Baraff's Theory Research Articles

Diagnosing breakdown mechanisms in monocrystalline silicon solar cells via electroluminescence imaging

The local breakdown behavior may be harmful to solar cells and could possibly permanently damage the cell. Therefore, understanding the breakdown mechanisms in commercially competitive photovoltaic devices such as monocrystalline silicon (Si) solar cells is of great importance. Here, by using the reverse-biased electroluminescence (ReBEL) imaging technique, we observed three types of breakdown phenomena in monocrystalline Si solar cells: defect-induced breakdown, avalanche breakdown, and early breakdown. We have applied a variety of methods to diagnose each breakdown mechanism. The positions of defect-induced breakdown were first determined by combining EL and ReBEL imaging. An innovation method, the distributed circuit modeling was further introduced to trace the formation of different defect-induced breakdown sites. It is firstly applied this approach in the analysis of the breakdown mechanism. Then, avalanche breakdown was demonstrated by the temperature coefficient. The origin of its emission spectra was analyzed by the Si energy band structure combined with Baraff theory. Moreover, the characteristic of early breakdown was found to be consistent with the Zener effect, which may be caused by the metal stains such as aluminum (Al) during the manufacturing process.

Impact ionization process in amorphous selenium

Temperature and electric field dependences of impact ionization rates α (for electron) and β (for hole) in a-Se have been determined by photo-multiplication measurements on sandwich type photo-cells. It has been found that both α and β decrease with decreasing temperature, in contrast to those of crystalline semiconductors. The results obtained at room temperature have been fitted to those calculated by Baraff's theory taking the geminate recombination process into account. The observed temperature dependences suggest characteristic mechanisms of the impact ionization process in this material.

Lucky-drift mechanism for impact ionisation in semiconductors

A simple analytic expression for the ionisation coefficient for impact ionisation is derived on the basis of a new approach which exploits the difference between momentum- and energy-relaxation rates for hot electrons. The basic mechanism whereby an electron gains sufficient energy to ionise is lucky to drift in which the electrons relax momentum but not energy. The electrons gain energy by drift and not by ballistic motion, and a few lucky ones reach the threshold. Those which thermalise may also contribute through the lucky-drift mechanism, starting from the average hot-electron energy. Good agreement with Baraff's theory is obtained. It is shown that neither the Schockley lucky electron nor the Wolff thermalised electron contribute significantly, in agreement with Baraff. However, the concept of Schockley's lucky electron is an essential part of the lucky-drift mechanism. The theory is simply extended to accommodate electrons injected at energies above zero, and some calculations are presented on this topic. A discussion is given of the effect of real band structure and it is concluded that the theory based on parabolic bands remains good provided the mean free path is taken as an average quantity over the relevant energy range. It is argued that the theory has wide application to semiconductors with moderate-to-large energy gaps because of the predominance of nonpolar scattering at high energies. A specific model of a nonparabolic band structure is discussed in which the electron distribution function has a Gaussian form, rather than the Maxwellian form associated with parabolic bands, and a weak negative differential resistance is exhibited.

Wavelength and temperature dependence of RAPD laser detectors

Wavelength and temperature-dependent characteristics of silicon reach-through avalanche photodiodes (RAPD) are studied using the modified Baraff's theory. The temperature and wavelength regions discussed are 100-500 K and 0.655-1.06 microm, respectively, for Si photodetectors. The effects of breakdown voltage, depletion region width, and efficiency on the avalanche region width are widely studied. Both n(+) (front) side and p(+) (back) side illumination are also considered. The noise equivalent power is significantly reduced with light incident on the p(+) surface with little sacrifice of efficiency. An RAPD structure is proposed in which the direction of radiation incidence causes photogeneration to precede avalanche multiplication reducing the multiplication noise substantially. This result should be useful in the design of RAPD laser detectors.

An improved empirical fit to Baraff's universal curves for the ionization coefficients of electron and hole multiplication in semiconductors

Since its introduction in 1966, an empirical quadratic fit to Baraff's curves due to Crowell and Sze, has been widely used, in conjunction with the use of Baraff's theory to extrapolate experimental data for electron and hole ionization coefficients to conditions-notably temperature-differing from those under which those data were derived. The quality of that quadratic fit is reexamined, and an improved cubic fit is proposed.

Characteristics of P-I-N laser detectors: their dependence on wavelength and temperature

Wavelength and temperature-dependent characteristics of silicon P-I-N laser detectors are studied using the modified Baraff theory. Both the electron or hole injection effect and photogeneration effect are considered in the calculation of the power spectral density of multiplication noise and efficiencies. The results thus obtained are compared with previous papers where the photogeneration effect was neglected.

