An analytical model for the epitaxial bipolar transistor

In the n⁺pn^?n⁺ transistor, high-current effects in the base and collector regions are linked within the current ranges of practical interest. To describe such effects, we have derived an analytical model that is based primarily on five assumptions: (1) the structure is approximately one-dimensional; (2) recombination is negligible in the base and collector quasi-neutral regions, and in the three space-charge regions; (3) high-current effects are negligible in the emitter and n⁺-substrate regions; (4) the Fletcher boundary conditions (or the Misawa boundary conditions) can be used for the three space-charge regions; and (5) the ambipolar approach can be used for the base and collector quasi-neutral regions. The primary findings predicted by the n⁺pn^?n⁺ transistor model are: In current ranges of practical interest (usable current gain), the electron concentration profile has a significant “vertical step” located at the collector-base metallurgical junction for all values of collector current. In the limit of extremely-high-current operation, this step tends to vanish. In the current range where the current gain begins to decline rapidly with increasing collector current, the electron concentration at the base boundary of the collector-base space-charge region goes approximately as the square of the hole concentration at the collector boundary of the same region. Because of this relationship, a charge-control calculation is more difficult than a straightforward calculation of carrier concentration for a given degree of accuracy. The n⁺pn^?n⁺ transistor model (which consists of twelve algebraic equations) is particularly useful for the practically important case of an epitaxial bipolar transistor having a very thin, heavily-doped base region.     

Modelling of perimeter recombination in GaAs solar cells

To investigate perimeter recombination current in heteroface GaAs solar cells, two models were proposed; the first concerned the analysis of recombination at the surface that intersects the space-charge layer and the second dealt with recombination at the quasi-neutral region. Recombination at the depleted layer surface has a 2kT character and was treated in a similar way to that of the bulk, using the model of Sah, Noyce and Shockley. The electric field at the surface due to Fermi level pinning is different from that of the bulk. We suggested a simple model to obtain an analytical form of the perimeter current at the space-charge region surface that yielded values of the product of the characteristic length by the surface recombination velocity (L_sS₀) that agreed well with experimental values. The recombination current outside the space-region is of two dimensional nature and has a kT behaviour, the model adopted consisted mainly of solving numerically the bidimensional continuity equation. An effective recombination velocity was introduced to account for bend bending caused by the charged surface states. As the ratio of perimeter to area (P/A) is increased the perimeter current acquired significant proportions, thus the expected 2kT current due to bulk deep levels existing in the depletion layer is two to three orders of magnitude too small to account for.     

Carrier recombination at grain boundaries and the effective recombination velocity

The recombination of excess minority carriers at grain boundaries, or other interfaces with space-charge regions, is treated theoretically for general energy distributions of interface states (recombination centers). The distinction is made between minority carrier recombination velocity at the (grain-boundary) interface itself, and the effective recombination velocity for the collection of these carriers by the adjacent space-charge region. Calculations of the effective recombination velocity are made, as a function of the excess minority-carrier concentration at the edge of the space-charge region, since this is the quantity of most convenience for device modelling.     

The influence of illumination on the majority-carrier quasi-fermi-level in the Schottky-barrier diode

We present an analysis of the behaviour under illumination, of a Schottky-barrier diode. It is shown that significant changes in the position of the majority-carrier quasi-fermi level may occur in the space-charge region. Such changes enhance the forward current of the Schottky-diode, and so degrade the cell output. Further bias dependent effects may arise when bulk recombination in the neutral regions, or minority carrier leakage, across the n-n⁺ episubstrate interface occurs. Recent published data on gold-silicon devices is used to compare predicted and experimental results. Good agreement in both qualitative and quantitative behaviour is found.     

An analytical model for the edge-illuminated silicon solar cell under concentrated sunlight

An analytical model for the edge-illuminated p⁺nn⁺ solar cell is derived. The model employs the Fletcher boundary conditions for the p⁺n and nn⁺ space-charge regions and the ambipolar approach for the low region, the lightly-doped n-type base region. For high-level condition, the ambipolar approach yields complete information about the low region, including the ohmic drop, the Dember voltage, and the hole concentration profile.     

