Noise In Semiconductors Research Articles

Monte Carlo calculation of electronic noise in semiconductors

We present a general theory to investigate the electronic noise in the presence of scattering as well of generation recombination processes under the application of an electric field of arbitrary strength. An exact decomposition procedure of the current spectral density is given which, in addition to fluctuations in carrier velocity and number, shows the presence of a cross term coupling both fluctuations. Four correlation functions are thus found to be needed to evaluate all terms. To this purpose, the Monte Carlo method is shown to provide a unifying microscopic calculation of these functions and thus of each term contributing to the total spectral density. In this way, scatterings in the conducting band as well as capture to and release from the traps are treated for the first time on the same kinetic level of description. In particular, the Poole-Frenkel effect is included when necessary. As an application, we consider the case of p-Si at77 K with a generation-recombination mechanism given by the capture at shallow impurities assisted by acoustic phonons. Then, the theoretical results are compared with existing mesoscopic theories as well as with available experimental results.

A model current spectral density for hot-carrier noise in semiconductors

Analytical expressions are presented for the spectral density of current fluctuations derived from a rigorous theoretical analysis which can be applied at any electric-field strength. The main peculiarities of these spectra are discussed from an analytical point of view and in terms of the physical processes involved at increasing electric fields. Then, two different expressions are provided for an analytical fitting of spectra based on physical parameters related to a rigorous eigenvalue expansion of the correlation functions. These model spectra are in good agreement with the experiments and the results of Monte Carlo simulations for the case of p-type Si at 77 K.

Fluctuating deep-level trap occupancy model for 1/f noise in semiconductor resistors

A quantitative theoretical model for 1/f and low-frequency noise due to bulk traps in semiconductor resistors has been developed. The model is based on the fact that random fluctuations of the steady-state deep-level-trapped electron density, at some point in a depletion layer, decay exponentially with a relaxation time which depends on the local free electron density, the intrinsic properties of the semiconductor and the trap energy. The model, which is valid for relaxation times which are much longer than the free electron transit time, was applied to the case of a Schottky-barrier field effect resistor. Our results show that the low-frequency noise spectrum generated by deep-level traps with a broad spatial distribution throughout the depletion layer, is very sensitive to Fermi-Dirac trap statistics. The discrete distribution of flatband trap energy levels is the crucial parameter which determines the spectral density and range of the low-frequency noise. Monoenergetic traps generate a considerably broadened Lorentzianlike low-frequency noise spectrum which is highly sensitive to temperature. Traps with an arbitrary distribution over a set of discrete energy levels may exhibit 1/f noise or generic low-frequency noise. We deduce the condition that has to be satisfied in order for an arbitrary discrete distribution of bulk traps over energy to exhibit 1/f noise and derive an exact integral and approximate analytical expressions for the spectral density and range of bulk 1/f noise in semiconductors. The temperature dependence of the 1/f noise spectrum is discussed while in the process elucidating the subtle temperature-dependent relationship between 1/f and low-frequency noise arising from bulk traps. Experimentally observed low-frequency and 1/f noise characteristics are explicitly accounted for by the model. A qualitative argument for the application of the model to 1/f noise generated by surface traps is given.

Correlation functions and electronic noise in doped semiconductors.

We present an original Monte Carlo study of correlation functions for the general case of a doped semiconductor under the influence of an electric field of arbitrary strength. Number, velocity, and energy of the carriers are taken as relevant variables. These lead to a set of 25 correlation functions that, for the case of a cubic semiconductor and an electric field in the 〈100〉 direction as investigated in this paper, reduce to 11 nonvanishing functions. By using an analytical model based on coupled Langevin equations together with the results of the Monte Carlo simulations, we have quantitatively analyzed the different coupling processes as functions of the electric field. The simulations are performed for lightly doped p-type Si at 77 K. We demonstrate that even at equilibrium the coupling between energy relaxation and generation-recombination processes can lead to a strongly nonexponential decay of the corresponding correlation functions. At higher fields, we find the interesting result of a transition from two real relaxation rates for energy and longitudinal velocity to a pair of complex-conjugate values, which indicates some kind of ordering in the system driven by the electric field. At the highest fields, this ordering disappears and the rates again become real. The theory so developed is shown to provide a rigorous scheme for a microscopic interpretation of noise-spectroscopy measurement.

