Hole Ionization Coefficients Research Articles

Temperature dependence of ionisation coefficients in silicon derived from physical model

Electron and hole ionisation coefficients from 200 to 500 K have been calculated using the lucky drift model of impact ionisation calibrated to measurements made at 300 K. The results are fitted to two- and three-parameter empirical relationships for the ionisation coefficient against field, which can be used in device modelling.

Ionization coefficients in Ga0.96Al0.04Sb

Ionization coefficients of holes and electrons (kp and kn) in Ga0.96Al0.04Sb have been derived from the variations of the photocurrent multiplication as a function of the reverse bias in Be-implanted p+Ga0.96Al0.04Sb/n Ga0.96Al0.04Sb/n+ GaSb mesa diodes. Three wavelength values have been used for the illumination in order to obtain pure hole injection, nearly pure electron injection, and mixed injection. The kp and kn values thus determined for electric fields varying from 18 to 32 V/μm exhibit a high ratio value showing the interest of this material for avalanche photodiodes devices.

Dependence of ionization coefficients on well and barrier widths for GaAs/AlGaAs multiple quantum wells

The impact ionization coefficients in GaAs/Al 0.3Ga 07As multiple quantum well structures, having well and barrier thicknesses in the range 30–500 Å, have been experimentally determined. For MQW structures having equal well and barrier thicknesses, both the electron ionization coefficient α, and the hole ionization coefficient β reduce with decreasing well dimension. There is no appreciable change in the ratio α/ β over the range of dimensions and electric fields studied.

Hole impact ionization enhancement in AlxGa1−xSb

The threshold energy and scattering rate for impact ionization in AlxGa1−xSb have been calculated for compositions x near the value where the spin-orbit-split gap Δ equals the band gap Eg. We have found that a minimum in the threshold energy for impact ionization near the Δ=Eg composition cannot explain the enhancement of the hole ionization coefficient, although it has been proposed as a possible mechanism. Rather, an increased scattering rate is responsible for this enhancement. It is caused by a minimum change of momentum in the hole ionization near the threshold and the mixing of an s-like state into the valence-like state induced by a composition disorder in this ternary compound. Our results indicate that the maximum hole ionization coefficient will occur at a composition x that lies between zero and the composition at which Δ=Eg.

Impact ionization coefficient and energy distribution function at high fields in semiconductors

Impact ionization coefficients in semiconductors are numerically calculated following Keldysh’s method [Sov. Phys. JETP 21, 1135 (1965)]. This requires deriving expressions for an energy-dependent mean free path l(ε) and an energy-dependent impact ionization scattering rate rii(ε). In the derivation of rii(ε), a nonparabolic ε-k relation as well as a smooth transition from the phonon-assisted impact ionization to the phononless impact ionization are considered. Numerically calculated impact ionization coefficients for electrons and holes in Ge, Si, and GaAs agree very well with experimental data. The calculated Keldysh energy distribution function is also compared with the standard Maxwellian distribution. The average mean free path l̄, which is a function of the electric field, has values within the range often quoted in the literature.

Impact ionization in AlxGa1−xAs for x=0.1–0.4

The impact ionization coefficients in AlxGa1−xAs have been experimentally determined for compositions x≤0.4. These data are necessary for accurate device design and modeling. Both α, the electron ionization coefficient, and β, the hole ionization coefficient, decrease with increasing x, and there is no appreciable change in the ratio α/β over the range of compositions and electric fields studied.

Studies On Ionization Coefficients of Targets in an Amorphous Selenium APD for Pick-up Tubes by New Type Least Squares

The ionization coefficients of electrons and holes (i.e. α and β) have been determined only by the voltage and current characteristics of targets of a-Se APD in the operation state of pick-up tubes. These determinations were based on selfconsistently solving 12 simultaneous transcendent Webb's equations by using random numbers and linear approximations. The values obtained for β and α(1/cm) varied from β=7.36×106 exp (-8.24×106/E) and α=8.09×102 exp (-0.04×106/E), to β=24.6×106 exp (-9.80×106/E) and α=3.60×102 exp (-0.11×106/E) (unit of E; V/cm). The excess noise factor (K') for a gain equaling 10 varied from 2 to 3. The differences in the obtained values were attributed to differences in sample histories.

