Page 121 - Science at the nanoscale

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June 9, 2009
6.1. From 3D to 0D Nanostructures
exist in identical energy states. As such, at 0 K they collect in the
lowest available energy states and build up a “Fermi sea” of elec-
tron energy states.
understanding the electrical and thermal properties of solids.
Both ordinary electrical and thermal processes involve energies of
a small fraction of an electron volt; for instance, at room tempera-
ture, the thermal energy kT = 0.026 eV. However, the Fermi ener-
gies E F of metals are of the order of electron volts (see Table 6.1),
so most electrons cannot receive energy from such processes since
there are no available energy states for them. The Fermi velocity
is the average velocity of an electron in an atom at 0 K, and is
defined by:
s
2E F
(6.1)
v F =
m e
where m e is the mass of the electron. The Fermi temperature is
Table 6.1 Fermi energy, Fermi temperature, and Fermi velocity of
selected metals.
Fermi
Fermi
Fermi
4
6
Temperature × 10 K
Energy eV
Element
Velocity × 10 m/s
1.29
Li
5.51
4.74
Na
3.77
1.07
3.24
K
0.86
2.12
2.46
2.15
0.81
1.85
Rb The concept of the Fermi energy is crucially important in 111 ch06
Cs 1.59 1.84 0.75
Cu 7.00 8.16 1.57
Ag 5.49 6.38 1.39
Au 5.53 6.42 1.40
Be 14.3 16.6 2.25
Mg 7.08 8.23 1.58
Ca 4.69 5.44 1.28
Sr 3.93 4.57 1.18
Ba 3.64 4.23 1.13
Nb 5.32 6.18 1.37
Fe 11.1 13.0 1.98