Bandgap Narrowing Effect Research Articles

Effects of heavy impurity doping on electron injection in p+-n GaAs diodes

Measurements of electron injection currents in p+-n diodes are presented for a range of p-type dopant concentrations. A successive etch technique was used to characterize the electron injection current in terms of the product (noDn). Measurements are presented for Zn-doped GaAs solar cells with p-layer hole concentrations in the range 6.3×1017−1.3×1019 cm−3. The results demonstrate that so-called band-gap narrowing effects substantially increase the injected electron current in heavily doped p-type GaAs. These heavy doping effects must be accounted for in the modeling and design of GaAs solar cells and heterostructure bipolar transistors.

Measurement of bandgap narrowing effects in p-GaAs and implications for AlGaAs/GaAs HBT performance

The authors report the first electrical measurements of bandgap narrowing effects in p/sup +/-GaAs and explore their influence on the performance of AlGaAs/GaAs heterojunction bipolar transistors (HBTs). A sequential etch technique was used to measure electron injection currents in MOCVD (metalorganic vapor-phase epitaxy)-grown p/sup +/-n GaAs diodes with Zn dopant concentrations ranging from 6.3*10/sup 17/ to 1.3*10/sup 19/ cm/sup -3/. The measurement consisted essentially of characterizing the n=1 electron injection current as a function of thickness of the p-type layer. From the measured n=1 saturation current density, the product, n/sub ie//sup 2/D/sub n/ was determined, where n/sub ie/ is the effective intrinsic carrier concentration and D/sub n/ is the minority-carrier diffusion coefficient. This product was observed to increase greatly with doping and was still a factor of two to three greater than expected, even when bandgap shrinkage was accounted for. This affects AlGaAs/GaAs n-p-n HBTs by increasing the electron current injected into the base. Bandgap narrowing effects increase the collector current by more than one order of magnitude when the base doping exceeds 10/sup 19/ cm/sup -3/. These results demonstrate the importance of treating bandgap narrowing effects when modeling and designing HBTs. >

Statistics of electrons and holes in heavily doped n-silicon

In an earlier paper [1] the authors have given a model for the effective electrical bandgap narrowing in silicon at moderate levels of doping by considering the impurity-band broadening. In this paper more elaborate calculations have been done for uncompensated n-doped silicon by defining a partition function for the electron distribution within the impurity band and a mobility edge above which electrons can be considered as free. Also, calculations have been done by incorporating the effect of potential energy fluctuations on the density of states within the conduction and valence bands. It has been shown that these fluctuations considerably increase the effective density of states within these bands, though the tail states are mainly due to the impurity band. The calculations show that the electrical bandgap narrowing is largely nonrigid. The rigid band shift is comparatively small.

Role of lifetime and energy-bandgap narrowing in diffused-junction silicon solar cells

The effects of bandgap narrowing, surface recombination and lifetime on the performance of n+p-diffused-junction silicon solar cells are analysed, and experimental results are given to show that the bulk recombination in the n+-diffused region plays an important role in limiting the open-circuit voltage of solar cells. The analysis shows that the surface effects are relatively unimportant in diffused-junction solar cells with surface doping concentration above 1020/cm3 because of the low lifetime due to phonon-assisted recombination in addition to Auger recombination in the heavily doped layer.The analysis also brings out the effects of bandgap-narrowing models and lifetime models on the estimated carrier-concentration distributions, short-circuit currents and open-circuit voltages of solar cells. The theoretical results are compared with the experimental data obtained on n+p solar cells having different n+-layer thicknesses and different surface concentrations, to demonstrate the tenability of the bandgapnarrowing and lifetime models used in the analysis.

An indirect measurement of energy gap for silicon and germanium

Using temperature characteristics obtained from the reverse saturation current of p- n junctions and the forward-bias voltage, the energy gaps of Si and Ge can be indirectly measured at 0 K by means of linear extrapolation. Considering the different components of the saturation currents of p- n junctions for Si and Ge, we have forsaken the methods prevalent in the usual CAD of electronic circuits and, instead, have derived two distinct equations to measure the E g0 of Si and Ge. The paper shows, after including band-gap narrowing effects, that the extrapolated intrinsic E g0 of the sample Si approaches the generally accepted values, with an error within 0.8–1.0% for Si. The E g0 for doped Ge is 0.67–0.75 eV approximately, when using, a small power transistor as sample. The model of physics used in the test has been shown to be clear-cut and simple, thus providing a simple way for testing the parameter E g0 , both practically and pedagogically.

