Explain the idea of ballistic transport, including the various length scales that define different transport regions.Ripunjay Tiwari
Ans. Conductivity is a bulk parameter, and is derived assuming a large number of electrons and a large number of collisions between electrons and phonons, impurities, imperfections, etc. In particular, if length L of a conduction path is reduced to become much less than the mean free path ·Lm, one would expect that no collisions would take place.
Collisions are of two types –
(i) An electron can collide with an object such that there is no change in energy. This type of collision is called an elastic collision, and typically, collisions between electrons and fixed impurities are elastic. For example, think of a ball bouncing off of a fixed surface.
(ii) In the second type of collision, the energy of the electron changes although the total energy is conserved. This type of collision is caused an inelastic collision, and typically results from collisions between electrons and phonons or between electrons and electrons. ·
It has been possible to experimentally investigate resistance at the nanoscale. Much progress has been made in understanding the underlying physics of nanoscale and macroscopic transport. Macroscopic refers to size scales between microscopic (atomic) and macroscopic (sizes of everyday objects). For
example, carbon nanotubes are often macroscopic, having nanometer radius values yet having anywhere from nm to em lengths. The overarching idea is that at very small length scales, electron transport occurs ballistic ally. it can be appreciated that .ballistic transport will be important in many future
Various length scales are –
(i) L is the system length.
(ii) Lm is the mean free path.
(iii) Lϕ is the length over which an electron can travel before having ah inelastic collision. This is also called the phase coherence length, since it is the length over which an electron wave function retains its coherence i.e., retains its· phase memory.
Transport Regimes – Electron transport divided into two regimes –
(i) For L >> Lϕ, Lm, we have classical transport, which is the familiar macroscopic. Ohm’s law applies, and momentum and phase relaxation occur frequently as charges move through the system. Because of this, we cannot solve Schrodinger’s equation over the whole conductor length L. It is
fortunate that semi classical or even classical models generally work well in this case. ·
(ii) For L << Lm, Lϕ we have ballistic transport. Ballistic transport occurs over very small length scales, and is obviously coherent; the electron doesn’t “hit” anything. as it travels through the material, and therefore, there is no momentum or phase relaxation. Thus, in a ballistic material, the electron’s wave function can be obtained from Schrodinger’s equation.
The application of ballistic transport is in ultra-short channel semiconducting PETs or carbon nanotube transistors. Sh01t interconnects may also exhibit ballistic transport properties.