Experimental determination of the avalanche region of one-sided abrupt barriers

In this paper is presented an experimental method for the determination of the width of the avalanche region of one-sided abrupt barriers at breakdown. The ionization rates of both electrons and holes are determined using the same experiments. The method is based on multiplication measurements corresponding to a primary current coming from the highly doped side of the junction. This primary current is obtained by varying the wavelength of a light spot applied to the highly doped side. This method is used to control the avalanche behaviour of P⁺N and N⁺P Si abrupt junctions. The avalanche region and ionization rates obtained are in good agreement with values already published.     

Interaction of electrons with optical phonons localized in a quantum well

The scattering rate of electrons in a quantum well by localized polar optical and interface phonons is considered. The dependence of the force of the electron-phonon interaction on the frequency of optical phonons in materials of the heterostructure forming the electron and phonon quantum wells is determined. It is shown that, by varying the composition of semiconductors forming the quantum well and its barriers, it is possible to vary the scattering rates of electrons by a factor of several times. The scattering rates of electrons by polar optical phonons are calculated depending on the fractions In _x and In _y in the composition of semiconductors forming the In _x Al_{1 ? x} As/In _y Ga_{1 ? y} As quantum wells. Dependences of the mobility and saturated drift velocity of electrons in high electric fields and quantum wells In _y Ga_{1 ? y} As on the composition of the In _x Al_{1 ? x} As barriers introduced into quantum wells are determined experimentally. The electron mobility increases, while the saturated drift velocity decreases as the fraction of In _x in the composition of barriers is increased.     

Low avalanche noise characteristics in thin InP p+-i-n+ diodes with electron initiated multiplication

We have performed electron initiated avalanche noise measurements on a range of homojunction InP p⁺-i-n⁺ diodes with “i” region widths, w ranging from 2.40 to 0.24 μm. In contrast to McIntyre's noise model a significant reduction in the excess noise factor is observed with decreasing w at a constant multiplication in spite of α, the electron ionization coefficient being less than β, the hole ionization coefficient. In the w=0.24 μm structure an effective β/α ratio of approximately 0.4 is deduced from the excess noise factor even when electrons initiate multiplication, suggesting that hole initiated multiplication is not always necessary for the lowest avalanche noise in InP-based avalanche photodiodes     

Analysis of inelastic scattering of quasi-two-dimensional electrons of a superlattice by acoustic phonons with allowance made for the miniband dispersion

Formulas for the effective momentum-relaxation time and mobility of quasi-two-dimensional electrons of a superlattice with consideration of inelastic scattering by acoustic phonons and the dispersion of the miniband energy spectrum as a function of the longitudinal wave vector have been obtained. Numerical calculation was performed for a nondegenerate gas of quasi-2D electrons in a symmetrical GaAs/Al_0.36Ga_0.64As superlattice with a quantum well width of 5 nm at T=77 K. It was shown that consideration of the elasticity of scattering and the dispersion of the miniband energy spectrum gives rise to a significant increase in the electron mobility.     

Noise properties and time response of the staircase avalanche photodiode

The staircase avalanche photodiode is a novel graded-gap superlattice device that is expected to detect photons quite noiselessly. It is designed in such a way that only electrons impact-ionize, thereby eliminating the feedback noise associated with conventional two-carrier avalanche devices. Because the electron multiplication can occur only at a small number of discrete locations in the device, the variability of the number of electrons generated per detected photon is minimized. The excess noise and the electron counting distribution are obtained as a function of the number of stages in the device and the impact-ionization probability per stage, for instantaneous multiplication. The (single-photon) impulse response function is calculated when the effects of (random) transit time are incorporated into the carrier multiplication process. Inclusion of the time dynamics is essential for determining the time course of the current generated by the device in response to pulses of light. This, in turn, permits bit error rates to be calculated for systems incorporating the device. For a five-stage quaternary device the gain-bandwidth product is calculated to be in the vicinity of 600 GHz.     

Noise properties and time response of the staircase avalanche photodiode

The staircase avalanche photodiode is a novel graded-gap superlattice device that is expected to detect photons quite noiselessly. It is designed in such a way that only electrons impact-ionize, thereby eliminating the feedback noise associated with conventional two-carrier avalanche devices. Because the electron multiplication can occur only at a small number of discrete locations in the device, the variability of the number of electrons generated per detected photon is minimized. The excess noise and the electron counting distribution are obtained as a function of the number of stages in the device and the impact-ionization probability per stage, for instantaneous multiplication. The (single-photon) impulse response function is calculated when the effects of (random) transit time are incorporated into the carrier multiplication process. Inclusion of the time dynamics is essential for determining the time course of the current generated by the device in response to pulses of light. This, in turn, permits bit error rates to be calculated for systems incorporating the device. For a five-stage quaternary device the gain-bandwidth product is calculated to be in the vicinity of 600 GHz.     