Monte Carlo method for the simulation of electronic noise in semiconductors.

We present a general theory to investigate the electronic noise in the presence of scattering as well as of generation-recombination processes. An exact decomposition procedure of the current spectral density is given that, in addition to fluctuations in carrier velocity and number, shows the presence of a cross term coupling both fluctuations. Four correlation functions are thus found to be needed to evaluate all terms. To this purpose, the Monte Carlo method is shown to provide a unifying microscopic calculation of these functions. We consider the case of p-type Si at 77 K with a generation-recombination mechanism given by the capture at shallow impurities assisted by acoustic phonons. Then, the theoretical results are compared with existing mesoscopic theories as well as with available experimental results.

Extensions of Handel's 1/f-noise equations and their semiclassical theory.

By replacing the change in velocity \ensuremath{\Delta}v by the low-frequency Fourier transform ${\mathrm{F}}_{a}$(0) of the electron acceleration a(t), Handel's equations for the Hooge parameter ${\ensuremath{\alpha}}_{H}$ are put in equivalent forms that are not only applicable to collision 1/f noise in semiconductors but also to acceleration 1/f noise in long semiconductor resistors. To prove these expressions semiclassically, one evaluates first the bremsstrahlung energy dE of a single radiation pulse in a frequency interval df, and then defines dn=dE/hf as the number of photons of a single radiation pulse in a frequency interval df and finally dr=dn/${\ensuremath{\tau}}_{a}$=dE/hf${\ensuremath{\tau}}_{a}$ as the rate of photon emission in a single pulse in a frequency interval df. It is then found that the expression for dr already contains the Hooge parameter ${\ensuremath{\alpha}}_{H}$. It thus seems that the Hooge parameter depends only on the bremsstrahlung emission process but not on the details of the electron-photon interaction. This may explain why Handel's expressions for ${\ensuremath{\alpha}}_{H}$ so often agree with experiment. One must now bear in mind that the elementary current event is described by a current pulse i(t) of duration ${\ensuremath{\tau}}_{a}$ having a Fourier transform ${\mathrm{F}}_{i}$(0). If one next defines ${S}_{r}^{\mathcal{'}\mathcal{'}}$(f)=dr/df, then the current noise spectrum is obtained by multiplying ${S}_{r}^{\mathcal{'}\mathcal{'}}$(f) first by ${2\mathrm{F}}_{i}^{2}$(0), to obtain the effect of a single elementary event per second, and then multiply by \ensuremath{\lambda}, the number of elementary events per second. This leads immediately to the Hooge equation and to the Hooge parameter ${\ensuremath{\alpha}}_{H}$. .AE

Fluctuations in hot charge carriers mobility and [formula omitted] noise in semiconductors

The 1f noise in semiconductors with hot charge carries is explained as a result of fluctuations in impurity scattering. This model contradicts the proposal by Hooge, Kleinpenning and Vandamme [Rep. Prog. Phys. 44 (1981) 479], attributing the 1f noise to lattice scattering. It is shown that the noise may be caused by the 1f fluctuations in the number of neutral scattering centres in the volume of the sample. This noise source modulates the mobility of the charge carriers, i.e. the mobility fluctuations are the secondary effect. The interpretation of the known experimental data is suggested here as well.

Generalized semiclassical quantum 1/f noise theory. I. Acceleration 1/f noise in semiconductors

A generalized derivation of van der Ziel’s semiclassical 1/f noise theory is given. It includes 1/f noise in collision-free devices and collision 1/f noise in collision-dominated devices, but also acceleration 1/f noise in the latter devices; this is a new noise source. In all cases the Hooge parameter αH can be expressed in a similar form. The Hooge parameter of the third noise source varies as the square of the device length d as long as d is not too large. For very large d the Hooge parameter may saturate and this saturated value may correspond to Handel’s coherent state 1/f noise. For very large drift times τd deviations from the 1/f spectrum may occur.

