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We have obtained a simple expression that determines the effective minority carrier lifetime in macroporous silicon with periodic arrangement of infinitely long macropores as a function of bulk lifetime, surface recombination velocity of minority carriers, pore radius and the distance between the centers of macropores. This expression can be applied also to macroporous silicon with randomly distributed pores by replacing the pore radius and the distance between the centers of macropores with their average values. The distribution of steady-state excess minority carriers in macroporous silicon is calculated for the analytical model proposed by us. The calculation is made for the case when both the outer surface of macroporous silicon and the bottom of pores are illuminated with light. We observed two peaks of the distribution of steady-state excess minority carriers in macroporous silicon near the surfaces illuminated with light of wavelength 0.95 m. At the same time, if macroporous silicon was illuminated with light with the wavelength of 1.05 μm, we observed only one maximum in the distribution function of the excess minority carriers, in spite of the fact that the pore bottom was also illuminated with light. It is shown that the distribution of excess minority carriers in macroporous silicon with through pores is similar to the distribution in single crystal silicon. But in this case, the effective lifetime of minority charge carriers in the effective medium of macroporous silicon, which includes silicon and the surface of pores, corresponds to the bulk minority-carrier lifetime in monocrystalline silicon.

The voltage and current oscillations occasionally occur during the reverse recovery transient of the superjunction MOSFET body diode. This paper identifies the unique reverse recovery oscillation characteristics of the superjunction MOSFET body diode. Base on the experimental investigation and theoretical analysis, the various reverse recovery oscillation mechanisms are clarified. At first, with a discrete 650 V/47 A superjunction MOSFET utilized, the high-frequency and low-frequency oscillation characteristics during the reverse recovery transient are obtained by the double-pulse test. After the theoretical analysis, it is found that the superjunction MOSFET body diode has various oscillation mechanisms depending on its drift region injection level. Under high-level injection condition, the high-frequency oscillation occurs due to the plasma extraction transient-time (PETT) effect. Under low-level injection condition, the body diode’s snappy reverse recovery results in the low-frequency LC oscillation. In the end of the paper, the oscillation behaviors under both high and low level injection conditions are reproduced by the mixed-mode numerical simulation, the simulation results validate the proposed oscillation mechanisms.

A model consisting of Shockley Read Hall (SRH) recombination under steady state conditions of constant photon injection is proposed in this work to study the steady state minority carrier lifetime in CdS/CdTe thin film solar cells. The SRH recombination rate versus optical injection level is analytically approximated in the junction and neutral regions. In the neutral region, it is found that the recombination rate through certain defect levels has one constant value under lower optical injection conditions and another constant value under higher optical injection conditions with the transition occurring at a critical optical injection level. By simultaneously solving the equations of charge neutrality, charge conservation and SRH recombination in the neutral region, it is found that the compensation of doping and the reduction of minority carrier lifetime by donors in the p-type semiconductor can each be remedied by optical injection. It is also demonstrated that this optical-dependent SRH recombination is significant in large bandgap thin films. The measured minority carrier diffusion length in a CdS/CdTe solar cells, as determined from the steady-state photo-generated carrier collection efficiency, shows the predicted transition of minority carrier lifetime versus optical injection level. A numerical fitting of the indirectly-measured minority carrier lifetime by assuming the minority carrier mobility gives a non-intuitive picture of the p–n junction with a low free hole concentration but a narrow depletion region width.

