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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

The classical impedance field method is one of the most powerful techniques to calculate electronic noise in semiconductor structures. This method fails when applied to deep submicron devices due to the presence of spatial correlations between noise sources. To overcome this drawback, a new technique (generalised impedance field) has been developed in the frame of a hydrodynamic simulator. Analogously to the classical method, the calculation of electronic noise requires the knowledge of two quantities: the local noise sources and the generalised impedance fields. Instead of using a hydrodynamic approach to obtain the generalised impedance fields and a Monte Carlo simulation for the noise sources, we have used a microscopic simulator (the Scattered Packet Method) to compute both quantities.

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.

The time‐and‐frequency behavior of hot‐carrier noise in submicrometer n + nn + GaAs diodes is investigated theoretically using the Monte Carlo method. We have continuously investigated the noise from current‐to‐voltage operation mode by calculating the noise‐power spectrum at the terminals of a noiseless load‐resistance R connected in series with the diode. By varying appropriately the value of R we have calculated the small‐signal impedance of the diode and then obtained the full spectrum of the noise temperature. Under voltage‐operation mode the current–noise spectrum exhibits two resonant peaks at the transit‐time and plasma frequencies, respectively. Under current operation mode, all current oscillations are effectively damped, and the voltage–noise spectrum exhibits a quasi‐Lorentzian shape, which vanishes at the transit‐time frequency. The behavior of hot‐carrier noise closely parallels the frequency dependence of the diode small‐signal impedance, which exhibits a dynamic negative differential resistance in the frequency range corresponding to the transit‐time resonance.

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.

We investigate the possibility to suppress the diffusion noise in semiconductor bulk materials by adding to the constant electric field a fluctuating contribution characterized by a gaussian distribution and a characteristic time. The general theory is applied to the specific cases of Si and GaAs and investigated by Monte Carlo simulations. Numerical results confirm the possibility to suppress the intrinsic noise and the best conditions to realize this effect are analyzed in detail.

We investigate the possibility to suppress the diffusion noise in bulk semiconductors by adding to a constant electric field a fluctuating contribution characterized by a gaussian distribution and a characteristic time. To this purpose, Monte Carlo simulations are performed applied to the case of GaAs at room temperature. Numerical results confirm the possibility to suppress the total noise power by an appropriate choice of the externally added noise.

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.

A theoretical model for the noise properties of n+nn+ diodes in the drift-diffusion framework is presented. In contrast with previous approaches, our model incorporates both the drift and diffusive parts of the current under inhomogeneous and hot-carrier conditions. Closed analytical expressions describing the transport and noise characteristics of submicrometer n+nn+ diodes, in which the diode base (n part) and the contacts (n+ parts) are coupled in a self-consistent way, are obtained.

International audience

The article presents a critical discussion on the evaluation of the impedance field for noise analysis by means of several transport models. The models considered are the drift-diffusion model, the full hydrodynamic model, and the scattered packet method for the direct solution of the Boltzmann transport equation. The comparison is carried out on a canonical Si p+pp+ diode at ambient temperature. The agreement found between the approaches is good, thus suggesting that the evaluation of the impedance field does not require any additional care with respect to other, more conventional operating conditions.

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.

The time-domain formulation of the transfer-impedance method is developed to calculate the impedance field of two-terminal semiconductor structures. The voltage noise spectrum associated with velocity fluctuations is then calculated for overmicron and submicron n+nn+ GaAs diodes in the framework of a closed hydrodynamic approach based on the velocity and energy conservation equations. Transit-time effects are found to influence substantially the noise spectrum in a wide frequency range above 10 GHz. The good agreement found with Monte Carlo simulations validates the proposed theoretical approach.

International audience

International audience

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 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 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 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.

International audience; The variation of the diffusion coefficent D(E) versus the electric field strength E, is determined at 300 K in n-type GaAs (N(D) = 3 x 10(-17) cm-3), using pulsed high-frequency noise measurements. D(E) is found to increase slightly at low field, then to decrease down to one tenth of its ohmic value near the threshold field. "Long" (greater-than-or-equal-to 4-mu-m) real n+-n-n+ Gunn diodes, with an arbitrary doping profile, can be modeled. Comparisons are made, and excellent agreement is found, between experimental and theoretical characteristics of two real diodes, with notch and with gradual doping profiles. The doping profile N(D)(x) is shown to have a considerable influence on the diode behavior, concerning the electric field profile as well as the noise characteristics. Using the impedance field method, the noise current is modeled and found to be very sensitive in the D(E) variation law, in particular in the range of 2.5-4 kV/cm. The agreement between the experimental noise and the computed noise of real diodes is found to be quite satisfactory when using D(E) determined in the present work, and important discrepancies occur when using other D(E) variations, both theoretical and experimental, found in the literature.

International audience; A theoretical investigation and experiments on the noise spectra of lightly doped p-type Si (boron) at 77 K are presented. Noise spectra in the high-frequency range 0.22 less-than-or-equal-to f less-than-or-equal-to 10.5 GHz have been measured at different electric fields 100 less-than-or-equal-to E less-than-or-equal-to 2500 V/cm for two acceptor concentrations N(A) of 4 X 10(14) and 3 X 10(15) cm-3. The experimental results are interpreted within a Monte Carlo simulation, which includes at a microscopic level the mechanism of generation and recombination from impurity centers. The different sensitivity on the parameters in fitting first- and second-order transport coefficients is shown to provide a formidable check to support the physical plausibility of the model used.

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.

Contrairement aux affirmations habituelles, les sources de bruit locales en deux points differents sont correlees sur de courtes distances, de l'ordre d'une fraction de micron. La fonction de correlation est calculee pour des porteurs chauds dans des semiconducteurs, pour des diffusions aleatoires. Le coefficient de diffusion dependant de la frequence, pour les porteurs chauds, est donne sous la forme d'une integrale contenant la fonction de distribution

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..

One of the basic hypothesis involved in the Boltzmann equation is that the collisions are instantaneous. In this paper it is shown that, for usual scattering processes in semiconductors, the collision duration can be estimated to be ≈ 5 x 10-13 sec, which is therefore not at all negligible compared with the mean free flight duration.