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10610310010-310-610-910-1210-1510-18 109
Semiconductors Conductors
1012
Conductivity (Ωm)-1
AgGraphiteNiCrTeIntrinsic Si
DegeneratelyDoped Si
Insulators
Diamond
SiO2
Superconductors
PETPVDF
AmorphousAs2Se3
Mica
Alumina
Borosilicate Pure SnO2
Inorganic Glasses
Alloys
Intrinsic GaAs
Soda silica glass
Many ceramics
MetalsPolypropylene
Figure 2.24: Range of conductivites exhibited by various materialsFrom Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca
Conductivity (σ) = 1/Resistivity(ρ)
Vibrating Cu+ ions
u∆x
Ex
V
(a) (b)
Fig. 2.2 (a): A conduction electron in the electron gas movesabout randomly in ametal (with a mean speedu) being frequently and randomly scattered by bythermal vibrations of the atoms. In the absence of an appliedfield there is no netdrift in any direction. (b): In the presence of an applied field, Ex, there is a netdrift along thex-direction. This net drift along the force of the field issuperimposed on the random motion of the electron. After many scattering eventsthe electron has been displaced by a net distance,∆x, from its initial positiontoward the positive terminal
From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca
τI
Strained region by impurity exerts ascattering force F = - d(PE) /dx
Fig. 2.5: Two different types of scattering processes involving scatteringfrom impurities alone and thermal vibrations alone.From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca
τΤ
From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca
(b)
Fig. 2.31: Grain boundaries cause scattering of the electron andtherefore add to the resistivity by Matthiessen's rule. For a verygrainy solid, the electron is scattered from grain boundary to grainboundary and the mean free path is approximately equal to themean grain diameter.
Grain 1
Grain 2
GrainBoundary
(a)
From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca
D
Jx
Fig. 2.32: Conduction in thin films may be controlled byscattering from the surfaces.
Fig. 2.6: The resistivity of various metals as a function of temperatureabove 0 °C. Tin melts at 505 K whereas nickel and iron go through amagnetic to non-magnetic (Curie) transformations at about 627 K and1043 K respectively. The theoretical behavior (ρ ~ T) is shown forreference.[Data selectively extracted from various sources including sections inMetals Handbook, 10th Edition, Volumes 2 and 3 (ASM, MetalsPark, Ohio, 1991)]
ρ ∝ T
Tungsten
Silver
Copper
Iron
Nickel
Platinum
NiCr Heating Wire
Tin
Monel-400
Inconel-825
10
100
1000
2000
100 1000 10000Temperature (K)
Res
istiv
ity (
nΩ m
)
From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca
0.00001
0.0001
0.001
0.01
0.1
1
10
100
1 10 100 1000 10000Temperature (K)
0
0.5
11.5
2
2.5
3
3.5
0 20 40 60 80 100T (K)
ρ ∝ T
ρ ∝ T5
ρ = ρRρ = ρR
ρ ∝ T5
ρ ∝ T
ρ (nΩ m)
Fig.2.7: The resistivity of copper from lowest to highest temperatures(near melting temperature, 1358 K) on a log-log plot. Above about100 K, ρ ∝ T, whereas at low temperatures, ρ ∝ T 5 and at thelowest temperatures ρ approaches the residual resistivity ρR . The
inset shows the ρ vs. T behavior below 100 K on a linear plot ( ρRis too small on this scale).From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca
Res
istiv
ity (n
Ω m
)
Temperature (K)
0
20
40
60
0 100 200 300
ρT
ρI
ρCW
100%Cu (Annealed)100%Cu (Deformed)
Cu-1.12%NiCu-1.12%Ni (Deformed)
Cu-2.16%Ni
Cu-3.32%Ni
Fig. 2.8: Typical temperature dependence of the resistivity ofannealed and cold worked (deformed) copper containing variousamount of Ni in atomic percentage (data adapted from J.O. Linde,Ann. Pkysik, 5, 219 (1932)).
From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca
Re
sist
ivity
(nΩ
m)
Superconductivity
State of zero resistivity at low temperature, low current, low magnetic field.