We verify a fast and simple analytical model for locally contacted rear surface passivated solar cells by three dimensional numerical simulations. For low level injection conditions the analytical model shows good agreement with the numerical results. For intermediate injection levels and for the injection dependent bulk lifetime in oxygen contaminated silicon, the present analytical model deviates from the numerical results. The accordance clearly improves when including injection dependent recombination and conductance in the analytical model. For intermediate to high injection levels, it is crucial to implement additional corrections for injection effects, being emphasised by the low recombinative front side and bulk material of the device structure investigated in this work. When accounting for these deviations from low level injection, analytical modelling turns out being a fast way to predict the optimum contact spacing as well as the electrical parameters of locally contacted rear surface passivated solar cells even for intermediate injection conditions

Double side collecting silicon solar cells such as the emitter wrap through and the both sides contacted and collecting concept are one possibility to maintain high efficiencies even on low lifetime material. To investigate the intrinsic advantages and limitations of this concept we use the solution of the continuity equation under low level injection conditions for a double side collecting (n + pn + ) and a single side collecting (n + pp + ) solar cell. In general, compared to the single side collecting structure, the double side collecting structure yields the highest advantages concerning the roduct of the short circuit current density and the open circuit voltage Jsc·Voc on highly doped material with diffusion lengths in the range of half the cell thickness. A realistic calculation of the fill factor of such devices is done using two dimensional numerical simulations. It is shown that a major reduction of the fill factor is caused by laterally varying voltage induced non-generation losses and ohmic losses, both caused by the majority carrier flow in the base. Electro- and photoluminescence images verify and illustrate the lateral voltage distribution under different illumination levels and terminal voltages.

Exact expressions for the out of phase modulated photocurrent (MPC), the so-called Y signal, with a clear physical insight for density of states (DOS) spectroscopy are derived without any approximation. It is found that, apart from the capture rate of the majority carriers into the probed gap states, additional mixed contributions from the recombination processes of the free majority carriers with trapped minority carriers may be important for the Y signal of lower frequencies. These additional contributions prevent the extraction of a reliable DOS. They become important as long as the capture coefficient for the majority carriers of the recombination centers, where the minority carriers are trapped, is comparable to or higher than that of the recombination centers were the majority carriers are trapped. In this case, the recombination rate is relatively high and the mixed contributions from the recombination processes can be detectable in the experimental Y signal and may also induce a phase lead. Taking...

Electrical characteristics and neutron dosimetry properties of silicon based p-i-n diodes are presented in support of the applications in the sensors for beam monitoring and medical physics. Both the current-voltage (I-V) and capacitance-voltage (C-V) characteristics of silicon planar p-i-n diode sensors with cylindrical geometry have been theoretically modeled and experimentally measured. The shifts of the forward and reverse diode characteristics of the sensors versus the neutron dose have been obtained. It is shown that the neutron irradiation caused shift of the forward voltage of the p-i-n diodes is proportional to the current at which it is measured in the case of the low level injection or to the square root of the current in the case of the high level injection. The C-V characteristics and the full depletion voltages of the diodes have been estimated and experimentally verified. It is shown that the sensitivity of planar cylindrical structures as neutron sensors can be optimized by the selection of the device geometry and the current at which the measurement is performed.

We have extensively measured and analyzed the current mismatch of a small-size n-channel MOS transistor of 2 /spl mu/m/spl times/2 /spl mu/m operated in weak inversion with its p-well-to-n/sup +/-source junction forward and reverse biased. The case of slightly forward biasing the well-to-source junction represents the action of a gated lateral bipolar transistor in low level injection. The measured dependencies of the mismatch in weak inversion on the back-gate forward and reverse biases have been successfully reproduced by a new simple statistical model. From the experimental data, we suggest that i) subthreshold circuits should be carefully designed for suppression of mismatch arising from back-gate reverse bias, and ii) a gated lateral bipolar action in low level injection may be utilized as a new method of improving the transistor matching.

Sidegating in GaAs metal‐semiconductor field‐effect‐transistors (MESFETs) is widely attributed to space‐charge‐limited (SCL) conduction through the semi‐insulating (SI) substrate. But often sidegating is accompanied by low sidegate currents and occurs at sidegate voltages that are too small to initiate SCL conduction. We suggest that this is due to low‐level hole injection from a MESFET into the substrate. An analytical treatment of carrier, field, and potential distribution in a SI substrate under conditions of low‐level injection shows that an electric field overshoot may develop in the vicinity of the MESFET when hole injection occurs. This results in a large portion of the applied voltage being dropped across the channel‐substrate interface and, consequently, in sidegating. One result for short structures is the electric field outside the narrow region of overshoot is below the value expected for ohmic conduction. Consequently, over a wide range of applied voltages the field in most portions of the structure is below the critical value required for intervalley electron transfer.

