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1.1
Material Types and Electric Conduction
Intrinsic Un-doped Silicon
At room temperature (27oC, 300°°K), in intrinsic silicon a hole-electron
pair is generated for each bond broken by thermal agitation and the
number of free electrons, no, is equal to the number of free holes, po,
in the un-doped material. Both electrons and holes take part in the
electrical conduction process and hence the term ‘bipolar
semiconductor’. For intrinsic silicon, since the conducting charge
carriers are generated in pairs, they have equal concentrations at any
temperature so that:
no = po = ni
nopo = ni2
This is known as the Law of Mass Action
At room temperature, (300°°K),
n i ≈ 1.5××1010/cm3
Conduction band
e- e- e-
e-
Ec Edge of conduction band
Eg
Ef
Energy
gap
h
h
+
-
e
-
e
h
+
h
+
Fermi Energy level
E v Edge of valence band
Valence band
Fig 1.1
Electron and Hole Generation in Intrinsic Silicon
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1.2 n-Type Material (see Fig. 1.2)
In this case, the silicon is doped with impurity atoms having five
electrons in their outer shell. Four of these take part in the covalent
bonding of the silicon crystal structure. The extra free electron
originally occupies the donor energy level, Ed, just below the
conduction band of the silicon. At room temperature, practically all of
the electrons of the impurity atoms gain sufficient energy to leave the
donor level and enter the conduction band. Hence the donor levels are
almost all empty and do not take part in the conduction process. The
number of electrons in the conduction band in n-type material due to
doping far exceeds those generated by thermal agitation of the silicon.
Consequently, in n-type material, current conduction is primarily due
to the electrons in the conduction band. This is so to such an extent
that the electron concentration in the conduction band can be taken as
equal to the doping concentration of n-type impurities present, i.e.
no ≈ Nd . Moreover, the increased concentration of electrons in the
conduction band also increases the rate of carrier recombination in the
doped material. Hence, the concentration of holes in the valence band
of n-type material is much lower than is the case for un-doped
material. However, the Law of Mass Action still holds so that n0p0 = ni2.
1.3
p-Type Material (See Fig 1.3)
In this case, the silicon is doped with impurity atoms having only
three electrons in their outer shell. These all take part in the covalent
bonding of the silicon crystal, but for each impurity atom there is a
vacant energy level, Ea , termed an acceptor level, just above the
valence band of silicon. At room temperature, enough electrons are
excited from the valence band to fill the acceptor levels. Hence, the
acceptor levels take no part in the conduction process. The electrons
excited into the acceptor levels, however, leave behind a plentiful
supply of holes in the valence band so that the number of holes
present far exceeds those generated by thermal agitation.
Consequently, in p-type material, current conduction is primarily due
to the holes in the valence band. The hole concentration in the valence
band can, be taken as equal to the doping concentration of the p-type
impurities present in the silicon, i.e. po ≈ Na . Moreover, the increased
concentration of holes in the valence band also increases the rate of
carrier recombination in the doped material. Hence, the concentration
of electrons in the conduction band of p-type material is much lower
than is the case for un-doped material. Again, n0p0 = ni2.
2
Conduction
band
EC
Ed
EF
Donor level
Fermi level
n -type
material
EV
e-
h+
Fig. 1.2
Valence
band
n-type Silicon Semiconductor
Conduction
band
EC
p type
material
EF
Ea
EV
Fermi level
Acceptor level
e-
h+
Valence band
Fig. 1.3
n - type material
no po = ni 2
no ≈ Nd >> ni
ni 2
po ≈
<< ni
Nd
p-type Silicon Semiconductor
p - type material
n op o = n i 2
majority carriers
po ≈ Na >> ni
ni 2
minority carriers
no ≈
<< ni
Na
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1.4 The Effect of an Electric Field
In the absence of any external influence other than temperature above
0°°K, carriers undergo thermal agitation only and move randomly within
the crystalline structure. There is no net flow of charge in any direction
within the semiconductor, and hence, no current flows through the
material. The energy of carriers in a given band is also constant
throughout the material.
Conduction band
V
e-
qV
EC
h+
semiconductor
+
E
EV
-
Valence band
Direction of electric field
+
E
-
Direction of electric field
Fig. 1.4
Effect of an Electric Field on Energy Bands
When an electric field is applied across the semiconductor, by way of a
battery or power supply for example, an electrostatic force is exerted
on the charge carriers in the material. The carriers, as a result of the
force they experience in the field, gain electrostatic energy. This gives
rise to a gradient in the energy bands occupied by the carriers in the
direction of the electric field as shown in Fig. 1.4.
Since electrons will seek to occupy the lowest energy status
available, they will move from locations of higher electrostatic energy
to locations of lower energy. This gives rise to a net movement of
carriers through the material and hence sets up a flow of current.
Electrons, because of their negative charge, will move in a direction
opposite to the electric field while holes will move in the direction of
the field. Current flow is, by convention, in the direction of the electric
field and is referred to as a drift current.
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1.5 Carrier Mobility
The net drift of carriers under the influence of an electric field depends
on the relative ease with which they can move within the crystalline
structure of the semiconductor. Carrier mobility is defined as the
velocity with which a carrier will drift, on average, in unit field
strength of 1 Vm-1 and is given as:
µ
qτ n
=
m *e
n
µ =
for electrons
and
p
qτ p
m*p
for holes
where:
m e*
and
m *p
are the effective masses of electrons and holes
respectively.
τ
n
,
τ
p
are the mean free times of the carriers spent between
collisions.
q is the magnitude of the charge on the carrier.
Generally, the mobility of electrons in the conduction band is
somewhat greater than that of holes in the valence band, i.e.
µ n > µ p and has units of m2V-1s-1.
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1.6 Drift Current
When charge carriers drift in a uniform manner across a piece of
homogeneous semiconductor material, there is a constant and uniform
flux of charge through the material. The charge flow per unit area is
referred to as the Charge Flux Density as seen in Fig. 1.5).
E lectric
F ield
E
J drift = nqµ n E (electrons )
n
A
C h arge
F lu x
D en sity
J drift = pqµ p E
p
(holes)
J
Fig. 1.5
Charge Flux Density in an Electric Field
where:
n and p are the respective charge carrier concentrations
q is the magnitude of the charge on the carriers
µ ,µ
n
p are the respective carrier mobilities
E is the electric field strength.
Electrons and holes will drift in opposite directions in a given electric
field. However, since the charge on the electron is negative, both
electrons and holes will make positive contributions to conventional
current specified in the direction of the field. When both flux
components are integrated over the area, A, of the semiconductor, the
total drift current is obtained as:
Idrift = Jn drift A + Jp drift A = AEq(nµn + pµp )
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