High injection phenomena in p+in+ silicon solar cells

A very simple analytic analysis of p⁺in⁺ solar cell structures is undertaken based in the quasi-neutrality condition (n = p), which validity is verified. The only differential equation to be solved in the model is the classical continuity one. Non linearities, appea ronly in the boundary conditions. This model can be applied to p⁺nn⁺ or n⁺pp⁺ cells under very high injection conditions. High carrier concentrations are required to support the current flow even in short-circuit conditions, so enhancing the recombination which, on the other hand, is reduced by high injection lifetime increase. Under-linearity between the short-circuit current and the photon flux is also deduced at very high irradiance. The short-circuit current under bifacial illumination is higher than the sum of those currents under front and back illumination alternatively, so leading to inherently better bifacial cells. In the V_oc vs J_sc curve values of m in the logarithmic slope mkT/q range from values slightly below one to two. The value m = 1 is not to be expected even if the base recombination is negligible due to Dember potential effects.     

Characteristics of three-terminal metal-tunnel if oxide-n/p+ devices

The device described here comprises a p⁺ substrate containing an epitaxial n-layer, on the surface of which is grown a thin (～50 Å) tunnel oxide. A metal cathode is deposited on the oxide surface, and a metal anode on the back side of the p⁺ substrate. A third terminal, the gate electrode, is connected to the n epilayer to provide for biasing the n-p⁺ junction.The I-V characteristic exhibit two stable states: a high-impedance state and a low-impedance state which are separated by a negative-resistance region. The high-impedance state is stable for applied voltages up to the intrinsic threshold voltage, V_s. When the switching voltage is exceeded, the device switches rapidly to the low-impendance state, which is characterized by a current that increases with little increase in the voltage across the device.The switching voltage may be reduced below V_s by current or voltage biasing of the n-p⁺ junction by means of the gate electrode. Gate efficiencies, the ratio of the change in switching voltage with d.c. gate voltage or current, of 10 V/V and 1.0 V/μA have been observed. Pulsed gate measurements are also presented, and it found that for pulse widths down to 0.1 μs the gate switching characteristics follow the d.c. characteristics. For pulse widths less than 0.1 μs the gate efficiencies are degraded. Suggestions for improving the device characteristics and the turn-on and turn-off time of the device and device reliability are discussed.     

Post-breakdown bulk oscillations in gold-doped silicon p+−i−n+ double-injection diodes

Experimental work on post-breakdown bulk oscillations in n-type gold-doped phosphorus-compensated p⁺?i?n⁺ double-injection diodes is presented. An empirical relationship for the frequency of oscillation in this region is derived for the first time and discussed.     

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.     

Noise in near-ballistic n+nn+ and n+pn+ gallium arsenide submicron diodes

Direct-current (d.c.) characteristics and noise measurements in the range 1 Hz-25 kHz are reported for n⁺nn⁺ and n⁺pn⁺ near-ballistic devices, with n regions (p regions) of 0.4 μm (0.45 μm), fabricated by molecular beam epitaxy at Cornell. The n⁺nn⁺ mesa structures show very low 1/? noise. indicating a Hooge parameter α_H = 6.0 × 10^?. This very low noise is attributed to the near absence of phonon collisions. The thermal (? like) noise above 1 kHz is equal to Nyquist noise at the lowest currents, rising to slightly above Nyquist noise for high currents, indicating the presence of carrier drag effects. The n⁺pn⁺ noise, on the contrary, is quite high. It seems to be associated with the ambipolar effects occurring for low injection of electrons in the p region. The importance of noise measurements for confirming ballistic or near-ballistic behavior is discussed.     

Heat flow resistance measurements of silicon p+-v-n+ diodes under forward and reverse biased conditions

A detailed study of the heat flow resistance measurements in a p⁺-v-n⁺ diode is studied in both forward and reverse biased conditions. Measurements are made by continuously switching the diode from the power dissipation state into the temperature measuring state. Safe operating power limits are identified for the diodes depending upon their mode of operation either as a microwave switch or as an IMPATT oscillator.     

Quenched-in centers in silicon p+n junctions

Silicon p⁺n junctions heat treated at high temperatures (1200°C) for a long time (2–20 hr) and then quenched to room temperatures or below shows two deep donor levels (E_C?264meV andE_C?542meV) in the n-type side of the junction depletion layer which appear to originate from the same imperfection center. The concentration of these levels ranges from 10¹³ to 10¹⁴ cm^?3. The junction leakage current comes from carrier generation at the deeper level in the depletion region. Phosphorus gettering was found ineffective in reducing the concentration of these quenched-in levels, but they are annealed out by very slow cooling (25°C/hr to 650°C then quench to room temperatures). The thermal emission and capture rates of electrons and holes at these levels are measured as a function of temperature and electric field by the junction high frequency capacitance and d.c. leakage current transient techniques. It is demonstrated that the detailed balance relationship does not hold. The origin of this double donor center is yet to be identified.     

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.     

