Bulk Negative Differential Conductivity Research Articles

Phase diagrams for periodically driven Gunn diodes

A simulation model of the electron transfer mechanism for bulk negative differential conductivity in n-GaAs is applied to investigate the formation and propagation of subsequent high field domains in the presence of an external microwave field. Phase diagrams for the distribution of modes are drawn for two different values of the non-equivalent intervalley relaxation time. The domain mode is found to entrain with the microwave signal in a variety of different frequency-locked solutions. At higher microwave amplitudes, period-doubling and other forms of mode-converting bifurcations take place. In this region, spatio-temporal chaos may also be observed, as indicated by a positive value of the largest Lyapunov exponent. At still higher amplitudes, transitions to delayed, quenched, and limited space charge accumulation modes occur. The D q -curve characterizing the multifractal structure is calculated for a typical chaotic solution.

Bifurcation and stability of dynamical structures at a current instability

We investigate bifurcation and stability of nonuniform current states at a voltage-controlled current instability. We consider a model which exhibits bulk negative differential conductivity due to Bragg scattering of hot electrons. The system is described by balance equations for momentum and energy densities of the carriers. These transport fields are coupled to Maxwell's equations. The uniform stationary current state is unstable against long-wavelength dielectric relaxation modes at a critical field. We find that the softening of these modes gives rise to a family of periodic travelling waves and to a solitary solution (dipole domain). We show that the periodic travelling waves are unstable, wheras the dipole domain can be stabilized by coupling the sample to a suitable external circuit, if the static impedance of the sample in the domain state is negative. The model describes therefore a discontinuous nonequilibrium transition to a large amplitude domain state.

Hydrodynamic modes, soft modes and fluctuation spectra near the threshold of a current instability

We give a full threedimensional treatment of the stability and the fluctuations of the uniform stationary current state in a voltage-controlled current instability. We consider a model which exhibits bulk negative differential conductivity due to Bragg scattering of hot electrons. The model consists of Langevin equations for the mean momentum and the mean energy of the charged carriers, coupled to Maxwell's equations. We investigate the normal modes and the fluctuation spectra of this system, in particular the occurrence of soft modes and of critical fluctuations at the stability limit of the uniform current state. It is shown that the nature of the normal modes is strongly determined by the electromagnetic interactions between the carriers, giving rise to hydrodynamic flux modes and to dielectric relaxation modes. As the threshold field is approached, the dielectric relaxation modes soften and couple strongly to the flux modes. It is shown that as a consequence of this coupling the exponential decay of the correlation functions due to ordinary dielectric relaxation is followed at very long times by a power law decay due to the hydrodynamic modes.

Travelling dipole domains and fluctuations for a current instability due to Bragg scattering

We investigate the stability of uniform and nonuniform current states for a model in which Bragg scattering of hot electrons leads to bulk negative differential conductivity. The system is described by phenomenological balance equations for momentum and energy densities of the carriers. For fixed total current, we find a family of periodic travelling-wave solutions and a solitary solution (dipole domain) which can be stabilized by coupling to a suitable external circuit, if the static domain impedance is negative. The model describes therefore a discontinuous nonequilibrium phase transition to a large-amplitude domain. In order to study fluctuations, we add stochastic forces to the balance equations and discuss the resulting fluctuation spectra.

Dynamic bulk negative differential conductivity in semiconductors : J. C. McGroddy and P. Guéret. Solid State Electron.14 (1971), p. 1219

