ELECTRICAL CONDUCTIVITY
in order of conductivity: superconductors,
conductors, semiconductors, insulators
conductors: material capable of carrying electric
current, i.e. material which has mobile charge carriers
(e.g. electrons, ions,..) e.g. metals, liquids with ions
(water, molten ionic compounds), plasma
insulators: materials with no or very few free charge
carriers; e.g. quartz, most covalent and ionic solids,
plastics
semiconductors: materials with conductivity between
that of conductors and insulators; e.g. germanium Ge,
silicon Si, GaAs, GaP, InP
superconductors: certain materials have zero
resistivity at very low temperature.
some representative resistivities ():
R = L/A, R = resistance, L = length, A = cross section area;
resistivity at 20o C resistivity in m
resistance(in )(L=1m, diam =1mm)
aluminum 2.8x10-8 3.6x10-2
brass 8x10-8 10.1x10-2
copper 1.7x10-8 2.2x10-2
platinum 10x10-8 12.7x10-2
silver 1.6x10-8 2.1x10-2
carbon 3.5x10-5 44.5
germanium 0.45 5.7x105
silicon 640 6x108
porcelain 1010 - 1012 1016 - 1018
teflon 1014 1020
blood 1.5 1.9x106
fat 24 3x107
ENERGY BANDS IN SOLIDS:
In solid materials, electron energy levels form bands of
allowed energies, separated by forbidden bands
valence band = outermost (highest) band filled with
electrons (filled = all states occupied)
conduction band = next highest band to valence band
(empty or partly filled)
gap = energy difference between valence and
conduction bands, = width of the forbidden band
Note:
electrons in a completely filled band cannot move,
since all states occupied (Pauli principle); only way
to move would be to jump into next higher band -
needs energy;
electrons in partly filled band can move, since
there are free states to move to.
Classification of solids into three types, according to
their band structure:
insulators: gap = forbidden region between highest
filled band (valence band) and lowest empty or
partly filled band (conduction band) is very wide,
about 3 to 6 eV;
semiconductors: gap is small - about 0.1 to 1 eV;
conductors: valence band only partially filled, or (if
it is filled), the next allowed empty band overlaps
with it
Band structure and conductivity
INTRINSIC SEMICONDUCTORS
semiconductor = material for which gap between
valence band and conduction band is small;
(gap width in Si is 1.1 eV, in Ge 0.7 eV).
at T = 0, there are no electrons in the conduction band,
and the semiconductor does not conduct (lack of free
charge carriers);
at T > 0, some fraction of electrons have sufficient
thermal kinetic energy to overcome the gap and jump
to the conduction band;
fraction rises with temperature;
e.g. at 20o C (293 K), Si has 0.9x1010 conduction
electrons per cubic centimeter; at 50o C (323 K) there
are 7.4x1010 .
electrons moving to conduction band leave hole
(covalent bond with missing electron) behind;
under influence of applied electric field, neighboring
electrons can jump into the hole, thus creating a new
hole, etc. holes can move under the influence of
an applied electric field, just like electrons;
both contribute to conduction.
in pure Si and Ge, there are equally many holes (p-
type charge carriers) as there are conduction
electrons (n-type charge carriers);
pure semiconductors also called intrinsic
semiconductors.
Intrinsic silicon:
DOPED SEMICONDUCTORS:
doped semiconductor: (also impure, extrinsic) =
semiconductor with small admixture of trivalent or
pentavalent atoms;
n-type material
donor (n-type) impurities:
dopant with 5 valence electrons (e.g. P, As, Sb)
4 electrons used for covalent bonds with
surrounding Si atoms, one electron left over;
left over electron is only loosely bound only small
amount of energy needed to lift it into conduction
band (0.05 eV in Si)
n-type semiconductor, has conduction
electrons, no holes (apart from the few intrinsic
holes)
example: doping fraction
of 10-8 Sb in Si yields about 5x1016 conduction
electrons per cubic centimeter at room
temperature, i.e. gain of 5x106 over intrinsic Si.
