Handout 28

# Handout 28 - Handout 28 Ballistic Quantum Transport in...

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1 ECE 407 – Spring 2009 – Farhan Rana – Cornell University Handout 28 Ballistic Quantum Transport in Semiconductor Nanostructures In this lecture you will learn: • Electron transport without scattering (ballistic transport) • The quantum of conductance and the quantum of resistance • Quantized conductance Rolf Landauer (1927-1999) Lester F. Eastman (1928-) ECE 407 – Spring 2009 – Farhan Rana – Cornell University Conductors and Dissipation Traditional View of Conductors: V I L A σ L V E = E J = R V GV V L A E A AJ I = = = = = Power Dissipation in Conductors: E&M (energy continuity equation) tells us that the power dissipation per unit volume of a resistor is: 2 2 J E E J = = = Power dissipation in the entire resistor is: () G I R I A L A J AL J AL E J P 2 2 2 2 2 = = = = = R L A G 1 = =

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2 ECE 407 – Spring 2009 – Farhan Rana – Cornell University Mean Free Path The mean free path is defined as the distance an electron travels before it scatters. It is given by: where v c is the characteristic electron velocity and τ is the scattering time. c v = l Mean Free Path: Characteristic Velocity: The characteristic velocity is the average velocity of those electrons that contribute to the conductivity: () [] k v E k v E f k d e J o d d r r r r r r r . 2 2 FBZ 2 × = π () () = E f k d k v k v E f k d v o d d o d d c FBZ FBZ 2 2 . 2 r r r r r r Recall the formula for the current density obtained from the Boltzmann equation: For metals and heavily doped semiconductors at low temperatures: For low doped semiconductors at high temperatures: F c v v = e c m KT d v = ECE 407 – Spring 2009 – Farhan Rana – Cornell University Ballistic Transport: When the length L of the conductor becomes much smaller than the mean free path the transport is termed “ballistic” meaning that the electrons do not scatter during the time it takes to travel through the conductor Ballistic transport condition: l << L Questions: • What happens when L << ? • The formulas for conductivity that have the scattering time in them are clearly no longer valid since there is no scattering • What about dissipation?
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Handout 28 - Handout 28 Ballistic Quantum Transport in...

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