A mechanism related to crystallographic defects has been proposed by Hsu, Whittier, and Mead to explain the characteristics of burst (popcorn) noise. This paper extends their results to include sources of burst noise both in bulk material and more importantly at the surface. Experimental results are presented on specially fabricated transistors, some of which were gold doped. Experimental data are interpreted in order to substantiate the proposed burst noise model.Un mécanisme se rapportant aux défauts de cristallographie a été proposé par Hsu, Whittier et Mead pour expliquer les caractéristiques du bruit d'éclatement (popcorn). Ce document élargit ses résultats pour comprendre les sources de bruits d'éclatement dans les matériaux en vrac et plus spécialement en surface. Les résultats présentés sont ceux d'expériences sur des transistors fabriqués spécialement, certains étant recouverts d'or. Les données expérimentales sont interprétées de manière à substancier le modèle proposé de bruit d'éclatement.Zur Erklärung des burst-(popcorn)-Rauschens wurde von Hsu, Whittier und Mead ein Mechanismus vorgeschlagen, der mit kristallographischen Defekten verknüpft ist. Die vorliegende Arbeit ergänzt diese Ergebnisse unter Einschluß von burst-Rauschquellen im Volumen und vor allem an der Halbleiteroberfläche. Es werden experimentelle Ergebnisse an speziell hergestellten Transistoren mitgeteilt, die z.T. mit Gold dotiert waren. Die gewonnenen Daten werden interpretiert, um das vorgeschlagene Rauschmodell zu beweisen.

Measurement of bulk negative differential conductivity in n-type silicon

Velocity field characteristics of electrons in silicon were measured for temperatures between 34K and 62K with the electric field along the 〈100〉 direction. At 52K and below a region of bulk negative differential conductivity is found.

Nonequilibrium Carrier Phenomena inn-Type InSb

Four nonequilibrium carrier phenomena, namely, the hot-electron effect, injection, impact ionization, and bulk negative differential conductivity (BNDC), produce nonlinear conduction in $n$-InSb in a strongly interrelated manner. These interrelationships are shown in detail. The hot-electron effect causes more decrease in average conduction under most transport conditions than injection causes increase and thus injection is not so easily observed. As the electric field strength is increased into the impact ionization range which begins at \ensuremath{\simeq} 225 V/cm, the generation rate progressively exhibits an ${e}^{E}$, an ${e}^{\frac{1}{E}}$, and then an ${e}^{\frac{1}{{E}^{2}}}$ dependence. The distribution of the carriers in energy space shifts from a peaked distribution for $225 \mathrm{V}/\mathrm{c}\mathrm{m} \ensuremath{\lesssim}E\ensuremath{\lesssim}425 \mathrm{V}/\mathrm{c}\mathrm{m}$ to an isotropic distribution for $E\ensuremath{\gtrsim}500$ V/cm. While the carriers are in a peaked distribution, the polar-optical-phonon scattering changes from small-angle scattering to large-angle as $E$ is increased. The origin of type-$S$ BNDC is explained, as is its temporal and spatial relationship to type-$N$ BNDC. The $S$-BNDC results from the presence of copious excess carriers that are generated by impact ionization within the propagating high-field domain (HFD) associated with the Gum effect and the $N$-BNDC. A low-electric-field-strength region is responsible for the $S$-BNDC, a region that propagates in the wake of the HFD associated with type $N$. A HFD in InSb makes a single transit as a result of impact ionization within the domain. The $N$-BNDC in $n$-InSb decays in typically 10 nsec, the transit time for a HFD, whereas the $S$-BNDC persists for several hundred nanoseconds. Radiative recombination measurements show conclusively that the $S$-BNDC is caused by excess carrier generation as proposed. The decay of these excess carriers is found to be characterized by two times. The faster, \ensuremath{\sim}27 nsec, persists for typically \ensuremath{\sim}150 nsec, a much shorter duration than the $S$-BNDC decay time, and is not understood at this time. However, the longer excess-carrier decay time prevails well beyond the $S$-BNDC disappearance, a phenomenon that is explainable by the hot-electron effect.

Dynamic bulk negative differential conductivity in semiconductors

The Gunn effect results from the existence of a static negative differential conductivity that is, the real part of the differential conductivity σ r ′( ω) is negative at zero frequency for a certain range of bias fields; at some high frequency, σ r ′( ω) passes through zero, and eventually approaches zero from above the axis as ω → ∞. We have investigated the possibility of the existence of a dynamic negative differential conductivity in bulk semiconductors that is, the existence of cases where σ r ′( ω) is positive at low frequencies, but becomes negative at high frequencies, finally approaching zero from below the axis. The relation of the structure of σ r ′( ω) to the impulse response of the semiconductor has been analyzed, and two model calculations which show the desired effect are presented.

