Ionization rates for electrons and holes are extracted from photomultiplication measurements on silicon p+n mesa diodes for electric fields of 2·0 × 105−7·7 × 105 V/cm at temperatures of 22, 50, 100 and 150°C. These results are particularly pertinent to the analysis of high-frequency (∼ 100 GHz) silicon IMPATT diodes. The rates obtained here are in reasonable agreement with previously published data of van Overstraeten and DeMan, although slightly larger in magnitude. Calculated curves of breakdown voltage vs background doping level are presented using the room temperature ionization rates. Also a comparison is made to previously reported rates. The new rates provide a closer agreement between predicted and measured breakdown voltages for breakdown voltages less than 70 V.

Electron and hole ionization rates in epitaxial silicon at high electric fields

We used the high local electric fields at the junction between the suspended and supported parts of a single carbon nanotube molecule to produce unusually bright infrared emission under unipolar operation. Carriers were accelerated by band-bending at the suspension interface, and they created excitons that radiatively recombined. This excitation mechanism is ∼1000 times more efficient than recombination of independently injected electrons and holes, and it results from weak electron-phonon scattering and strong electron-hole binding caused by one-dimensional confinement. The ensuing high excitation density allows us to observe emission from higher excited states not seen by photoexcitation. The excitation mechanism of these states was analyzed.

https://science.sciencemag.org/content/sci/310/5751/1171.full.pdf

Bright infrared emission from electrically induced excitons in carbon nanotubes.

Chalcogenide glasses are widely used in phase-change nonvolatile memories and in optical recording media for their ability to rapidly change their structure to crystalline, thus obtaining different electrical resistance and optical reflectivity. Chalcogenide glasses universally display threshold switching, that is a sudden, reversible transition from a high-resistivity state to a low-resistivity state observed in the current-voltage $(I\text{\ensuremath{-}}V)$ characteristic. Since threshold switching controls the operating voltage and speed of phase-change memories, the predictability of the switching voltage, current, and speed is of critical importance for selecting the proper chalcogenide material for memory applications. Although threshold switching has long been recognized to be an electronic process with an intimate relation to localized states, its detailed physical mechanism is still not clear. In this work, threshold switching is explained by the field-induced energy increase in electrons in their hopping transport, moderated by the energy relaxation due to phonon-electron interaction. The energy increase leads to an enhancement of conductivity and a collapse of the electric field within the amorphous chalcogenide layer, accounting for the observed negative differential resistance at switching. Threshold switching is found to obey to a constant electrical-power condition. The proposed model generally applies to low-mobility semiconductors featuring a deep Fermi level and hopping-type conduction, and can predict the thickness, temperature, and material dependence of threshold voltage and current.

Threshold switching mechanism by high-field energy gain in the hopping transport of chalcogenide glasses

Impact ionization in thick multiplication regions is adequately described by models in which the ionization coefficients are functions only of the local electric field. In devices with thin multiplication lengths, nonlocal effects become significant, necessitating new models that account for the path that a carrier travels before gaining sufficient energy to impact ionize. This paper presents a new theory that incorporates history-dependent ionization coefficients, and it is shown that this model can be utilized to calculate the low-frequency properties of avalanche photodiodes (APD's) (gain, noise, and breakdown probability in the Geiger mode) and the frequency response. A conclusion of this work is that an ionization coefficient is not a fundamental material characteristic at a specific electric field and that any experimental determination of ionization coefficients is valid only for the particular structure on which the measurement was performed.

A new look at impact ionization-Part I: A theory of gain, noise, breakdown probability, and frequency response

The effect of dead space on the statistics of the gain in a double-carrier-multiplication avalanche photodiode (APD) is determined using a recurrence method. The dead space is the minimum distance that a newly generated carrier must travel in order to acquire sufficient energy to become capable of causing an impact ionization. Recurrence equations are derived for the first moment, the second moment, and the probability distribution function of two random variables that are related, in a deterministic way, to the random gain of the APD. These equations are solved numerically to produce the mean gain and the excess noise factor. The presence of dead space reduces both the mean gain and the excess noise factor of the device. This may have a beneficial effect on the performance of the detector when used in optical receivers with photon noise and circuit noise. >

Effect of dead space on gain and noise of double-carrier-multiplication avalanche photodiodes

Ionization coefficients in semiconductors: A nonlocalized property

A simple expression for the ionization coefficient of charged carriers in a semiconductor as a function of electric field and lattice temperature has been developed by simultaneously fitting three physical asymptotic cases to Baraff's result. These cases are for low field (Shockley), high field (Wolff), and limitations imposed by energy conservation at high electric field or when the energy loss by phonon scattering is negligible. Given the threshold energy for ionization and the optical-phonon energy, our expression requires a single additional parameter to predict experimental results. Although the final expression is thus essentially a one-point fitting, it reproduces experimental data over as much as four decades of ionization coefficient with better accuracy than frequently used empirical two-parameter expressions. Excellent fits with much of the existing electric field dependence of the ionization coefficients for electrons and holes in Ge, Si, GaAs, and GaP were obtained. The temperature dependence was examined in the cases of GaAs and Si and excellent agreement was obtained in the case of GaAs. Some data on Si were found to be in considerable error in the sense that the data do not appear to be consistent with energy conservation.

Y. Okuto

Papers

Ionization coefficients in semiconductors: A nonlocalized property

Energy-Conservation Considerations in the Characterization of Impact Ionization in Semiconductors