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International audience; We extend the iterative matrix method for the solution of the Boltzmann transport equation in multi-band semiconductors to the calculation of second order parameters such as correlation functions and the noise temperature. The method allows also the extraction of the diffusion coefficient in each valley. The results for the case of GaAs with two valleys show that the diffusion in this material is dominated mainly by interactions in the Γ valley. The calculated noise temperature is in good agreement with Monte Carlo results

We use a full band iterative matrix method to study the high-field transport in n-type GaAs for the first time using three non-parabolic valleys (Γ, L, and X). The new simulation of transient electrons in GaAs shows that, even if there exist carriers in the X-valley beginning from an electric field E = 10 kV/cm, the two-valley model (r and L) remains still valid until E = 20 kV/cm. We present results for the distribution functions, in the transient and permanent regimes in GaAs in the Γ-, L-, and X-valleys, for electric fields in the range 1 to 60 kV/cm. These functions allow to calculate all parameters of the first order in both regimes. We obtain good agreement with the experimental velocity-field curves.

We present a new numerical method to calculate the correlation functions in semiconductor materials by a direct solution of the Boltzmann equation. The correlation function is calculated solving a set of time-dependent Boltzmann equations corresponding to different initial conditions. As application, we present the calculation of the correlation function of velocity fluctuations and the noise temperature for holes in silicon at T=300 K. The results are in good agreement with Monte Carlo calculation as well as with experimental data.

In this paper, a new method for three-dimensional object envelope construction is proposed using the chaining approach. The object is seen by three cameras placed on an orthonormal basis (OXYZ) axes. From these projections, respective contours are extracted and then transformed into a list of chains presenting contour pixels of each projection. These chains are restructured to be used for arbitrary-object shape envelope construction. The constructed 3-D object can be viewed on the screen using perspective or parallel projections under arbitrary viewpoint angles Θ and φ A one-pixel precision is reached for recovered objects.

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 analytical expressions for the differential‐mobility spectra which are obtained from a linear analysis of the balance equations under stationary and homogeneous conditions. The expressions are rigorously related to an eigenvalue expansion of the response matrix and are applicable to ohmic as well as to non‐ohmic conditions. The coefficients appearing in the formula can be calculated from the knowledge of three parameters as functions of the electric field, namely, the reciprocal effective mass, the drift velocity, and the average energy of the carriers. The theory is applied to the case of holes in Si at T=300 K and validated by comparison with the results obtained by a direct numerical resolution of the perturbed Boltzmann equation.

International audience

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 numerical method is developed for solving the transient Boltzmann equation. The scattered packet method (SPM) gives the carrier distribution function when an electric field is applied. Using that method we can also follow the evolution and the spreading in the k‐space of a packet of carriers, due to the field and the collisions with the lattice and ionized impurities. The current correlation function and the diffusion coefficient can then be computed in a simple way.

The purpose of that paper is to compute the noise temperature through the Boltzmann and Einstein equations. Using the scattered packet method, described in Ref. 1, we can solve the Boltzmann equation and compute the diffusion coefficient when an electric field is applied. In order to obtain the noise temperature it is then necessary to know the differential (a.c.) mobility of the carriers. At low frequency we can calculate the slope of the velocity field characteristic but this method is not enough accurate at low frequency and even not valid at all at high frequency. We have developed a program enabling us to solve the small signal Boltzmann equation and to obtain the a.c. mobility.

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.