Frank L. Madarasz

Blocked impurity band detectors—an analytical model: Figures of merit

We are presenting an analytic model for the figures of merit of a novel extrinsic infrared quantum detector—the blocked impurity band (BIB) detector. The detector consists of top and bottom contacts, a heavily doped active layer, and a nearly intrinsic layer, called the blocking layer, to stop the motion of hopping carriers in the impurity band. The responsivity, gain, excess noise factor, and detectivity of the BIB detector are calculated as functions of the device dimensions, doping concentrations, and the applied reverse bias, which controls the electric field in the depletion region, devoid of hopping carriers, of the device underneath the blocking layer. Central to our model is the inclusion of impact ionization of carriers in the calculation of the detector response and of the associated noise. For practical detector dimensions and doping concentrations, and at 2‐V reverse bias, we calculate the responsivity to be on the order of 2 A/W, and detectivities, with 1012 photons/cm2u2009s background photon fl...

Effective masses for nonparabolic bands in p‐type silicon

The nonparabolic nature of the valence bands of silicon gives rise to an explicit temperature dependence in the density of states effective mass as defined through the carrier concentration as well as an energy dependence in the mass defined through the density of states itself. Both masses are important to those researchers interested in fitting electronic transport data. In the past the temperature dependent effective mass of Barber has been most commonly used. The approximations that have gone into the Barber mass are somewhat oversimplified in that he only approximated the actual band structure. We present a more complete calculation, and compare it with the results of Barber for nondegenerate p‐type silicon. There is a significant difference, a factor of about 1.4, between our results and his in the temperature range 300–600u2009K. The difference is quite noticeable in calculating electronic transport quantities such as carrier concentration or conductivity mobility.

Temperature dependent density of states effective mass in nonparabolic p‐type silicon

Previously, an exact calculation was made for the temperature dependent density of states effective mass in p‐type silicon. This calculation was made for the nondegenerate regime and included the full nonspherical‐nonparabolic nature of the valence band structure. For those researchers interested in using this mass for the analysis of their transport data we offer a polynomial fitted expression. The values generated are within 1% of the theoretical values.

Temperature dependence of the figures of merit for blocked impurity band detectors

In a recent paper [F. Szmulowicz and F. L. Madarasz, J. Appl. Phys. 62, 2533 (1987)] we introduced details of an analytical model for a top side illuminated blocked impurity band infrared detector operating under background limited conditions (BLIP). In the present paper we extend that model to a bottom side illuminated detector operating in the presence of thermally generated carriers (non‐BLIP case) as well as the optically generated background carriers. We display results of a parametric study including gain, quantum efficiency, the excess noise factor, and hence the detector figures of merit responsivity and detectivity, as functions of the detector temperature. Our study of the thermal noise includes the Poole–Frenkel effect. The results of the present calculation determine optimal operating temperatures as well as bias voltages. We show that Si:As blocked impurity band detectors, doped to 5×1017 cm−3, will be background limited below 13.5 K at low background, 1010 photons cm−2u2009s−1 operation, with re...

Intrinsic carrier concentrations in Hg1−xCdxTe with the use of Fermi–Dirac statistics

The intrinsic carrier concentrations in Hg1−xCdxTe are calculated with the use of the Fermi–Dirac statistics thus expanding on our previous calculation which employed the Boltzmann statistics. The use of Boltzmann statistics for Hg1−xCdxTe is limited to x≥0.20 and is not appropriate for the narrow band gap x<0.20 compositions. Our present treatment improves on existing calculations by using composition and temperature dependent momentum matrix element squared, which is the input to the Kane’s ku2009⋅u2009p theory, and by making no approximations to the band structure beyond those inherent to Kane’s theory. We find that our results for x≥0.20 using both statistics are in excellent agreement. We also compare our results with those of Hansen and Schmit. Good agreement is found for the range of 0.15≤x≤0.40.

Barrier formation in graded Hg1−xCdxTe heterojunctions

The problem of equilibrium barrier formation in graded Hg1−xCdxTe heterojunctions is solved with the use of a highly accurate computer model. The present calculation incorporates several features designed to improve on past efforts. The Poisson equation is solved as a nonlinear integro‐differential equation. Fermi–Dirac statistics are used to allow for the degeneracy associated with inversion for narrowly graded junctions and the degeneracy of the native defect donors. The band structure is obtained from the numerical solution of the secular equation. Fermi–Dirac statistics are taken to govern the degree of ionization of the acceptors and acceptorlike traps. Acceptors are treated as divalent flaws and their ionization energies as linear functions of the cadmium composition. The results are compared to the recent work of Bratt and Casselman [J. Vac. Sci. Technol. A 3, 238 (1985)], and the earlier work of Migliorato and White [Solid‐State Electron. 26, 65 (1983)]. Significant differences are found. The resu...

Effect of light attenuation on the responsivity and detectivity of transverse and longitudinal detectors

It is shown that when account is taken of the attenuation of incident radiation into the bulk of a photoconductor, as a result of the absorption, the expressions for the responsivity and detectivity are modified. An earlier derivation [Infrared Phys. 20, 385 (1980)] attributed the difference in the operation of the detectors in the transverse and longitudinal geometries to carefully defined ‘‘effective’’ quantum efficiencies. Here we show that a more physically motivated view attributes the difference to the different photoconductive gains for the two geometries. It is shown that the appropriate gains for the responsivity and detectivity are not the same.

Photoconductive gain of a longitudinal detector with an arbitrary absorption profile

It is shown that the photoconductive gain of a longitudinal detector is given by the ratio of the average carrier lifetime to the interelectrode transit time regardless of the absorption profile of the detector. Both corpuscular and macroscopic points of view are considered.

Time dependence of optical absorption in np‐layered superlattice structures

Recent experimental data measuring channel conductance in np‐layered superlattice structures during optical excitation have been used in a phenomenological calculation to determine the optical absorption coefficient as a function of time. Additionally, internal fields and depletion widths as functions of time are calculated. With the appropriate data one may also determine these quantities as a function of irradiation intensity and energy. This type of information should prove valuable in electro‐optical device applications.