Ionization Threshold Energy Research Articles

Investigation of the transition from tunneling to impact ionization multiplication in silicon p- n junctions

White noise spectra of diodes breaking down between 1·5 and 5 V have been used to investigate the details of the transition from tunneling to avalanche breakdown in silicon p- n junctions. It is found that the transition and carrier multiplication in these junctions is dominated by the influence of the threshold energies for ionization. Because this influence is not explicitly taken into account in the existing theories of carrier multiplication and noise, they are not applicable to low breakdown voltage diodes. Consequently, a multiplication onset model and alternate schemes for calculating the DC multiplication and noise in low breakdown voltage diodes are developed. Analysis of the noise data indicates that the threshold energies for ionization depend slightly on junction widths and, for the diodes employed in this study, range between 1·66–1·9 eV for electrons and 1·79–2·04 eV for holes. The minimum distance between ionizing collisions is found to range from 190 to 240 A for electrons and 200 to 250 A for holes. Application of the threshold energies for ionization to the multiplication onset model permits evaluation of the doping densities on both sides of the step junctions. From it, it is determined that the solubility of aluminum in silicon is N A = 9·5 ± 0·5 × 10 18 cm −3.

Threshold energy for impact ionization by electrons in GaAs considering the nonparabolicity of the central valley

A theoretical calculation of the threshold energy for impact ionization by electrons in GaAs has been presented considering the nonparabolicity of the central valley. The results obtained for the process with the lowest threshold energy differ by about 10% from those obtained by assuming a parabolic central valley. In case of other processes the difference is less marked.

Ionization coefficients in semiconductors: A nonlocalized property

In the light of energy-conservation considerations a nonlocalized concept (NLC) has been introduced to describe the avalanche ionization effect in semiconductors. From this formulation it appears that the intrinsic electron and hole ionization coefficients cannot be directly compared with experimental data. We show the coupled relationships between these parameters and experimentally obtainable apparent ionization coefficients. The conventional definition of ionization coefficient is modified to maintain its relevance for high-electric-field situations via a pseudolocal approximation. With the use of a previous estimate of the average distance for the ionization scattering given by Okuto and Crowell, apparent ionization coefficients have been calculated for Si, Ge, GaAs and GaP. The agreement with the existing experimental results for high electric fields is especially satisfactory for Si in which an anomalously large high-field threshold energy had previously been reported. We also show that for any material at a given electric field there exists a critical multiplication factor beyond which the pseudolocal approximation does not hold. To examine the importance of this limit an exact formulation was solved for selected $p\ensuremath{-}i\ensuremath{-}n$ junctions. The results indicate the importance of boundary corrections associated with the threshold energies for ionization scattering but indicate that the pseudolocal approximation can be appropriately modified for use even at high multiplications.

Threshold energy for impact ionization by holes in GaAs

Various processes have been considered for impact ionization by holes in GaAs and the corresponding threshold energies have been reported.

Impact ionization thresholds in semiconductors

A method of deriving accurate values for impact ionization threshold energies in semiconductors from realistic band structures is described. The method is applied to two different band structures for both Si and Ge. The sensitivity of the various thresholds to the precise details of the band structure is thereby investigated, and reliable information on the thresholds in these materials is obtained. In most cases it is found that impact ionization can take place when the hot electron has an excess energy not much greater than the energy gap. This is in agreement with the conclusions of Anderson and Cromwell based on less accurate values of threshold energies calculated by a different method. Threshold energies derived from approximate band models are discussed in relation to the results for the genuine bands. It is found that the lowest thresholds are not provided correctly by such models.

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

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.

Threshold Energies for Electron-Hole Pair Production by Impact Ionization in Semiconductors

Threshold energies for energy- and momentum-conserving impact ionization of electron-hole pairs in actual semiconductors are determined by differential analysis of the energy-wave-vector relations of the participating charge carriers and phonons. A necessary condition for the initiating carrier to have minimum energy consistent with pair production is that the resultant carriers and all phonons involved have identical real-space velocities. This criterion allows calculations of ionization threshold energies for any semiconductor for which the one-electron-energy-wave-vector relationship is known. A step-by-step graphical procedure is presented for the calculation of threshold energies when the final particles are traveling along a principal axis of a semiconductor. Threshold energies resulting from the application of this procedure are presented for Si, Ge, GaAs, GaP, and InSb. Each of these materials exhibits numerous threshold energies for phononless ionization initiated by either type of carrier. The lowest thresholds for electron-initiated ionization without phonon assistance are 1.1, 0.8, 1.7, 2.6, and 0.2 eV relative to the conduction-band minima in Si, Ge, GaAs, GaP, and InSb, respectively. For ionization initiated by holes, the corresponding results are 1.8, 0.9, 1.4, 2.3, and 0.2 eV relative to the valence-band maximum.

Alfvén's Critical Velocity Hypothesis

IN his theory on the origin of the solar system1, Alfven makes an assumption which is central to the entire theory2. This assumption is that when there is a relative velocity between a plasma and a neutral gas in the presence of a magnetic field, a strong ionization process will set in when the relative velocity reaches a critical value Ucrit such that where mg and Vi are the mass and ionization potential of the gas atom. Using this assumption, Alfven has been able to predict fairly accurately the mass distribution of the planets and satellites in the solar system. A study of the ionization mechanism leads to some difficulties, however; first, the threshold energy for ionization in a collision between a gas atom and an ion of the same gas is 2 eVi (ref. 3) and, second, the ionization cross-section of ions is very small compared with that of electrons, except at very high energies. It has been suggested4 that the ionization must be caused by the electrons and that energy is transferred from the ions to the electrons by some kind of space charge mechanism which is not discussed in detail. The purpose of this communication is to point out three simple ionization mechanisms which lend support to the critical velocity hypothesis.

Higher autoionization processes in argon and xenon

A study has been made of electron impact ionization of argon and xenon. It has been found that singly and doubly charged metastable ions are produced near the threshold energies for double and treble ionization respectively. These excited ions were found to decay by autoionization. Measurements were made of the excitation functions of these ions and in some instances the lifetime and production cross section. Argon was studied in most detail, but similar processes were found to occur in Ne and Kr although the results are not reported in this paper.