Fabrication and study of p-n structures with crystalline inclusions in the space-charge region

A new model of connecting elements for monolithic multijunction solar cells based on III–V compounds is proposed, in which p-n junctions with crystalline inclusions of a foreign semiconductor material in the space-charge region are used instead of p ⁺⁺-n ⁺⁺ tunnel junctions. The study shows that the introduction of crystalline inclusions to the space-charge region of the p-n junction in a GaSb-based structure allows current densities of ～50 A/cm² at an ohmic loss of ～0.01 Ω cm². The obtained characteristics of the connecting elements with crystalline inclusions show their applicability to multijunction solar cells for concentrated light conversion.     

Tunneling recombination in silicon avalanche diodes

Distribution of the tunneling-recombination current over the space-charge region in a p-n junction was simulated mathematically. It is shown that the recombination rate saturates if the probability of tunneling is low. An expression for current-voltage characteristics of the p-n junction in the case of tunneling recombination is derived. The current-voltage characteristics of silicon avalanche diodes containing dislocations were studied experimentally. The results of numerical calculations based on the tunneling-recombination model are consistent with experimental data.     

Recombination properties of a diffused pn junction determined by spectral response measurements

The theoretical spectral responsivity of a diffused pn junction is computed in the case of a silicon n⁺p junction which employes a rather deep (4, 7 μ) and lightly doped N⁺ front region.Comparing experimental results with theoretical predictions the diffusion length L and surface recombination velocity S₀ can be determined. Several cases are examined: the influence of an oxide layer on the front and of gettering processes on L and S₀ are presented and the overall sensitivity of the method is discussed.     

Die räumliche verteilung der rekombination in legierten silizium-psn-gleichrichtern bei belastung in durchlassrichtung

Making use of the emitted infrared radiation, the charge carrier distribution n(x) in p-s-n diodes that were biased in forward direction was measured on cross-cuts. The sagging of this distribution depends on the lifetime and yields in conjunction with the stored charge a measure for that part i_m of the current density i which recombines in the weakly doped center region. The current density i, on the other hand, is a measure for the recombination in the entire diode. Therefore, infrared measurements in conjunction with determinations of the stored charge make it possible to determine for a given forward current density i the distribution i_m/i of the recombination between the weakly doped center region and the highly doped border regions.Since the radiation measurements are performed on small rectangular polished specimens (1 × 4 mm) that have been cut from the diode wafer, the measurements can be noticeably influenced by surface recombination. This influence is discussed in detail. As it turns out, only an upper limit can be given for the recombination distribution i_m/i. However, this is sufficient to ensure that already at current densities of 100–200 A cm^?2 the recombination takes place predominantly in the highly doped border regions. At current densities of 1000–3000 A cm^?2 the contribution of the center region to the recombination practically vanishes.     

Mechanism of forward current transport in modified-surface Au-CdTe photodiodes

Current-voltage characteristics of surface-barrier diodes based on n-CdTe substrates treated in aqueous solutions of alkali metal salts were studied. It was found that the forward current is controlled by recombination processes in the space-charge region and the above-barrier carrier transport.     

Low-frequency noise due to carrier recombination in a p-n junction

The noise due to recombination in the space-charge region of an abrupt Si p-n junction is calculated numerically for low and moderate forward bias. Then an expression is given for the recombination noise in the bulk region at high injection. The results show that the low frequency ratio ξ(0) of the equivalent shot-noise current to the recombination current depends both on doping density and on injection level. The value of ξ(0) approaches 1 asymptotically for low and high injection independently of the doping level, and its minimum is near 0.75 in the case of a relatively highly doped diode at moderate injection. Finally the numerical values of ξ(0) are compared with the analytically estimated values as well as the experimental results.     

Effective lifetimes in high quality silicon devices

A correct interpretation of pn junction current-voltage and pulsed MOS capacitance-time data allows space-charge region width dependent generation parameters to be separated from bulk controlled recombination parameters. This is very important for the correct extraction of generation lifetime and minority carrier diffusion length, especially for intrinsically gettered devices where the recombination center density varies through the device. Methods to do this are discussed in this paper.     

