Semiconductors
„
Conductivity (σ
(σ) increases (exponentially)
with temperature; compare to metals
Semiconductors
„
Calculate the fraction of Si atoms that
provide a conduction e- at room
temperature and compare this to the
value obtained for Cu.
„
[density (Si) = 2.33g/cm3; M(Si)
M(Si) = 28.09 g/mol; carrier density ne =
„
Ans:
Ans: fraction = 2.8 x 10-13 cf 1.23
Exercise: convert 1eV and 6eV to kJ/mol
„
14 x 1015 m-3 ]
Semiconductors:
Semiconductors
change in the Fermi function (f
(f(E)
(E) with temperature
1
f (E) =
[exp(E − EF ) / kT ] + 1
f (E) =
1
[exp(E − EF ) / kT ] + 1
Calculate the probability of an e- being
thermally promoted to the conduction
band of Si (E
(Eg = 1.07eV) at 25 °C
Ans:
Ans: f(E)
f(E) = 4.39 x 10-10
Semiconductors
Band gaps, Eg(eV)
Semiconductors: Arrhenius plot
of electrical conductivity
„
conductivity is proportional to the density of charge carriers
since
and
σ = nq( μ e + μ h )
n ∝ exp( − E g / 2kT )
∴ ln(σ ) = ln(σ 0 ) −
from f(E)
f(E)
Eg 1
2k T
1
Semiconductors: Arrhenius plot
of electrical conductivity
∴ ln(σ ) = ln(σ 0 ) −
Eg 1
2k T
„
Note: although
conductivity will decrease
as T increases in all
materials due to thermal
vibration, but this is only
significant in metals
„
see example
Semiconductors
To characterize a new semiconductor one can find the
band gap by measuring conductivity at different
temperatures (Note: this can also be done
spectroscopically).
spectroscopically).
Example: The conductivity of a new material is 250
Ω-1m-1 at 20°
20°C and at 100°
100°C it is 1100 Ω-1m-1. What is
its band gap, Eg?
Ans:
Ans: 0.349 eV
Intrinsic semiconductors
Intrinsic semiconductors
„
„
„
range of band gaps
conductivity in an intrinsic (pure) semiconductor depends on the band
gap energy and temperature.
Examples of intrinsic semiconductors are Si, Ge,
Ge, Se, GaAs,
GaAs, CdS
„
electrons can also be excited into the
conduction band by light of the correct
energy: E=hc/
λ. Conversely, light can be
E=hc/λ
emitted (tunable
(tunable LED’
LED’s).
Ex: Calculate the photon wavelength (nm)
needed to promote an e- to the conduction
band in Si.
p- and n-doped semiconductors
band structure
p- and n-doped semiconductors
„
„
small amounts of dopants (from 0.01 atom% to less than 1 atom in 109)
can be added to modify the conductivity (“
(“extrinsic semiconductors”
semiconductors”)
and subsequently to make electronic devices.
(see periodic table to decide on pp- or n-dopants)
dopants)
„
p- and n-dopants modify the band structure of a semiconductor;
effectively adding either ‘donor’
donor’ or ‘acceptor’
acceptor’ bands.
p-dopant
2
p- and n-doped semiconductors:
band structure
„
n-dopant
Extrinsic semiconductors
Extrinsic semiconductors exhibit an ‘exhaustion range’
range’ at a certain
temperature when all “extra electrons”
electrons” have been promoted to the
conduction band.
„
The p-n junction
„
Current flow in a p-n junction
The p-n juction is one of the simplest and most common applications
using semiconductors in a variety of devices (transistors, silicon
silicon
chips, photocells, LED’
LED’s, thermistors)
thermistors)
„
„
NanoNano-CdSe:
CdSe: optical properties vary with
particle size
„
The p-n junction acts as a solidsolid-state rectifier, allowing current to
flow only in one direction
NanoNano-CdSe:
CdSe: synthesis by organometallic
methods
Radius (nm)
0.9
1.4
1.9
2.4
3
„
NanoNano-CdSe semiconductor
Insulators
„
Insulators
Insulators
„ Piezoelectric and pyroelectric effects
(see text books: AR West)
Barium titanate structure and the Piezoelectric effect
(see text books)
„
Electrical properties of solids:
Summary
Insulators
„
Other perovskite structures (solid solutions)
Band gaps; range of conductivity; examples
„
„
„
„
„
„
„
„
Conductors can be classified according to their response to temperature:
temperature:
conductors, semiconductors & superconductors.
The electronic properties of solids can be rationalised using band
band theory
For metallic conductors, resistivity is proportional to temperature.
For semiconductors, conductivity increases exponentially with
temperature. The population of the conduction band as a function of
temperature is given by the FermicFermic-Dirac distribution.
Radiation of the correct energy can also excite electrons into the
the
conduction band. Conversely light of different wavelengths (Eg
(Eg)) can be
emitted.
Extrinsic semiconductors have a higher conductivity than similar intrinsic
ones at low temperature.
The conductivity of extrinsic semiconductors is accurately controlled
controlled by
the concentration of the dopant;
dopant; wide temperature range possible.
Superconductivity phenomena can be explained in terms of ‘Cooper pairs
of electrons’
electrons’, which can conduct electricity with zero resistance
4