High-low Junction Research Articles

Determination of the minority carrier lifetime in the base of a back-surface field solar cell by forward current-induced voltage decay and photovoltage decay methods

Theoretical expressions are derived for both the forward current-induced voltage decay (FCVD) and the photovoltage decay (PVD) in a base-dominated back-surface field (BSF) solar cell of arbitrary thickness. The expressions apply to the general case where the effective surface recombination velocity S at the edge of the low-high junction in the base can have any value. If the value of S is taken as infinity, the expressions become applicable to conventional cells with finite base thicknesses. The case of an effective BSF cell in which S = 0 and that of a conventional cell in which S = ∞ are considered in detail. Large errors were found to occur in the values of minority carrier lifetimes τ B when lifetimes in the bases of thin conventional cells were determined by the FCVD method using the formula obtained previously; this formula applies only to thick cells. The difference between the FCVD and the PVD is large for W = ∞ ( W = w/ L B where w is the width of the base and L B is the diffusion length), as shown in previous papers by other workers. As W decreases, the FCVD and the PVD plots become linear, approach each other and are almost identical for W ⩽ 0.5, both for S = 0 and for S = ∞. For S = 0, however, the decay becomes slower as W decreases and the reciprocal of the slope of the FCVD or the PVD plot is equal to the minority carrier lifetime in the base. In contrast, for S = ∞ the voltage decay rate increases rapidly as W decreases, i.e. the FCVD and the PVD plots become steeper; the reciprocal of the slope then becomes equal to τ B/(1 + π 2/4 W 2). For small W the advantage of using PVD rather than FCVD for the determination of τ B disappears. The PVD in both effective BSF and conventional cells after light pulses of very short duration, and of arbitrary duration, is also discussed. It is shown that in a thick base solar cell the PVD after short pulse excitation can conveniently be used to determine the minority carrier lifetime, even if the pulse is of arbitrary duration, provided that 1/α (where α is the absorption coefficient) is larger than L B. However, if the base is thin ( W ⩽ 0.5), the FCVD, the PVD and the PVD after short pulse excitation become almost identical. The method by which the lifetime and the effective surface recombination velocity S can be determined from the observed PVD or FCVD is also discussed for the general case when S is not zero.

New experimental evidence for minority-carrier reflection at negative-barrier MIS contacts

Recently, measurements of the open-circuit voltage of solar cells with negative-barrier metal-insulator-semiconductor (MIS) back contacts have been used to demonstrate that such contacts can function as the electrical analogues of metallurgical high-low junctions. In this brief, further experimental evidence for the minority-carrier reflecting properties of the negative-barrier MIS junction is presented. First, it is shown that a negative-barrier Mg-SiO <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf> -nSi back contact can be used to enhance the long-wavelength photoresponse of p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> -n solar cells in the same manner as a diffused n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> back-surface field. Secondly, measurements of the effective surface-recombination velocity for an Mg-SiO <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf> -nSi contact and for a diffused n-n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> high-low junction formed on an identical substrate are reported. Both junctions gave very low values of recombination velocity, on the order of 50 cm/s.

Temperature coefficients of the open-circuit voltage of p-n junction solar cells

An analytic expression for the tempoerature coefficient of the open-circuit voltage has been derived in general, which may be applied to different kinds of p-n junction solar cells. Based on the dominance of the saturation dark current density, the simplified expression have also been developed and justified by experimental measurements. It has been shown that the negative temperature coefficient of the open-circuit voltage is decreased with the increasing light level and the interaction between minority carriers and the high-low junction. Hence, the temperature coefficient of the open circuit voltage is good measure for providing a guide to test the effectivness of a high-low junction in a back-surface-field (BSF) solar cell. Moreover, based on the measured temperature coefficient of the open-circuit voltage from the BSF solar cells fabricated on thin epitaxial substrate, a new method for measuring the effective energy-gap narrowing in the highly doped emitter has been proposed and studied. It has shown that the effective energy-gap narrowing measured is in good agreement with the eempirical expression proposed by Slotboom.

