Page 94 - Principles and Applications of NanoMEMS Physics

82 Chapter 3

N
N = ¦ T (E ) , (7)
Effective n F
i1
where T is the transmission coefficient of band n. Clearly, casting the
n
conductance in terms of the transmission coefficient uncovers its dependence
on the wave nature of the electron.

3.1.1.2 Quantum Point Contacts

In deriving the quantized electrical conductance of a quantum wire above
it was pointed out that it is proportional to N, the number of bands through
which transport is operative. The quantum point contact (QPC), Fig. 3-3,
represents a virtually zero-length quantum wire, in which the details of T n
dominate transport and are made patently manifest in the conductance.
Top V iew
Top V iew

2D E 2D E
2D EG G
2D EG G
E F2
E F1
E F1 E F2
I I
V V
(a)
Cross Sectio
Cross Section n
Split-G ate
Split-G ate
Split-G ate
50 nm n-AlGa
50 nm n-AlGaA A
50 nm n-AlGaAs s s
20 nm AlGaAs
20 nm AlGaAs
20 nm AlGaAs
GaAs
GaAs
GaAs
C onfined 2D
C onfined 2D EG G G
C onfined 2D E E
(b)
3 3 2 2
Conductance (e 2 /h) Conductance (e 2 /h) 1 1 0 0 0 0 0.6K 0.3K
0.6K
0.3K
0 0 0 0
-2 -2 -1 -1.8 .8 -1
-1.6 .6
Gate Voltage (V
Gate Voltage (V ) )
Figure 3-3. Quantum point contact. (a) Top view. (b) Cross-section. (c) Conductance versus
gate voltage. (After [114].)
In the QPC a constriction is formed by modulating via, e.g., depletion
regions, the width of the channel between two two-dimensional electron gas