The carrier recombination rates in semiconductor quantum wells are found to be structure dependent. Under high levels of excitation they generally do not follow the recombination rule of the bulk material. Through a differential carrier-lifetime measurement in the strained-layer InGaAs/GaAs quantum wells, it is shown that in quantum wells with lower potential barrier or thinner well width, the recombination rates are smaller due to a larger portion of the injected carriers populating the confinement layers where the carriers recombine more slowly owing to dilute carrier volume density. >

In the analysis, the full-range transient response of the gate is calculated using closed-form analytical expressions. This is achieved by generalizing and improving the method used by J.M.C. Stork (IEDM Tech. Dig., p.550, 1988) for the determination of the propagation delay. The proposed model is applicable at low-level injection, unity fan-in, and unity fan-out. The delays related to the transit time, the load, and the junction capacitances are considered. For ECL gates, the emitter follower delay is also included. Various delays (risetime, propagation delay, etc.) calculated using the proposed model agree perfectly with the results of SPICE computer simulations and with the reported experimental values. >

Measured minority and majority carrier mobility temperature dependencies in heavily doped n- and p-GaAs are compared. Majority carrier mobilities in heavily doped GaAs are essentially temperature ~T! independent while minority carrier mobilities exhibit a roughly 1/T dependence. Majority carrier freezeout, which reduces both majority–minority carrier and ionized impurity scattering, is shown not to be responsible for the 1/T minority carrier mobility dependence. The difference in minority and majority carrier mobility T dependencies is explained in terms of the increased degree of degeneracy of majority carriers with decreased temperature, which decreases majority–minority carrier scattering.

Knowledge of both carrier bulk lifetime τb and surface recombination velocity S are necessary to analyze and model electron devices. In this paper, the analytical results of Luke and Cheng [J. Appl. Phys. 61, 2282 (1987)] are applied to examine excess carrier decay due to pulsed Gaussian optical excitation to extract values of τb and S under low level injection. The nondestructive, contactless measurement technique utilizes a visible pulsed laser pump beam and a CW infrared laser probe beam. Values for τb and S are obtained for a number of different Si samples. The effect of varying the pump beam frequency is examined. The technique is simple to use in the laboratory and the parameter extraction from the measured data is straightforward.

The carrier recombination rate in GaAs‐AlGaAs single quantum well layers is investigated using a small‐signal technique for carrier densities from 1017 to 1019/cm3. For carrier densities up to mid 1018/cm3, the inverse of the differential carrier lifetime, 1/τd, increases linearly with the carrier density. The differential rate, however, saturates at higher carrier densities and remains nearly constant for carrier densities higher than 1019/cm3. The deviation from the bulk recombination behavior is due to a portion of the injected carriers populating the semicontinuum states where the rate for the radiative transition is much smaller. The experimental data indicate that the runaway increase of threshold current with decreasing cavity length commonly observed in the short‐cavity lasers is mainly due to the loss of carrier confinement at high carrier densities rather than due to fast carrier‐depleting processes, such as Auger recombination.

This paper presents an accurate and practical mathematical model of time-resolved photoluminescence (PL) response from silicon wafers generated by fast repetitive excitation pulses. The model is valid under low level injection condition and takes into account the depth dependence of carrier generation, diffusion, and surface recombination. Finite element analysis is employed for the carrier density and PL computations. By comparing computational results with results obtained from PC1D (a computer program solving fully coupled nonlinear equations for quasi-one-dimensional carrier transportation in crystalline semiconductor devices, especially focusing on photovoltaic devices), the validity of this method is confirmed. Early stage application and the limitations of this method have been studied, and future work has been proposed.