Effect of thickness on silicon solar cell efficiency

Semiconductor material cost is one of the factors which determines the performance-cost ratio and economical feasibility of silicon solar cells for terrestrial power generation. Decreasing the cell thickness would lower the silicon material cost. The energy conversion efficiency of a back-surface field solar cell will have a peak as the silicon film thickness is reduced due to two opposing factors: 1) the open-circuit voltage increases and 2) the short-circuit current decreases with decreasing cell thickness. A computer-aided-design study on the dependence of this efficiency peak on the concentrations of the recombination and dopant impurities is presented in this paper. The illuminated current-voltage characteristics of over 100 cell designs were obtained using the transmission line circuit model to numerically solve the Shockley equations. Using an AM1 efficiency of 17 percent as a target value, which is the highest encapsulated silicon cell efficiency used in the Block IV modules of the Low-Cost Solar Array Project, it is shown that the efficiency versus thickness dependence has a broad maximum which varies less than 1 percent over more than a three-to-one range of cell thickness from 30 to 100 µm. Optical reflecting back surface will give only a slight improvement of AM1 efficiency, about 0.7 percent, in this thickness range. The sensitive dependence of efficiency on patchiness across the back-surface field low-high junction in thin cells is noted.

The effect of substrate–epitaxial interface on the capacitance–voltage characteristics of Schottky barriers formed on sputtered films of gallium arsenide

The capacitance–voltage characteristics of Schottky diodes fabricated on sputtered GaAs do not yield straight line plots on a 1/C2 vs V curve. This anomalous behavior may be due to any one of the following mechanisms: (1) defective Schottky barrier fabrication, (2) the effect of an insulating interfacial layer, (3) nonuniform donor distribution, (4) the effect of deep traps, or (5) the effect of the substrate–epitaxial interface. Only the effect of the substrate–epitaxial interface capacitance adequately explains the anomalous behavior observed. Measurements of capacitance at 1 kHz and at 1 MHz coupled with complex impedance measurements led to a small signal linear circuit model. The temperature dependence of the circuit elements identified appropriately with physical phenomena yielded information about the Schottky barrier and the barrier formed at the epitaxial layer–substrate interface. The strong temperature dependence of the low–high junction barrier capacitance is explained using this model.

Ineffectiveness of low-high junctions in optimized solar cell designs

Exact numerical calculations for the back-surface field (BSF) type of silicon solar cell show that the base doping level for optimum overall performance is sufficiently high that the BSF is essentially ineffective. This implies that an optimized conventional cell will perform roughly as well as a BSF design and accounts for the fact that the highest efficiency cells to date have low resistivity bases. A second generic cell type, the high-low emitter, is also modeled. Again, no significant advantage of this cell over the conventional device is found. Summaries of optimized design performances of the different cell types are given.

Effect of double reflection on the forward current-voltage characteristics of a silicon p+- s- n+ epitaxial diode

The behaviour of both majority and minority carriers in a p +- s- n + epitaxial diode (where s may be p or n) has been investigated in this paper. Forward current-voltage characteristics of the diodes are obtained by exact numerical analysis, taking into account the effects of energy-gap narrowing, Auger recombination and carrier-carrier scattering. As with previous authors, it is found that the forward current increases with increasing middle layer thickness. The present analysis shows that such increase occurs only upto a specific applied bias, after which the forward current decreases with increasing middle layer thickness. This behaviour is attributed to double reflection, i.e. the reflection of both majority and minority carriers by the p- n junction and high-low junction respectively. Beyond the specific bias so determined, junction reflection loses its effectiveness. Distribution of carrier concentration and junction voltages for several device configurations are given to illustrate these features. The majority carrier reflection by the p- n junction is found to have a dominating effect in all cases.

Effect of the back-surface field on the open-circuit voltages of p +-n-n + and n +-p-p + silicon solar cells

The effect of the back-surface field (BSF) on the open-circuit voltages V oc of front-illuminated p +-n-n + (p/n BSF) and n +-p-p + (n/p BSF) silicon solar cells was investigated. A theory based on the assumption that the front emitter has a unit injection efficiency was formulated and this theory can be applied to both low and high level conditions in the bulk regions of p/n and n/p BSF cells. The effect of perfect and imperfect minority carrier blocking at the low-high (L-H) junction end of the bulk region was analysed. The theory gives some insight into the physics of the BSF cells. It shows that the minority carrier blocking at the L-H back junction both by itself and by causing a back reflection of minority carriers towards the front-junction end of the bulk region leads to an improvement in the open-circuit voltage of the cells. The contribution of back reflection is independent of the intensity of illumination and the resistivity ϱ B of the bulk region, whereas the contribution of minority carrier blocking increases with both the intensity of illumination and ϱ B . For low level conditions the improvement in V oc is mainly due to the contribution of back reflection. However, for high level conditions the contribution of minority carrier blocking can be quite large. For high level conditions the increase in recombination at the front surface and in the front region is more harmful to the V oc value of a p/n BSF cell. However, a decrease in the minority carrier blocking at the L-H junction is more harmful to the V oc value of an n/p BSF cell. The fact that V oc for BSF cells is independent of ϱ B is attributed to the high level conditions in their bulk regions.