Degradation mechanism for silicon p+-n junctions under forward bias

Leakage current degradation has been observed during forward bias stressing of silicon integrated p⁺-n junctions. Detailed characterization results of the anomalous leakage behavior are discussed in this paper. From these results an electric field-enhanced impurity diffusion mechanism has been proposed to explain both the strong temperature and forward bias dependencies on leakage current time-to-saturation. An activation energy has been determined for this mechanism (0.48±0.04 eV) and is in good agreement with that previously determined for diffusion of interstitial copper in p-type silicon. Subsequent Secondary Ion Mass Spectrometer elemental analysis has confirmed the presence of copper near the surface of the epitaxial layer containing the p⁺-n device.     

Effective recombination velocity at the NN+ interface

The effective recombination velocity S_nn⁺ at the nn⁺ interface in buried layer (nn⁺p) and n epi-n⁺ substrate structures has been studied using a model which takes into account the retarding outdiffusion region, recombination and bandgap narrowing. The variation of S_nn⁺ with diffusion length and bandgap narrowing has been estimated taking into consideration their doping-dependence. An attempt has been made to explain the wide range in the reported values for S_nn⁺ using the results of this study.Results indicate clearly the difference between the S_nn⁺ of the two structures. This difference arises from the collection by the p-substrate which accounts for a significant part of the S_nn⁺ of the buried layer structure over a wide range of values of diffusion length. This collection component of S_nn⁺ is sensitive to bandgap narrowing.On the other hand, the S_nn⁺ of the nn⁺ structure is largely determined by the recombination in the outdiffusion region which is sensitive mainly to the value of diffusion length in that region. The component of S_nn⁺ representing recombination in the n⁺ substrate is sensitive to bandgap narrowing. The present study indicates the dependence of S_nn⁺ on the structure and processing of the devices in which the nn⁺ interface occurs.     

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.     

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.     

Low field study of P+NN+ or P+PN+ structures in the forward direction

It is shown, on the basis of P⁺NN⁺ and P⁺PN⁺ models, how injection processes modify the field distribution in two-electrode systems, and thereby the effective resistivity.     

The effect of current suppression in the pn−n+ diode of integrated injection logic

The j-V characteristics of the pn^?n⁺ diode are derived by combining the different current components in the n^? region of the diode for various bias voltages. For infinitly fast recombination, the expression for the current density as a function of bias reduces to that of a conventional one-dimensional theory. For finite recombination, however, the expression deviates significantly from the usual expression. In fact, contrary to what would be expected from the conventional theory, the current increases as the width of the neutral n^? region increases for a constant bias. Finally the results of the analysis of the pn^?n + diode are applied to an analysis of the current gain in the integrated injection logic (I²L) device. A qualitative discussion of the current gain for the lateral pnp transistor and for that of the vertical npn transistor is given.     

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.     

Stabilizing effects for the supercritical GaAs n+nn+-transferred electron amplifier

In this paper effects of importance for the stabilization of supercritical n⁺nn⁺ GaAs transferred electron devices are considered. By small-signal impedance calculations and measurements it is shown that doping- as well as temperature gradients of correct polarity reduce the device negative resistance and enhance stability. It is also found that an increasing doping density reduces the negative resistance. Finally it is demonstrated that relaxation effects have a profound influence on the impedance, and that such effects have to be included in a small-signal analysis in order to give reasonable agreement with measurements.     

A discrete element small-signal equivalent circuit for forward-biased p+n diodes containing deep levels

A discrete element small-signal equivalent circuit model for p-n diodes containing deep defect levels is developed, by extending an existing model for undamaged devices. With the aid of a simple analytical expression which accurately describes the forward bias d.c. current, the enhanced small-signal conductance due to carrier recombination in the depletion region is included in the model. The influence of trapped charge on the space charge capacitance is incorporated using a simplified version of the analysis of Beguwala and Crowell. The predictions of the model are verified by experimental data from silicon p⁺n diodes, in which deep levels have been induced by electron irradiation. It is shown that the deep level activation energies may be estimated from the forward bias capacitance-voltage characteristics, yielding values which agree well with those obtained by established techniques.     

Surface recombination effects on the performance of n+p step and diffused junction silicon solar cells

Effect of front and back surface recombination velocity (SRV) on the performance of n⁺p step and diffused junction Si solar cells has been investigated. Assuming the impurity profile to be Gaussian in the diffused region, the influence of built-in field and field gradient on the cell performance parameters have been discussed. It has been found that relatively higher front SRV can be tolerated for terrestrial utilisation than for space application. The improvement in conversion efficiency due to the reduction in back SRV is more if the cell thickness is smaller and the junction is shallower. The benefits of a lower back SRV are limited by the value of front SRV and recombination losses in the front region. The built-in field in the front region counteracts the recombination losses at the top surface and in the front region provided the field gradient is small.     

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.     

The mobility of a nickel-related centre in reverse biased germanium n+p diodes

The motion of a nickel-related centre (E_v + 0.14 eV) in reverse biased germanium n⁺p junction has been observed using deep level transient spectroscopy. The concentration profile of this deep acceptor defect is presented as a function of the duration of the electric field application. An estimated mobility of 2.0 ± 1.1 × 10^?13 cm²Vs^?1 at 25°c was obtained for the nickel-related centre.