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v y
a
G a s a to m s
A re a A
a
S q u a re C o n ta in e r
a
F a c e A
F a c e B
v x
The gas molecules in the container are in random motion
Fig 1.16
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
vxv z
v y
TRANSLATIONAL MOTION
x
Iy
y ax is ou t o f pap er
z
y
Ix= 0
Iz
ROTATIONAL MOTION
Possible translational and rotational motions of a diatomic molecule.Vibrational motions are neglected.
Fig 1.17
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
x
y
z
(b )
(a )
(a) The ball-and-spring model of solids in which the springsrepresent the interatomic bonds. Each ball (atom) is linked to itsneighbors by springs. Atomic vibrations in a solid involve 3dimensions.(b) An atom vibrating about its equilibrium position stretches andcompresses its springs to the neighbors and has both kinetic andpotential energy.
MOLAR HEAT CAPACITY Cm
monatomic
diatomic
solid
Fig 1.18
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Interatom ic separation, r0
U o
ro
BC
K E
U (r) = PE
B C rav
T 2
T 1
U m in
A
A
U m in = U o
Energy
The potential energy PE curve has a minimum when the atoms inthe solid attain the interatomic separation at r = ro. Due to thermalenergy, the atoms will be vibrating and will have vibrational kineticenergy. At T = T1, the atoms will be vibrating in such a way that thebond will be stretched and compressed by an amount correspondingto the KE of the atoms. A pair of atoms will be vibrating between Band C. Their average separation will be at A and greater than ro.
Fig 1.21
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
H o t o v enE f fu s in g g a s a tom s
C o ll im a tin g s l i ts
S 1S 2
D e te c to r
V e lo c ity s e le c to r
R o ta tin g d isk s
H o le
L
S chem atic d iagram of a S te rn typ e experim en t fo r de term in ing th ed is tribu tion o f m olecu lar speeds .
Fig 1.22
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
0
0 .5
1
1 .5
2
2 .5
0 500 1000 1500 2000S peed (m /s)
1 0 0 0 K (72 7 °C )
2 9 8 K (25 °C )
v*v avv rm s
v*v a vv rm s
Relativenumberofmolecules
perunitvelocity(s/km)
Maxwell-Boltzmann distribution of molecular speeds in nitrogengas at two temperatures. The ordinate is dN/(Ndv),the fractionalnumber of molecules per unit speed interval in (km/s)-1
Mawell-Boltzmann Distribution
# of atoms per unit volume per unit energy at an energy E
Fig 1.23
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
E nergy, E
T 1
T 2 > T 1
E A
A ve rag e KE a t T 1 .
A verag e KE a t T 2
Num
ber
ofat
oms
per
unit
ener
gy,n
E
Energy distribution of gas molecules at two different temperatures.The number of molecules that have energies greater than EA is theshaded area. This area depends strongly on the temperature asexp(EA/kT).
The mean energy is (3/2) kT monatomic gas with three degrees of freedom
N = total number of molecules, nE dE = the fraction of the particles in the range E to (E + dE)
then we can answer the question:“What is the probability, given a molecule, that its energy is in the range from E to (E+dE)?”
Fig 1.24
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
M V
m
v
G as A tom
SO L ID
G A S
Solid in equilibrium in air. During collisions between the gas andsolid atoms, kinetic energy is exchanged.
Fig 1.25
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
m
m
m
x < 0
x = 0
x > 0
C om p re s s io n
E x ten s io n
E qu ilib rium
t
E x te n s io nC om p re s s io n x
Fluctuations of a mass attached to a spring due to randombombardment by air molecules
Fig 1.26
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Random motion of conduction electrons in a conductor results in electrical noise.
Fig 1.27
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Charging and discharging of a capacitor by a conductor due to the random thermal motions of the conduction electrons.