Page 46 - Microsensors, MEMS and Smart Devices - Gardner Varadhan and Awadelkarim

28 ELECTRONIC MATERIALS AND PROCESSING

E d, then
'

where eo is the permittivity of free space, e r is that of the semiconductor, and m* is
the effective electron mass in the semiconductor crystal. The energy E n is discussed in
Section 3.1 of the following Chapter. When the phosphorus atom in silicon is ionised,
the released electron becomes a free electron that is available for conduction. The phos-
phorus atom is, hence, called a donor atom because it donates a free electron to the
crystal. All atoms with five valence electrons, that is, Group V elements, can behave in
a similar manner to phosphorus in silicon, that is, donate a free electron to the semicon-
ductor crystal. However, the amount of energy required, E d, for this process to occur
may differ from one type of donor atom to another. All Group V atoms will donate
electrons if they substitute for host atoms in crystals of Group IV elemental semiconduc-
tors. Consequently, Group V elements, such as phosphorus or arsenic, are called donor
atoms or simply donors, and the doped semiconductor is now referred to as an extrinsic
semiconductor. This may be contrasted to an intrinsic (undoped) semiconducting material.
Now consider the introduction of a large concentration of phosphorus atoms in an
otherwise pure silicon crystal, for example, a phosphorus atom concentration of ~10 15
-3
cm . With a minimal energy supply, each of these phosphorus atoms will donate an
electron to the crystal, amounting to a concentration of electrons in the conduction band
on the order of 10 15 cm -3 at room temperature. This concentration of electrons is to
be contrasted with the concentration of conduction electrons in intrinsic silicon at room
-3
temperature, which is on the order of 10 10 cm . Thus, with this doping level, a five-
order-magnitude increase in the free-electron concentration has been achieved. Note that
there are about 10 22 to 10 23 atoms/cm 3 in a solid and that a doping level of 10 15 cm -3
8
is equivalent to merely replacing one silicon atom in every 10 7 to 10 atoms/cm 3 by a
phosphorus atom. Obviously, this level of doping introduces a very insignificant change
in the overall crystal structure but its effect on the free-electron concentration is clearly
very significant. Note that conduction in this phosphorus-doped silicon will therefore
be dominated by electrons. This type of extrinsic (Group IV) semiconductor, or more
specifically, silicon, is called an n-type semiconductor or n-type Si. The term n-type
indicates that the charge carriers are the negatively charged electrons. The example
discussed in the preceding text was specific to silicon doped with phosphorus; however,
the conclusion arrived at will apply generally to all elemental semiconductors doped with
a higher group element. The values of the ionisation energies Ed for several Group V
donors in silicon are given in Table 2.7 together with those for some acceptors.

Table 2.7 Common donor and acceptor atoms in silicon

Atom Atomic number Type Ionisation energy in Si (eV)
Boron 5 Acceptor 0.045
Aluminum 13 Acceptor 0.057
Phosphorus 15 Donor 0.044
Gallium 31 Acceptor 0.065
Arsenic 33 Donor 0.049
Indium 49 Acceptor 0.16
Antimony 51 Donor 0.039