By Supriyo Datta
Together with the most complex recommendations of non-equilibrium quantum statistical mechanics, this publication provides the conceptual framework underlying the atomistic thought of subject. No previous acquaintance with quantum mechanics is believed. Many numerical examples offer concrete illustrations, and the corresponding MATLAB codes may be downloaded from the net. Videostreamed lectures associated with particular sections of the booklet also are on hand via net entry.
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Extra info for Quantum Transport: Atom to Transistor
Example text
Calculate the current vs. 25 eV, using the SCF approach and compare with Fig. 6. 2. Calculate the current vs. gate and drain voltages for a nanotransistor as shown in Fig. 1 using the SCF equations summarized in Eqs. 5 nm, vR = 107 cm/s. 3. Thermoelectric effect: In this chapter we have discussed the current that flows when a voltage is applied between the two contacts. 2 m1 − e Fig. 3 You should get a plot like this showing the reversal in the direction of the current from p-type (µ1 < ε) to n-type (µ1 > ε) samples.
However, the coupling to the contacts decreases inversely with the length L of the conductor, since the longer a conductor is, the smaller is its coupling to the contact. While the DOS goes up with the volume, the coupling to the contact goes down as 1/L, so that the conductance G ∼ S L/L = S However, Ohm’s law tells us that the conductance should scale as S/L; we are predicting that it should scale as S. The reason is that we are really modeling a ballistic conductor, where electrons propagate freely, the only resistance arising from the contacts.
5b) too (without the s-contact), it was argued in Meir and Wingreen (1992) that [G n (E)] can be similarly eliminated if [ 1 ] is equal to a constant times [ 2 ]. However, this can be true only for very short channels. Otherwise, the source end is distinct from the drain end, making [ 1 ] a very different matrix from [ 2 ] since they couple to different ends. We then need additional equations to determine both [A(E)] and [G n (E)]. There is an enormous amount of physics behind all these matrices (both the diagonal and the off-diagonal elements) and we will introduce and discuss them in course of this 30 Prologue: an atomistic view of electrical resistance book: the next five chapters are about [H], Chapter 7 is about [ρ], Chapter 8 is about [ ], Chapter 9 combines these concepts to obtain the inflow/outflow diagram shown in Fig.