Perfect diamagnetism: Complete repellence of external magnetic field.Application: levitation by applied external magnetic field.
• 1911: Dutch physicist Heike Kamerlingh Onnes. Resistivity of mercury at 4K disappears. In 1913 he won Noble prize for his research in this area
• 1933. Walter Meissner and Robert Ochsenfeld discovered that a superconducting material will repel a magnetic field.
- A magnet moving by a conductor induces currents in the conductor. This is the principle upon which the electric generator operates. But, in a superconductor the induced currents exactly mirror the field that would have otherwise penetrated the superconducting material - causing the magnet to be repulsed. This phenomenon is known as diamagnetism and is today often referred to as the "Meissner effect".
- See levitation of magnet over a superconductor
Reference: http://superconductors.org/
History of Superconductor History of Superconductor (continued)
1941: niobium-nitride was found to superconduct at 16 K.
1953: vanadium-silicon displayed superconductive properties at 17.5 K.
1957: The first widely-accepted theoretical understanding of superconductivity was advanced in by American physicists John Bardeen, Leon Cooper, and John Schrieffer (below). Their Theories of Superconductivity became know as the BCS theory - derived from the first letter of each man's last name - and won them a Nobel prize in 1972.
Reference: http://superconductors.org/
1962: scientists at Westinghouse developed the first commercial superconducting wire, an alloy of niobium and titanium.
1986: A truly breakthrough discovery: Alex Müller and Georg Bednorz(below), researchers at the IBM Research Laboratory in Switzerland, created a brittle ceramic compound (Lanthanum, Barium, Copper and Oxygen compound) that superconducted at the highest temperature then known: 30 K.
1993: Prof. Dr. Ulker Onbasli at the University of Colorado discover the current system of ceramic superconductors with the highest transition temperatures are the mercuric-cuprates.
A. Schilling, M. Cantoni, J. D. Guo, and H. R. Ott of Zurich, Switzerland hold the world record Tc of 138 K. It is a thallium-doped, mercuric-cupratecomprised of the elements Mercury, Thallium, Barium, Calcium, Copper and Oxygen.
History of Superconductor (continued)
Reference: http://superconductors.org/
Type of Superconductor
Type 1: Metals at extremely cold temperature
They require incredible cold to slow down atomic vibrations sufficiently to facilitate unimpeded electron flow.
0.85 K Zinc (Zn)
0.915 K Molybdenum (Mo)
1.083 K Gallium (Ga)
1.175 K Aluminum (Al)
1.38 K Thorium (Th)
1.40 K Protactinium (Pa)
3.72 K Tin (Sn)
4.15 K Mercury (Hg)
4.47 K Tantalum (Ta)
4.88 K Lanthanum (La)
7.196 K Lead (Pb)
Critical temperatureMetal
• Has a distinct critical temperature• Completely repel magnetic field
Type of Superconductor
Type 2: metallic compounds and alloys
93 KY2Ba4Cu7O15
93 K YBa2Cu3O7+
126 K Tl1.6Hg0.4Ba2Ca2Cu3O10+
127-128 KTl2Ba2Ca2Cu3O10
133-135 K HgBa2Ca2Cu3O8
138 KHg0.8Tl0.2Ba2Ca2Cu3O8.33
Critical temperatureMetal• Critical temperature is broad
• Allow some penetration of magnetic field
N
S
MagnetSuperconductor above Tc
N
S
Magnet
Surface currents Superconductor below Tc
Figure 8.45: Left: A magnet over a superconductor becomes levitated.The superconductor is a perfect diamagnet which means that there canbe no magnetic field inside the superconductor.Right: Photograph of a magnet levitating above a superconductorimmersed in liquid nitrogen (77 K). This is the Meissner effect.(SOURCE: Photo courtesy of Professor Paul C.W. Chu.)From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca
Why repulsion? Magnetic field is partly excluded from the superconductor. Hence, the same repulsion as between a magnet and a diamagnetic.