Temperature-dependent characteristics of a reach-through avalanche photodiode (RAPD) in Ge, Si and GaAs

A theoretical assessment is presented based on a modification of Baraff's theory in order to compare the temperature dependence of several characteristics, including breakdown voltage, excess noise factor, effective ionization rate ratio and efficiency in Ge, Si and GaAs reach-through avalanche photodiodes (RAPD). The temperature coefficient of avalanche breakdown voltage in a depletion region is studied. The response time of a reach-through APD in these materials is also discussed. Finally a comparison of the characteristics between PIN APD and RAPD is presented. The theoretical data have also been substantiated experimentally by Kanedaet al.

Temperature dependent characteristics of a PIN avalanche photodiode (APD) in Ge, Si and GaAs

A theoretical assessment is presented based on a modification of Baraff's theory in order to compare the temperature dependence of several characteristics, including breakdown voltage, excess noise factor, effective ionization rate ratio and efficiency in Ge, Si and GaAs PIN avalanche photodiodes. The temperature coefficient of avalanche breakdown voltage in a high field region is studied. Finally the response time of a PIN APD in these materials is discussed.

Magnetoreflection of the semimetals for circularly polarized radiation

Interband magnetoreflection measurements were made on arsenic, antimony, and bismuth, using circularly polarized radiation. A clear Fermi level cut-off was observed for an arsenic trigonal face, and the valence band Fermi energy at Q is deduced to be 12.5 meV. The observed deviation from the two-band model are discussed in terms of the Baraff theory.

Charge multiplication in Au-SiC (6H) Schottky junctions

The avalanche multiplication rate for carriers in 6H polytype SiC has been determined from photocurrent data with the assumption of equal hole and electron rates. The optical-phonon mean free path was determined by fitting to the Baraff theory to be λ=58 Å at 300 K. Avalanche breakdown voltages were in accord with Sze’s empirical prediction.

Temperature effects in silicon avalanche diodes

Gain-voltage curves for reach-through avalanche photodiodes are computed using the ionization rate data of van Overstraeten and de Man and Lee et al. and compared with measured curves. Noise spectral density measurements are also made and compared with McIntyre's avalanche noise theory. Agreement between computed and measured k-values as obtained from the noise measurements and between the computed and measured gain-voltage relationship can only be obtained with the ionization rate data of Lee et al. Gain-voltage curves were measured over the temperature range −17 to +55°C and compared with computed curves in which temperature dependence of the ionization rate data of Lee et al. is computed using the modified Baraff theory. Excellent agreement between theory and experiment is obtained.

Temperature Dependence of Ionization Rates in Ge

The ionization rates of electrons and holes in Ge have been measured from 200 to 300°K and were fit to the Baraff theory, in which the optical-phonon mean free path is verified to be temperature dependent and fits to the formula λ=λ0 tanh(Ep/2KT), where Ep is the average optical-phonon energy. The asymptotic optical-phonon mean free paths deduced from experiments are λ0e=76 Å and λ0h=84 Å for electrons and holes, respectively, which are in good agreement with Miller's data obtained at room temperature. A simplified approach to calculate the ionization rates from the photomultiplication data has also been deduced for the one-sided abrupt junction.

Temperature dependence of breakdown voltage in silicon abrupt p-n junctions

Temperature dependence of breakdown voltage in silicon abrupt p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> -n junctions has been calculated using a modified Baraff theory [1]-[3] and measured experimentally from 77°K to 500°K, with substrate doping from 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">15</sup> cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> to 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">18</sup> cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> . Experimental data are in good agreement with the results of theoretical calculations. These results strongly substantiate the validity of the modified Baraff theory which has been pointed out by Sze and Crowell.

Low‐Energy Electron Irradiation of Thin Paraffin Hydrocarbon Films

Low‐energy photoelectrons are excited through thin paraffin hydrocarbon films at 77°K. The photocurrent is measured as a function of film thickness which is increased in steps of 20–80Aå. The attenuation length or range for electrons of approximately 1 eV initial energy is 65Aå for 3‐methylpentane, 59Aå for hexane, and 55Aå for nonane. The mean free paths determined from Baraff Theory are of the order of 12Aå.

Electron-hole pair production by impact ionization in zinc selenide

Measurements have been made of the ionization coefficient as a function of electrical field in znse. Hole and electron ionization coefficients are equal within the limits of the experiments. The results obtained are consistent with baraff's theory. Values of the scattering length lamda lie in the range 25-50 aa. An empirical relation has been found between lamda and the concentration of ionized impurities. The results are discussed in terms of the band structure of znse. The ionization coefficients are consistent with those of similar materials.

