Electrical properties

2
• Scanning electron microscope images of an IC:
• A dot map showing location of Si (a semiconductor):
--Si shows up as light regions.
• A dot map showing location of Al (a conductor):
--Al shows up as light regions.
Fig. (a), (b), (c) from Fig. 18.0, Callister 6e.
Fig. (d) from Fig. 18.25, Callister 6e. (Fig. 18.25 is courtesy Nick Gonzales, National Semiconductor Corp., West Jordan, UT.)
(a)
(b)
(c)
(d)
VIEW OF AN INTEGRATED CIRCUIT

3
• Ohm's Law:
ΔV = I R
voltage drop (volts)
resistance (Ohms)
current (amps)
• Resistivity, ρ and Conductivity, σ:
--geometry-independent forms of Ohm's Law
E: electric
field
intensity
resistivity
(Ohm-m)
J: current density
conductivity
• Resistance:
ELECTRICAL CONDUCTION

4
• Room T values (Ohm-m)
-1
Selected values from Tables 18.1, 18.2, and 18.3, Callister 6e.
CONDUCTIVITY: COMPARISON

5
• Question 18.2, p. 649, Callister 6e:
What is the minimum diameter (D) of the wire so that
ΔV < 1.5V?
< 1.5V
2.5A
6.07 x 10 (Ohm-m)
7
-1
100m
Solve to get D > 1.88 mm
EX: CONDUCTIVITY PROBLEM

6
• Metals:
-- Thermal energy puts
many electrons into
a higher energy state.
• Energy States:
-- the cases below
for metals show
that nearby
energy states
are accessible
by thermal
fluctuations.
CONDUCTION & ELECTRON TRANSPORT

7
• Insulators:
--Higher energy states not
accessible due to gap.
• Semiconductors:
--Higher energy states
separated by a smaller gap.
ENERGY STATES: INSULATORS AND SEMICONDUCTORS

• Imperfections increase resistivity
--grain boundaries
--dislocations
--impurity atoms
--vacancies
8
These act to scatter
electrons so that they
take a less direct path.
• Resistivity
increases with:
--temperature
--wt% impurity
--%CW
Adapted from Fig. 18.8, Callister 6e. (Fig. 18.8 adapted from J.O. Linde, Ann. Physik 5, p. 219 (1932); and C.A. Wert and R.M. Thomson, Physics of Solids, 2nd ed., McGraw-Hill Book Company, New York, 1970.)
METALS: RESISTIVITY VS T, IMPURITIES

9
• Question:
--Estimate the electrical conductivity of a Cu-Ni alloy
that has a yield strength of 125MPa.
Adapted from Fig. 18.9, Callister 6e.
Adapted from Fig. 7.14(b), Callister 6e.
EX: ESTIMATING CONDUCTIVITY

10
• Data for Pure Silicon:
--σ increases with T
--opposite to metals
electrons
can cross
gap at
higher T
material
Si
Ge
GaP
CdS
band gap (eV)
1.11
0.67
2.25
2.40
Adapted from Fig. 19.15, Callister 5e. (Fig. 19.15 adapted from G.L. Pearson and J. Bardeen, Phys. Rev. 75, p. 865, 1949.)
Selected values from Table 18.2, Callister 6e.
PURE SEMICONDUCTORS: CONDUCTIVITY VS T

• Electrical Conductivity given by:
11
# electrons/m
3
electron mobility
# holes/m
3
hole mobility
• Concept of electrons and holes:
Adapted from Fig. 18.10, Callister 6e.
CONDUCTION IN TERMS OF ELECTRON AND HOLE MIGRATION

12
• Intrinsic:
# electrons = # holes (n = p)
--case for pure Si
• Extrinsic:
--n ≠ p
--occurs when impurities are added with a different
# valence electrons than the host (e.g., Si atoms)
• N-type Extrinsic: (n >> p)
• P-type Extrinsic: (p >> n)
INTRINSIC VS EXTRINSIC CONDUCTION

13
• Data for Doped Silicon:
--σ increases doping
--reason: imperfection sites
lower the activation energy to
produce mobile electrons.
Adapted from Fig. 19.15, Callister 5e. (Fig. 19.15 adapted from G.L. Pearson and J. Bardeen, Phys. Rev. 75, p. 865, 1949.)
• Comparison: intrinsic vs
extrinsic conduction...
--extrinsic doping level:
1021/m3 of a n-type donor
impurity (such as P).
--for T < 100K: "freeze-out"
thermal energy insufficient to
excite electrons.
--for 150K < T < 450K: "extrinsic"
--for T >> 450K: "intrinsic"
Adapted from Fig. 18.16, Callister 6e. (Fig. 18.16 from S.M. Sze, Semiconductor Devices, Physics, and Technology, Bell Telephone Laboratories, Inc., 1985.)
DOPED SEMICON: CONDUCTIVITY VS T

14
• Allows flow of electrons in one direction only (e.g., useful
to convert alternating current to direct current.
• Processing: diffuse P into one side of a B-doped crystal.
• Results:
--No applied potential:
no net current flow.
--Forward bias: carrier
flow through p-type and
n-type regions; holes and
electrons recombine at
p-n junction; current flows.
--Reverse bias: carrier
flow away from p-n junction;
carrier conc. greatly reduced
at junction; little current flow.
P-N RECTIFYING JUNCTION

15
• Electrical conductivity and resistivity are:
--material parameters.
--geometry independent.
• Electrical resistance is:
--a geometry and material dependent parameter.
• Conductors, semiconductors, and insulators...
--different in whether there are accessible energy
states for conductance electrons.
• For metals, conductivity is increased by
--reducing deformation
--reducing imperfections
--decreasing temperature.
• For pure semiconductors, conductivity is increased by
--increasing temperature
--doping (e.g., adding B to Si (p-type) or P to Si (n-type).
SUMMARY