Modeling the efficiency of multijunction solar cells

The efficiency of multijunction solar cells (MSCs) η is calculated taking into account radiative recombination, Shockley-Read recombination, front and rear surface recombination, recombination in the space-charge regions, and recombination at heterojunctions. Calculation is performed by self-consistent solution of the photocurrent, photovoltage, and heat-balance equations. MSC cooling by increasing the numbers of cells n and improvement in the conditions of heat removal is taken into account. An effect leading to a decrease in the photocurrent with increasing n, associated with narrowing of the energy ranges of photons incident on the MSC cell, is considered. It is found that a significant increase in the MSC efficiency can be achieved by improving the heat-removal conditions, in particular, through the use of radiators and increasing the MSC grayness factor to unity. The results obtained are compared to those of other authors. It is shown that the calculated dependences η(n) are in agreement with experimental values.     

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.     

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.     

Vertical silicon-on-nothing FET: Threshold voltage calculation using compact capacitance model

The threshold voltage (V_th) model of the novel vertical fully-depleted silicon-on-nothing FET (VFD SONFET) structure is extracted from the compact capacitance equivalent circuit. Due to the absence of the transistor substrate in the VFD SONFET, the channel region is coupled to the source and drain through the buried oxide. Electrostatically, the VFD SONFET resembles the SOI device with thick buried oxide and recessed source/drain, and the developed model can also be applied to these structures. This property is modeled by two-dimensional buried oxide capacitance (C_BOX), which competes for the inversion charge with gate oxide capacitance (C_GOX). Therefore, the V_th is primarily influenced by the ratio of buried and gate oxide capacitances, with the negligible effect of the silicon body equivalent capacitance and the silicon body charge. The relative impact of C_BOX increases with the down-scaling of the effective channel length. In the VFD SONFET structure, the inversion channel can be formed at the back interface of the channel region, due to its coupling to the n⁺ source and drain regions. However, it is shown by the model that the V_th value is minimally changed in this case, due to a small potential change in the silicon channel. The model accurately predicts V_th in comparison to physical simulations, especially in the long channel region, whereas accuracy drops for shorter channels. The maximum absolute deviation is below 50 mV for the channel lengths above 30 nm.     

Monte Carlo simulation of GaAs Schottky barrier behaviour

The transport of carriers through the space-charge region (SCR) of a GaAs Schottky barrier is studied by the Monte Carlo simulation technique. Simulation results indicate that the carrier distribution is significantly perturbed from a Max-wellian near the metal-semiconductor boundary, limiting the validity of the commonly used thermionic diffusion model. Phenomena related to the disturbed distribution include increased recombination velocity at the interface and reduced carrier concentration near the junction. The interface recombination velocity is found to be constant with applied bias and the Bethe condition is shown to be more than sufficient to ensure the validity of the thermionic emission model.     

A computer method for the characterization of surface-layer ohmic contacts

The paper presents a general computer model for the calculation of the specific resistance of ohmic contacts with a heavily doped surface layer. A computer program is developed for the calculation. The theoretical model makes use of the depletion approximation. Two distinct cases are considered: the space-charge region extends beyond the surface layer and the space-charge region is contained in the surface layer, respectively. Curves, illustrating the specific resistance dependence on the bulk doping, with the surface layer doping and thickness as parameters are numerically computed. By fitting the theoretical curves with published experimental data the surface layer parameters are determined for Al/p-Si, Ni/n-Si and Au/n-GaAs contacts.     

Avalanche-induced 1/f noise in bipolar transistors

It has been proposed that degradation of low current hFE, as a result of avalanching the emitter-base junction of a bipolar transistor, can be attributed to an increase in surface recombination velocity within the emitter-base space-charge region. This work shows that 1/fnoise is also increased during avalanche and that this increase is consistent with a previously reported correlation between surface recombination velocity and 1/fnoise.     

Influence of the dopant density profile on minority-carrier current in shallow,heavily doped emitters of silicon bipolar devices

Experimental determination of the dependence of recombination current in p⁺ and n⁺ regions on the dopant profile for shallow emitters of ion-implanted silicon solar cells is described. The results are analyzed by extending a previous analytical model for the transport of minority carriers in heavily doped regions. The extension accounts for an effective electric field, defined by heavy-doping effects at the surface, and suggests that the energy-gap narrowing for p⁺ silicon is slightly smaller than that for n⁺ silicon and/or that minority-carrier diffusivities are substantially lower than the majority-carrier ones at comparable dopant densities. The very high dopant densities achieved with the ion implantation/laser annealing technique provide an in situ surface passivation that supresses surface recombination and minimizes the emitter recombination current.