S.C. Jain

The energy of an array of dislocations: Implications for strain relaxation in semiconductor heterostructures

Abstract An exact closed-form formula is given for the energy of an array of dislocations, arranged periodically on the interface between an epitaxial layer and its substrate, when these are modelled as elastically isotropic with the same elastic constants. In the course of the formulation, the exact equivalence of equilibrium theories originating in the work of Frank and van der Merwe and of Matthews and Blakeslee is established. The new formula allows the exact assessment of arrays of dislocations in equilibrium, for layers thicker than critical. This demonstrates that previous approximations may be seriously in error.

A new study of critical layer thickness, stability and strain relaxation in pseudomorphic gexsi1-x strained epilayers

Abstract The predicted energy of an array of dislocations in semiconductor epilayers is considerably reduced due to interactions between the dislocations. It is found that when the effects of interactions are taken into account, the existing expression for critical layer thickness hc becomes invalid. A method to calculate the correct critical layer thickness hci taking into account the interactions, is given. Values of hci are always smaller than hc but the difference hc—hci is small. The concentration of dislocations present in thick epilayers (i.e. with hhci) in stable equilibrium increases considerably due to interactions. The rates of plastic flow and strain relaxation on annealing the metastable epilayers also increase. The values of phenomenological constants present in the plastic flow theories which are used to interpret experiments are much reduced when interactions are properly taken into account.

Photovoltage decay in p‐n junction solar cells including the effects of recombinations in the emitter

The expressions for the open circuit photovoltage decay in a p‐n junction solar cell are derived, including the effects of recombinations in the emitter. It is shown that for a cell with base thickness wB≫LB, the base diffusion length, the voltage decay rate for small values of time depends on the emitter dark saturation current JE0; the larger the value of JE0 , the faster is the initial rate of voltage decay. For large values of time, the rate of voltage decay is solely determined by the minority carrier lifetime in the base τB and is independent of JE0 . However, for a cell with wB≲LB, the voltage decay is linear from the very beginning and the decay rate is of the form (kT/e)[(1/τB) +(1/t1)]. The time constant t1 is independent of τB . It, however, depends on the base thickness, the effective back surface recombination velocity, and the emitter dark saturation current JE0 . The value of JE0 depends on emitter thickness, front surface recombination velocity, drift field in the emitter, band‐gap narrowi...

Theory and experiments on open circuit voltage decay of p‐n junction diodes with arbitrary base width, including the effects of built‐in drift field in the base and recombinations in the emitter

An expression for the forward current induced open circuit voltage decay of a p‐n junction diode with a finite base width is derived. The expression includes the effects of recombination in the emitter and the built‐in drift field in the base which may arise due to a nonuniform impurity profile. The voltage decay rate is dependent on the base thickness, base drift field, emitter dark saturation current, the effective surface recombination velocity at the back contact, and the minority carrier lifetime in the base. The effects of the drift field in the emitter, emitter lifetime, and surface recombination velocity at the emitter surface are completely taken into account by the emitter saturation current. Experimentally observed voltage decay plots for thin base hyperabrupt varactor diodes with retrograded impurity gradients in the base are reported. It is shown that the experimental results can be interpreted satisfactorily using the above theory. The values of the minority‐carrier lifetime in the base are ...

Open circuit voltage decay in p-n junction diodes at high levels of injection

Abstract The open circuit voltage decay (OCVD) in p - n junction diodes at high levels of injection is discussed in this paper. Theoretical results are given for thick base diodes and for BSF solar cells including the effect of recombination in the emitter. It is found that the recombination in the emitter becomes important at high levels of injection and makes the voltage decay faster. The experimental results in BSF solar cells at high levels of injection are also reported and found to be in good agreement with the theoretical results derived in this paper.

Comment on ’’Normal modes of semiconductor p‐n junction devices for material‐parameter determination’’

During the open circuit voltage decay (OCVD) in a diode with τB/τE≫1 (τB and τE are the lifetimes of the minority carriers in the base and emitter, respectively), the quasistatic approximation is found to be valid in the emitter but not in the base. If the band‐gap narrowing ΔEg is significant, τE,τB, as well as ΔEg determine the OCVD for t<τB. For t≫τB [and exp (qV/kT)≫1] OCVD vs t plot is approximately linear with its slope ∼1/τB, irrespective of the magnitude of ΔEg.

Electron microscope study of silver colloids in KCl : Ag

Transmission electron microscope studies of the colloids of silver in KCl : Ag crystals show that the colloidal particles are spherical in shape and have a size distribution among them. Using the observed size distribution and modified optical constants for small metal particles by the Kawabata‐Kubo method and Mies theory, the calculated shapes of the optical bands agree well with the observed band shape.

Discussion of the validity of Kuno’s relation to determine the base lifetime from a reverse recovery experiment

It is shown that Kuno’s modified relation ts/τeff =ln[1+(JF/JR)]+B, is valid for all diodes irrespective of whether or not heavy doping effects are important and whether the emitter and base thickness are small or large provided ts is large or JR/JF is small). The slope of the ts vs ln[1+(JF/JR)] straight line plot gives τeff. For a large base thickness, τeff≂τB. For a short base, 1/τeff=1/τB+1/t1, where t1 depends on the base thickness, the emitter properties, and the surface recombination velocity at the base contact. For small ts/τB, B is not constant anymore, and the ts vs ln[1+(JF/JR)] plot becomes curved in all cases. The effects of photoexcitation and of drift field in the quasineutral regions are also considered.

Reverse recovery in p-n junction diodes with built-in drift fields

Abstract This paper extends the earlier analysis of Moll, Krakauer and Shen of the reverse recovery of a symmetrical p-n junction diode with built-in retarding drift field in the base to the diodes in which the effect of bulk recombinations in the base is important. It is shown that the effect of bulk recombination becomes important if J f J R ⪆ 0.5 (JF and JR are the forward and the reverse currents respectively) even when the drift field is very strong. For very strong retarding fields, ts vs ln (1 + J F J R ) plot is linear and has a slope very close to the minority carrier lifetime τB in the base even for small values of time. Hence, τB can be conveniently determined by this method for such diodes. Expressions for the charge left in the base at the end of the storage phase and for the decay of the current in the second phase are also derived and discussed.

The influence of heavy doping effects on the reverse recovery storage time of a diode

Abstract During the reverse recovery process in a modern Si p - n junction diode, the value of J EO / J BO (the ratio of emitter to base dark saturation currents) increases and the recombination of carriers in the emitter becomes important due to heavy doping effects. A theory is developed to take these effects into account. The emitter and the base components of the current during the reverse recovery phase are found to vary with time. However, their sum remains equal to the constant reverse current J R , which flows in the external circuit. The ratio of the total quantity of charge present in the base to that present in the emitter is found to increase rapidly with time. Values of the storage time t s for different values of J EO / J BO are calculated. In a typical case, the storage time is reduced by a factor 5 in a diode with J EO / J BO = 2. In such cases, the values of lifetime τ B calculated using measured t s values and the Kingstons formula, become inaccurate. Theoretical expression for the total charge Q BS left in the base at t = t s in a base dominated diode is derived. An earlier semi-empirical formula known as Kunos formula is derived theoretically. It is found that the formula is valid both for the base dominated diode as well as in a diode with large contribution of the emitter but only when J R / J F is small. According to this formula t s vs 1n(1 + J F / J R ) plot is approximately a straight line with slope approximately equal to τ B in both cases. For large values of J R / J F when t s values are small, the correct formula shows that the plot is highly curved. An analysis of this part of the curve yields a value of J EO / J BO .