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Experimental results on microwave noise in $n$-type GaAs $(n=3\ifmmode\times\else\texttimes\fi{}{10}^{17}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}3},$ 80 K) at electric fields below a few hundred $\mathrm{V}/\mathrm{c}\mathrm{m}$ are interpreted combining the analytic approach and Monte Carlo simulation. The analytic approach is based on applicability, due to high frequency of interelectron collisions, of the electron temperature approximation. Monte Carlo simulation shows a rather low sensitivity of the conductance to the electron heating, accompanied by small deviations from the Ohm law, these circumstances favoring a nearly isotropic noise temperature and an approximate validity of the Price fluctuation-diffusion relation. The degree of violation of this relation caused by the interelectron-collision-born correlation is found to depend on the applied electric field and the donor compensation by acceptors, remaining below 0.01 in typical partially compensated $n$-type GaAs channels. This enables one to obtain the field-dependent electron diffusion coefficients from calculated and/or measured noise and current characteristics in a wide range of electric fields including those where the interelectron collisions are essential.

We present a theoretical analysis of number and current fluctuations in homogeneous n-Si resistors of submicron dimensions at increasing electric field strengths. To this purpose, we calculate the corresponding correlation functions. In the ballistic regime a simple scaling relationship of the transit time accounting for carrier heating is found to hold over the whole range of fields considered. In the diffusive regime different time scales associated with diffusion, drift and dielectric relaxation are found to characterize the behaviour of number fluctuations.

After recalling the definition of the noise temperature, the macroscopic expressions for noise sources are shown not to be specific to the hot carrier regime, though dependent on the electric field strength. Careful modeling allows one to obtain important information on transport parameters from noise measurements. The microscopic noise source expressions, via the transition rates, give a unified view of the noise sources. In particular, it is clarified that noise sources are intercorrelated, and that there is also space correlations over lengths of a few mean free paths. Recent developments are reviewed, concerning noise modeling using direct numerical methods for solution of the Boltzmann equation. Finally, impedance field methods for modeling noise of devices are briefly evoked. >

A direct numerical method is developed for solving the electron transient coupled Boltzmann equations in the Gamma and L valleys in InP. The complicated shape of the transient distribution function is obtained with a great accuracy. Fine structures of the velocity and the energy are obtained in the Gamma and L valleys when the population of L valleys is very small.

We present a theoretical analysis of the thermal conductivity of charge carriers in semiconductors under nonequilibrium conditions due to an applied electric field. The theory is based on a correlation-function formalism which directly relates this kinetic coefficient to four spectral densities involving carrier velocity and energy flux fluctuations. Monte Carlo calculations performed for the cases of p-Si and n-GaAs give an evidence of a strong dependence of the thermal conductivity on increasing electric fields.

We present a hydrodynamic-Langevin scheme to describe electronic noise in unipolar structures and evaluate the cross-correlation functions of conduction current fluctuations entering the transfer impedance method. The theory is developed in terms of microscopic fluctuations of carrier velocity and energy taking place during scattering events. Applications to submicron n+nn+ GaAs structures show that the contribution of stochastic velocity rate prevails over that of the energy rate in determining the cross-correlation function of conduction current fluctuations.

We propose a novel numerical procedure to calculate the hot-carrier thermal conductivity in bulk semiconductors. The method is based on combining Monte Carlo and hydrodynamic simulations of carrier transport in submicron inhomogeneous structures. Application to a Si structure indicates a decrease over one order of magnitude of the thermal conductivity of electrons at electric fields over , in close agreement with recent results obtained within the correlation-function formalism.

It is shown that in nitrides the instabilities based on the transit-time resonance inside the optical-phonon sphere of momentum space as well as the intervalley transfer of electrons can be realized in the TeraHertz frequency region. In both cases the maximum frequency of the instability is proportional to the effective rate of polar optical phonon emission.

By using the Monte Carlo method, submicron Si n+nn+ structures are analysed at different bias voltages and lengths of the n region. The autocorrelation function of current fluctuations and the variance of carrier number in different parts of the device is used to investigate the correlations induced by the self-consistent solution of the Boltzmann and Poisson equations and the influence of the modelling of the contacts.

The authors present a numerical method that allows them to solve the transient Boltzmann equation in p-Si with accuracy as high as in previous methods, but up to 200 times faster than is possible by the direct method. It consists in expanding the carrier distribution into a set of displaced Maxwellian functions and using a least-squares-like approximation method.

