Page 70 - Principles and Applications of NanoMEMS Physics

2. NANOMEMS PHYSICS: Quantum Wave-Particle Phenomena 57

grown by MBE, and metal and semiconductor nanoparticles up to several
nanometers, e.g., ~1-6 nm, in size. Because of their small size, which is
2
comparable to that of the Bohr exciton, a = = ⋅ ε 2 m e , electron
ex ex
energy levels in QDs are quantized. Electron transport through a QD is
mediated by tunnel barriers, see Fig. 2-8, and is effected via a series of
individual tunneling events across the barriers.
Energy
Energy
Barrier
Barrier DOT Barrier
Barrier
DOT
e- e-
V V

L L
(a)

C C Γ Γ C C R, Γ Γ R R
R,
L,
L, L L QD
QD
I I
C C 0 0
V
V G G
+ +
- -
-
+
-
+
-
V V + - V V +
V R R R
V L L L
(b)
Figure 2-8. (a) Sketch of quantum dot energy level diagram. The continuous line denotes
equilibrium, while the dashed line denotes reflects an applied voltage, V. The dashed arrow
denotes suppressed current due to Coulomb blockade by QD electrons. (b) Equivalent circuit
of QD.
The tunneling rate across the barriers is characterized by the change in free
energy, ∆ , resulting from the tunneling event, and the tunnel resistance, R
t
(R >> h e ), and is given by [70], [71] Eq. (39).
2
t
∆
Γ = . (39)
§ § − ∆ · ·
e 2 R ¨ − exp1 ¨ ¸ ¸
t ¨ ¨ ¸ ¸
© © k B T ¹ ¹