Direct Energy, 2018a

204 9.2 Measures of the Ability of Charges to Flow
energy level represents the energy level at which the probability of nding
an electron is 0.5. At T =0 K, it is at the middle of the energy gap.
In the gure, it is shown as a dotted line. Qualitatively, it represents
the amount of energy needed to remove the next electron. No electrons
have exactly that energy because there are no allowed states in the gap.
For a doped semiconductor, a semiconductor with crystalline defects, or
a semiconductor not at absolute zero temperature, the Fermi level is near
but not quite at the middle of the gap.
The right part of the gure shows the same energy level diagram labeled
using terms more commonly used by chemists to describe isolated
atoms than by physicists to describe solid semiconductors. Chemists sometimes
use the term highest occupied energy level instead of valence band.
This term is most often used to refer to energy levels of isolated atoms or
molecules because some authors reserve the term band for an energy level
shared between neighboring atoms. Similarly, chemists sometimes use the
term lowest unoccupied energy level in place of conduction band. As discussed
below in Secs. 9.2.3 and 9.2.4, the term chemical potential μ chem
is used in place of Fermi energy level E f , and the energy gap E g may be
called twice the chemical hardness.
9.2.2 Mulliken Electronegativity
One measure that chemists use to describe the ability of charges to ow is
electronegativity, and this term has multiple denitions in the literature.
One denition is by Mulliken in 1934 [130], and this measure will be referred
to as the Mulliken electronegativity. Mulliken approximated the energy in
a chemical bond by averaging the ionization energy I ioniz and the electron
anity A aff . Mulliken electronegativity is dened
χ Mulliken = I ioniz + A aff
. (9.1)
2
Ionization energy is the energy needed to remove an electron from an atom
or ion, and electron anity is the energy change when an electron is added
to an atom or ion [12]. All of these quantities, χ Mulliken , I ioniz , and A aff ,
are measured in the SI units of
J
atom
or occasionally in other units like
eV
atom or mol kJ .
This denition is simpler than other denitions of electronegativity, and
reference [131] calls this an operational and approximate denition. It is
useful because it involves strength of chemical bonds, and we can relate it to
the measures used by semiconductor researchers. Qualitatively, ionization
energy is represented by the energy needed to rip o an electron. In Fig.