Download Allowed and Forbidden Energy Bands may overlap, as in (a)

Allowed and Forbidden Energy Bands
- allowed energy bands associated with different atomic orbitals
may overlap, as in (a)
- the regions between allowed energy bands are called forbidden
bands or band gaps
Electrical Conductivity and Energy Bands
- in sodium (a good metal conductor) there are 2(2l+1) with l = 0
available electron states per atom in the 3s shell only one of which is
filled with the single valence electron
- as a result the 3s shell of sodium is only half filled (see figure)
- thus the electrons are free to change their energies within the 3s
band
- this allows electrons to pick up a kinetic energy from an applied
electric field leading to a electron drift velocity generating current
that makes Na a good metallic conductor
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- magnesium (Mg) has an electron configuration 1s2 2s2 2p6 3s2, i.e. it has a filled 3s shell
- therefore the filled 3s shell on its own would not allow for electrons to gain energy, if the 3p
band was separated by a gap from the 3s band
- in Mg however, the 3s and 3p bands overlap in energy (see figure)
- the 3p band can accommodate 2(2l+1) = 6 electrons per atom, i.e. jointly the 3s and the 3p
orbitals form a band that can accommodate 8 N electrons
- thus the conduction band is only 25 % filled rendering Mg a good conductor
Insulators
- in insulators the electron states in the valence band are
completely filled
- the next higher available energy band, the conduction
band, is separated from the valence band by a band gap
- in an insulator the band gap is large enough in energy so that electrons are not thermally
excited across it
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- carbon (C, 1s2 2s2 2p2) is an insulator even
though it has a only partially filled p band
- at some intermediate C-C separation an
overlapping sp band accommodating 8N electron
states is formed
- at the equilibrium separation however the band
is split into two bands accommodating 4N
electrons (hybridization) each that are separated
by an energy gap of 6 eV making Carbon
(diamond) an insulator
- similar reasoning applies to silicon (Si, 1s2 2s2 2p6 3s2 3p2)
- for Si the energy gap is only 1 eV
- at room temperature a noticeable number of electrons are thermally excited across the energy
gap, where states are available and electrons can gain energy and conduct current
- because of the intermediate conductivity such materials are called semiconductors
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Impurity Semiconductors
- small amounts of impurities can drastically change the conduction in semiconductors
- consider arsenic atoms (As, 4s2 4p3) embedded in a Si crystal, 4 of the electrons form
covalent bonds with the Si, the fifth electron is only weakly bound (0.05 eV) and can easily
move in the crystal and contribute to conduction
- the arsenic provides electronic energy levels, called
donor levels, close to the conduction band
- these donor levels supply electrons (negative charges) to the current transport (n-type
semiconductor)
- similar reasoning applies for gallium (Ga, 4s2 4p1) impurities embedded in Si that can act
as acceptor levels
- in this case an electron misses to form 4 covalent bonds
- at little energy cost an electron can fill the vacancy,
but leaving another vacancy (a hole) behind
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Electron and Hole Current Transport
- in a semiconductor doped with n-type impurities (P,
Sb, Bi, As) electrons are the dominant (majority)
charge carriers responsible for electrical current
- in a p-doped (Ga, In, Tl) semiconductor holes are the
dominant charge carries
- in an applied field holes move in the opposite direction
of electrons but contribute a current in the same
direction (see figures)
- in semiconductors small amounts of dopants on the
order of 1 ppb can drastically change the conductivity
by orders of magnitude
- this control of conductivity is of enormous importance
in all semiconductor technology
- other semiconductors are (group IV) Ge
and (groups III-V) GaAs, GaP, InSb, InP
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Semiconductor Devices
- most microelectronics devices used industrially consist of junctions (interfaces) between ntype and p-type doped semiconductors
- with modern photolithography technology millions of such junctions (and additionally
capacitors, resistors and inductors) can be fabricated on a single chip of a few square
millimeter area
fabrication technology:
- diffusion of (p,n) dopants in vapor form into a single crystal semiconductor wafer
through a mask
- the mask is generated optically by exposing a light sensitive material (resist) through a
metalized mask containing an image of the structure
- the resolution is (diffraction) limited by the wavelength of the light (e.g. 193 nm UV
light) used in this process to about 65 ~ 100 nm
- future reduction in the feature size may require use of alternative radiation sources (Xrays, electron or ion beams)
phys4.18 Page 6
Electronic Circuits
basis of modern information and communication based society
intel dual core processor (2006)
first transistor at Bell Labs (1947)
2.000.000.000 transistors
smallest feature size 65 nm
clock speed ~ 2 GHz
power consumption 10 W
phys4.18 Page 7
Junction Diode
- in a junction between a p-type and an n-type material current
transport occurs preferentially in one direction, see I-V curve
- in the p-region current is transported by holes, in the nregion by electrons
At no bias voltage (V=0):
- in the p-region electrons are thermally excited
from the valence band into acceptor states
generating free holes (p majority carriers)
- also electrons are thermally excited into the
conduction band creating free electrons (p-side
minority carriers)
- equivalently, in the n-region electrons are
thermally excited from donor states into the
conduction band generating free electrons (nside majority carriers)
- also electrons are thermally excited into the
conduction band creating holes in the valence
band (n-side minority carriers)
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Thermal and Recombination Currents
- the minority carriers (electrons on the p-side, holes on the n-side) can diffuse across the
junction interface (electrons from p to n and holes from n to p) generating a small thermal
current Ith
- the majority carriers (holes on the p-side and electrons on the n-side) are thermally excited
across the barrier recombining with majority carriers in the other part of the junction
(electrons with holes on the p-side and holes with electrons on the n-side) generating a
recombination current Ir
- with no bias applied the thermal and recombination currents are small and balance each
other and there is no net transport current
- the Fermi energy is identical in both regions
- the recombination current is very sensitive to bias voltage across the junction (because of
the bias dependence of the thermal barrier), whereas the thermal current is independent of
bias, this fact is responsible for the asymmetry of the current voltage characteristic
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Reverse Bias (V < 0)
- voltage applied to the junction with p-end
negative and n-end positive
- holes diffuse to the p-end, electrons to the n-end
which suppresses recombination current
- electron hole pairs are still thermally excited
and sustain a small constant reverse current
Forward Bias (V>0)
- voltage applied to the junction with p-end
positive and n-end negative pushing electrons
and holes into the junction area
- recombination current increases at the
junction because of the constant supply of
electrons and holes and the increase of the
electron energy on the n-side by eV
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p-n Junction
- acts as a rectifier for electrical current, i.e. a large forward
recombination current flows for positive bias and a small
reverse thermal current flows for negative bias
- a depletion region is formed at the p-n junction interface
where at zero bias electrons from the donor levels on the n-side
recombine with holes of the acceptor levels on the p-side
reducing the number of charge carriers
- the extent of the depletion region is typically a few micron
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Light Emitting Diodes (LEDs)
- carrier recombination can generates photons in a forward biased diode
• efficiency ~ 20 %
• semiconductor diodes
(GaAs)
• power P ~ 0.01 - 5 W
• General Electric (1962)
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Applications
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