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.     

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.     

Theory for nonequilibrium behavior of anisotype graded heterojunctions

An analysis for the terminal behavior and capacitance of anisotype graded heterojunctions is presented. A closed form expression for the I–V characteristics is derived using the depletion approximation and the rigid band model. The expression is valid for uniform nondegenerate doping and low-level injection. The transition region is modeled to extend beyond the space-charge region with a constant bandgap gradient. Variations of the dielectric constant, carrier lifetime and mobility are ignored. The nonsaturating nature of the reverse current is demonstrated. The effects of variations of bandgap and electron affinity on the I–V characteristics and junction capacitance are discussed. Numerical results for a graded nGe-pGaAs device are given.     

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.     

Improved physics for simulating submicron bipolar devices

The conventional device physics in most numerical simulations of bipolar transistors may not predict the measured electrical performance of shallow heavily doped emitters and bases. This paper summarizes improved device physics for numerical simulations of solid-state devices with dopant densities up to about 3 × 10²⁰cm^-3and with junction depths as small as 0.1 µm. This improved device physics pertains to bandgap narrowing, effective intrinsic carrier concentrations, carrier mobilities, and lifetimes. When this improved physics is incorporated into device analysis codes such as SEDAN and then used to compute the electrical performance of n-p-n transistors, the predicted values agree very well with the measured values of the current-voltage characteristics and dc common emitter gains for devices with emitter-base junction depths between 10-0.16µm.     

Properties of Au,Pt, Pd and Rh levels in silicon measured with a constant capacitance technique

Measurements of emission rates and majority carrier capture cross-sections of Au, Pt, Pd and Rh centres in silicon are reported, and the activation energies associated with the different levels of these centres are determined. Where appropriate, our results are compared with values reported in the literature; other results have not been previously reported. The measurement depends on the emission and capture of majority carriers on the centres in the depletion layer of a p-n junction or Schottky barrier. The change in charge state of the centres is monitored by measuring the change in reverse bias applied to the junction necessary to keep the junction capacitance constant. The advantage of this technique, compared with the usual method of keeping the bias voltage constant and measuring the change in capacitance, is demonstrated.     

Numerical evaluation of the scanning method for the determination of minority carrier diffusion length in p-n junctions

A numerical model for the scanning method for determining minority carrier diffusion length is presented to include the effect of the built-in field and high-level injection. A numerical simulation is presented which shows that the scanning method for diffusion length measurements will not give accurate results for minority carrier diffusion length in the region where the presence of a built-in field is significant. No matter how poor the junction is made, the accuracy of the measurement method increases away from the depletion region. The problem of low magnitude in the induced short circuit current away from the physical junction could be overcome by increasing the generation level. For substrate dopant concentrations between 2.0 × 10¹⁵cm⁻³ and 6.0 × 10¹⁶cm⁻³ the distance into the device from the surface where the error of the measurement will be greater than 10% is expressed as a semi-empirical formula relating dopant concentration. When there are irregularities in minority carrier lifetime closer to the physical junction, the measurement method will accurately determine the minority carrier diffusion length in a particular region only if the width of that region is much larger than its diffusion length.     

Effect of heavy doping on the properties of high-low junction

The minority carrier reflecting properties of the high-low junction have been studied, taking into account the heavy doping effects. It has been observed that the junction leakage velocity attains a minimum value for a particular value of impurity concentration in the heavily doped region, when an empirical relationship giving bandgap narrowing as a function of impurity concentration in silicon is utilized.     

Two-dimensional field distribution analysis of reverse biased p-n junction devices

A two-dimensional Poisson equation is solved for a reverse biased p-n junction diode structure without introducing a cumbersome movable boundary treatment of depletion layer edge determination. An investigation is made of the field distribution of a glass-passivated transistor having sidewalls perpendicular to the junction plane. The influences of the glass dielectric constants and glass charge densities will be studied. Positive charges in the glass are shown to induce an undesirable high field near the semiconductor surface and degrade the device breakdown characteristics. The peak field value due to the positive charges increases as the glass dielectric constant decreases. An estimate for permissible operating voltage is obtained for various conditions.     

Boundary conditions and current-voltage relations for heavily doped p-n diodes

Boundary conditions at the edges of the space-charge region of a p-n diode have been developed by two different methods. Both of the methods make use of a tractable empirical approximation for the reduced Fermi level experessed in terms of effective intrinsic carrier concentrations. In procedure 1, the excess minority carriers are derived in terms of band-gap narrowing and a parameter F(u) resulting due to degeneracy of the majority carriers in the same side of the junction. In procedure 2, in addition to these two parameters, the spatial dependence of the band structure has been taken into consideration. The analyses are valid for low and reasonably high injection levels. These are also general enough to be applicable to both degenerate and non-degenerate semiconductors. For non-degenerate semiconductors all these relations reduce to ones obtained on the basis of Maxwell-Boltzmann statistics. The boundary conditions are applied to derive current-voltage relations of long-base diodes. The results are found to depend on the majority carrier degeneracy and band-gap narrowing.     