Les photodiodes à avalanche Hg0,4Cd0,6Te à λ = 1,55 μm. Bruit près de la résonance due au couplage spin-orbite

This contribution is devoted to the electrical and optical characterization of three Hg 1−x Cd x Te avalanche photodiodes from planar technology with composition parameter x near 0.6. This alloy composition leads to devices that are well suited for 1.55 μm detection. From the noise analysis under multiplication we intend to show the tight dependence of the ratio K=β/a ― of the hole and electron ionization coefficients respectively ― upon the ratio Δ/E g or x. It so turns out that in these Hg 1−x Cd x Te alloys around x=60%, Δ is very close to E g therefore k reaches its maximum value. Due to this physical property, this II-VI alloy may be considered as a good candidate among the semiconductor materials from which 1.3 to 1.6 μm avalanche photodiodes could be made and used in the fibre optics transmission systems [1,2] On presente une caracterisation electrique et optique d'un essai de photodetecteurs a avalanche pour de futures applications aux reseaux câbles par fibres optiques dans la fenetre λ=1,55 μm

On the physics of impact ionization and its application to superlattice avalanche photodiodes

The enhancement in superlattices of α/β (electron to hole ionization coefficient ratio) in AIGaAs/GaAs and in AllnAs/GalnAs, and of β/α in InP/GalnAs, is modelled using lucky-drift theory. Agreement with observation in the case of AIGaAs/GaAs is obtained only if the old 85 :15 band-edge discontinuity rule is assumed and geometrical reduction factors are ignored. The theory of the ionization rate for nearly parabolic bands is recalled, and the crucial role of overlap integrals is discussed. Simple theory predicts that ionization processes involving light holes are much more rapid than for heavy holes. An estimate of the rate near threshold for GaAs is made and it is shown to be over a hundred times smaller than the phonon-scattering rate. The impact ionization threshold for GaAs is therefore ‘soft’, in contrast to what is normally assumed. A soft threshold has important implications for the efficient working of staircase avalanche photodiodes (APDs), and for the modelling of the impact ionization process.

Theory of the GaInAs/AlInAs-doped quantum well APD: A new low-noise solid-state photodetector for lightwave communication systems

We present calculations of the electron and hole ionization coefficients, the excess noise factor, and gain for a doped quantum well APD made from the Al 0.48 In 0.52 As/Ga 0.47 In 0.53 As material systems. The ionization rates are calculated based on an ensemble Monte Carlo method. The effect of all of the device parameters, i.e., doping concentrations, layer widths, and the overall dc bias field, on the carrier ionization coefficients and the deterministic ionization probabilities, P and Q , is determined. These results in conjunction with recent noise theory results are utilized to determine an optimal device design that provides high gain at very low noise. A complete design including number of stages and individual stage design is presented for the lowest noise, highest gain device realizable in this system. It is anticipated that this device can be used as a new ultralow-noise high-gain receiver in lightwave communications systems.

Theory of the doped quantum well superlattice APD: A new solid-state photomultiplier

A new superlattice avalanche photodiode structure consisting of repeated unit cells formed from a p-i-n Al 0.45 Ga 0.55 As region immediately followed by near intrinsic GaAs and Al 0.45 Ga 0.55 As layers is examined using an ensemble Monte Carlo calculation. The effects of various device parameters, such as the high-field layer width, GaAs well width, low-field AlGaAs layer width, and applied electric field on the electron and hole ionization coefficients is analyzed. In addition, the fraction of electrons which ionize in a spatially deterministic way, at the same place in each stage of the device, is determined. As is well known, completely noiseless amplification can be achieved if each electron ionizes in each stage of the device at precisely the same location while no holes ionize anywhere within the device. A comparison is made between the doped quantum well device and other existing superlattice APD's such as the quantum well and staircase APD's. It is seen that the doped quantum well device most nearly approximates photomultiplier-like behavior when applied to the GaAs/AlGaAs material system amongst the three devices. In addition, it is determined that none of the devices, when made from GaAs and AlGaAs, fully mimic ideal photomultiplier-like performance. As the fraction of electron ionizations per stage of the device is increased, through variations in the device geometry and applied electric field, the hole ionization rate invariably increases. It is expected that ideal performance can be more closely achieved in a material system in which the conduction band edge discontinuity is a greater fraction of the band gap energy in the narrow-band gap semiconductor.