Channel length dependence of the 1/f noise in silicon metal-oxide-semiconductor field-effect transistors. II. Verification of the acceleration 1/f noise process

A systematic study of the 1/f noise dependence on the channel length in p- and n-channel silicon MOSFETs (metal-oxide-semiconductor field-effect transistors) is presented. Devices made by the same procedure on the same chip were used. In this way, the nonuniformity of noise sources, which strongly depend on the fabrication procedure (like 1/f noise produced by surface trapping), was avoided. Hooge’s parameter αH was used as a measure of the magnitude of the 1/f noise in the device. The αH was found to vary as the square of the channel length in p MOSFETs and in the most of the n MOSFETs. Existing theories and known noise mechanisms do not explain this dependence. The incorporation of a recent theory involving the acceleration 1/f noise in semiconductors, developed by van der Ziel, explains the experimental data very well. The αH was found to be independent upon the electric field and the extraction of an effective time constant was used for comparison between theory and experiment.

Unified presentation of 1/f noise in electron devices: fundamental 1/f noise sources

1/f noise in semiconductors, semiconductor devices, and collision-free devices (like vacuum tubes) is presented from a unified point of view, using an extended version of the F.N. Hooge equation (Physica, vol. 83b, p.9, 1976), which is generalized to all collision-dominated systems involving mobility, diffusion, and cross-section fluctuations. It also applies to collision-free processes involving vacuum tubes, Schottky barrier diodes operating in the thermionic mode, and in devices such as p-i-n diodes in which collision processes are not the determining factor. A generalized schematic is given for expressing the noise spectrum S/sub 1/(f) in the external circuit in terms of distributed noise sources of the nonuniform devices in terms of alpha /sub H/, so the latter can be determined from the former. It is then found that the Hooge parameter. alpha /sub H/ introduced by this equation can be used as a general measure of the noisiness of a system or device. Several cases in which the noise does not obey the quantum 1/f noise theory are discussed. Measurements on many different devices are examined, and an attempt is made to correlate measured values of the Hooge parameter with the values calculated from P.H. Handel's quantum theory of 1/f noise (1975, 1980).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Spatial correlation measurements of [formula omitted] noise in semiconductors

One of the proposed models for 1 ƒ noise, thermal fluctuations theory, involves a diffusive mechanism which implies spatial correlation of the fluctuating quantity within a frequency-dependent correlation length. In order to test this prediction, we have performed spatial correlation measurements on p-type conductive diffused strips of silicon at temperatures between 20 and 295 K. The frequency span was from 10 Hz to 10 kHz. We have not found any correlation between the 1 ƒ fluctuations in two different segments of the strip separated by 2.5 mils, making diffusion mechanism an unlikely origin of the noise.

Monte Carlo algorithm for generation-recombination noise in semiconductors

We present an original Monte Carlo procedure to account for generation-recombination noise through impurity centers in semiconductors. Numerical calculations are specialized to the case of holes in Si at 77 K. Results are found to compare favorably with available experiments.

Hot-electron noise in two-valley semiconductors: An analytic model.

We present results for the hot-electron noise in two-valley semiconductors, such as GaAs, where intervalley transfer plays an important role. The noise is calculated by a Boltzmann--Green-function method. We obtain an analytic solution for a model with two valleys and three relaxation times. Using the measured low-field mobility, lower-valley mass, and valley separation energy \ensuremath{\Delta}, while adjusting three upper-valley parameters, we obtain good agreement with both experimental time-of-flight measurements and microwave noise measurements. We find that the hot-electron noise is very sensitive to the transport parameters, much more so than the velocity-field curve. In particular, the noise is very sensitive to the \ensuremath{\Gamma}-to-L scattering rate and our results indicate that experimental noise measurements might be used for determining this parameter.

Nonequilibrium current fluctuations in semiconductors: A Boltzmann-equation-Green-function approach.