Analysis of the photo voltage decay (PVD) method for measuring minority carrier lifetimes in P-N junction solar cells

When the diffusion length of minority carriers becomes comparable or even larger than the thickness of a P-N junction solar cell, the characteristic decay of the photogenerated voltage becomes a mixture of contributions with different time constants. The minority carrier recombination lifetime τ and the time constant l2/D, where l is essentially the thickness of the cell and D the minority carrier diffusion length, determine the signal as a function of time. It is shown that for ordinary solar cells (N+-P junctions), particularly when the diffusion length L of the minority carriers is larger than the cell thickness l, the excess carrier density decays according to exp(−t/τ−π2Dt/4l2), τ being the lifetime. Therefore, τ can be readily determined by the photo voltage decay (PVD) method once D and l are known. For ideal back-surface-field (BSF) cells (N+-P-P+ junctions) under the same circumstances the excess number density of carriers decays purely exponentially as exp(−t/τ). However most BSF solar cells are not ideal, possessing an effective surface recombination velocity seff of 100 to 1000 cm/sec at the high-low junction. Therefore, PVD measurements for BSF cells must be treated with caution and must be supplemented with other nonstationary methods recently developed. These facts are important for a determination of diffusion lengths since steady-state methods are notoriously unreliable when the cell thickness is smaller than the diffusion length. Finally a connection will be made with older work on the same subject.

High-low junctions for solar cell applications

A new theoretical model to calculate the effective surface recombination velocity ( S eff) of a high-low junction with an arbitrary impurity distribution is presented. The model is applied to erfc-diffused pp + junctions using experimental data of bandgap narrowing, lifetime and mobility. Bandgap narrowing is shown to degrade the minority carrier reflecting properties of the high-low junction. Computer results are applied for the design of BSF solar cells and to study other solar cells structures based on high-low junctions.

Transport velocity transformation: A convenient method for performance analysis of multilayer solar cell structure

With the trend to the use of drift fields and high-low junctions in the front and base regions of solar cells, the need arises for simple modeling of structures with at least three layers in a region. A forerunner treated a one-dimensional two-layer model in closed form and showed an expansion to a third layer for a very simple case [10]. Since direct expansion of the closed-form method to additional layers is too cumbersome, a layer-by-layer modeling method was developed, based on the representation of current densities across layer interfaces by the product of the carrier density and a transport velocity. In the ease of low-level injection, space-charge quasi-neutrality, and spatially constant material parameters, including an electrostatic field, the individual layer can be treated analytically, and the basic solar cell performance parameters evaluated from three equations. The first represents the transformation of the transport velocity across the layer from the other layer boundary. The second determines the light-generated current output from the layer interface, under the influence of the transport velocities and minority-carrier density at both layer boundaries and of bulk recombination. The third equation describes the flow of these carriers across other layers. The power of the approach lies in its facility for analysis of the solar cell's performance layer by layer, giving a clear picture of the individual layer's influence on the cell efficiency. It thus greatly eases the task of cell-design optimization. Where the parameters are not constant within a layer, the method allows approximation by stepwise-constant parameter approach, after subdividing the layer into a suitable number of sublayers.

Operating limits of Al-alloyed high-low junctions for BSF solar cells

Experimental estimations of the effective surface recombination velocity of the high-low junction ( S eff) and of the base diffusion length are carried out for Al-alloyed n + pp + bifacial cells and the results are presented in form of histograms. These results agree with calculated values of S eff when the characteristics of the recrystallized Si layer and heavy doping effects are taken into account. It is concluded that thick Al layers and high alloying temperatures (over 800°C) are necessary to obtain low values of S eff. This conclusion agrees with experimental results of other authors. Recomendations to avoid diffusion length degradation are given and the operating limits of the Al alloying technology are discussed.

