Transcript Slide 1

Sinai University Faculty of Engineering Science
Department of Basic science
7/17/2015
2
Course name: Electrical materials
Code: ELE163
Text references
1- Principles of Electronic Materials and Devices, 3rd edition
2- Kittel, Introduction to Solid State Physics
3-College Physics , Serway, 7th edition
4-Lecture notes (power points)
5- Internet sites
Prepared by
Pr Ahmed Mohamed El-lawindy
[email protected]
7/17/2015
Faculty site: www.engineering.su.edu.eg
3
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Ch 2 Electrical and thermal conductions in solids
Objectives
1- Understand and derive the equation of electrical and thermal
conductivities in solids using classical mechanics
2-Apply such equations to explore the behavior of such
materials, which shows these phenomena
3-Solve problems related to such phenomena.
4-Relate the attained knowledge to explain the electrical and
thermal conduction of materials, measured in the laboratory.
Introduction
Electrical conduction involves the motion of charges in the
material under the influence of electric field
Material electrical classification:
1-Super conductors
2- Conductors
3-Semiconductors
4-Insulators
Valence electrons
Conduction electrons
Metallic bond, electron cloud
Ex
net displacement, Mobility
Material thermal classification:
Also, conduction electrons take part
2.1 Classical theory: The Drude model
2.1.1 Metals and conduction by electrons
Drift of electrons in a conductor in the
presence of an applied electric field.
Electrons drift with an average velocity vdx
in the x-direction. (Ex is the electric field.)
1
vdx  [vx1  vx 2  vx 3    v xN ]
N
vdx = drift velocity in x direction, N = number of conduction electrons, vxi = x direction
velocity of i th electron
n=N/V,
N=nV
In time Dt
Dq= enA Dx
Fig 2.1
distance Dx
vdx= Dx/ Dt
Dx= Dt vdx
Current Density and Drift Velocity
Jx (t) = envdx(t)
Jx = current density in the x direction, e = electronic charge, n =
electron concentration, vdx = drift velocity
what is the relation between J(t) and Ex (t)?
Electrons in a crystal is similar to a gas in a cylinder
In gas K.E. is Temperature dependence=3/2 kT
But in solids, is not
Due to the electrostatic attraction, P.E.av~ K.E.av=Few eV
Then
Fig 2.1
u~ 106 m/s, i.e. temperature independent
(a) A conduction electron in the electron gas moves about randomly in a metal (with
a mean speed u) being frequently and randomly scattered by thermal vibrations of
the atoms. In the absence of an applied field there is no net drift in any direction.
(b) In the presence of an applied field, Ex, there is a net drift along the x-direction.
This net drift along the force of the field is superimposed on the random motion of
the electron. After many scattering events the electron has been displaced by a net
distance, Dx, from its initial position toward the positive terminal
Fig 2.2
Ex, Fx=eEx
In general
1- Metal crystals are not perfect
Crystal defects:
-Vacancies
-Dislocation
-Impurities
So electron will scatter more
2- Thermal vibration of ions
In case of no Ex
Displacement: Dx~0
In case of Ex
v=v0+at
eE x
v xi  u xi 
(t  t i )
me
1
v dx  [v x1  v x 2  v x 3  ....... v xN ]
N
Velocity gained in the x direction
eE x N
e x
at time t from the electric field (E )
v dx 
(t  t i ) 
Ex
for three electrons. There will be N
me N
me
electrons to consider in the metal.
  (t  t i )  the average collision tim e
x
Definition of Drift Mobility
vdx = dEx
Jx (t) = envdx(t)
vdx = drift velocity, d = drift mobility, Ex = applied field
Drift Mobility and Mean Free Time
e
d 
me
d = drift mobility, e = electronic charge,  = mean scattering time
(mean time between collisions) = relaxation time, me = mass of an
electron in free space.
 = conductivity,
vdx   d E x
J x (t )  envdx  en d E x
J x  E x
e 2 n
  en d 
me
e = electronic charge,
n = number of electrons per unit
volume,
d = drift velocity,
= mean scattering (collision) time =
relaxation time,
me = mass of an electron in free
space.
Drift Velocity
Dx
 vdx
Dt
Dx = net displacement parallel to the field, Dt = time interval,
vdx = drift velocity
2.2 Temperature dependence of resistivity
A- Ideal pure metal
A vibrating metal atom
Scattering of an electron from the thermal vibrations of the atoms. The electron
travels a mean distance  = u between collisions. Since the scattering cross-sectional
area is S, in the volume s there must be at least one scatterer, Ns (Su ) = 1,
where Ns is the concentration of scattering centers.
Fig 2.5
Mean Free Time Between Collisions
1

SuN s
 = mean free time, u = mean speed of the electron, Ns =
concentration of scatterers, S = cross-sectional area of the scatterer
Resistivity Due to Thermal Vibrations of the
Crystal
T = AT
T = resistivity of the metal, A = temperature independent constant, T
= temperature
Matthiessen’s Rule
2-Non pure metals
Crystal defects:
1




1
T
1


1
d


1
-Vacancies
-Dislocation
-Impurities
I
e
me  d

1
L

1
I
1
1
1


en d en L en I
T 
1
en d
and  I 
1
en I
  T   I
Matthiessen`s rule
 I becom es R , residual reistivity
  T   R
Fig 2.6
Two different types of scattering
processes involving scattering from
impurities alone
and from thermal vibrations alone.
Matthiessen’s Rule
 =  T + I
= effective resistivity,
T = resistivity due to scattering by thermal vibrations only,
I = resistivity due to scattering of electrons from impurities only.
 = T +  R
= overall resistivity,
T = resistivity due to scattering from thermal vibrations,
R = residual resistivity
= AT+B
Definition of Temperature Coefficient of Resistivity
1   
o   
o T T To
o = TCR (temperature coefficient of resistivity),  = change in the
resistivity, o = resistivity at reference temperature To , T = small
increase in temperature, To = reference temperature
Temperature Dependence of Resistivity
 [1 + o(TTo)]
 = resistivity, o = resistivity at reference temperature, 0 = TCR
(temperature coefficient of resistivity), T = new temperature, T0 =
reference temperature
  AT is approxim ate for pure m etal
Frequently
T 
  o  
 T0 
n
for
pure
m etal
The resistivity of various metals as a function of temperature above 0 °C. Tin melts at
505 K whereas nickel and iron go through a magnetic to non-magnetic (Curie)
transformations at about 627 K and 1043 K respectively. The theoretical behavior
( ~ T) is shown for reference.
[Data selectively extracted from various sources including sections in Metals Handbook,
10th Edition, Volumes 2 and 3 (ASM, Metals Park, Ohio, 1991)]
Fig 2.7
The resistivity of copper from lowest to highest temperatures (near melting temperature,
1358 K) on a log-log plot. Above about 100 K,   T, whereas at low temperatures,
 T 5 and at the lowest temperatures  approaches the residual resistivity R. The inset
shows the  vs. T behavior below 100 K on a linear plot (R is too small on this scale).
Fig 2.8
Power radiated from a light bulb is equal to the electrical power dissipated
in the filament.
Fig 2.10