Dependence of scattering of quasi-two-dimensional electrons by acoustic phonons on the parameters of a GaAs/Al<Subscript>x</Subscript>Ga<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>As superlattice

The time of relaxation of quasi-two-dimensional electrons in a GaAs/Al_xGa_1?xAs superlattice in the case of scattering by acoustic phonons was calculated numerically in relation to the quantum-well width and the width and height of the potential barrier. The probability of scattering for electrons of the lower miniband was calculated using an approximate envelope wave function without consideration of the dispersion of the periodic component of the Bloch function in relation to the wave vector. A comparative analysis of the calculated relaxation times and the values obtained using the well-known approximate formula was performed.     

Ionization coefficient measurement in GaAs by using multiplication noise characteristics

Multiplication noise measurements for p⁺n type (100) GaAs avalanche photodiodes with various n-layer dopings ranging from 6 × 10¹⁵ to 9 × 10¹⁶ cm^?3 confirmed that the ionization coefficient of electrons α is about two times larger than that of holes β in the electric field range from 2.4 × 10⁵ to 5.6 × 10⁵ V/cm. When pure electrons were injected into the avalanche region, the multiplication noise power was proportional to the 2.7th power of the multiplication factor and the ionization coefficient ratio $\text{k =}\text{β}\text{α}$ was constant, where k = 0.5 in the above electric field range. The result was consistent with the multiplication factor dependence on light wavelength. Using the constant ionization coefficient ratio k and the multiplication factor dependence on applied bias voltage, ionization coefficients α and β for electrons and holes were estimated.     

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 × 10¹⁸ cm^?3.     

Mean energy of photoexcited hot electrons in high magnetic fields

Several authors have determined the mean energy of a photoexcited electron gas in the absence of magnetic field. Assuming a Maxwellian distribution for the electrons, they used the power balance equation to find the electron temperature T_e. Noting that when a strong magnetic field is applied, the electron collision integral vanishes in the extreme quantum limit, we derive a theoretical expression for T_e using a similar approach. Recombination and various scattering processes by optical and acoustical phonons are considered and the dependence of T_e on magnetic field, lattice temperature and laser excitation freqeuency is studied.     

An avalanche photodiode with metal-insulator-semiconductor properties

A new design of the avalanche photodetector combining the avalanche photodiode and MIS structure properties was tested. The noise and high-frequency properties of the device were studied. The device exhibited a noise factor of less than 10 at a high multiplication factor (M>1000) even with hole injection. This is indicative of a drastic change in the effective ratio of the coefficients of impact ionization by electrons and holes in favor of the latter. Measurements of the photosensitivity distribution over a photodetector area for M=8000 showed a high uniformity.     

Carrier multiplication in silicon <Emphasis Type="Italic">P-N</Emphasis> junctions

The dependences of carrier multiplication factors M on the voltage applied to p-n Si junctions with an avalanche breakdown voltage of 10–3000 V are considered. Analytical expressions for the approximation of these dependences for electrons, holes, and generation current are suggested. In the range of varying the multiplication factors of 1.01–3.0, the relative rms error of approximation (M?1) is several percent. This is more than an order of magnitude more accurate compared with the approximation by the widely known Miller-Moll expression. It is assumed that the analytical expressions of the form suggested will be suitable for the approximation of dependences of multiplication factors on the voltage applied for most semiconductor materials.     

The effect of acoustic phonon confinement on electron scattering in GaAs/Al<Subscript>x</Subscript>Ga<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>As superlattices

The relaxation time of quasi-two-dimensional (quasi-2D) electrons in the lowest miniband of the GaAs/Al_0.35Ga_0.65As superlattice is calculated for the case of scattering by acoustic phonons. It is shown that electron scattering is affected only slightly by the quantization of the phonon spectrum in terms of the elasticity theory. The scattering is well described based on the phonon spectrum of the bulk semiconductors that form the superlattice.     

Photoelectric characteristics of infrared photodetectors with blocked hopping conduction

It is shown that the current-voltage characteristics of Si:As-based structures that have blocked hopping conduction (blocked-impurity-band, or BIB, structures) and are subjected to infrared radiation in the photosensitivity range have two distinct portions. In the first portion, the photocurrent is controlled by an infrared-radiation flux and by an avalanche impurity-related breakdown. In the second portion, the photocurrent is controlled by merging of the depletion region with the contact N ⁺⁺ region. It is shown that the avalanche-multiplication mode can be used in focal multielement photodetector systems. The uniformity of photoelectric parameters over an array of elements in a system of focal multielement photodetectors operating in the avalanche-multiplication mode compares well with that observed in BIB arrays operating without avalanche multiplication.     