An operational method to model carrier degeneracy and band gap narrowing

In this paper an operational method of modeling heavily doped silicon to include effects of carrier degeneracy and band gap narrowing is presented. The issue of carier degeneracy on majority carrier flow is discussed together with the question of the ambiguity in the electrostatic potential associated with identifying which band edge is narrowed. Using an exact numerical analysis of a bipolar transistor as an example it is shown that when modeling carrier flow in quasi-neutral regions, classical statistics can be used for the majority carrier and the ambiguity in the electrostatic potential can be ignored. Overall, it is shown that for the same quasi-neutral heavily doped regions the effects of carrier degeneracy and band gap narrowing are accurately modeled within the context of classical statistics by adding the quasi field term to the minority carrier transport equation that is based on the commonly used “band gap narrowing” data available from measurements of minority carrier transport in heavily doped regions. While it is recognized that this is not rigorously correct the result of this paper is to establish the accuracy for the operational method most commonly used to model heavy doping effects.     

Rigid band analysis of heavily doped semiconductor devices

The conventional carrier transport equations used in device analysis must be modified for heavily doped semiconductor regions. The modifications to Shoekley's auxiliary equations relating the carrier densities to their corresponding quasi-Fermi levels are derived for the rigid band model. We include the effects of asymmetric bandgap narrowing and of carrier degeneracy (Fermi-Dirac statistics). Emphasis is placed on writing the equations in a simple form that indicates the effect of changes in the band structure due to heavy doping. In this form they can serve as a basis for computer-aided analysis and design. We show that, in general, the effective intrinsic carrier density nieas well as the electron and hole current densities depend on the asymmetry in bandgap narrowing. However, for the special case of low-level injection, nieand the minority current density depend only on the total bandgap narrowingDeltaE_{g}. Furthermore, we indicate that interpretation of experiments with theory using Boltzmann statistics, instead of Femi-Dirac statistics, will underestimateDeltaE_{g}in degenerate material.     

STI stress-induced increase in reverse bias junction capacitance

A new contribution to reverse-biased junction capacitance is reported. This component arises from trench isolation stress-induced bandgap narrowing that changes the built-in potential. Experimental junction capacitance measurements show good correlation to simulated oxidation stresses. The reported data agrees well with the predicted values from basic device equations. Stress induced capacitance increase of 12% (7.5%) at 3.3 V reverse bias for p⁺/n (n⁺/ p) junctions, respectively is observed. In addition, well-understood reverse junction leakage relation to stress is also reported. This phenomenon will become increasingly important as trenches become shallower and more tightly spaced     

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.     

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.     

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.     

Influence of carriers on the capacitance of p-n junctions with deep donors

Applying the definition of p-n junction capacitance [1], which takes into account the effect of carriers in the space-charge region, a sufficiently accurate approximate expression is derived for the low-frequency capacitance of an abrupt p-n junction containing both deep and shallow donor impurities within the n-region. The capacitance expression can be written in conventional Schottky form, putting the intercept voltage if V_in instead of the diffusion potential. It is shown that V_in differs considerably from the generally known V_i0 expression obtained on the basis of the depletion layer approximation. This difference increases with the degree of p-n junction asymmetry, or the decrease of deep donor impurity ionisation energy, and is dependent also on the concentration ratio of deep and shallow donors. The most important difference between V_in and V_i0 lies in the fact that V_i0 in contrast to V_in, is independent of the applied voltage, and is therefore applicable only with very high reverse voltages, where equivalence between V_in and V_i0 is valid.     

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.     

Heavily doped transparent-emitter regions in junction solar cells, diodes, and transistors

An analytical treatment of heavily doped transparentemitter devices is presented that includes the effects of bandgap narrowing, Fermi-Dirac statistics, a doping concentration gradient, and a finite surface recombination velocity S at the emitter surface. Transparency of the emitter to minority carrier is defined by the condition that the transit time τtis much smaller than the minority carrier lifetime in the emitter τp,tau_{t} ll tau_{p}. As part of the analytical treatment, a self-consistency test is formulated that checks the validity of the assumption of emitter transparency for any given device. The transparent-emitter model is applied to calculate the dependence of the open-circuit voltage VOCof n⁺-p junction silicon solar cells made on low-resistivity substrates. The calculated VOCagrees with experimental values for highS_{P}( geq5 \× 10^{4}cm/s) provided the effects of bandgap narrowing (modified by Fermi-Dirac statistics) are included in the transparent-emitter model.