Page 91 - Principles and Applications of NanoMEMS Physics
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Chapter 3
NANOMEMS PHYSICS: QUANTUM WAVE
PHENOMENA
3.1 Manifestation of Wave Nature of Electrons
The principles of nanoscale devices are based on the physics dominating
this dimensional regime. In particular, as the device size is reduced below
about 100nm, the electron behavior stops obeying classical physics, in which
its momentum and energy are continuous, and starts obeying quantum
mechanics, in which it behaves as waves with quantized energy, Figure 3-1.
Fig.3-1 Continuous Energy
p 2
p = mv E ~
2 m
L z
L y
L x
Size ReductionÆ Quantized Energy
p = h E = h ω
λ 2
y
¨
x
z
E ( ,nn ,n )= h ª «¨ §n π · ¸ 2 + §n π · ¸ + §n π · ¸ ¸ 2 º »
¨
¨
¨
y
x
z
2m « © L ¸ ¹ ¨ L ¸ © L ¹ »
¬ x © y ¹ z ¼
~
<
L i 100 nm ∆x ⋅ ∆p x > ~ h
Figure 3-1. Size-dependent behavior of electrons.