Optimization of the surface impurity concentration of passivated emitter solar cells

The optimum emitter surface dopant concentration (Ns) in passivated silicon solar cells is found for different base resistivities with the help of a computer model. The model takes into account not only the band-gap narrowing, Auger and surface recombination effects on the dark saturation current, but it also considers the variation of series resistance as the impurity concentration changes. The results obtained with the model show different behavior for passivated and nonpassivated solar cells. The open-circuit voltage and the conversion efficiency of nonpassivated solar cells is almost independent of the surface impurity concentration when this parameter is greater than 2×1019 cm−3. On the other hand, for passivated solar cells the optimum value is in the range 2.5×1019 cm−3 ≤Ns<5×1019 cm−3 for typical base resistivities. Furthermore, it is confirmed that even when Ns is high (Ns>1×1020 cm−3) there is an advantage in efficiency of passivated solar cells over those which have a high recombination at the surface. However, in order to increase the efficiency appreciably Ns has to be optimized. The model also gives a procedure to optimize the grid design simultaneously with the surface concentration, assuming the other parameters are optimum.

Electrical and optical transport in undoped and indium-doped zinc oxide films

Electrical conduction in undoped and indium-doped ZnO films in as-deposited, vacuum-annealed and oxygen-annealed states has been studied. The as-deposited and oxygen-annealed films contain a large density (≥ 1017 m−2) of trap states due to chemisorbed oxygen at the grain boundaries. The role of these trap states has been analyzed in terms of the grain boundary carrier trapping model. The vacuum-annealed films are free of chemisorbed oxygen, and the conduction in these films is controlled by scattering due to ionized impurities and grain boundary barriers. In the case of undoped ZnO films, intrinsic trap states at the grain boundaries also play a significant role. The optical behavior of all films in the UV and visible regions is dielectric-like and the optical bandgap shows a dependence on free carrier concentration that is controlled by a bandgap narrowing effect due to electron-electron and electron-impurity interactions as well as the Moss-Burstein effect of bandgap widening. In the IR region the optical behavior is metal-like due to free-electron effects and follows the Drude model.

Waveguide infrared photodetectors on a silicon chip

A novel infrared (IR) photodetector structure is discussed. It represents a waveguide in which the core is a strained-layer Ge <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf> Si <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</inf> /Si superlattice (SLS) sandwiched between Si layers of a lower refractive index. Absorption of infrared radiation occurs in the core region due to interband electron transitions, and photogenerated carriers are collected in the Si cladding layers. Due to the recently discovered effect of bandgap narrowing by the strain in alloy layers the fundamental absorption threshold of the SLS is shifted to longer wavelengths, so that the detector can be operated in the range of silica-fiber transparency, 1.3-1.55 µm. The optimum SLS composition and thickness have been estimated from the known material properties and waveguide theory. The detector quantum efficiency grows with the optical path length, remaining consistent with the requirements of high-speed fiber-optical communications. A major advantage of the proposed structure is the possibility of obtaining avalanche gain in the silicon cladding. First experimental results have demonstrated the validity of the concept.

Arbitrary space charge to bulk boundary model of Auger recombination for semiconductor power diodes

An arbitrary semiconductor junction is used to obtain an equation for junction current density in terms of the conditions at the boundaries between the space charge and the quasineutral bulk regions on each side of the junction. Included are the effects of recombination in the space charge volume as well as bandgap narrowing and ambipolar diffusion effects in the bulk regions at these boundaries. The equation also accounts for the effects of drift field, which is neglected in other theories, and demonstrates that it exerts a form of cross-coupled modulation upon current flow. Under certain conditions, it may be shown that the current density is largely determined by the carrier density gradient at the space charge to bulk boundaries. A solution for carrier density gradient, which is obtained by one integration of the diffusion equation, does not require a precise solution for carrier density profile and may be used to model bulk region Auger recombination with the aid of the derived equation for current density. This contribution may find use in the design of snubber diodes.

Doping effects on the band structure in n- type silicon at 300 K

Based on two screened donor potential models and taking into account the electron-electron interaction effect in the electron-donor interaction, the band-gap narrowing (BGN) in n-type doped silicon at 300 K is investigated. The BGN effect is expressed in terms of physical BGN ( ΔE g ), a change in density of conduction-band states ( Γ n ) and the change in effective electron (hole) mass ( γ n ( γ p )). In fact, electrical BGN is found to be given by ΔE g, elec. ∗ = ΔE g + Γ n γ n + Γ p + ΔE g, fd ≅ ΔE g + Γ n , where ΔE g, fd represents the Fermi-Dirac statistics effect. Our results of ΔE g and ΔE tg, elec. ∗ agree fairly with corresponding observed results, and the large values of Γ n ≅ ΔtE g, elec. ∗ − ΔE g obtained at high donor concentration are in good agreement with a qualitative discussion given by Marshak and Van Vliet. Finally, the present results for the effective intrinsic-carrier concentration n ie are compared with corresponding results observed by Tang.

