EE 2 Fall 2007
Class 9 slides
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Outline
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Review of last class
Extrinsic semiconductors
Donor and acceptor impurities
Majority and minority carries in extrinsic semiconductors
Thermal equilibrium carrier densities
Law of mass action
Compensated semiconductor
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Extrinsic semiconductors
• Extrinsic semiconductors are those in which controlled (and trace)
amount of specific impurities are incorporated in the semiconductor
lattice to increase the electron density or the hole density.
Depending on the type of impurity the electron or the hole density
will be increased by the number of impurities added. Whereas in an
intrinsic semiconductor the electrons and holes arise due to thermal
excitation of electrons from the valence band to the conduction
band, in an extrinsic semiconductor electrons (or holes) will be
excited to the conduction band (or to the valence band) from the
impurity atoms with energy levels in the band gap close to Ec for
increasing the electron density (or Ev for increasing the hole
density). The material is called extrinsic since its properties depend
on the externally added impurities.
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Extrinsic semiconductors
• The impurities are said to be substitutionally added since the
impurity atoms substitute the original atoms in the material.
• For example in silicon an impurity atom will sit in the site previously
occupied by a silicon atom.
• If you recall the discussion in an earlier class the semiconductors
crystallize in diamond structure because in such a structure each
atom say silicon is surrounded by four nearest neighboring silicon
atoms
• The s2p2 electron configuration in silicon gives rise to the covalent
bond whereby each atom shares an electron with the four neighbors
forming the diamond structure.
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Extrinsic semiconductors
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Extrinsic semiconductors
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Extrinsic semiconductors
• Elements of group V of the periodic table have five valence
electrons. When one of these impurity atoms is substituted for
silicon in the crystal lattice, four of the five electrons complete the
four covalent bonds and the fifth electron is not participating in the
covalent bond and is weakly bound to the site of the impurity atom. It
takes very small amount of energy to break the fifth electron from
this site and make the electron free to move in the crystal i.e., we
have now an electron in the conduction band. The impurity atom
contributes (or donates) an electron to the conduction band and
hence the impurity atom is called a donor atom. We have an
electron in the conduction band for each ionized donor atom. Each
ionized donor atom has a localized positive charge. In a piece of
extrinsic semiconductor we have an electron in the conduction band
for each ionized donor atom.
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Extrinsic semiconductors
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Extrinsic semiconductors
• In an extrinsic semiconductor with donor impurities, electrons arise
in the conduction band due to two processes one due to thermal
excitation from the valence band and the other due to ionization of
donor atoms. It takes a very small amount of energy to ionize the
donor atom and thus even at moderate temperature such as room
temperature most of the donor atoms are ionized.
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Extrinsic semiconductors
• Typical donor type of impurities used in silicon and germanium are
phosphorous (P), arsenic (As), antimony (Sb) and bismuth (Bi) all
from column V of the periodic table. The ionization energy in silicon
and germanium for these impurities are given in the bottom of page
53 in the course reader material.
• The donor is modeled as a hydrogen atom with a central charge of
+q coulomb and the fifth electron as the single electron in the
hydrogen atom.
• The ionization energy is the same as the ionization energy of the
hydrogen atom as corrected for the permittivity of the silicon material
by dividing the value of ionization energy in hydrogen atom by the
square of the dielectric constant of the semiconductor material.
• It is customary to approximate the ionization energy as 0.05 eV for
all the donor atoms in silicon material.
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Extrinsic semiconductors
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Elements of the third column of the periodic table have only three valence
electrons and when they are used as substitutional impurity in the site of
semiconductor atom say silicon, the three valence electrons are able to
complete the covalent bond with only three of its neighbors and the bond
with the remaining (fourth) neighbor remains incomplete.
An electron from a covalent bond in a neighboring silicon site breaks away
generating a hole and jumps into the site where the bond with the impurity
atom is incomplete and the four covalent bonds are completed for the
impurity atom. The site of the impurity atom is negatively charged.
