518 CHAPTER 13: Liquids and Solids
CC Research & Technology
HEMISTRY IN USE
Semiconductors
A semiconductoris an element or a compound with filled
bands that are only slightly below, but do not overlap with,
empty bands. The difference between an insulator and a semi-
conductor is only the size of the energy gap, and there is no
sharp distinction between them. An intrinsicsemiconductor
(i.e., a semiconductor in its pure form) is a much poorer con-
ductor of electricity than a metal because, for conduction to
occur in a semiconductor, electrons must be excited from
bonding orbitals in the filled valence bandinto the empty con-
duction band.Figure (a) shows how this happens. An electron
that is given an excitation energy greater than or equal to the
band gap (Eg)enters the conduction band and leaves behind
a positively charged hole(h, the absence of a bonding elec-
tron) in the valence band. Both the electron and the hole
reside in delocalizedorbitals, and both can move in an elec-
tric field, much as electrons move in a metal. (Holes migrate
when an electron in a nearby orbital moves to fill in the hole,
thereby creating a new hole in the nearby orbital.) Electrons
and holes move in opposite directions in an electric field.
Silicon, a semiconductor of great importance in electron-
ics, has a band gap of 1.94 10 ^22 kJ, or 1.21 electron volts
(eV). This is the energy needed to create one electron and
one hole or, put another way, the energy needed to break one
SiXSi bond. This energy can be supplied either thermally or
by using light with a photon energy greater than the band
gap. To excite one moleof electrons from the valence band
to the conduction band, an energy of117 kJ/mol1.94 10 ^22 kJ
electron6.022 1023 electrons
molis required. For silicon, a large amount of energy is required,
so there are very few mobile electrons and holes (about one
electron in a trillion—i.e., 1 in 10^12 —is excited thermally at
room temperature); the conductivity of pure silicon is
therefore about 10^11 times lower than that of highly
conductive metals such as silver. The number of electrons
excited thermally is proportional to eEg/2RT. Increasing the
temperature or decreasing the band gap energy leads to
higher conductivity for an intrinsic semiconductor. Insulators
such as diamond and silicon dioxide (quartz), which have
very large values of Eg, have conductivities 10^15 to 10^20 times
lower than most metals.
The electrical conductivity of a semiconductor can be
greatly increased by dopingwith impurities. For example,
silicon, a Group IVA element, can be doped by adding small
amounts of a Group VA element, such as phosphorus, or a
Group IIIA element, such as boron. Figure (b) shows the
effect of substituting phosphorus for silicon in the crystal
structure (silicon has the same structure as diamond, Figure
13-31a). There are exactly enough valence band orbitals to
accommodate four of the valence electrons from the phos-
phorus atom. However, a phosphorus atom has one more
electron (and one more proton in its nucleus) than does sil-
icon. The fifth electron enters a higher energy orbital that is
localized in the lattice near the phosphorus atom; the energy
of this orbital, called a donor level,is just below the con-
duction band, within the energy gap. An electron in this
orbital can easily become delocalizedwhen a small amount of
thermal energy promotes it into the conduction band.
Because the phosphorus-doped silicon contains mobile, neg-
ativelycharged carriers (electrons), it is said to be doped
n-type. Doping the silicon crystal
with boron produces a related, but
opposite, effect. Each boron atom con-
tributes only three valance electrons to
bonding orbitals in the valence band,
and therefore a holeis localized near
each boron atom. Thermal energy
is enough to separate the negativelySi Si Si SiSi Si Si SiSi Si Si SiValence bandConduction bandThermal or
Eglight energySi Si Si Si SiSi Si Si Si SiSi Si Si Si SiSi Si Si Si Sieh(a)Generation of an electron–hole pair in
silicon, an intrinsic semiconductor. The electron
(e) and hole (h) have opposite charges, and
so move in opposite directions in an electric
field.