LECTURE NOTE -11
Complete Ionization
● If we assume Ed-EF >> kT or EF-Ea >> kT ( e.g. T= 300
K), then that is, the donor/acceptor states are almost
completely ionized and all the donor/acceptor
impurity atoms have donated an electron/hole
to the conduction/valence band.
Fre
eze
out
At T = 0K, no electrons from the donor state are thermally elevated
into the conduction band; this effect is called freeze-out.
At T = 0K, all electrons are in their lowest possible energy state; that is
for an n-type semiconductor, each donor state must contain an electron,
therefore, nd =Nd or Nd+=0, which means that the Fermi level must be
above
the
donor
level.
Charge Neutrality
Charge neutrality occurs when all the charge in a volume adds to zero; it is neutral,
neither positive or negative. The equation for charge density (Coulombs/cm3) is:
= q(whatever has charge)
where q = electronic charge.
In a semiconductor, the most common and most prominent sources of charge are
electrons holes, and ionized acceptors and ionized donors.
The zero net charge does not mean that the electrons, holes, ionized donors, and
ionized acceptors are not present in the semiconductor. It simply states that in a
uniformly doped semiconductor the negative charge associated with an electron or
ionized acceptor would be canceled by the positive charge associated with a hole
or ionized donor. This does not mean that the actual electrons, holes, and ionized
impurities have ceased to exist in the semiconductor, it means that
= 0.
If = q(po - no + ND - NA) = 0, then the sum of the charges associated with the
carriers must equal zero:
po - no + N D - N A = 0
This equation is useful in many areas, including computing po and no in
equilibrium. We usually consider NA and ND to be known, so it gives us one
equation to relate two unknowns, po and no. We also know that pono=ni2 and ni is
considered known, so we can use the two equations to solve for po and no in terms
of ND, NA, and ni
*
In thermal equilibrium, the semiconductor is electrically neutral.
The electrons distributing among the various energy states creating
negative and positive charges, but the net charge density is zero.
* Compensated Semiconductors: is one that contains both donor and
acceptor
impurity
atoms
in
the
same
region.
A n-type compensated semiconductor occurs when Nd > Na and a p-type
semiconductor
occurs when Na > Nd.
* The charge neutrality condition is expressed by
* where no and po are the thermal equilibrium conc.
of e- and h+ in the conduction band and valence band, respectively.
Nd+ is the conc. Of positively charged
donor states and Na - is the conc. of negatively charged acceptor states.
Compensated Semiconductor
Energy band diagram of compansated semiconductor
showing ionized and un-ionized donor and acceptor
Compensated Semiconductor
* If we assume complete ionization, Nd+ = Nd and Na- = Na, then
is used to calculate the conc. of holes in valence band
Compensated Semiconductor
Electron concentration versus temperature showing the 3 regions Partial Ionization
Extrinsic intrinsic
Energy band diagram showing the redistribution of electrons when donor are added
Compensation and Space Charge Neutrality
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Semiconductors can be doped with both donors ( ) and acceptors ( )
simultaneously.
Assume a material doped with >
predominantly n-type
lies
above
acceptor level Ea completely full, however, with
above ,
the hole concentration cannot be equal to .
Mechanism:
o Electrons are donated to the conduction band from the donor level
o An acceptor state gets filled by a valence band electron, thus creating
a hole in the valence band.
o An electron from the conduction band recombines with this hole.
o Extending this logic, it is expected that the resultant concentration of
electrons in the conduction band would be
instead of .
o This process is called compensation.
By compensation, an n-type material can be made intrinsic (by making =
)
or
even
p-type
(for
>
).
Note: a semiconductor is neutral to start with, and, even after doping, it
remains neutral (since for all donated electrons, there are positively charged
ions ( ); and for all accepted electrons (or holes in the valence band), there
are negatively charged ions ( ).
Therefore, the sum of positive charges must equal the sum of negative
charges,
and
this
governing
relation,
given by
(2.17) is referred to as the equation for space charge
neutrality.
This equation, solved simultaneously with the law of mass action (given by
) gives the information about the carrier concentrations.
Note: for ,
.