D.J. Roulston

A simple expression for band gap narrowing (BGN) in heavily doped Si, Ge, GaAs and GexSi1−x strained layers

Abstract This paper presents simple but accurate closed form equations for Band Gap Narrowing (BGN) for n and p type, Si, Ge, GaAs and GexSi1−x alloys and strained layers. The equations are derived by identifying the four components of BGN: exchange energy shift of the majority band edge, correlation energy shift of the minority band edge and impurity interaction shifts of the two band edges. In the simple parabolic band approximation, the BGN is determined by the effective masses of the carriers and the relative permittivity of the semiconductor. For real semiconductors, known corrections due to anisotropy of the bands, due to multi-valleys in a band and due to interactions between sub-bands are used. The values of BGN for n Si, n Ge and n and p GaAs calculated using this simple formulation agree closely with the theoretical values calculated by other authors using advanced but complex many body methods and the Random Phase Approximation for screening effects. For p Si and p Ge ours appear to be the first calculations taking all interactions into account. Experimental values of BGN for all semiconductors except for p Ge for which no data could be found, are also in very good agreement with our theory. The Fermi level for n and p Si and p GaAs is determined using the published luminescence data. In heavily doped p type semiconductors, the values are found to be considerably smaller than those calculated using the known values of the effective density of states. The values of apparent BGN for n and p Si and p GaAs calculated using experimentally determined Fermi levels are in remarkably good agreement with the experimental values derived from device measurements. All results are presented in a form which lends itself to numerical computer simulation studies.

Band‐gap narrowing in novel III‐V semiconductors

A predictive model for band‐gap narrowing has been applied to several III‐V semiconductors. Band‐gap narrowing is expressed as ΔEg =AN1/3+BN1/4+CN1/2 ; values for A, B, and C are predicted for these materials. The commonly used N1/3 relation is shown to be valid for the p‐type materials considered, but not for n‐type materials.

Modeling and measurement of minority-carrier lifetime versus doping in diffused layers of n + -p silicon diodes

The results of minority-carrier lifetime measurements in heavily phosphorus-doped n+diffused layers of p-n junction diodes using a spectral response technique are reported in this paper. Exact modeling of current-flow equations, modified to include bandgap reduction due to high carrier concentration and Auger recombination, is used to compute the dependence of diffused-layer photocurrent Jpthon the incident light energy and intensity. The photocurrent in the diffused layer is also obtained by subtracting the theoretical value of the space charge and uniformly doped p-region component from the experimentally measured photocurrent of the diode at each wavelength. Note that all calculated values based on light intensity include computed transmittance/reflectance through the oxide layer at each wavelength. The comparison of the values of Jpthwith Jpexp, using nonlinear least square techniques, then directly gives the lifetime profile in the diffused layer. A simple expression is given for lifetime as a function of doping which may be used in modeling and prediction of device performance. Using this experimental technique it was found that the lifetime in the diffused layer is an order of magnitude less than that corresponding to uniformly doped bulk-silicon values and is very much process dependent; its value being 3.72 × 10-11s for surface concentration of 3.0 × 1020cm-3and increases to 2.9 × 10-8s at doping concentration of 1.0 × 1017cm-3.

Drift hole mobility in strained and unstrained doped Si/sub 1-x/Ge/sub x/ alloys

Results of the drift hole mobility in strained and unstrained SiGe alloys are reported for Ge fractions varying from 0 to 30% and doping levels of 10/sup 15/-10/sup 19/ cm/sup -3/. The mobilities are calculated taking into account acoustic, optical, alloy, and ionized-impurity scattering. The mobilities are then compared with experimental results for a boron doping concentration of 2*10/sup 19/ cm/sup -3/. Good agreement between experimental and theoretical values is obtained. The results show an increase in the mobility relative to that of silicon. >

Simplified computer-aided analysis of double-diffused transistors including two-dimensional high-level effects

An approximate two-dimensional numerical analysis has been developed for studying double- (or triple-) diffused transistors. The program supplies dc and hf terminal characteristics (e.g., h fe , r bb , f T , I B , V BE ) over a wide range of operating collector currents and voltages for a given set of physical device parameters (mask dimensions, impurity profile, etc.). The approach is based on obtaining a set of differential equations describing current flow in the longitudinal (emitter-collector) direction and a separate differential equation describing current flow in the lateral direction. The assumption is made of space-charge or space-charge-neutral regions with current- and voltage-dependent boundaries. The equations are valid for arbitrary injection levels and automatically include such high-level effects as conductivity modulation, base widening, and emitter current crowding. Both theoretical and experimental results are given for transistors with f T values between 100 MHz and 3 GHz. The validity of the approach is confirmed and some areas requiring further study are outlined. The technique described is felt to be particularly attractive for the design and optimization of high-power microwave devices, due to the small computer execution time and memory requirements.

