Voltage dependence of the differential capacitance of a p +-n junction

The dependences of the differential capacitance and current of a p ⁺-n junction with a uniformly doped n region on the voltage in the junction region are calculated. The p ⁺-n junction capacitance controls the charge change in the junction region taking into account a change in the electric field of the quasi-neutral n region and a change in its bipolar drift mobility with increasing excess charge-carrier concentration. It is shown that the change in the sign of the p ⁺-n junction capacitance with increasing injection level is caused by a decrease in the bipolar drift mobility as the electron-hole pair concentration in the n region increases. It is shown that the p ⁺-n junction capacitance decreases with increasing reverse voltage and tends to a constant positive value.     

Differential capacitance of a <Emphasis Type="Italic">p</Emphasis><Superscript>+</Superscript>-<Emphasis Type="Italic">p</Emphasis> junction

The differential capacitance of a p ⁺-p junction formed by charge redistribution near the junction, has been investigated taking into account the electric field in the quasi-neutral p region. The dependence of the capacitance and current of the p ⁺-p junction on its voltage is obtained. It is shown that a change in the sign of the p ⁺-p-junction capacitance with an increase in the injection level is caused by a decrease in the bipolar drift mobility in the p-type region. It is also demonstrated that a change in the sign of the p ⁺-p-junction capacitance with an increase in the reverse voltage determines the charge reduction near the junction, as the increase in the negative charge of acceptor ions predominates over the increase in the positive charge of holes.     

Current dependence of capacitance of germanium p +-p junctions in the temperature range of 290–330 K

The current dependence of differential capacitance of germanium p ⁺-p junctions with the p-region resistivity of 45, 30, and 10 Ω cm is investigated in the temperature range of 290–350 K. It is shown that the current dependence of the p ⁺-p-junction capacitance varies with an increasing junction temperature. At the temperature of 290 K, the capacitance decreases with an increasing reverse current, changes sign from positive to negative, and increases with the forward current. At 330 K, the capacitance decreases to the lowest positive value with an increasing reverse current and changes sign to negative with increasing the forward current. At 310 K, the p ⁺-p-junction capacitance can change the sign from positive to negative with increasing the forward and reverse current. It is assumed that the positive and negative p ⁺-p-junction capacitance is caused by the change in the junction-region charge by the external voltage.     

On the forward current-voltage characteristics of p+-n-n+ (n+-p-p+) epitaxial diodes

The forward-biased current-voltage characteristics of p⁺-n-n⁺ and n⁺-p-p⁺ epitaxial diodes are derived theoretically. Effects of the energy-gap shrinkage, the high-low junction built-in voltage, the high-level injection, and the minority-carrier life time on the forward-biased current-voltage characteristics are included. Good agreements between the theoretically derived results and the experimental data of Dutton et al. are obtained. The developed theory predicts that the leakage of the high-low junction is dominated by the recombination of minority carriers in the highly doped substrate, not by the recombination of minority carriers in the high-low space charge region, which is opposite to the previous prediction of Dutton et al.     

Effect of neutron irradiation on the structure of silicon p-n junctions of voltage limiters

Changes in capacitance-voltage characteristics of p-n junctions with a linear or close-to-linear uncompensated charge distribution under neutron irradiation are analyzed. It is confirmed that an intrinsic conductivity region is formed near the p-n junction due to such exposure. Empirical formulas are derived which describe the dependence of the sizes of this region and the effective concentration gradient of uncompensated charge on the neutron fluence in a wide range of initial (before neutron irradiation) concentration gradients (from 3 × 10¹⁸ to 2 × 10²⁰ cm^?4) and initial silicon resistivities (from 0.3 to 2 Ω cm).     

Mechanism of reverse current in the Al/p-InP schottky diodes

Reverse current-voltage characteristics of the Al/p-InP Schottky diodes based on Zn-doped InP epilayers were measured in relation to bias and temperature. Temperature dependence of reverse current is characterized by the activation energies of 0.75 and 0.51 eV in the high-temperature region and at temperatures T<280 K, respectively. Results are explained by the phonon-assisted tunneling generation of charge carriers from the surface states of a semiconductor with regard to the Frenkel emission mechanism. It is found that, in the low-temperature region, tunneling occurs via the centers with energy levels of 0.51 eV. Comparing experimental results with theory, we estimated electric-field strength in the barrier at (5–13)×10⁷ V/m and the surface density of the hole charge in the boundary layer of the semiconductor.     