In this paper we show experimental results that indicate that trapping-related increase of the apparent carrier lifetime can be directly accompanied by a decreased recombination lifetime. This effect cannot be described with the traditionally used trapping model of Hornbeck and Haynes [1,2,3] (H&H). In order to obtain a physically consistent theoretical description of the observed correlation between trapping and recombination we use the Shockley, Read [4] and Hall [5] (SRH) formalism. We assume trap states with non-zero capture cross sections for majority carriers, which may nevertheless be several orders of magnitude smaller than the minority carrier capture cross sections. In this way we define a Recombination-Active Trap state (RAT) that allows a simultaneous description of trapping effects and a reduction of the recombination lifetime in low level injection.

We present spatially resolved and injection dependent excess carrier lifetime measurements on silicon. At low level injection conditions an anomalous increase often interferes in such measurements. The origin of the anomalous increase is discussed. Assuming trapping as the origin, highly resolved images of trap parameters together with low level injection recombination lifetimes with strongly reduced trapping effects have been obtained. A theoretical model for infrared lifetime imaging based on the Hornbeck and Haynes model [J. A. Hornbeck and J. R. Haynes, Phys. Rev. 97, 311 (1955)] is presented which describes the trapping effect on the measured lifetime. This model is fitted to experimental spatially resolved data to extract trapping parameters, particularly trap density and the trap-escape ratio, i.e., the ratio between escape rate of minority carriers from the trap level into the minority band (detrapping) and trap rate from the minority band into the trap level (trapping). An upper bound for the low level injection recombination lifetimes is determined. Lifetime and trapping parameters are compared with dislocation density maps. A strong correlation is found between the total trap density and the crystal defect density.

The present investigation deals with the distributed parameter analysis of the p–n junction solar cell in the current-induced case at low level injection. The theory, for the first time, takes into account the metal–semiconductor contact resistance, along with the base bulk resistance and the diffused layer shear resistance. The transcendentally nonlinear differential equations for the emitter layer current and voltage have been solved analytically. Additionally, expressions for the I–V characteristic and equivalent ‘lumped’ series resistance have been established. Such physical parameters are very useful in the optimisation of the contact finger width and separation. Inclusion of the contact resistance, even for very small values, corresponds to the nonuniform carrier generation within the metallic grid. Therefore, the results are affected both qualitatively and quantitatively. The most important effect has been calculated in the I–V characteristics resulting from an additional contribution to the series resistance. Analysis reveals that the series resistance and the diode quality factor vary with applied current.

When collector current of a reverse biased epitaxial bipolar transistor exceeds a critical value, the transistor goes into current mode second breakdown and its terminal voltage abruptly decreases to a low value. The current is localized at the centre of the emitter stripe where high current densities will be reached. At high collector current densities, high level injection is encountered in the base region. Here, a simple analytic expression accounting for high injection effects in the base is derived for the critical collector current. The result is applied to a planar transistor structure. The approach presented in this paper is different from those given by previous authors where they treated current crowding phenomena only for low level injection.

When radiative (band to band) lifetimes and nonradiative (multiphonon via flaws) lifetimes become comparable, as is the case for GaAs, the customary diffusion equation for minority carriers under low level injection conditions must be augmented by terms originating from photon transport. Using the generalized van Roosbroeck–Shockley relation between absorption and emission as well as radiative transfer theory, the relevant equations for free carrier transport are derived. Subsequently, it is shown that the influence of the reabsorbed recombination radiation on carrier transport while unimportant at low doping levels becomes important for n‐type GaAs at high doping levels. We also determine the external luminescence flux taking due account of multiple emission and absorption events inside the sample.