Impact ionization coefficients in In0.2Ga0.8As/GaAs strained-layer superlattices

The impact ionization coefficients for electrons and holes have been measured in In0.2Ga0.8As/GaAs strained-layer superlattices (SLS’s) for transport perpendicular to the superlattice. The pure electron and hole initiated primary photocurrents were produced in p+n mesa photodiodes having In0.1Ga0.9As alloy photon absorption regions and an SLS active region carrier concentration of 7.4×1015 cm−3. The impact ionization coefficient for electrons is found to be larger than for holes with a ratio that varies from 1.8 at 2.7×105 V/cm to 1.4 at 3.8×105 V/cm.

The determination of impact ionization coefficients in ln0.2Ga0.8As/GaAs strained-layer superlattice mesa photodiodes

Sandia National Laboratories, Albuquerque, NM 87185 Photocurrent multiplication measurements have been performed on two different In0.2Gao0.8As/GaAs strained-layer superlattice (SLS)p +n photodiode structures which are designed to permit simultaneous injection of electrons and holes. Initial devices were found to suffer from low quantum efficiencies produced by small electron diffusion lengths as well as mixed injection caused by lower than expected optical absorption coefficients in the SLSn + contact layers for hole injection conditions. Using a second device structure having a thicker n+ contact region, the electron multiplication factors are found to be larger than that of holes with a ratio of the electron to hole ionization coefficient of 1.4 for fields between 2.9 and 3.4 x 105V/cm.

Temperature dependence of impact ionization coefficients in InP

Impact ionization coefficients for electrons and holes in InP were measured experimentally at 25–175 °C in the 400–600 kV/cm electric field range with planar avalanche photodiodes, in which the n-InP avalanche region was separated from the light absorbing InGaAs and/or InGaAsP layers. α and β monotonically decreased with elevated temperatures; β/α slightly decreased with increasing temperature. Comparison of the experimental results with Okuto–Crowell formula on the impact ionization coefficient gave the phonon energy ERO=46 meV and the phonon scattering mean free path λ0=41.7 Å for electron impact ionization and ERO=36 meV and λ0=41.3 Å for hole impact ionization, respectively. Curves calculated by using these parameters agree with the experimental results quite satisfactorily at each temperature.

Optical control of W-band impatt oscillators

Results are presented for analytical computer modelling and experimental studies of optically induced frequency tuning of W-Band (75–110 GHz) impatt oscillators. Predictions from an analytical theory are compared with those from a large-signal time-domain computer model, and the effect of unequal electron and hole ionisation coefficients on the tuning performance is illustrated. Experimental measurements are presented showing an optical tuning range of about 10 MHz for an optically generated current of 20 μA, and comparisons are made with the theoretical predictions.

Electron and hole impact ionization coefficients in (100) and in (111) Si

The impact ionization coefficients for electrons and holes in both (100)- and (111)-oriented Si have been determined from photocurrent measurements performed on reach-through avalanche photodiodes. The results for both orientations are similar, indicating that the ionization coefficients are isotropic. Monte Carlo calculations of the impact ionization coefficients compare favorably with the experimental results.

Impact ionization in InP and GaAs

Abstract The experimental techniques that are critical in the determination of impact ionization coefficients in semiconductors are reviewed. The experimental results for the electron and hole ionization coefficients in InP and GaAs will be given. A discussion of Monte Carlo calculations of the ionization coefficients in these materials is included.

Electron and hole impact ionization coefficients in GaAs-AlxGa1−xAs superlattices

Electron and hole multiplication and impact ionization coefficients have been measured with pure carrier injection in p+-n−-n+ and p+-n diodes grown by molecular beam epitaxy. Values of the electron and hole ionization coefficient ratio α/β=2–5 are measured for superlattices with well width Lz≥100 Å and α/β>10 is measured in a graded band-gap superlattice with a total well and barrier width LB+LZ=120 Å. The ratio decreases and becomes less than unity for smaller well sizes. This is caused by an increase in β(E) while α(E) remains fairly constant. The results have been interpreted by considering varying hole confinement and scattering in the coupled quantum wells.

Noise Investigation of the Impact Ionization in GaAs

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Impact ionization coefficients of electrons and holes in

The arsenic composition dependences of electron and hole ionization coefficients, α and β, in