On the maximum thickness of the space-charge region of reverse biased <Emphasis Type="Italic">p</Emphasis><Superscript>+</Superscript>-<Emphasis Type="Italic">n</Emphasis> junctions with a positive bevel

Two-dimensional potential and electric-field strength distributions in edge regions of sharply asymmetric reverse biased p ⁺-n junctions with a positive bevel were numerically simulated. It was shown that the maximum thickness of the space-charge region W _nM nonmonotonically depends on the angle θ between the bevel surface and junction plane: the function W _nM (θ) reaches a maximum at θ decreasing from 60° to 35° as the parameter Q _s /ɛ _s ɛ₀ EvM increases from 0 to 0.02 (here Q _s is the surface charge density, ɛ _s ɛ₀ is the absolute permittivity of the semiconductor, and E _vM is the maximum field strength in the space-charge region of the p ⁺-n junction far from the bevel). The results obtained may be useful in designing high-voltage thyristors based on Si, SiC, and other materials.     

Modified drift field model for high-low transition in solar cells

A theoretical discussion is presented for the understanding of the back surface pp⁺ transition used in solar cells. It is shown that quasi-neutrality of space charge is a good approximation if the back surface diffusion is fairly deep. The error involved in the drift field model developed by assuming a quasi-neutrality of the space charge is compared with that inherent in the abrupt high-low junction model. The analysis shows that the back surface boundary, when measured from the heavily doped p⁺ side, effectively exists at a distance much larger than the impurity diffusion depth and the recombination current in the base is always less than its value estimated from the abrupt junction model. The voltage in the pp⁺ transition is due to the change in electric field by the excess carriers injected by light and drops across those regions of the cell where the injected carrier density is appreciable.     

Doping and temperature dependences of minority-carrier diffusion length and lifetime deduced from the spectral response measurements of p-N junction solar cells

The minority-carrier diffusion length in the base region of p⁺?n (n⁺?p) junction solar cells has been deduced from the relative spectral response in the long wavelength. The doping and temperature dependences of minority-carrier diffusion length have also been characterized. It has been shown that the minority-carrier diffusion length is slightly increased with increasing temperature and is decreased with increasing doping concentration. Based on the known minority-carrier diffusivity as functions of doping concentration and temperature, the doping and temperature dependences of minority-carrier lifetimes have been deduced. It has been verified that the empirical relationship between minority-carrier lifetime and doping concentration deduced by other method is in good agreements with our experimental measurements. Moreover, it has been shown that the minority-carrier lifetime is increased with increasing temperature, which is consistent with that measured by the open-circuit voltage decay (OCVD) method.     

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.     

Electron-beam-induced conductivity in self-organized silicon quantum wells

Electron-beam diagnostics are used to study self-organized quantum wells which form within ultrashallow silicon p ⁺-n junctions under the conditions of nonequilibrium boron diffusion. The energy dependence and current-voltage characteristics of the electron-beam-induced conductivity are investigated with relative dominance of both longitudinal and transverse quantum wells, which are oriented parallel and perpendicularly to the p-n junction plane, respectively. Current-voltage characteristics of the electron-beam-induced conductivity are exhibited for the first time with both reverse and forward biasing of the silicon p ⁺-n junction. This became possible because of the presence of self-organized transverse quantum wells within the ultrashallow p ⁺ diffusion profile, while self-organized longitudinal quantum wells promote the appearance of electron-beam-induced conductivity only when the p ⁺-n junction is reverse-biased. The distribution of the probability for the separation of electron-hole pairs across the thickness of the crystal derived from the energy dependences of the electron-beam-induced conductivity reveals effects of the avalanche multiplication of the nonequilibrium carriers as a result of the spatial separation of electrons and holes in the field of a p ⁺-n junction that contains self-organized transverse quantum wells. Fiz. Tekh. Poluprovodn. 33, 851–857 (July 1999)     

Numerical analysis on abnormal thyristor forward voltage increase due to heavy doping in gated p-base layer

An abnormal forward voltage increase was observed for a p-base gated double diffused n⁺pn^?p⁺ high power thyristor with high impurity concentration at the n⁺-p emitter-base junction. Accurate numerical analysis shows that heavy doping effects are the most responsible mechanism for the abnormality and that depletion layer formation at the center junction accompanies it.It will be shown that appropriate control of the impurity concentration at the emitter-base junction is necessary to avoid this abnormality by realizing the common base transistor current gain of greater than 0.73 for n⁺n^?-portion.     