Theory of the high base resistivity n+p p+ silicon solar cell and its application to radiation damage effects

High-resistivity (84 and 1250 Ω cm) n+pp+ silicon solar cells, with thickness ranging from 56 to 250 μm, were irradiated by 1-MeV electrons and their performance evaluated using a specially developed analytical model. It was found experimentally that, contrary to expectations based on previous performance data for lower resistivity cells, the greatest cell degradation occurred for the present higher-resistivity cell. In addition, the degradation was found to be much greater than that observed for cells with base resistivities typical of those currently used in space. Relevant details of the analytical model are presented. Computer calculations of optically injected minority carrier distributions, and all voltage components at the maximum power point, are used to interpret the experimental results. The analytical model is valid for both low and high injection and includes the effects of band-gap narrowing in the cell’s heavily doped regions. It was concluded that, for the thicker higher-resistivity cell, lack of conductivity modulation, leading to a large ohmic drop in the cell base, was the predominant cause of cell degradation. Although still a significant factor, the magnitude of the ohmic component is less important in the thinner 1250 Ω cm cell. In the thicker 84 Ω cm cell, absence of conductivity modulation becomes comparable to loss in collection efficiency as a loss mechanism while in the 84 Ω cm thinner cell loss in collection efficiency begins to emerge as a dominant loss mechanism. Our results indicate that lack of conductivity modulation is a fundamental roadblock toward achieving increased radiation resistance simply by indefinitely increasing the base resistivity of silicon solar cells.

On the shifting and broadening of impurity bands and their contribution to the effective electrical bandgap narrowing in moderately doped semiconductors

The role of shifting and broadening of the impurity band in determining the effective bandgap narrowing in moderately doped semiconductors, as obtained from the electrical transport experiments, has been discussed. A model complementary to Lee and Fossum's model (which is based on band tails and many body effects and would hold true at comparatively higher dopant concentrations at which the impurity ionization energy has completely disappeared)has been proposed here. It is shown that Mahan's variational calculations when seen in the right perspective explain the movement of impurity states toward the conduction band. Morgan's formulation has been used for the calculation of the density of states in the impurity band. The model quite satisfactorily explains the electrical bandgap narrowing data for dopant concentrations N < N <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> . For phosphorous-doped silicon, N <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> is found to be 3×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">19</sup> cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> .

Computer simulation with scale down I2L

AbstractScaling down of solid state devices is indispensable for large‐scale integration of circuits. Understanding the characteristic tendency and the limitation of the scaling down provides a useful guideline in recent scaling‐down efforts. This paper discusses scaling down of bipolar transistors, especially the I2L, for which little has been reported. the collector dimension of the I2L is chosen as the scale‐down parameter. Important characteristics such as the current gain, capacitance and delay time are studied by similarly reducing the device with an identical shape from 5 μm to 0.5 μm. In the analysis, the bandgap narrowing effect and the Auger recombination are considered and the two‐dimensional computer simulation program CADDET‐B is used. It is expected that the minimum delay time is reduced to about 200 ps and the power dissipation‐delay time product is improved to about 3 fJ when the collector dimension is scaled down to 0.5 μm.

Measurements of the p-n product in heavily doped epitaxial emitters

A new method is described for the measurement of the p-n product in the heavily doped epitaxial emitters of biopolar tansistors. Quantitative electron-beam-induced conductivity is used to determine the diffusion length in the emitter as well as the emitter thickness. I - V characterization and other standard methods are then used to measure the p-n product. The principal advantage of this method is that corrections for recombination in both the emitter and the base can be made based on measurements on identical regions of the same device. A key problem with other methods for determining the p-n product is their inability to separate changes in the p-n product (bandgap narrowing) from recombination, based on measurements taken on the same region of the device. New data for the p-n product at ∼ 1020.cm3free-carrier electron density are uniformly compared to other published data. The importance of the effective bandgap narrowing parameter both for comparing experimental data and for device modeling is stressed. Diffusion length measurements on the more heavily doped emitters yield lifetimes longer than expected based on published lifetimes determined by the decay of optical luminescence in heavily doped silicon. Possible reason for this difference are discussed and attributed to gettering in our samples.

Heavy doping effects on donor-acceptor spectra of polar semiconductors at low temperatures

The heavy doping effects on donor-acceptor (DA)-pair spectra at small DA-pair distances R are investigated, basing on an effective screened impurity potential model given by Morgan and on the results of the R-dependent electron (hole)—longitudinal optical phonon interaction energy obtained by Kartheuser et al. It is suggested that the deviation of the electron—hole recombination energy by dense impurities (or at small R), found from the energy of the emitted photon for a zero-phonon transition, results from the band-gap narrowing effect. At large R, we have found that the energy gap of the pure ZnSe crystal is equal to 2.827 eV, in good agreement with observed results. Finally, at small R, our numerical results applied to ZnSe doped with ln and Li impurities are compared with other theories and with observed results.

