Page 324 - Semiconductor For Micro- and Nanotechnology An Introduction For Engineers

Inhomogeneities
operating frequencies. Here the limitation is the dielectric relaxation
time of the semiconductor.
Biased For the Schottky contact diode, under forward biasing conditions, three
Junction transport mechanisms are identified:

• Conduction band electrons can drop over the potential barrier into the
metal;
• Conduction band electrons can tunnel through the potential barrier
into the metal;
• Recombination can occur between conduction band electrons and
holes that are injected from the metal into the semiconductor. Recom-
bination can take place in the space-charge region, or immediately
adjacent to the space-charge region, also known as the neutral region.

Thermionic The first mechanism above dominates the transport process, and is
Emission explained as thermionic emission of electrons into the metal. We will not

derive the expression, but shortly explain the idea following [7.17]. Con-
duction band electrons that have energies higher than the barrier can be
injected. If we assume that the available electrons have all their energy in
the form of kinetic energy, and an effective mass given by the energy
band shape, then we can convert the electron density expression for the
distribution of electrons from a dependency of energy, i.e.,
dn = N E()FE()dE to one of velocity dn = N v()Fv()dv . Now, using
∞
J S → M = ( ∫ E F + Φ B ) qv n and a an estimate for the electron distribution,
d
we obtain the current
Φ
2 B qV
J S → M = A∗ T exp – --------- exp ------- (7.186)
k T kT
B
2
where A∗ = 4πqm∗ k ⁄ h 3 is called the effective Richardson constant.
For n-type 111〈 〉 silicon, A∗ 〈 111〉 = 264 , and for n-type 100〈 〉 silicon,
A∗ 〈 100〉 = 252 .

Semiconductors for Micro and Nanosystem Technology 321