Threshold and subthreshold characteristics theory for a very small buried-channel mosfet using a majority-carrier distribution model

Simple expressions of threshold and subthreshold characteristics for a very small buried-channel MOSFET is derived from a model of majority-carrier distribution along the channel. The carrier distribution is determined from the Poisson equation for a high-low junction. The basic formula for the subthreshold characteristic is derived from the majority-carrier drift-current equation. The theory is compared with the measured threshold voltages and the measured inverse semilogarithmic slopes of subthreshold current. The theoretical curves are in a reasonable agreement with experimental results. It is shown for a buried-channel MOSFET having a channel length less than 1 μm that the threshold and subthreshold characteristics change abruptly as the channel length is reduced because the majority-carrier concentration increases through the carrier diffusion from the source and drain terminals. The theoretical estimation shows that buried-channel MOSFETs will have the less short-channel effect than surface-channel MOSFETs for a small drain voltage. The theory also predicts that the buried-channel MOSFET can be scaled down in the same way as the surface-channel MOSFET.

A general solution for step junctions with infinite extrinsic end regions at equilibrium

We present here a unified solution to determine the potential profiles for step junctions in equilibrium. The complete solution is determined by solving for the two sides of the junction separately. The generalized solution consists first of a curve corresponding to majority-carrier accumulation, i.e, the low side of high-low junction. Second, it consists of a family of curves corresponding to majority-carrier depletion, i.e., the high side of a high-low junction and either side of a p-n junction. The curves in the latter case approach a common asymptote that by itself constitutes a solution for all but lightly doped sides of asymmetric p-n junctions.

A method for improving the spatial resolution of frontside-illuminated CCD's

A method is proposed for improving the spatial resolution of frontside-illuminated silicon CCD imagers. The technique involves building the device on an epitaxial layer deposited on a more highly doped substrate of the same conductivity type, creating a high-low junction. A simple theoretical model for the carrier diffusion limited modulation transfer function (MTF) is developed for this structure. Calculations of the MTF using this model are compared to similar calculations for other configurations, e.g., a thinned, backside-illuminated device and a frontside-illuminated imager built on a uniformly doped substrate. The calculations show that the new structure has MTF performance comparable to or better than the backside-illuminated device and has, for λ = 1.06 µm and Nyquist spatial frequency, an MTF which is nearly an order of magnitude higher than that for the nonepitaxial frontside-illuminated device. At the same time, the quantum efficiency of the epitaxial device is reduced by about one order of magnitude. The effects of substrate doping and epitaxial layer thickness are also explored.

Determination of lifetimes and recombination currents in p-n junction solar cells, diodes, and transistors

New methods are presented and illustrated that enable the accurate determination of the diffusion length of minority carriers in the narrow regions of a solar cell or a diode. Other methods now available are inaccurate for the desired case in which the width of the region is less than the diffusion length. Once the diffusion length is determined by the new methods, this result can be combined with measured dark I-V characteristics and with small-signal admittance characteristics to enable determination of the recombination currents in each quasi-neutral region of the cell-for example, in the emitter, low-doped base, and high-doped base regions of the BSF (back-surface-field) cell. This approach leads to values for the effective surface recombination velocity of the high-low junction forming the back-surface field of BSF cells or the high-low emitter junction of HLE cells. These methods are also applicable for measuring the minority-carrier lifetime in thin epitaxial layers grown on substrates with opposite conductivity type.

Current gain of high-low junction emitter bipolar transistor structure with uniformly doped profiles

The analytic expressions for the maximum current gain and the transit times across the neutral emitter and base region in the case of uniformly doped high-low junction emitter bipolar transistor structure are calculated in detail, which include the effects of energy-gap narrowing in highly doped semiconductor, doping-dependent minority-carrier diffusivities, contact-surface and bulk recombinations. It is shown that the high-low junction emitter with the doping in the low-concentration emitter higher than that of the base region will give higher maximum current gain and better frequency response than those of the LEC structure originally proposed by Yagi et al. Numerical results for the optimal design of the high-low junction emitter are given and discussed.

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.

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.

Physics underlying the performance of back-surface-field solar cells

A description of the physics of back-surface-field (BSF) solar cells is presented, in which several key approximations, valid for effective BSF cells, have been used to express the results of the analysis in ways that make them useful in understanding the performance of high-efficiency BSF cells. A silicon p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> -n-n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> BSF solar cell, developed in conjunction with the theoretical treatment, provides experimental support for the theory. Measured current-voltage characteristics, together with the analysis, are used to describe the important physical mechanisms that control the performance of the BSF solar cell. For example, the analysis enables the determinations of the carrier lifetimes in the base region and of the effective surface recombination velocity at the low-high junction.