Q.12. Define drift velocity, mobility and
conductivity of a semiconductors. Obtain an expression for the electrical
conductivity of an intrinsic semiconductor.(AKTU. 2015 - 16)
Ans. Drift Velocity: -
The drift velocity is the average velocity that a particle, such as an
electron, attains in a material due to an electric field. It can also be
referred to as axial drift velocity. In general, an electron will propagate
randomly in a conductor at the Fermi velocity. An applied electric field will
give this random motion a small net flow velocity in one direction.
In a semiconductor, the two main carrier scattering
mechanisms are ionized impurity scattering and lattice scattering.
Because current is proportional to drift velocity,
which in a resistive material is, in turn, proportional to the magnitude of an
external electric field, Ohm's law can be explained in terms of drift velocity.
The most elementary expression of Ohm's law is:
u = mE
where u is the drift
velocity, ยต is the electron mobility (with units m2/(V·s)) of the material and E is the electric field
(with units V/m).
Electron Mobility: -
In
solid-state physics, the electron mobility characterizes how quickly an
electron can move through a metal or semiconductor, when pulled by an electric
field. In semiconductors, there is an analogous quantity for holes, called hole
mobility. The term carrier mobility refers in general to both electron and hole
mobility in semiconductors.
Electron and hole mobility are special cases of
electrical mobility of charged particles in a fluid under an applied electric
field.
Conductivity is proportional to the product of
mobility and carrier concentration. For example, the same conductivity could
come from a small number of electrons with high mobility for each, or a large
number of electrons with a small mobility for each. For metals, it would not
typically matter which of these is the case, since most metal electrical
behavior depends on conductivity alone. Therefore mobility is relatively
unimportant in metal physics. On the other hand, for semiconductors, the
behavior of transistors and other devices can be very different depending on
whether there are many electrons with low mobility or few electrons with high
mobility. Therefore mobility is a very important parameter for semiconductor
materials. Almost always, higher mobility leads to better device performance,
with other things equal.
Electrical Conductivity
Of An Intrinsic Semiconductor: -
When an
electric field is applied across an intrinsic semiconductor, in addition to the
thermal motion, the free electrons and holes exhibit a steady drift constituting
a current flow.
The current density contributed by electron flow is
given by
jn = nevn ...............(i)
where e is the charge of
electron and vn is the drift velocity free electrons.
The current density contributed by hole flow is given
by
jp = pevp ...............(ii)
where vp is the drift
velocity of the holes.
Then, the conductivity due to electrons is given by
...............(iii)
Where E is the applied
electric field and is the mobility of
free electrons defined as the drift velocity of electrons when subjected to
unit electric field.
Similarly, the conductivity
due to the holes is given by
...............(iv)
where is the mobility of holes.
As both electrons and holes
contribute to current flow in an intrinsic semiconductor, the total
conductivity in an intrinsic semiconductor is given as
si = sn + sp = eni(mn + mp) ...............(v)
where si is called the intrinsic conductivity.