We present a unifying scheme for the hydrodynamic calculation of electronic noise in semiconductor devices operating under various conditions. In the framework of the Green-function formalism the noise sources corresponding to the Langevin forces originated by single scattering events are included into the equations describing medium properties. The scheme is validated by numerical calculations of the voltage and current noise in submicron n + nn + GaAs structures.

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We present an analytical modeling of the noise temperature associated with velocity fluctuations obtained in the framework of the linear‐response theory around a steady state. The expressions are rigorously related to an eigenvalue expansion of the response matrix and are applicable to ohmic as well as to nonohmic (hot‐carrier) conditions. Theory requires as input parameters the reciprocal carrier effective mass, the drift velocity, the carrier energy, the variance of velocity fluctuations, and the covariance of velocity‐energy fluctuations as functions of the electric field in stationary and homogeneous conditions. The analytical results obtained for the case of holes in Si and electrons in GaAs at T=300 K are validated by comparison with experiments.

We present a detailed investigation of the transient transport regime in InP at room temperature based on an original method to solve numerically the coupled hot-phonon--hot-carrier time-dependent Boltzmann equations for the case of a steplike high dc electric field pulse. The method enables a study of the perturbation of the phonon distribution function induced by hot carriers and the corresponding modifications of the carrier distribution function. The numerical accuracy of the method is far beyond other existing methods, and, as a consequence, the time behavior of the main transport parameters can be resolved in great detail. The presence of nonequilibrium phonons is found to be responsible for an overall increase in the time duration of the transient regime. Modifications in the time evolution of the main transport parameters are also observed; in particular, the carrier drift velocity exhibits a second overshoot for electric fields near the threshold value for negative differential mobility. The sensitivity of the results to the value of the phonon relaxation time is also discussed. \textcopyright{} 1996 The American Physical Society.

We present a theoretical investigation on the electronic noise of submicron n+nn+ GaAs diode under the conditions when the electrical characteristics of the diode exhibit a pronounced near‐oscillatory macroscopic behavior caused by velocity fluctuations of single particles at the microscopic level. Two kinds of spontaneous oscillations, related to transit time and plasma oscillations, and their contributions to the diode noise are investigated by a Monte Carlo simulation. A simple analytical model which provides an excellent fit of the macroscopic features of the noise obtained by the Monte Carlo simulation is developed.

We present an analysis of number and current fluctuations in homogeneous n‐Si resistors of submicron dimensions by employing analytical and Monte Carlo calculations. Results show the presence of long‐time tails in the ballistic regime, which vanish when the length of the sample becomes comparable with the carrier mean‐free‐path. In the diffusive regime different time‐scales related to diffusion, drift, and dielectric relaxation are shown to characterize the behavior of fluctuations.

We have solved the transient {k} and space dependent Boltzmann equation in n‐type silicon. The transient distribution function f(k,z,t) is obtained in the k space and along the direction of the applied electric field (along the z axis). The material is assumed to be homogeneous so that the Poisson equation is not taken into account. Hence we can follow the spreading of a packet of carriers initially located around z=0. By a simple integration over the whole k space we obtain f(z,t), v(z,t), and e(z,t). The longitudinal diffusion coefficient is computed using the slope of the variance of the carriers’ positions.

A matrix method for the numerical determination of steady-state hot-phonon and nondegenerate hot-electron distribution functions is presented. The coupled Boltzmann equations for the longitudinal-optical phonons and for the electrons, in the \ensuremath{\Gamma} and L valleys of III-V semiconductor compounds, are iteratively solved with high accuracy under typical hot-electron conditions. The phonon distribution is shown to be significantly disturbed from thermal equilibrium. In turn, nonequilibrium phonons induce a substantial disturbance of the hot-electron distribution. Computations are performed for InP at 300 K, taking into account all relevant scattering mechanisms. It turns out that the electron transport parameters are strongly affected in the field range from 0 to 10 kV/cm: the drift velocity is increased by about 42% at 2 kV/cm and the Ohmic mobility by 37%. These effects are shown to be due to the drag and reduced cooling of the carriers by the nonequilibrium LO phonons.

The longitudinal diffusion coefficient of holes in Si has been measured with time‐of‐flight and noise techniques at 300 K for field strengths ranging from about 0.5 up to 40 kV/cm. As the electric field increases, the diffusion coefficient decreases to about 0.3 of its Ohmic value much more sharply than results previously reported in literature. The experimental results are interpreted by a Monte Carlo simulation which includes warping and nonparabolicity effects of the heavy‐hole band.

