Self‐consistent calculations of phonon scattering rates in the GaAs transistor structure with one‐dimensional electron gas

Abstract

Self-consistent calculations of acoustic and polar optical phonon scattering rates in GaAs quantum wire transistor structures were carried out with account of collisional broadening. The influence of the gate bias on the scattering rates was examined, too. It was shown that in order to treat the scattering rates rigorously it is important to search for electron energy levels by means of the self-consistent solution of Schrodinger and Poisson equations and to take into account the collisional broadening.Modern technologies in micro-and nanoelectronics allow different semiconductor device structures of very small sizes and various geometry to be created. In particular, high-speed field effect GaAs transistors with one-dimensional electron gas (1DEG) or, in other words, quantum wire transistors [1,2] have been successfully created and actively investigated. It is supposed that on the basis of these transistors a new generation of high-speed GaAs ULSI circuits can be produced.It is known that the efficient design of such devices today is a very hard problem without numerical simulation of their electrical characteristics. In this regard, one of the most promising simulation methods is the Monte Carlo one [3]. Its correct implementation is possible when the rigorous expressions for the scattering rates for all dominant scattering mechanisms in the simulated structure are known. In this connection it is necessary to note that acoustic and polar optical phonon scattering are two of the important scattering mechanisms in GaAs structures with 1DEG [4][5][6][7].Several works were devoted to the calculation of acoustic and polar optical phonon scattering rates (A&POPSR) in quantum wires. Particularly, in the papers [5,7] expressions for the A&POPSR in the rectangular quantum wires were proposed taking into account the collisional broadening (in case of intersubband scattering being the same as the broadening of the energy levels) in the first order approximation. It was shown that the functions of A&POPSR versus electron kinetic energy have not any singularity points. The latter is especially important for the direct use of the derived expressions in Monte Carlo procedures as it naturally eliminates the tendency to infinity of A&POPSR in singularity points related to the features of the density of states in quantum wires. Besides, the rigorous incorporation of the phonon scattering into the charge transport simulation by means of Monte Carlo method requires the exact knowledge of electron subband energy levels in the considered quantum well as they directly enter into the expressions for A&POPSR. These energy levels in real device structures with an arbitrary quantum well can be found only by means of numerical self-consistent solution of the corresponding Schrodinger and Poisson equations.In this work we present the results of calculation of A&POPSR in the GaAs-transistor structure (see Fig. 1), with taking into account the collisional broadening caused by only acoustic and polar optical phonon scattering, and exa...

Influence of scattering processes on electron quantum states in nanowires

“…(2) is valid. However, when the scattering rates are calculated taking into account high-order quantum effects such as the collisional broadening [4][5][6][7][8] …”

“…Thus, the considering contradiction (see Eqs. (3) and (4)) is caused by violation of the approximations that the electron quantum states are stable or/and one-particle while calculating the electron scattering rates taking into account the high-order quantum effects [4][5][6][7][8].…”

“…To do it we use the results of Refs. [5][6][7][8]. In these studies the scattering rates in GaAs quantum wires have been calculated taking into consideration the collisional broadening of the initial electron quantum states (electron energy uncertainty).…”

“…In this case according to Refs. [5][6][7][8] to take into account the quantum correlations between scattering events it is sufficient to consider the collisional broadening of the final electron quantum states as well as initial and final states identity at k initial = k final . In result, the equations for the self-consistent calculation of the function E = E(k) for the one-dimensional electron gas in the electric quantum limit and thermodynamic equilibrium can be derived by…”

“…At the same time while developing a similar model of electron transport in nanowires, taking into account the high-order quantum effects (the collisional broadening and the quantum correlations between scattering events) (see, for example, Refs. [4][5][6][7][8]), we have met a problem. It is turned out that some obtained results are in contradiction to the fundamental physical principles.…”