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Review of Basic Device Physics
into bands. This results in an effective decrease in the ionization energy until
finally the impurity band merges with the CB (or VB) and the ionization energy
becomes zero. Under these circumstances, the silicon is said to be degenerate.
Strictly speaking, Fermi statistics should be used for the calculation of electron concentration when E E
kT
c
f
−
(
) ≤ [20]. For practical purposes, it is a good
approximation within a few kT to assume that the Fermi level of the degenerate
n+ silicon is at the CB edge, and that the degenerate p+ silicon is at the VB edge.
2.2.5 Carrier Transport in Semiconductors
In thermal equilibrium, mobile (CB) electrons are in random thermal motion
with an average velocity of thermal motion, v th ≅ 1 × 10 7 cm sec –1 at 300° K.
However, due to the random thermal motion of electrons, no net current
flows through the material. On the other hand, in the presence of an electric
field E, electrons move opposite to the direction of E. This process is called
electron drift and causes a net current flow through the material. Also, if there
is a carrier concentration gradient in the material, the carriers diffuse away
from the region of higher concentration to the lower concentration, producing a net current flow in the semiconductor. Thus, the carrier transport or
current flow in a semiconductor is the result of two different mechanisms:
(1) the drift of carriers (electrons and holes), which is caused by the presence
of an electric field and (2) the diffusion of carriers, which is caused by an
electron or hole concentration gradient in the semiconductor. We will now
consider factors involved in both phenomena.
2.2.5.1 Carrier Mobility and Drift Current
When an electric field is applied to a conducting medium containing free carriers, the carriers are accelerated in proportion to the force of the field. However,
the accelerating carriers within a semiconductor will collide with various
scattering centers including the atoms of the host lattice (lattice scattering),
the impurity atoms (impurity scattering), and other carriers (carrier–carrier
scattering). In the case of an electron, these different scattering mechanisms
tend to redirect its momentum and in many cases tend to dissipate the energy
gained from the electric field. Thus, under the influence of a uniform electric
field, the process of energy gain from the field and energy loss due to the scattering balance each other and carriers attain a constant average velocity, called
the drift velocity (v d ). At low electric fields, v d is proportional to the electric field
strength E and is given by
v
E
d = µ
(2.28)
where:
μ is the constant of proportionality and is called the mobility of the carriers
in units of cm 2 V –1 sec –1
Review of Basic Device Physics
into bands. This results in an effective decrease in the ionization energy until
finally the impurity band merges with the CB (or VB) and the ionization energy
becomes zero. Under these circumstances, the silicon is said to be degenerate.
Strictly speaking, Fermi statistics should be used for the calculation of electron concentration when E E
kT
c
f
−
(
) ≤ [20]. For practical purposes, it is a good
approximation within a few kT to assume that the Fermi level of the degenerate
n+ silicon is at the CB edge, and that the degenerate p+ silicon is at the VB edge.
2.2.5 Carrier Transport in Semiconductors
In thermal equilibrium, mobile (CB) electrons are in random thermal motion
with an average velocity of thermal motion, v th ≅ 1 × 10 7 cm sec –1 at 300° K.
However, due to the random thermal motion of electrons, no net current
flows through the material. On the other hand, in the presence of an electric
field E, electrons move opposite to the direction of E. This process is called
electron drift and causes a net current flow through the material. Also, if there
is a carrier concentration gradient in the material, the carriers diffuse away
from the region of higher concentration to the lower concentration, producing a net current flow in the semiconductor. Thus, the carrier transport or
current flow in a semiconductor is the result of two different mechanisms:
(1) the drift of carriers (electrons and holes), which is caused by the presence
of an electric field and (2) the diffusion of carriers, which is caused by an
electron or hole concentration gradient in the semiconductor. We will now
consider factors involved in both phenomena.
2.2.5.1 Carrier Mobility and Drift Current
When an electric field is applied to a conducting medium containing free carriers, the carriers are accelerated in proportion to the force of the field. However,
the accelerating carriers within a semiconductor will collide with various
scattering centers including the atoms of the host lattice (lattice scattering),
the impurity atoms (impurity scattering), and other carriers (carrier–carrier
scattering). In the case of an electron, these different scattering mechanisms
tend to redirect its momentum and in many cases tend to dissipate the energy
gained from the electric field. Thus, under the influence of a uniform electric
field, the process of energy gain from the field and energy loss due to the scattering balance each other and carriers attain a constant average velocity, called
the drift velocity (v d ). At low electric fields, v d is proportional to the electric field
strength E and is given by
v
E
d = µ
(2.28)
where:
μ is the constant of proportionality and is called the mobility of the carriers
in units of cm 2 V –1 sec –1