Bulk Negative Differential Conductivity in a Near Cathode Region in n-Type Germanium

Sinusoidal current oscillations up to 0.2 A (rms) are observed in n-type germanium at 77°K. The oscillations occur at a frequency near 1 GHz and for an average threshold electric field of approximately 1 kV/cm. The germanium samples were cut from single crystal n-type germanium with carrier concentration 6×1014/cm3, and were approximately 2.0×0.5×0.5 mm. Using a capacitive probe, the oscillation is found to occur in a region of bulk negative differential conductivity which causes traveling high electric field domains. The domain movement confines itself to a 0.3-mm region starting 0.1 mm beyond the cathode contact. The electric field in this region, at the threshold applied voltage, is approximately 2800 V/cm, the same as that previously measured for bulk negative differential conductivity in germanium. A discussion of the effect of a cathode boundary electric field is included. It is shown that cathode boundary conditions can lead to a stable high electric field at the cathode, which in turn gives rise to traveling high-field domains which are confined to a region near the cathode.

Gunn Effect in InAs Under Hydrostatic Pressure

We have studied the high electric field conductivity of n-type InAs at pressures up to 29 kbar. Carrier multiplication due to impact ionization of valence band electrons is the predominant phenomenon at lower pressures, while the Gunn effect is observed at higher pressures. Above about 25 kbar no carrier multiplication is observed below the threshold electric field for Gunn effect. The bulk negative differential conductivity underlying the Gunn effect is presumed to be due to the transferred carrier mechanism. From the change in character of the high-field transport near 25 kbar, and from some recently published studies on the In1-xAlxAs alloy system, we eliminate the subsidiary minima involved in the carrier transfer to lie about 1.2±0.05 eV above the top of the valence band at atmospheric pressure, and to have L1 symmetry. The results are compared with an earlier report of Gunn effect in InAs under uniaxial stress.

Combined doping and geometry effects on transferred-electron bulk instabilities

The behavior of transferred-electron bulk negative differential conductivity devices with nonuniform geometries and various doping profiles is analyzed. Computer solutions were obtained for appropriate transport equations generalized by a scheme to simulate arbitrary areal variation. The solutions show that the effects of doping and geometrical nonuniformities on domain dynamics are similar. The product of doping and transverse area plays an important role in determining the space-charge properties. An important practical implication of the above result is demonstrated by a scheme for device design using combinations of geometrical and doping nonuniformities to achieve a desired control characteristic. Various equivalent device configurations yielding a linear frequency-voltage characteristic over a wide frequency range are proposed.

TYPE S BULK NEGATIVE DIFFERENTIAL CONDUCTIVITY IN n-InSb

The relationship between type S and type N (Gunn effect) bulk negative differential conductivity (BNDC) is shown in n-InSb at 77 K and atmospheric pressure. The results of conduction measurements and of radiative recombination measurements, both in time and space, shown that an S-BNDC is created in the wake of a propagating high-field domain and that the large currents associated with the S-BNDC are caused by strong impact ionization in the domain.

Domain velocity in semiconductors with field-dependent carrier diffusion

Recently several analytical formulas for the velocity of high-field domains in materials with bulk negative differential conductivity and field-dependent carrier diffusion have been published. The formulas were derived under the conventional "invariant domain" condition, and they thus represent solutions of the fundamental equations which are not necessarily stable. Numerical calculations of mathematically stable domains, allowing independence of one space dimension and time, have been made and are reported here. The results are consistent with the analytical formulas.

Current oscillations and negative differential conductivity in n-type germanium

The existence of several types of high-frequency majority carrier current instabilities in [100] and [110] oriented samples of n-type germanium has led to a renewed interest in the conductivity of germanium in a strong electric field. We review the experimental situation with regard to these instabilities and show how their properties can be understood in terms of bulk negative differential conductivity, which has been shown to occur in this material for temperatures below about 120°K. The present state of understanding of the origin of this BNDC effect in terms of the band structure and scattering mechanisms in germanium is summarized.

