices. Results agree well with McIntyre's theory of breakdown probability. The data further indicate that the probability of any given carrier initiating breakdown is independent of carrier concentration over the three orders of magnitude investigated.     

Some investigations on secondary breakdown in p-n junctions considering the effect of thermally generated carriers

The V-I characteristic of a p-n junction under breakdown is calculated taking the thermally generated carriers into account. The current density distributions computed under different conditions have been given. The light emission and other characteristics reported by Chiang and Lauritzen and others have been explained.     

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.     

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.     

Alteration of diffusion profiles in semiconductors due to p-n junctions

Concentration profiles of diffusing species in semiconductors are calculated including the effects of the electric fields at p-n junctions. The junction electric field can significantly alter diffusion behavior near the junction at the growth temperature, and thus affect dopant uniformity and junction placement for some commonly occurring epitaxial growth conditions. The junction electric field affects diffusion in the same manner as the internal electric field that results from a dopant concentration gradient. The field can produce diffusion profiles with either enhanced or retarded diffusion rates at the junction and pile-up or depletion of the diffusing species near the junction. Several experimental examples for diffusion of Mg across a p-n junction in (Al, Ga). As during growth by liquid phase epitaxy are presented.     

Experimental results on transient space charge limited currents in p-n junctions

This paper shows the first experimental evidence of transient space charge limited currents in totally depleted surface barrier p-n junctions. For this experiment surface barrier diodes excited by electrons bursts supplied by a pulsed accelerator were used.     

Fabrication and characterization of p-n junctions based on ZnO and CuPc

p-n Junctions based on zinc oxide (ZnO) and copper-phthalocyanine (CuPc) were fabricated using pulsed laser deposition and thermal evaporator techniques, respectively. Current-voltage (I-V) characteristics of the ZnO-CuPc junction showed rectifying behavior. Various junction parameters such as barrier height and ideality factor were calculated using I-V data and observed to be 0.63 ± 0.02 eV and 4.0 ± 0.3, respectively. Cheung and Norde’s method were used to compare the junction parameters obtained by I-V characteristics.     

Avalanche breakdown voltage of multiple epitaxial pn junctions

Calculation of the peak electric field at breakdown for two-sided step junctions with arbitrary doping levels on each side is presented. The theoretical predictions are compared with the results of experimental breakdown studies of a series of carefully prepared and characterized high voltage diodes. Calculations based upon the ionization coefficients determined by Van Overstraeten and De Man are shown to be in better agreement with experiment than those based on the ionization coefficients of Lee et al.     

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.     

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.     

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.     

Effect of reabsorbed recombination radiation on the saturation current of direct gap p-n junctions

The radiative transfer theory for semiconductors recently developed is applied to p-n junctions under conditions of low level injection. By virtue of the interaction of the radiation field with free carriers across the depletion layer or space charge region, the saturation current density j₀ in Shockley's expression j = j₀[exp (qV/kT) ? 1] for the diode current is reduced at high doping levels from the customary value which neglects radiation effects altogether. While the effect is insignificant in p-type material, it is noticeable in n-type material owing to the small magnitude of the electron effective mass in direct gap III–V compounds. At an equilibrium electron concentration of 2 × 10¹⁸ cm^?3 in GaAs, a reduction of j₀ by 15% is predicted.     

On the small-signal equivalent circuit of p-n junctions in the condition of finite carriers multiplication

A new version of the equivalent circuit of the space-charge region of the reverse biased p-n junction is evaluated and the expressions for the circuit parameters are given. The basic idea is to separate the equivalent circuit in to the “conductive” and “displacement” branches and in this way the equivalent circuit parameters have physical meaning. The results are applicable to conditions of the finite multiplication factors and unequal ionization coefficients in a wide range of frequency and in the presence of the generation of carriers (thermal or outside induced) in the space-charge region. The numerical results for two complementary abrupt silicon p-n junctions and for low-frequency are given. The equivalent circuit of the multiplication noise source of the p-n junction is discussed.     

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.