We have very recently developed a theory of the fluctuations of the state occupancy function in semiconductors, including a new expression of the noise source term instead of the classical one which was shown to be erroneous. In the present paper, we show that this theory can apply to practical situations, since it allows us to actually compute the transverse diffusion coefficient versus the electric field intensity in the range 0–50 kV/cm, in p-type silicon at 300 K. Also the variance of the number of particles in a volume is computed.

We present the first direct numerical computation of the distribution function as a solution of the Boltzmann equation in the degenerate case. The method provides the transient and steady state distribution functions with a high accuracy. Increasing the concentration reduces hot carrier effects. The degenaracy has a significant influence on the distribution function at free carrier concentrations above 1019 cm−3. It has practically no influence on the drift velocity in bulk p-type Silicon, but it modifies significantly the average energy, which is shifted towards higher values, independantly from the electric field strength..

Taking into account the finite lenght of the gate of a JG FET and the variation of the mobility versus electric field, it is shown, through a self-consistent hypothesis, that the electrical and geometrical properties of the active conducting channel remain unchanged in the saturation range. Experimental results of noise measurements performed in the saturation range at 300 K and 77 K can easily be explained by this theory.

The differential relaxation time τ (k,F) defined in a previous paper for isotropic semiconductors in the hot‐carrier range is shown to depend on the orientation with respect to the field force F. τ (k,F) is expressed using the collision operator and the distribution function. In the Ohmic range τ (k,F=0) is found to be equal to the usual relaxation time τ (k) related to transition probabilities per unit time. Longitudinal τN(k,E) and transverse τn(k,E) differential relaxation times are numerically computed for p‐type germanium and are found to be actually different although of the same order of magnitude, namely 10−12–10−13 sec. It is proved that the distribution function for hot carriers may be a displaced Maxwellian only if τ (k) is k independent, which does not hold for most of the situations of physical interest. It is shown that the differential relaxation times involved in longitudinal D∥(E) and transverse D⊥(E) diffusion coefficients are τ∥(k,E) and τ⊥(k,E). D∥(E) and D⊥(E) are numerically computed...

Noise measurements at 77 K performed on JG FET 2 N 4416 (Texas Instruments Corporation) show an important disagreement with theoretical expressions given by Van der Ziel. By analogy with results obtained with p-type germanium samples in the presence of a moderately high electric field, the “warm-carrier” hypothesis is made for the FET channel. Experimental results in the range 77 K–300 K fit the theoretical laws deduced from this assertion.

Transverse ( T n⊥ ) and longitudinal ( T n| ) diffusion-noise temperatures are compared in isotropic semiconductors in the presence of an applied electric field E . It is shown that T n| > T n⊥ and that the ratio T n| / T n⊥ tends towards infinity at intense electric fields. Differential mobility is mainly responsible for the strong anisotropy induced by an electric field in the noise temperature. The study of such phenomena in anisotropic semiconductors requires a knowledge of the variation of the mobility tensor with the vector E .

Properties of the mobility tensor and differential mobility-tensor components in the hot-carrier range are investigated in cubic semiconductors as regards to symmetry and independently from any scattering mechanism. It is shown that all the components can be deduced from only one diagonal and one nondiagonal component. General relations between components are established. Considering conduction of each valley brings additional information which is explicated for semiconductors with valleys lying along the

It is proved that the three diffusion coefficients, related to noise, spreading of a bunch of carriers, and gradient of concentration, are identical. This demonstrates in the hot carrier regime the validity of the relation kTn(E)/q=D (E)(dvd(E)/dE)−1 which is an extension of the Ohmic Einstein relation (Tn is the noise temperature, D is the diffusion coefficient, vd is the drift velocity). Therefore the noise and time‐of‐flight techniques appear as being two ways which are quite different, leading to the same diffusion coefficient.

Measurements of the transverse differential conductivity of hot carriers in semiconductors are performed, for the first time, using an experimental setup described in the present paper. This allows the determination of the transverse diffusion coefficients.

A theoretical investigation and new experiments on the conductivity of lightly doped p‐Si (boron) at 77 K are presented. The conductivity is studied as a function of the electric field in the range 10

The theory of the fluctuations of the state occupancy function, recently developped, together with the differential relaxation time, allow getting the transverse diffusion coefficient, which is computed in p-type Silicon, as a function of the electric field, at 300 K, from 0 to 50 kV/cm.

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