Each ionized impurity atom accepts so to say an electron and these
impurities are called acceptors and there is a hole in the valence band for
each ionized acceptor atom.
The holes in a semiconductor with acceptor impurities arise from thermal
excitation from the valence band as well as from ionized acceptor atoms/
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Extrinsic semiconductors
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Extrinsic semiconductors
• The acceptor impurity atom can be modeled also as a hydrogen
atom with a central charge of -q coulomb with a hole orbiting around
it and the ionization energy can be modeled as was done for the
donor atom.
• The typical trivalent atoms that are uses as acceptors in silicon and
germanium are boron (B), gallium (Ga), Aluminum (Al), and Indium
(In) and the ionization energy is given in page 54 of the course
reader.
• It is customary to think the ionization energy of all acceptor atoms in
silicon as .05 eV.
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Extrinsic semiconductors
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Extrinsic semiconductors
• We will discuss the semiconductor physics using silicon as the
material although our discussion is valid for any semiconductor
• A semiconductor with donor type of impurity is called n-type
semiconductor since there are more electrons than holes.
• Similarly, a semiconductor with acceptor type of impurity is called ptype semiconductor since there are more holes than electrons.
• We denote the carrier density in the two types of semiconductors
with a subscript n or p, such as nn or np for electron density and pp
or pn for hole density. We use a second subscript 0 to denote
thermal equilibrium densities such as nn0 or np0 for electron density
and pp0 or pn0 for hole density.
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Extrinsic semiconductors
• Neutral n-type semiconductor:
• Total positive charge in the semiconductor per unit volume is equal
to q ( pn0 + ND+) where N is the density of donor atoms and the
superscript + denotes ionized donor atoms.
• Total negative charge per unit volume is equal to –q nn0
• In thermal equilibrium, there is no net charge and hence these two
must be equal in magnitude.
pn0 + ND+ = nn0
nn0 > pn0
Hence electrons are called majority carriers and holes are
called minority carriers
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Extrinsic semiconductors
• Neutral p-type semiconductor:
• Total negative charge in the semiconductor per unit volume is equal
to -q ( np0 + NA-) where NA is the density of acceptor atoms and
the superscript - denotes ionized acceptor atoms.
• Total positive charge per unit volume is equal to q pp0
• In thermal equilibrium, there is no net charge and hence these two
must be equal in magnitude.
pp0 = nn0 + NApp0 > nn0
Hence holes are called majority carriers and electrons are
called minority carriers
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Extrinsic semiconductors
• Thermal equilibrium career densities: nn0, pn0 in n-type material and
pp0 and np0 in p-type material.
• We can determine the electron and hole densities in extrinsic
semicondcutors the same way we did for intrinsic materials,
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Extrinsic semiconductors
• Non-degenerate semiconductor is one in which EF is less than Ec by
more than 3 kT and above Ev by more than 3 kT. In this case the
expression for the density of electrons and holes will be the same as
what we got in the case of intrinsic material.
• Therefore the law of mass action will be valid i.e.,
• nn0 x pno = ni2
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• pp0 x npo = ni2
• The non-degenerate assumption is valid as long as the majority
carrier density is less than 1019 cm-3. If the majority carrier density is
above this value, then the material is called degenerate and the law
of mass action is not valid
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Extrinsic semiconductors
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Extrinsic semiconductors
• Similarly it can be shown that in the case of a non-degenerate
p-type semiconductor, pp0 is approximately equal to NA-
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The thermal equilibrium minority carrier density can be written as
pno = ni2 / ND+ in n-type material and
npo = ni2 / NA- in p-type material
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Extrinsic semiconductors
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Extrinsic semiconductors
• Compensated semiconductors are those in which both donor and
acceptor impurities are present and the material will be n-type or ptype depending on which impurities are larger in number. It will be
determined by the net impurity type..
• For example in a semiconductor with ND larger than NA, the net
impurity will be donor type with a net concentration of ND – NA and
will be n-type.
• In order to fabricate semiconductor devices we need to make layers
of n and p type material and we use compensated material to make
alternately n and p type layers.
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