Tunnel Diode
- in a heavily doped p-n junction the depletion region is very
small (~ 10 nm)
- the bottom of the n-side conduction band overlaps the p-side
valence band, see (a)
- with a small forward bias electrons can directly tunnel
across the small depletion region from the n-side conduction
band into the p side valence band, see (b)
- for increased forward voltage the tunnel current ceases as the
two bands do not overlap anymore (regular pn junction)
- the current flowing is a very
sensitive function of the
voltage bias due to the
tunneling which makes the
device useful for applications
in which fast switching is
required
phys4.19 Page 1
Zener Diode
- for large reverse bias voltages p-n junctions called Zener diodes
show a sharp rise of current at the breakdown voltage
- such circuits are used widely in electronics for voltage
stabilization
- avalanche electron multiplication through impact ionization of atoms by electrons
accelerated across the depletion area contribute to reverse current rise
- Zener breakdown is the second mechanism arising from tunneling of electrons from the
valence band of the p-side to the conduction band on the n-side at high reverse bias voltages
phys4.19 Page 2
npn-Junction Transistor
- consists of a thin p-doped region called the
base electrode connected to an n-doped
emitter and collector electrode, see figure
- an npn transistor acts as an amplifier for small signals applied between the emitter and
base electrode that are amplified into a large base-collector signals
- the energy band structure of the npn
transistor at zero bias is shown
- the current in an npn transistor is carried
by electrons
- a pnp transistor would work in an analog
way for holes being the predominant charge
carrier
phys4.19 Page 3
Transistor Bias
- for transistor operation the emitter base
junction is weakly forward biased and the
base collector junction is strongly reverse
biased
- the current from the heavily doped emitter into
the base is carried by electrons
- electrons diffuse across the thin (~ 1 μm) weakly hole doped base electrode into the baseemitter junction and are accelerated by the large reverse bias into the collector
- the input signal power is then amplified at constant current by the large base collector
reverse bias voltage to a larger output power
- a limitation of the npn transistor amplifier is its low input impedance (or low input
resistance), also its power consumption and integration density are not the best
- for some applications an amplifier with higher input impedance, such as a field effect
transistor, is advantageous
phys4.19 Page 4
Field Effect Transistor (FET)
- an FET consists of a n-type channel
connecting source and drain and contacted by
a p-type gate; it is widely used as an
alternative to npn junction transistors
- electrons move from source to drain along an n-type channel
- the pn junction is reverse biased to create a depletion region at the interface, the carrier
density and the source-drain current depend sensitively on the magnitude of the reverse bias
- in reverse bias little current flows into the pn junction giving it a high input impedance
Metal Oxide Semiconductor Field Effect Transistor (MOSFET)
- semiconductor gate replaced by a metal film separated from the channel by a thin oxide
layer
- MOSFETs have high input impedance (up to 1015 Ω) due to capacitively coupled gate and
are also compatible with high integration density
phys4.19 Page 5
Superconductivity
- usual electrical conductors, even the very best ones, have finite resistance determined by
temperature and impurities in the material
- at very low temperatures some metals, alloys and some special chemical compounds can
transport current without resistance, an effect called superconductivity
- Kammerlingh Onnes discovered that resistance of
mercury (Hg) decreased like that of other metals down
to Tc ~ 4.15 K but then lost all of its resistance to
immeasurable levels below that critical temperature Tc
- the resistivity is actually zero as tested in persistent
current measurements
- usual critical temperatures for metallic
superconductors are in the range 0.1 - 10 K
- it is interesting to note that good usual conductors
such as copper (Cu) and silver (Ag) do not become
superconducting
phys4.19 Page 6
The Nobel Prize in Physics 1913
"for his investigations on the properties of matter at low
temperatures which led, inter alia, to the production of liquid
helium"
Leiden University, Leiden, the Netherlands
Heike Kamerlingh Onnes
b. 1853, d. 1926
The Nobel Prize in Physics 1987
"for their important break-through in the
discovery of superconductivity in ceramic
materials"
IBM Zurich Research Laboratory
Rüschlikon, Switzerland
J. Georg Bednorz
Germany
b. 1950
K. Alexander Müller
Switzerland
b. 1927
phys4.19 Page 7
Magnetic Effects
- the critical temperature Tc of a superconductor
depends on the magnetic field (see figure)
- in a type I superconductor the zero resistance
state disappears altogether at a threshold critical
field Bc that depends on the material and the
temperature
- the maximum critical field occurs at zero
temperature
Superconductor Tc and Bc
- because of the limited critical fields of type I
superconductors they are of limited use in
applications for field generation with coils
phys4.19 Page 8
material
Al
Hg
In
Pb
Sn
Zn
Tc [K]
1.18
4.15
3.41
7.19
3.72
0.85
Bc [T]
0.015
0.041
0.028
0.080
0.031
0.005
Meissner Effect
- superconductors are perfectly diamagnetic
- in a type I superconductor field below the
critical field is expelled completely from the
material when cooled through Tc , see figure
- in this Meissner effect screening currents
are induced in the superconductor to cancel the
externally applied field
- this effect distinguishes a superconductor from an ideal conductor
- type II superconductors below a first critical field Bc1 behave like type I superconductors,
above Bc1 and below a second critical field Bc2 magnetic flux can penetrate into the material
bringing it to a mixed superconducting/normal state
- Bc2 critical fields can be high so that these
materials are interesting for generating
magnetic fields
material
Nb3Sn
Tc [K]
18.0
Bc2 [T]
24.5
phys4.19 Page 9
Cooper Pairs and Bardeen-Cooper-Schrieffer (BCS) theory
- in conventional superconductors electrons attract each other through deformations induced
in the crystal lattice
- materials with strong lattice vibrations are usually poor conductors at room temperature but
maybe superconductors at low temperatures
- a hint of this fact was first found when it was noted that the Tc of different superconductors
depends on the isotope used, e.g. Tc(199Hg) = 4.161 and Tc(204Hg) = 4.126
- two electrons (Fermions) form a single Cooper pair (Boson) with the electrons being in a
singlet state with zero angular momentum
- the binding energy Eg, also called the gap energy, is
typically on the order of 1 meV and can be measured using
microwave absorption
- at temperatures above 0 K some Cooper pairs are broken up
by thermal fluctuations, the remaining electrons interact
with the Cooper pairs effectively reducing the gap energy
(see figure)
phys4.19 Page 10
- at the critical temperature Tc the energy gap disappears, there are no more Cooper pairs and
thus the material ceases to be superconducting
- electrons (fermions) in a superconductor form Cooper pairs with
total spin S = 0
- the Cooper pair is a boson, any number of bosons can be in the same quantum state ψ
- Cooper pairs in a super conductor form a Bose-Einstein condensate
- all Cooper pairs in a superconductor are described by a single macroscopic wave function
minimizing the system energy
where ρ is the Cooper pair density and φ their phase
- when a current flows in a superconductor, all Cooper pairs have the same non-zero linear
momentum
- no scattering of individual electrons that would lead to finite resistance can occur
phys4.19 Page 11
Flux Quantization
- Faraday's law relates the current I flowing through a
loop enclosing an area A and the magnetic flux Φ = A B
in the loop
- the flux Φ in the superconductor is quantized because
the wave function describing the Cooper pairs in the ring
must be a continuous periodic function around the loop
(compare to Bohr model)
- the flux quantization rule is
- with the magnetic flux quantum
phys4.19 Page 12