Full-Band Monte Carlo Simulation of HgCdTe APDs

A full-band Monte Carlo model has been developed for understanding the carrier multiplication process in HgCdTe infrared avalanche photodiodes. The proposed model is based on a realistic electronic structure obtained by pseudopotential calculations and a phonon dispersion relation determined by ab initio techniques. The calculated carrier–phonon scattering rates are consistent with the electronic structure and the phonon dispersion relation, thus removing adjustable parameters such as deformation potential coefficients. The computation of the impact ionization transition rate is based on the calculated electronic structure and the corresponding wavevector-dependent dielectric function. The Monte Carlo model is applied to investigate key performance figures of long-wavelength infrared (LWIR) and mid-wavelength infrared (MWIR) HgCdTe avalanche photodetectors such as carrier multiplication and noise properties. Good agreement is achieved between simulations and experimental results. The multiplication process in LWIR (λ _c = 9.0 μm at 80 K) and MWIR (λ _c = 5.1 μm at 80 K) devices is found to be initiated only by electrons, as expected from excess noise measurements. This single-carrier multiplication behavior can be traced back to the details of the computed valence-band structure and phonon scattering rates.     

Extremely Low Excess Noise in InAs Electron Avalanche Photodiodes

Measurements of the avalanche multiplication noise in InAs p-i-n and n-i-p diodes at room temperature demonstrate unambiguously that the avalanche multiplication process is dominated by impact ionization of electrons. This results in the excess noise factor for electron initiated multiplication asymptotically approaching a maximum value just less than two and becoming virtually gain-independent for higher gains. Measurements for predominantly hole initiated multiplication show corresponding high excess noise factors suggesting the electron to hole ionization coefficient ratios are comparable to those reported for $hbox{Hg}_{1-{x}}hbox{Cd}_{x}hbox{Te}$ electron avalanche photodiodes.      

HgCdTe electron avalanche photodiodes

Exponential-gain values well in excess of 1,000 have been obtained in HgCdTe high-density, vertically integrated photodiode (HDVIP) avalanche photodiodes (APDs) with essentially zero excess noise. This phenomenon has been observed at temperatures in the range of 77–260 K for a variety of cutoff wavelengths in the mid-wavelength infrared (MWIR) band, with evidence of similar behavior in other IR bands. A theory for electron avalanche multiplication has been developed using density of states and electron-interaction matrix elements associated with the unique band structure of HgCdTe, with allowances being made for the relevant scattering mechanisms of both electrons and holes at these temperatures. This theory is used to develop an empirical model to fit the experimental data obtained at DRS Infrared Technologies. The functional dependence of gain on applied bias voltage is obtained by the use of one adjustable parameter relating electron energy to applied voltage. A more quantitative physical theory requires the use of Monte Carlo techniques incorporating the preceding scattering rates and ionization probabilities. This has been performed at the University of Texas at Austin, and preliminary data indicate good agreement with DRS models for both avalanche gain and excess noise as a function of applied bias. These data are discussed with a view to applications at a variety of wavelengths.     

Scattering of hot electrons by neutral acceptors in GaAs/AlAs quantum well structures

The optical alignment of hot electrons and its destruction in a magnetic field under conditions when electron scattering by neutral acceptors plays a large role is investigated. This makes it possible to determine the probability of the scattering of hot electrons from an initial photoexcited state, as well as the times characterizing the energy and momentum relaxation of hot electrons on scattering by neutral acceptors. The experimental results are compared with calculations. Fiz. Tekh. Poluprovodn. 32, 866–875 (July 1998)     

Electrons and phonons in quantum wells

The modulation of electron and polar optical phonon states in an AlGaAs/GaAs/AlGaAs quantum well (QW) with an inserted thin AlAs barrier is considered. The OW width dependence of electron-phonon scattering rates are estimated. The large contribution to the change of the electron subband population, the photovoltaic effect, and the electron mobility in the QW accounts for the resonant intersubband scattering of electrons by interface phonons. The decrease of electron mobility limited by polar optical phonon scattering with increasing carrier concentration in the QW is established. The conditions for the increase of mobility in the QW by inserting the AlAs barrier are found. Fiz. Tekh. Poluprovodn. 33, 1049–1053 (September 1999) This article was published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Electron-phonon interaction in short-period (GaAs) m (AlAs) n (001) superlattices

The deformation potentials of electron scattering at short-wavelength phonons for intervalley transitions in the conduction band of short-period (GaAs) _m (AlAs) _n (001) (m, n = 1, 2, 3) superlattices are determined by the electron density functional method. The dependences of the electron and phonon states and deformation potentials on the layer thickness in the superlattices are analyzed. The results of ab initio calculations are in good agreement with the data of empirical calculation of the deformation potentials integrated over phonons, but differ from data on the corresponding potentials for partial scattering channels because of approximations of the phenomenological model of interatomic binding.