Negative differential conductivity effects in semiconductors

Abstract The discovery of the Gunn Effect has been heralded as the greatest breakthrough in semiconductor physics since the discovery in 1948 of transistor action in germanium. This article shows the basic physics of the effect and lays emphasis on the physics and applications of devices in which there is a bulk negative differential conductivity. Exciting new possibilities are opened up in the microwave region by a range of devices based on the peculiar properties of high field domains in semiconductors like GaAs.

Bulk Negative Differential Conductivity in Stressed n‐Type Germanium

AbstractThe velocity‐field characteristics of stressed n‐type germanium at 300 °K have been theoretically obtained assuming a Maxwellian velocity distribution function. It is found that the experimentally observed bulk negative differential conductivity cannot be explained if the carriers are assumed to be confined to the 〈111〉 valleys only. The experimental results on the other hand may be fitted if carrier scattering to the 〈100〉 valleys is taken into account and the mobility of the carriers in these valleys is taken to be 690 cm2 V−1 s−1.

Investigation of Electron Transfer in Stressed Many-Valley Semiconductors by Optical Anisotropy

A method is proposed for studying electron transfer between stress-split valleys in stressed many valley semiconductors exhibiting bulk negative differential conductivity in strong electric field. Field induced electron transfer causes carrier redistribution which in turn alter the anisotropy of high frequency dielectric constant. Hence, by observing the optical anisotropy in strong field, we can extract valuable information concerning electron transfer. One convenient method is piezobirefringence. Constructing a simple model for electron transfer in stressed many valley semiconductor, we investigate the behavior of optical anisotropy of stressed many valley semiconductor in strong electric field. It is shown that free carrier electro-optic effect in stressed many-valley semiconductors is expected to be strong so that its observation may be a valuable tool for studying electron transfer. With the advent of recent development of laser spectroscopy, this method may be a very efficient method.

Bulk Current Instabilities in Uniaxially Strained Germanium

Experimental studies of current instabilities in uniaxially compressed $n$- and $p$-type germanium are described. The instability reflects the presence of bulk negative differential conductivity due to transfer of carriers between the strain-split high-mobility and low-mobility states of the conduction or valence band. At low temperatures, threshold fields of the order of several hundred volts per centimeter are observed, which is an order of magnitude smaller than the threshold electric field for the Gunn effect in GaAs. In $n$-type Ge, the effect is observed at room temperature. The dependence of these phenomena on temperature, sample orientation, and stress magnitude is discussed. These results demonstrate the importance of intervalley transfer to the $X$ minima in determining the high-field transport properties of $n$-type Ge. Unsuccessful attempts to observe similar effects in strained $p$-type InSb and $n$-type Si are also described and discussed.

Negative Conductivity Effects and Related Phenomena in Germanium. Part I

This paper is the first part of a two-part review of recent work on current instabilities and related properties of germanium in high electric fields. In this part we discuss the general subject of high field transport in n-Ge with emphasis on the concept of saturated drift velocity. The oscillations which result from bulk negative differential conductivity (BNDC) in [100] and [110] directions at low temperatures are discussed and related to the saturation effects. A discussion of theoretical and experimental evidence with regard to the BNDC effects is presented. Finally, the anisotropy of the high-field conductivity is discussed and related to the Erlbach instability.

Bulk Negative Differential Conductivity in Germanium: Theory

Two mechanisms have been proposed for the bulk negative differential conductivity of n-type germanium first observed by Elliott et al. These are discussed with reference to recent Monte Carlo calculations in which effects due to intravalley acoustic phonon scattering, 〈100〉 and 〈000〉 minima and ellipsoidal constant energy surfaces are explored. Strong evidence is presented that electron transfer to 〈100〉 minima causes this negative conductance. The origin of its temperature and orientation dependence is discussed.