An exact transient solution is presented for the spatial and temporal variation of the injected minority carrier distribution and for the total number of injected minority carriers in a double heterojunction device, e.g., a light-emitting diode (LED) or diode laser, in the presence of interface recombination centers at the heterojunction boundaries, with finite minority carrier lifetime in the center region, and for current pulse excitation. The solution for the model assumed is completely general and can be applied to any material or dimensional situation; for purposes of illustration, numerical results appropriate for typical III-V or Pb-salt heterostructures are presented. It is shown that for the total number of injected minority carriers, an effective minority carrier lifetime can, in certain cases, be defined which is a function of the interfacial recombination centers, the minority carrier lifetime, and the middle or "active" region width. The practical implications of this and other results for device performance and analysis are discussed.

Majority and minority carrier trapping has been studied in neutron-irradiated silicon diodes by transient junction capacitance recovery as well as by capacitance-versus-frequency and pulsed field effect techniques. After exposure to damaging radiation, trapping results in a transient time dependence of depletion layer width which may determine the survivability of depletion layer devices in a radiation environment. Majority carrier traps have been found in n-type neutron-irradiated silicon at Ec -0.36 eV and in p-type silicon at Ev + 0.30 eV. The capture cross sections for both types of traps are of the order of 10-15 cm2. Following a burst of damaging radiation, traps with unequilibrated charge exist with concentration roughly an order of magnitude larger than observed in equilibrium. These unequilibrated states relax slowly via the majority carrier band but quite rapidly when minority carriers are deliberately injected. Capacitance-voltage characteristics of neutron-irradiated junctions recovered by minority carrier injection show that recovery occurs only within a diffusion length of the metallurgical junction. Capacitance and lifetime recovery effects can be qualitatively interpreted in terms of the Gossick model for the disordered region spacecharge layer modified to include minority, as well as majority, carrier trapping. Recovery in this model is attributed to a shrinking of the disordered region space-charge layer.

The influence of As surface concentration C SE on the emitter efficiency β γ and the temperature dependence of β γ are reported. The theoretical model that is used to explain the variation of β γ with C SE is based upon the difference in the effective energy bandgaps in the emitter and base regions \DeltaE_{g} . Experimental measurements of \DeltaE_{g} versus C SE are presented. Measurements of β γ versus C SE show that the effective emitter doping density Q_{E}/x_{eb} reaches a maximum value at C_{SE} \cong 1.5 \times 10^{20} atoms/cm3, corresponding to the threshold above which \DeltaE_{g} > 0 . For the case of a constant active base doping/cm2Q B , this also corresponds to an optimum in the emitter efficiency β γ . However, it is shown that in typical sequential diffusion processing of transistors, β γ increases monotonically with C SE because Q_{B} = Q_{B}(C_{SE}) decreases. In addition, for devices fabricated in this study, \Delta\beta_{\gamma}/\DeltaC_{SE} at C_{SE}=2 \times 10^{20} atoms/ cm3for As-diffused emitters (doped oxide) was ≈ 5 times greater than for ion-implanted-diffused As emitters, showing the superiority of implantation in controlling gain. Finally, transistors that were made with C_{SE} \siml 1.4 \times 10^{20} atoms/cm3( \DeltaE_{g} = 0 ) showed β gamma (85°C)/ β γ (-15°C) ≤ 1.05.

A solution of the continuity equations is obtained for the space charge distribution by assuming (1) that deviations from neutrality are small, and (2) that the space charge fields, which are a consequence of the terms containing ▿·E in these equations give rise to pure diffusion and pure ``drift‐wave'' terms with time dependent coefficients. It is, for equal numbers of holes and electrons initially injected, e[(p−p0)−(n−n0)]=−τρ∇ lim E·J[1−exp(−t/τρ)], where τρ equals K/4πσ, the relaxation time, J is the total current density including diffusion, as well as drift, and ∇ lim E means that the divergence does not operate on E (the electric field is held constant). In the differentiation ∂n/∂x and ∂p/∂x are considered to be equal, as are ∂2n/∂x2 and ∂2p/∂x2.Working independently, H. Brooks and W. van Roosbroeck arrived at expressions for both the ambipolar diffusion coefficient and the ``group mobility'' of the drift of a pulse of excess carriers. This theory yields the same results, and, in addition, transi...