p-type material
acceptor (p-type) impurities:
dopant with 3 valence electrons (e.g. B, Al, Ga,
In) only 3 of the 4 covalent bonds filled
vacancy in the fourth covalent bond hole
p-type semiconductor, has mobile holes, very
few mobile electrons (only the intrinsic ones).
advantages of doped semiconductors:
cantune conductivity by choice of doping
fraction
can choose majority carrier (electron or hole)
can vary doping fraction and/or majority carrier
within piece of semiconductor
can make p-n junctions (diodes) and
transistors
DIODES AND TRANSISTORS
p-n JUNCTION:
p-n junction = semiconductor in which impurity
changes abruptly from p-type to n-type ;
diffusion = movement due to difference in
concentration, from higher to lower concentration;
in absence of electric field across the junction,
holes diffuse towards and across boundary into n-
type and capture electrons;
electrons diffuse across boundary, fall into holes
(recombination of majority carriers);
formation of a depletion region
(= region without free charge carriers)
around the boundary;
charged ions are left behind (cannot move):
negative ions left on p-side net negative charge on
p-side of the junction;
positive ions left on n-side net positive charge on
n-side of the junction
electric field across junction which prevents
further diffusion.
Pn junction
Formation of depletion region in pn-junction:
DIODE
diode = biased p-n junction, i.e. p-n junction with
voltage applied across it
forward biased: p-side more positive than n-side;
reverse biased: n-side more positive than p-side;
forward biased diode:
the direction of the electric field is from p-side
towards n-side
p-type charge carriers (positive holes) in p-
side are pushed towards and across the p-n
boundary,
n-type carriers (negative electrons) in n-side
are pushed towards and across n-p boundary
current flows across p-n boundary
Forward biased pn-junction
Depletion region and potential barrier reduced
Reverse biased diode
reverse biased diode: applied voltage makes n-side
more positive than p-side
electric field direction is from n-side towards
p-side
pushes charge carriers away from the
p-n boundary
depletion region widens, and no
current flows
diode only conducts when positive voltage applied
to p-side and negative voltage to n-side
diodes used in rectifiers, to convert ac voltage to
dc.
Reverse biased diode
Depletion region becomes wider,
barrier potential higher
TRANSISTORS
(bipolar) transistor = combination of two diodes
that share middle portion, called base of
transistor; other two sections: emitter'' and
collector;
usually, base is very thin and lightly doped.
two kinds of bipolar transistors: pnp and npn
transistors
pnp means emitter is p-type, base is n-type, and
collector is p-type material;
in normal operation of pnp transistor, apply
positive voltage to emitter, negative voltage to
collector;
operation of pnp transistor:
if emitter-base junction is forward biased, holes
flow from battery into emitter, move into base;
some holes annihilate with electrons in n-type base,
but base thin and lightly doped most holes make it
through base into collector,
holes move through collector into negative terminal
of battery; i.e. collector current flows whose size
depends on how many holes have been captured by
electrons in the base;
this depends on the number of n-type carriers in the
base which can be controlled by the size of the
current (the base current) that is allowed to flow
from the base to the emitter; the base current is
usually very small; small changes in the base current
can cause a big difference in the collector current;
Transistor operation
transistor acts as amplifier of base current, since
small changes in base current cause big changes
in collector current.
transistor as switch: if voltage applied to base is such
that emitter-base junction is reverse-biased, no
current flows through transistor -- transistor is off
therefore, a transistor can be used as a voltage-
controlled switch; computers use transistors in this
way.
field-effect transistor (FET)
in a pnp FET, current flowing through a thin channel of
n-type material is controlled by the voltage (electric
field) applied to two pieces of p-type material on
either side of the channel (current depends on electric
field).
This is the kind of transistor most commonly used in
computers.