Numerical modeling of looped C-V Characteristics in Ap+n junction containing mid-bandgap electron traps

The capacitance of p⁺n junctions containing traps or deep centers depends on the time variation of the applied reverse voltage. Capacitance changes results from the time dependent variation of the density of traps filled with electrons within the depletion region. If a cyclical reverse voltage in applied to the junction, capacitance hysteresis due to the time-dependent charge variation within the depletion region should be observed. The hysteresis loops, as a function of the bias drive rate, temperature, and total concentration of traps provide some information on the characteristics of the traps.This paper presents a numerical analysis of looped C-V characteristics in a p⁺n junction containing midbandgap electron traps and also discusses the variation of loops as a function of the bias drive rate, dV/dt, total concentration of traps, N_T, and emission rates of electrons and holes, e_n and e_p, based on our numerical modeling.     

A low-high-junction solar-cell model developed for use in tandem cell analysis

A comprehensive low-high (L-H) junction solar cell model has been developed. It accounts for actual solar spectrum related photogeneration of carriers in all regions of the n-p-p⁺ cell and allows for any value of rear surface-recombination-velocity (SRV). In typical GaAs L-H junction solar cells, photogeneration in the p⁺ region, but not the p region, is found to be negligible. The L-H junction's space-charge-layer recombination current density is also negligible. Assigning a non-infinite value of rear surface SRV makes this model applicable to tandem multi-junction structures made from materials with different band gaps.     

A dynamic model of the p-n-n+ step recovery diodes for the numerical analysis of pulse circuits

A new p-n-n⁺ diode model for circuit transient analysis is developed. In contrast to existing circuit models, this model reflects all step-recovery diode (SRD) effects during switching on and off, including “ramp” of slow recovery phase. It is accomplished by taking into account the dynamic physical phenomena in the p-n-n⁺ diodes when switched. A non-linear dynamic diffusion capacitance of the diode model is determined by the dependence of the instantaneous base charge on the instantaneous diode voltage.The accuracy of the presented model is verified by comparison of the calculated and measured wave forms of some pulse circuits.The present model has been proved to be more accurate than SRD models previously published.     

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.     

Minority carrier lifetimes in silicon solar cells determined from spectral and transient measurements

Measurements of the spectral collection efficiency and short circuit current decay rate following an X-ray pulse have been made on three types of single crystal silicon solar cells. The cell types were n⁺ - p, p⁺ - n, and p⁺ - n - n⁺ with base resistivities of 0.3, 10 and 10 Ω-cm, respectively. Minority carrier lifetimes were determined from both experiments using analytical or device code calculations, as required. For the n⁺ - p and p⁺ - n cells, nominal lifetimes of 2 and 5 ωsec, respectively, were obtained. A lifetime greater than 100 ωsec was inferred for the p⁺ - n - n⁺ device. This value represents a minimum estimate since our analysis is inaccurate when the diffusion length exceeds the cell thickness, as is the case here. The difference in base lifetime for the p⁺ - n and p⁺ - n - n⁺ structures is attributed to gettering during the phosphorus diffusion to form the back surface field layer.     

Junction potentials of strongly illuminated n+ - p - p+ solar cells

The low-junction (LHJ) model is applied to an n⁺ - p - p⁺ solar cell having finite dimensions, in order to investigate its performance under intense illumination. Ambipolar transport equations are solved in the three sections of the cell using appropriate boundary conditions. Expressions for junction currents are derived, and the junction potentials under open-circuit conditions are computed by the Newton-Raphson method.The theory presented here includes the effects of high level injection. The generalized current density equations which are derived here for an n⁺ - p - p⁺ device are shown to reduce to the ideal Shockley diode equation with appropriate modifications. The effects of p - p⁺ low-high junction on the open-circuit voltage of the cell are explained. The theoretical results of this paper are consistent with the experimental results of others.     

The open-circuit voltage of back-surface-field (BSF) p-n junction solar cells in concentrated sunlight

Simple analytical expressions for the open-circuit voltage of the n⁺?p?p⁺ and p⁺?n?n⁺ BSF solar cells, which are valid for both the low- and high-levels of optical illumination, are derived. Based on the principle of superposition the open-circuit voltage of both the n⁺?p?p⁺ and p⁺?n?n⁺ solar cells are expressed in terms of the short-circuit current and the known saturated dark current. Effects of the high-low junction doping, the energy-gap shrinkage, and the dimensions of the BSF solar cells on the open-circuit voltage are included. The numerical results of the derived expressions are found to be in good agreement with the exact numerical analysis of Fossum et al. The optimal design considerations based on the known characteristics of the open-circuit voltage are also discussed.