A study is made to determine analytically the time variation of the terminal voltage of a p-n junction in response to a terminal current which starts with a large forward value and continues to decrease linearly until the reverse saturation is attained. It is shown that the period between the reversal of current and the reversal of voltage depends exclusively on the lifetime, diffusion length, and thermal equilibrium densities of minority carriers in both regions of the junction. For some cases, the period between the reversal of current and voltage reduces to half the lifetime of either of the two types of minority carriers. This property allows measuring the lifetime of minority carriers for certain p-n junctions by relatively simple means.

Two methods are described for the measurement of lifetime of minority carriers. One depends on pulse injection of carriers in a filament and detection, after a known time, at a collector. The second makes use of the decay of the conductivity modulation caused by minority carriers after injection at a single contact. Both measure the lifetime in a small region rather than the average value over a large part of the sample.

The possibility of backward injection of minority carriers in p‐n junctions is shown. It is predicted that in a forward‐biased p‐n junction where this type of injection occurs, heat energy is pumped out of the junction causing it to cool off. Some conditions which lead to backward injection of minority carriers are described. Theory is presented for a particular p‐n junction model in which this new cooling effect takes place. It is shown that a given dc electrical energy may be used to pump nearly an equal amount of heat energy from one of the junctions to the neighboring ones provided that the junction temperatures are sufficiently close to each other.

Electron trapping in metal‐oxide‐silicon structures and its dependence on the injected electron energy distribution and oxide field were studied. It is found that at high injection levels trapping efficiency and saturation level increase with the accelerating field in the Si, and decrease with increase in the oxide field. These results differ markedly from those obtained in low level injection, in which it is assumed that trapping is of electrons injected from the Si into the oxide conduction band. Based on the high level injection experimental results, it is proposed that significant electron trapping is obtained through direct tunneling of hot electrons with energy less than the potential barrier, into localized states in the oxide near the Si‐SiO2 interface.

Surface accumulation of carriers not only affects the conductance of a semiconductor sample, but is traditionally invoked as a means of reducing the effects of surface recombination velocity on minority carrier lifetime. It is shown that circumstances can easily arise where the latter effect is actually reversed, to the detriment of device performance. Simple expressions are derived for the effective surface recombination velocity, and the relationship between minority carrier lifetime and sheet conductance in truly surface dominated samples.

The mechanism proposed by Matsunaga et al. to explain the injection of minority carriers into the substrate of a saturated n-channel MOST cannot account for the size of the observed current. An alternative mechanism is suggested based on optical generation of minorities by radiation emitted by hot carriers in the drain depletion region. Evidence for this mechanism is presented.

An analysis of base widening and the current dependence of the cutoff frequency f T has been given previously by Kirk. His approximate analysis is based on the location of the edges of transition regions, whose definition becomes problematic in transistors having nonuniform base doping and at high current levels. An alternate theory of f T falloff at high currents has recently been given with the implication that base widening does not occur. This paper presents numerical solutions based on a one-dimensional model (with realistic doping profile) of an npn epitaxial transistor at low reverse collector bias at various current densities ranging from low level injection to high level injection. Solutions for electric field, hole and electron densities as functions of distance are shown. At low-injection levels, a high-field region exists near the transition between base and expitaxial layer. This high-field region is relocated to the interface between epitaxial layer and substrate under high injection conditions. Numerical solutions of delay time as a function of current density, calculated frown a charge control point of view, are also given. The results show that the delay time increases sharply in the current range where "field relocation" takes place. Whether "base widening" occurs is a matter of semantics. However, the physically observable effects predicted by Kirk for a one-dimensional structure are shown to occur.