An operational method to model carrier degeneracy and band gap narrowing

In this paper an operational method of modeling heavily doped silicon to include effects of carrier degeneracy and band gap narrowing is presented. The issue of carier degeneracy on majority carrier flow is discussed together with the question of the ambiguity in the electrostatic potential associated with identifying which band edge is narrowed. Using an exact numerical analysis of a bipolar transistor as an example it is shown that when modeling carrier flow in quasi-neutral regions, classical statistics can be used for the majority carrier and the ambiguity in the electrostatic potential can be ignored. Overall, it is shown that for the same quasi-neutral heavily doped regions the effects of carrier degeneracy and band gap narrowing are accurately modeled within the context of classical statistics by adding the quasi field term to the minority carrier transport equation that is based on the commonly used “band gap narrowing” data available from measurements of minority carrier transport in heavily doped regions. While it is recognized that this is not rigorously correct the result of this paper is to establish the accuracy for the operational method most commonly used to model heavy doping effects.

Photovoltaic investigation of minority carrier lifetime in the heavily-doped emitter layer of silicon junction solar cell

The minority carrier lifetime in a phosphorous-diffused layer of a conventional N+/P silicon photocell has been investigated experimentally. The photovoltages have been measured as a function of photon flux density from low to medium illumination levels. From the quasi-Fermi level analysis of Gray-Kao-Schroder, we have determined the carrier recombination lifetime as a function of the photogeneration rate 〈G〉 in the heavily-doped N+ layer. When the band gap narrowing effect is taken into consideration, the recombination processes can be described by (i) a ’’positive-field controlled’’ Shockley-Reed-Hall recombination at low photo injection level, (ii) a ’’positive-field influenced’’ Auger recombination at the medium injection level, and (iii) a ’’negative-field controlled’’ Auger recombination at the high injection level. Under a very high photoexcitation condition, the magnitude of the saturated open circuit voltage of the cell is limited by the recombination lifetime at the surface contact region.

An accurate design method of bipolar devices using a two-dimensional device simulator

The systematic application of two-dimensional analysis for the bipolar device design is described. In this analysis, surface recombination is taken into account by properly modifying the carrier lifetime term, in addition to mobility variations and bandgap narrowing effects. Moreover, an effective method to obtain terminal currents from the calculated current densities is introduced. The analysis of transistors with different emitter length demonstrates the validity of this procedure. The propagation delay time of IIL also is calculated using V-I characteristics and capacitances obtained by this two-dimensional analysis. The results give good agreement with experimental ones. IIL and SFL with subnanosecond gate delay time are designed with the suitable geometry and doping profiles by the two-dimensional analysis.

Analysis of high-efficiency silicon solar cells

Performance data on high-efficiency concentrator (>18 percent at 25 suns) silicon solar cells are compared to results from an exact numerical model in which all parameters for the calculation are taken from the existing literature on bulk silicon. The numerical solution of the transport equations includes the effects of Fermi-Dirac statistics, bandgap narrowing, and Auger recombination. Cell performances as a function of sunlight concentration are predicted with reasonable accuracy using this model. Evidence for the existence of bandgap-narrowing effects is found by comparing experimental data to calculated values of spectral quantum efficiencies and open-circuit voltages under a variety of lifetime assumptions. The validity of using superposition with simple diode equations to approximate the behavior of silicon solar cells also is examined.

Rigid band analysis of heavily doped semiconductor devices

The conventional carrier transport equations used in device analysis must be modified for heavily doped semiconductor regions. The modifications to Shoekley's auxiliary equations relating the carrier densities to their corresponding quasi-Fermi levels are derived for the rigid band model. We include the effects of asymmetric bandgap narrowing and of carrier degeneracy (Fermi-Dirac statistics). Emphasis is placed on writing the equations in a simple form that indicates the effect of changes in the band structure due to heavy doping. In this form they can serve as a basis for computer-aided analysis and design. We show that, in general, the effective intrinsic carrier density n ie as well as the electron and hole current densities depend on the asymmetry in bandgap narrowing. However, for the special case of low-level injection, n ie and the minority current density depend only on the total bandgap narrowing \DeltaE_{g} . Furthermore, we indicate that interpretation of experiments with theory using Boltzmann statistics, instead of Femi-Dirac statistics, will underestimate \DeltaE_{g} in degenerate material.