We present a method for calculating nonequilibrium current fluctuations (i.e., hot-electron noise) in semiconductors based on the Green function to the time-dependent Boltzmann equation. The method is valid for nondegenerate semiconductors for which the Boltzmann equation describes the normal (i.e., time-independent) transport properties. We illustrate the method in uniform systems within the relaxation-time approximation. We find that the noise can either increase or decrease from its equilibrium value, depending on the band structure and the energy dependence of the relaxation time.

A unified theory of noise in nondegenerate semiconductors

Explicit forms of the Langevin noise sources due to both intraband and interband scattering are given for the Boltzmann transport equations with the relaxation-time approximation in nondegenerate semiconductors. A generalized formula for the short-circuited noise currents, which holds in both homogeneous and nonhomogeneous one-dimensional nondegenerate semiconductors, is derived in a unified manner by solving the Langevin-type Boltzmann transport equations. From this generalized noise formula the short-circuited noise currents for thermal noise, generation-recombination noise, and 1/f noise in a homogeneous nondegenerate semiconductor bar are calculated. It is shown that for homogeneous nondegenerate semiconductors, Nyquist’s theorem always holds both at thermal equilibrium and under an applied dc electric field with either intraband scattering or interband scattering dominant. Generation-recombination noise is shown to be caused by the electrons or holes whose scattering mechanism is dominated by intraband scattering, and the derived generation-recombination noise formula is the same as the one derived by the conventional methods. It is also shown that 1/f noise may be caused by a very small number of electrons (or holes) lying just around the bottom of the conduction band (or the top of the valence band) when interband scattering is dominant over intraband scattering for these electrons (or holes). The contribution of these small number of electrons (or holes) to the electrical conductivity is negligible because of the smallness of the number of these carriers. The derived 1/f noise formula has the same functional form as the Hooge’s empirical relation [Physica 83, 14 (1976)].

Computer study of acoustoelectric current noise in semiconductors

Numerical simulation shows that the acoustoelectric current noise about the steady state saturated current in piezoelectric semiconductors is caused by the electron transfer processes where bunches of electrons trapped in potential troughs coupled to amplified acoustic waves via the piezolectric effect are transferred chaotically to their neighboring troughs.

Relativistic correction of the Hooge parameter for Umklapp [formula omitted] noise

If the 1 ⨍ noise in semiconductors is describable by the Umklapp 1 ⨍ noise process, a relativistic correction of the Hooge parameter is needed when the effective mass of the carriers is very small. This should apply to Hg 1− x Cd x Te resistors with x = 0.20 and low temperature when Umklapp 1 ⨍ noise is the predominant 1 ⨍ noise source.

Reply to ‘‘Comment on ‘Phonon fluctuation model for flicker noise in elemental semiconductors’ ’’ [J. Appl. Phys. 5 2, 2884 (1981)

Phonon fluctuation model for flicker noise in elemental semiconductors is consistent with then existing data. New experimental results may necessitate a reinterpretation of some of the axioms of the model. A further improvement in the model can result by reviewing some of the assumptions involved.

Phonon signatures in the 1/f noise parameter of copper, silver and silicon

Structures corresponding to phonomic energies were identified in the 1/ f noise parameter of copper, silver, and silicon. These results sustain that the phonon-carrier interaction is the common source of 1/ f noise in metals and semiconductors.

Low-frequency current noise with a 1/fspectrum in solids

The problem of low-frequency current noise with a 1/f spectrum in solids (flicker noise) is reviewed. The fundamental general properties of this noise are described: frequency-dependence of the spectral density, time-dependence of the correlation function, form of the distribution function of the fluctuations, dependence of the spectral density on the potential applied to the specimen, anisotropy of the fluctuations of the resistivity tensor, correlation length of the fluctuations, dependence of the noise on the dimensions of the specimen and on the concentration of current carriers, the empirical Hooge relationship, etc. A model of 1/f noise is presented and discussed that associates its spectrum with the presence in solids of an extensive hierarchy of relaxation times. Concrete models of systems having an exponentially broad spectrum of relaxation times are described (the McWhorter model, two-level tunneling systems, the disordered Ising kinetic model). The theory and experimental data on current noise caused by temperature fluctuations are analyzed. The problem is treated of surface noise in semiconductors and 1/f noise in metal films.