Ionization Rates in (AlxGa1−x)As

The ionization rates of (AlxGa1−x) As have been measured as a function of the Al content and the results are presented here. Values of both A and b are found to increase with Al content. It is also found that for low values of Al content, the ionization rates of (AlxGa1−x) As are consistent with Baraff's theory.

The Quantum Variation of Fermi Energy in Bismuth under High Magnetic Fields

Alfven wave transmission through bismuth single crystals is measured using 50 Gc microwave interferometer under pulsed magnetic field up to 200 kG at liquid helium temperatures. It is found that the mass densities change remarkably with magnetic field for all cases studied. These changes are ascribed to the quantum variation of Fermi energy at high magnetic field. The shifts of Fermi energy are determined as a function of magnetic field assuming the nonparabolic band for holes. From the analysis based on the Baraff's theory, it is found that the lowest Landau levels of light electrons go down linearly with magnetic field instead of the parabolic change expected from the modified two band model. It is also found that the lattice dielectric constant has an anisotropy. If \(\varepsilon_{\bot}{\doteqdot}100\) is adopted according to Boyle and Brailsford, we obtain \(\varepsilon_{//}{\doteqdot}60\) in the present experiments, where e // and e ⊥ are the dielectric constants for waves polarized along and perpend...

Giant Quantum Attenuation of Sound Waves in Bismuth. I. Spin Splitting Factors of Electrons and Holes

The giant quantum attenuation of longitudinal sound waves in bismuth was investigated in pulsed magnetic fields up to 170 kG, at a temperature of 1.65°K and at sound wave frequencies of 60 and 100 Mc/s. The angle between the sound wave vector q and the magnetic field vector H was varied by rotating a sample. By combining data in a previous paper with the present ones the anisotropy of the spin splitting factor for electrons in the principal pocket is completely determined for two cases H ∥ X Y -plane and H ∥ Y Z -plane, where X -, Y - and Z -axis refer to a binary, a bisectrix and the trigonal axis, respectively. The Baraff theory is successfully applied to interpret the anisotropy, and values of some parameters in the theory are determined. The hole spin splitting factor for the case H ∥ Z -axis is found conclusively to be (1.86±0.02).

Avalanche Breakdown and Multiplication in Silicon pin Junctions

The ionization rates of charge carriers and effective ionization rate were measured for field lower than 2.5×105 volts/cm by using high voltage pin junctions. The effective ionization rate is experimentally given by α=1.0×106exp (-1.66×106/E). The experimental ionization rates of electrons and holes, αn and αp, are just extended to the low field side of the previous experimental data and the dependence on the field is given by αnp≈anpexp (-bn,p/E) over the range of field (1.1–5.0)×105 volts/cm, but this formula does not sufficiently agree with Baraff's theory. For these junctions, the effective ionization rate is expressed by α≈(αn–αp)/ln (αn/αp). This approximation can be also extended to pn junctions. For some samples, anomalous multiplication characteristics were observed. They are closely related with diffusion process.

Avalanche Breakdown in Gallium Arsenidep−nJunctions

Charge multiplication and avalanche breakdown have been studied in relatively narrow diffused $p\ensuremath{-}n$ junctions in GaAs. For these studies both junctions with and without microplasma effects were available. From the charge multiplication studies in microplasma-free junctions, the ionization rate, $\ensuremath{\alpha}$, has been determined as a function of the field, $\mathcal{E}$. These results are unusual in that they give a decidedly better fit to Wolff's theory than to Shockley's; this is found to be consistent with the criterion, $e\mathcal{E}\ensuremath{\lambda}g(\mathrm{o}\mathrm{p}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l}\ensuremath{-}\mathrm{p}\mathrm{h}\mathrm{o}\mathrm{n}\mathrm{o}\mathrm{n}\phantom{\rule{0ex}{0ex}}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{r}\mathrm{g}\mathrm{y})$, discussed in a more recent theory due to Baraff which combines the approaches of both Wolff and Shockley. From detailed comparisons with Baraff's theory, the mean free path, $\ensuremath{\lambda}$, for the hot carriers between collisions involving optical phonon emission is 15\ifmmode\pm\else\textpm\fi{}2 \AA{} and the threshold energy for pair production is 1.7\ifmmode\pm\else\textpm\fi{}0.3 eV.Strong correlations were found between the quality of the breakdown (i.e., formation or absence of microplasmas) and the quality of the substrate crystal. Those junctions that exhibited microplasma noise and several multiplication peaks also had soft reverse characteristics, whereas the junctions that appeared to be free from microplasmas had hard breakdown characteristics. With the soft junctions, quantitative comparisons were made between the dark current and the number of microplasmas.