Transcript Conduction_Part_1

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Metal interconnects are used in microelectronics to wire the devices within the chip,
the intergraded circuit. Multilevel interconnects are used for implementing the
necessary interconnections.
|SOURCE: Dr. Don Scansen, Semiconductor Insights, Kanata, Ontario, Canada
Drift of electrons in a conductor in the presence of an applied
electric field. Electrons drift with an average velocity vdx in the xdirection.(Ex is the electric field.)
Fig 2.26
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Ex
u
x
+
Vibrating Cu ions
V
(b)
(a)
(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 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, x, from its initial position
toward the positive terminal
Fig 2.2
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Velocity gained along x
Present time
vx 1-u x1
Last collision
Electron 1
t1
vx 2-u x2
Free time
time
t
Electron 2
t2
t
time
v x3-u x3
Electron 3
t3
time
t
Velocity gained in the x-direction at time t from the electric field
(Ex) for three electrons. There will be N electrons to consider in
the metal.
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Electric field
E
s1
x
1
Collision
uy1
Start
0
Collision
p
t2
t1
ux1
3
t3
Finish
2
4
s = x
Distance drifted in total time t
The motion of a single electron in the presence of an electric field E. During a time
interval ti, the electron traverses a distance si along x. After p collisions, it has drifted
a distance s = x.
Fig 2.4
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
S =  a2
=u

a
u
Electron
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.
Fig 2.5
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Strained region by impurity exerts a
scattering force F = - d (PE) /dx
I

Two different types of scattering processes involving scattering from
impurities alone and thermal vibrations alone.
Fig 2.6
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Silicon electron mobility
1
t
1
m
=
=
1
+
1
t lattice t impurity
1
ml
+
1
mi
W.F. Beadle, et. al.,”Quick reference
manual for semiconductor engineers,”
Wiley, NY, 1985.
Diffusivity (cm2/s)
Mobility (cm2/V-s)
2000
Inconel-825
NiCr Heating Wire
1000
Iron
Tungsten
Resistivity (n m)
Monel-400
T
Tin
100 Platinum
Copper
Nickel
Silver
10
100
1000
10000
Temperature (K)
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
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)