Chemistry Reference
In-Depth Information
For a doped silicon, depending on the dopant, one type of carrier is the majority
carrier as its concentration far exceeds the other, even at low doping levels. For
example, for donor concentration
that is,
which
is nearly 10 orders of magnitude below the majority carrier concentration.
In the neutral region of a semiconductor, the number of positive charges must be
exactly balanced by the number of negative charges. This means
assuming all the dopant atoms are ionized. Thus, when there is only one dopant, either
donor or acceptor, for
n
-type material
and for
p
-type material
1.2.2.
Energy Levels in Electrolyte
The chemical potential of electrons for a redox couple is given by the Nernst
equation
where is the standard redox potential, and and are the activities of the
oxidized and reduced species of the redox couple, respectively.
The redox potential is generally referred to the standard hydrogen potential
relative to the energy of the free
electron in vacuum or at infinity. Thus, electrode potentials of redox couples can be
expressed on the absolute energy scale according to
(SHE), which has an exactly defined energy,
The negative sign of
in the equation is due to the different signs in the conventional
and the absolute electron energy scales.
has been found to be about -4.50 eV referred
86
to the vacuum level so that the electron energy of any redox couple is
1.2.3. Distribution of Energy Levels in Electrolyte
The redox potential reflects the average energy levels at equilibrium of all the
individual redox species, both reduced and oxidized forms. It can be further divided
into two levels: the energy level of the reduced species, and the energy level of
the oxidized species, with is the most probable energy level
for the oxidizing species and
E
red
is the most probable energy level for the reducing
species. In a liquid electrolyte, the energy levels of individual ions tend to fluctuate due
to the solvation effect of the polar solvent molecules surrounding the ions. The dipoles
associated with the solvent molecules constantly move to/away and rotate around the
ions, causing thermal fluctuation in the polarization.
