Quantum Transport Handout

Quantum Transport Handout - University of California,...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
- 140 - University of California, Berkeley EE230 - Solid State Electronics Prof. J. Bokor Quantum transport (Read Kittel, 8th ed., pp. 533-554) When we have structure in which many collisions take place as carriers transport across it, the quantum mechanical phase of the electron wavefunctions is essentially randomized, and the semiclassical approach that we have been following is appropriate. In nanoscale elec- tronic devices, especially at low temperatures: • device dimensions begin to approach the mean-free path between collisions • scattering processes play an decreasingly important role This is the regime of quantum transport . Electron transport becomes governed by princi- ples of quantum-mechanical wave propagation and interference, rather than the classical dif- fusive transport. Conductance quantization Consider the limit of a one-dimensional conducting wire with no collisions. Does it have resistance? Connect the wire between to contacts. We model the contacts as large, 3-D reservoirs with a voltage difference V between them. The right-going states of the wire are populated up to the electrochemical potential (quasi- Fermi energy) μ 1 and the left-going states will be populated up to the electrochemical poten- tial μ 2 where the potential difference is μ 1 - μ 2 = qV. The net current flowing through the wire is due to the excess right-moving carrier density Δ n is limited by the density of states in the wire. For the lowest transverse sub-band (or mode) of the wire: μ 2 μ 1 μ 2 qV + = left contact right contact wire
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
- 141 - University of California, Berkeley EE230 - Solid State Electronics Prof. J. Bokor We obtain the differential conductance, , as the small change in current for a small change in applied voltage. Then we can write the density of excess right-moving carriers as . We divide by 2 to get the density of states only for right moving carriers, and we divide by L to get the carrier density per unit length. We can re-write D(E) in terms of the carrier veloc- ity, v: . The net current (for electron flow) is then: and we obtain the famous result of quantized conductance: . The resistance quantum, R Q = 1/G Q = 12.906 k Ω. This is the conductance for carriers in the lowest sub-band of the wire. As additional subbands are populated, each adds one addi-
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 08/01/2008 for the course EE 230 taught by Professor Bokor during the Spring '08 term at University of California, Berkeley.

Page1 / 9

Quantum Transport Handout - University of California,...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online