Why attraction? The magnetic flux lines that managed to penetrate the superconductor get pinned (trapped) there by microscopic inhomogeneities. When the magnet is lifted up, the superconductor holds its magnetic lines and follows the magnet. How to help magnetic lines penetrate the superconductor? Place the superconductor close to the magnet already at high temperature (movie 2) or push the magnet hard towards the supercondictors (movie 3).
Fig: Schematic visualization of magnetic field lines
Reference: http://www.fys.uio.no/super/levitation/
Movie1: Levitation in action
A superconductor is immersed in liquid nitrogen to provide cooling below the critical temperature. A magnet is placed in the air above the superconductor and left there levitating. Nothing but magnetic interaction keeps the magnet from falling down.
Reference: http://www.fys.uio.no/super/levitation/
Movie2: Lifting superconductor without touching it
At room temperature magnetic field lines from the magnet penetrate the superconductor without restraint. After cooling by liquid nitrogen they get trapped by microscopic inhomogeneities in the superconductor. The trapped magnetic lines then serve as invisible threads holding the two objects together at a certain distance.
Reference: http://www.fys.uio.no/super/levitation/
Movie3: Smooth landing during warming up
When the superconductor is taken out of the liquid nitrogen, its temperature slowly starts increasing. As a result, the superconducting properties weaken, and the levitation force gradually gives way to the gravity.
Reference: http://www.fys.uio.no/super/levitation/
A small size with gigantic 5000 horse power motorusing superconductor wire in the coil.
• High-power motor
Uses of superconductors
Uses of superconductors
• Magnetic levitation (Maglev):
The Yamanashi MLX01 MagLev train opened in 1990. The newestversion attain the world record speed of 531 km/h (approximately thesame speed as of a commercial airplane)
However, bio-hazard possibility of very high magnetic field and high cost discourage commercialization.
Reference: http://www.rtri.or.jp/rd/maglev/
Uses of superconductors
• Magnetic Resonance Imaging (MRI)
By impinging a strong superconductor-derived magnetic field into the body, hydrogen atoms that exist in the body's water and fat molecules are forced to accept energy from the magnetic field. They then release this energy at a frequency that can be detected anddisplayed graphically by a computer.
Fig: MRI of a human skull
Reference: http://superconductors.org/
Semiconductivity
Conductivity:
Intrinsic Semiconductor: concentration of charge carrier depends of amount of availability of thermal energy for excitation of electrons to become conduction electrons. Hence, the higher is the temperature, the higher is the conductivity.
n is number of conducting speciesµ is mobility of the conducting species
Addition of Group III element adds available holes for movement of electrons
Ene
rgy
of e
lect
rons
Addition of Group IV element adds extra electrons for conduction
Ene
rgy
of e
lect
rons
Band gap (gap between valence band and conduction band) is characteristic of each kind of element or compound.
The smaller the band gap, the higher the conductivity.
Compound which exhibit semiconductivity:Transition metal oxides: Mixed valency semiconductor.Ex: NiO has low conductivity. Upon oxidizing in air at 800oC, it
becomes Ni1-XO. Conductivity is due to electron transfer between Ni2+ and Ni3+. Disadvantage: difficult to control the degree of oxidation (amount of Ni3+ in the system); therefore conductivity is not predictable.
One method to control amount of Ni3+ is by addition of Li+ as following
Applications: pn junction, transistor, etc.
Flow of electrons is possible when applying negative potential at n-type side.Flow of electrons in the opposite direction is not possible.This works as rectifier.
Conductivity1. Electronic Conductivity: charge carriers are electrons (or holes).
found in metals, superconductors, semiconductor.2. Ionic Conductivity: charge carriers are ions in the system.
found in liquid electrolyte, solid electrolyte.
Conduction by ions: This occurs when ions have enough thermal energy to escape from their sites, and move to adjacent lattice sites. Therefore, high temperature, at which thermal energy is high, and number of defect (vacancy) is also high.
Ex: NaCl at 800oC: σ = 10-3 (ohm-m)-1
at 25oC: σ = 10-12 (ohm-m)-1