Electrical Transport Properties in a Superlattice
01 May 1970-Journal of Applied Physics (American Institute of Physics)-Vol. 41, Iss: 6, pp 2664-2667
TL;DR: In this paper, the Boltzmann equation was solved for electrons in a one-dimensional superlattice under the influence of a uniform electric field; an energy independent scattering time and nonspherical energy bands were assumed.
Abstract: Boltzmann's equation is solved for electrons in a one‐dimensional superlattice under the influence of a uniform electric field; an energy independent scattering time and nonspherical energy bands are assumed. The current density‐electric field characteristic shows negative differential conductivity at fields of 103−104 V/cm independent of the detailed shape of the minibands.
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TL;DR: In this article, the transport properties of a finite superlattice from the tunneling point of view have been computed for the case of a limited number of spatial periods or a relatively short electron mean free path.
Abstract: We have computed the transport properties of a finite superlattice from the tunneling point of view. The computed I‐V characteristic describes the experimental cases of a limited number of spatial periods or a relatively short electron mean free path.
1,996 citations
TL;DR: In this paper, a quantum-statistical theory of the low-temperature behavior of Josephson junctions with very small capacitanceC and quasiparticle conductivityG, driven by a small currentI(t), is developed.
Abstract: A quantum-statistical theory of the low-temperature behavior of Josephson junctions with very small capacitanceC and quasiparticle conductivityG, driven by a small currentI(t), is developed. In such junctions the “secondary” quantum macroscopic effects (tunneling and interference) are significant for all values of the Josephson phase difference ϕ, so that new features in the junction dynamics arise, including quantum “Bloch-wave” oscillations. Here the junction dynamics is analyzed in detail starting from a simple macroscopic Hamiltonian. The simplest way to analyze the Bloch-wave oscillations turns out to be a Langevin-type equation for the operator of the junction “quasicharge”q. In particular, this equation shows that the frequencyf
B of these oscillations is related by the fundamental equation
$$f_B = (\bar I - G\bar V)/2e$$
to the dc current
$$\bar I$$
and voltage
$$\bar V$$
. The main effects suppressing or masking the Bloch-wave oscillations can be analyzed using the equation for the density matrix of the system traced over the states of the quasiparticles. This analysis has made it possible to establish the main conditions for the experimental observation of the predicted effects and to present a general picture of the low temperature dynamics of Josephson junctions.
478 citations
TL;DR: In this article, the standard transport theories for superlattices, i.e., miniband conduction, Wannier-Stark hopping, and sequential tunneling, are reviewed in detail.
454 citations
Additional excerpts
...If μ > Ea + 2|T a 1 | one obtains [96] n = ρ0(μ − Ea) and JMBT = e 2ρ0|T a 1 |2 ~ eFd~/τ (~/τ)2 + (eFd)2 for ...
[...]
TL;DR: Vue d'ensemble sur la preparation, la caracterisation, les proprietes de transport et les proprières magnetiques des superreseaux as mentioned in this paper, et.
Abstract: Vue d'ensemble sur la preparation, la caracterisation, les proprietes de transport et les proprietes magnetiques des superreseaux
253 citations
TL;DR: In this article, the electron states of an indirect optical semiconductor with two bands were calculated in the presence of an additional periodic one-dimensional potential (superlattice) in the semiconductor material.
Abstract: Starting from a model of an indirect optical semiconductor with two bands, the electron states are calculated in the presence of an additional periodic one-dimensional potential (superlattice) in the semiconductor material. These states are used to determine the transition probability connected with the absorption of a photon. This transition corresponds to an optical direct transition — no phonon takes part in this process. The optical direct and optical indirect transitions are compared. For optical frequencies near the band gap one expects only direct transitions, whereby the optical indirect transitions may be neglected.
207 citations
References
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TL;DR: The study of superlattices and observations of quantum mechanical effects on a new physical scale may provide a valuable area of investigation in the fieId of semiconductors.
Abstract: We consider a one-dimensional periodic potential, or "superlattice," in monocrystalline semiconductors formbeyd a periodic variation of alloy composition or of impurity density introduced during epitaxial growth. If the period of a superlattice, of the order of 100A, is shorter than the electron mean free path, a series of narrow allowed and forbidden bands is expected duet o the subdivision of the Brillouin zone into a series of minizones. If the scattering time of electrons meets a threshold condition, the combined effect of the narrow energy band and the narrow wave-vector zone makes it possible for electrons to be excited with moderate electric fields to an energy and momentum beyond an inflection point in the E-k relation; this results ina negative differential conductance in the direction of the superlattice. The study of superlattices and observations of quantum mechanical effects on a new physical scale may provide a valuable area of investigation in the fieId of semiconductors.
2,569 citations
TL;DR: In this article, a transport theory which allows for anisotropy in the scattering processes is developed for semiconductors with multiple nondegenerate band edge points, and the main effects of scattering on the distribution function over each ellipsoidal constant-energy surface can be described by a set of three relaxation times, one for each principal direction; these are the principal components of an energy-dependent relaxation-time tensor.
Abstract: A transport theory which allows for anisotropy in the scattering processes is developed for semiconductors with multiple nondegenerate band edge points. It is found that the main effects of scattering on the distribution function over each ellipsoidal constant-energy surface can be described by a set of three relaxation times, one for each principal direction; these are the principal components of an energy-dependent relaxation-time tensor. This approximate solution can be used if all scattering processes either conserve energy or randomize velocities. Expressions for mobility, Hall effect, low- and high-field magnetoresistance, piezoresistance, and high-frequency dielectric constant are derived in terms of the relaxation-time tensor. For static-field transport properties the effect of anisotropic scattering is merely to weight each component of the effective-mass tensor, as it appears in the usual theory, with the reciprocal of the corresponding component of the relaxation-time tensor.The deformation-potential method of Bardeen and Shockley is generalized to include scattering by transverse as well as longitudinal acoustic modes. This generalized theory is used to calculate the acoustic contributions to the components of the relaxation-time tensor in terms of the effective masses, elastic constants, and a set of deformation-potential constants. For $n$ silicon and $n$ germanium, one of the two deformation-potential constants can be obtained from piezoresistance data. The other one can at present only be roughly estimated, e.g., from the anisotropy of magnetoresistance. Insertion of these constants into the theory yields a value for the acoustic mobility of $n$ germanium which is in reasonable agreement with observation; a more accurate check of the theory may be possible when better input data are available. For $n$ silicon, available data do not suffice for a check of the theory.
1,003 citations
TL;DR: In this paper, the exact solution of the Boltzmann equation was given in the relaxation time approximation for general external fields and a general band structure, and its solution was obtained by an iteration of the solution.
Abstract: The exact solution of the Boltzmann equation was given in the relaxation time approximation for general external fields and a general band structure. The Boltzmann equation was considered with a general collision operator and its solution was obtained by an iteration of the solution in the relaxation time approximation. (C.E.S.)
21 citations