Comparison of experimental and computed results on arsenic- and phosphorus-doped polysilicon emitter bipolar transistors

This paper presents a detailed comparison of the measured and computed electrical characteristics of polysilicon emitter bi-polar transistors over a wide range of processing conditions. Detailed electrical measurements are made of both the emitter resistance and the base and collector current as a function of base-emitter voltage. Devices with arsenic- and phosphorus-doped emitters are considered, as well as both with and without a deliberately grown interfacial oxide layer. The theoretical characteristics are computed using a unified model that incorporates both transport and tunneling mechanisms. It is shown that the measured emitter resistances across a wide range of processing conditions can be satisfactorily explained using a tunneling model with a single value for the electron effective barrier height (0.4 eV). Values for the modeling parameters are obtained, in some cases uniquely by measurement, and in others by fitting the experimental results. In devices with a deliberately grown interfacial oxide, the base current is suppressed to such an extent that recombination in the single-crystal emitter and in the base becomes important.

Collector design tradeoffs for low voltage applications of advanced bipolar transistors

The values of BV/sub ceo/ are computed for transistors with highly doped collectors and with thin reach-through collectors, using various sets of ionization coefficients including new data. Computed values of BV/sub ceo/ are compared with experimental results. It is shown that transistors with thin reach-through collectors have higher current capability for any given BV/sub ceo/ compared to those with highly doped collectors. Tradeoffs in terms of BV/sub ceo/, maximum collector current and the maximum frequency of operation are studied for transistors with highly doped and thin reach-through collectors. >

Design study of AlGaAs/GaAs HBTs

The frequency performance of AlGaAs/GaAs heterojunction bipolar transistors (HBTs) having different layouts, doping profiles, and layer thicknesses was assessed using the BIPOLE computer program. The optimized design of HBTs was studied, and the high current performances of HBTs and polysilicon emitter transistors were compared. It is shown that no current crowding effect occurs at current densities less than 1*10/sup 5/ A/cm/sup 2/ for the HBT with emitter stripe width S/sub E/ >

Recombination dependent characteristics of silicon P+−N−N+ epitaxial diodes

Abstract The low level injection d.c. and transient characteristics of a P+−N−N+ diode are discussed from a theoretical point of view, using the minority carrier lifetime ‘τepi’ in the lightly doped region and the parameter α defining the properties of the high-low junction, as basic parameters. A value of α less than unity is predicted for typical epitaxial silicon structures. Detailed experimental studies involving both lifetime measurements (using optical techniques) on the original epitaxial layer and substrate and d.c. plus transient measurements on completed devices confirm the existence of a ‘blocking’ high low junction (α less than unity). However the measured value of α is still considerably higher than that predicted from the theory, thus indicating conclusively the presence of additional recombination mechanisms at the high low junction interface. An interesting and useful result of the study is the fact that using a combination of d.c. and transient measurement techniques, both α and the effective epitaxial layer width Wepi can be uniquely determined using the given theoretical curves.

Two-dimensional analysis of emitter resistance in the presence of interfacial oxide breakup in polysilicon emitter bipolar transistors

Two-dimensional computer simulations of the emitter resistance and majority carrier current flow in the presence of interfacial oxide breakup in polysilicon emitter bipolar transistors are shown and compared with published experimental results. The analysis reveals that the behavior of the emitter resistance with oxide layer breakup can be adequately predicted only if 2-D majority carrier current flow is taken into account. The interfacial layer plays an important role in determining the emitter resistivity only in very early stages of oxide layer breakup. Both the experimental data and the analysis reveal a much faster fall-off in emitter resistance with oxide layer breakup than previous 1-D dimensional theoretical analyses have suggested. The 2-D majority carrier modeling presented suggests that the emitter resistance decreases much more rapidly than the current gain in the early stages of oxide layer breakup. Physical mechanisms which explain the differences in the dependence of the emitter resistance and gain on oxide layer breakup are proposed. >