Light Emitting Diodes
OUTLINE
Semiconductor Band structure and p-n junctions: a
revision
Absorption and Luminescence processes
Materials
Bandstructure modification: Alloying
Electronic Bandstructure
In solid-state physics, the electronic band structure (or simply band
structure) of a solid describes those ranges of energy an electron is
"forbidden" or "allowed" to have
Band structure derives from the diffraction of the quantum
mechanical electron waves in a periodic crystal lattice with a specific
crystal system and Bravais lattice
The band structure of a material determines several characteristics,
in particular the material's electronic and optical properties
Metals
In a metal, the various energy bands (eg 2s, 2p, 3s etc)
overlap to give a single energy band that is only partially full
of electrons
There are states with energies up to the vacuum level,
where the electron is free
Metals have no forbidden band, because the valence band
overlaps the conduction band. Consequently, in metals all
electrons will contribute to the comparably high conductivity
The electrons in the energy band of a metal are loosely
bound valence electrons which become free in the
crystal and thereby form a kind of electron gas
It is this electron gas that holds the metal ions together in
the crystal structure and constitutes the metallic bond
Insulators
Contrarily, an insulator is characterized by a large energy
gap
Therefore, a relatively high energy is necessary to lift
valence band electrons into the conduction band
That is why the thermal generation of carriers is extremely
weak and at room temperature pretty unlikely, i.e. no
mobile charges are available within the insulator
Semiconductors
The intrinsic semiconductor is neither as a good
conductor as the metals are, nor an insulator
The electron and hole concentrations are equal
However the electron and hole concentrations can be
modified by doping
Semiconductor Bandstructure
k: wavevector in electron wave
function
In free space, momentum of
electron = ħk
Energy = ħ2k2 / 2mo
In a crystal, E = E(k)
The relation between E and k is the
semiconductor bandstructure
Top of VB in most semiconductors
occurs at k=0 (zero effective
momentum)
Doping
(a) intrinsic semiconductor: Fermi level in the centre of
bandgap
Fermi level: Under equilibrium conditions, the
Fermi level occurs where there is a fifty percent
probability of an electron occupying the level
n-type doping
By adding impurities that
donate additional
electrons to the CB, the
electron concentration n
will be larger than the
hole concentration p
The Fermi level must be
closer to Ec than Ev
p-type doping
By adding impurities to
the semiconductor that
remove electrons from
the VB and thereby
generating holes
The fermi level EF is
closer to Ev than EC
Forming a p-n junction
Two isolated p and n-type semiconductors (same
material) with same Eg
An important property of Fermi energy EF is that in a system in
equilibrium, the Fermi level must be spatially continuous
A difference in Fermi level is equivalent to electrical work eV, which
is either done on the system or extracted from it
When 2 semiconductors are brought together, the Fermi level must
be uniform through the 2 materials and the junction at M, which
marks the position of the metallurgical junction
Band banding is needed around the junction at M to
keep the bandgap the same
An electron on the n-side at Ec must overcome a PE
barrier to go over to Ec in the p-side
This PE barrier is eVo, where Vo is the built-in potential of
a pn junction
Band banding around M accounts not only for the
variation of electron and hole concentration in this
region, but also for the effect of the built-in potential
Open-circuit pn junction
No net current
Forward biased pn junction
PE barrier reduced
Electrons at Ec in the n-side can now readily overcome
the barrier and diffuse to the p-side
Reverse biased pn junction
PE barrier is increased
Diffusion current due to electrons is now negligible
Luminescence
Electrons injected into
excited state band and
relax to the lowest
available level
Drop to empty level in
ground state by emitting
a photon
Empty levels generated
by injection of holes
Basis of operation of an
LED
I-V characteristics of pn junction
Absorption in Semiconductor
Conversion of light into
electron-hole pairs
Ef Ei
Interband transitions possible
over a continuous range of
energies
E g
Creates hole in initial state,
electron in final state, thus
electron-hole pair
Application in photodetectors
Direct and Indirect Interband Transitions
Group IV vs III-V Semiconductors
Group IV: Silicon or Germanium
Naturally occuring
Si: bandgap of 1.2eV, but indirect
III-V, also know as compound semiconductors
Grown epitaxially by mixing group III and group V
elements
Lots of examples: GaAs, GaN, InP……..
Many have direct bandgaps: suitable for luminescence
Materials
Light emitted is close
to semiconductor
bandgap
For emission at a
particular desired
wavelength, one has
to choose a specific
semiconductor
What if it’s not available?
For instance,
InAs has a bandgap of 0.36 eV
GaAs has a bandgap of 1.42 eV
Desired wavelength of absorption/ emission is 0.96 eV?
Solution: BANDGAP ENGINEERING
Create a new material by combining different
semiconductors by alloying different materials
Alloying
An alloy (such as AlxGa1-xAs) can be formed by mixing two
semiconductors (such as AlAs and GaAs) via an appropriate
epitaxial growth technique such as LPE, MBE or MOCVD
In most semiconductors the two (or more) components of the
alloy have the same crystal structure so that the final alloy
also has the same crystal structure
For such materials the lattice constant obeys the Vegard’s Law for
the alloy AxB1-x
aalloy = xaA + (1-x) aB
The alloys should be grown on lattice-matched substrate
Lattice Matching
The bandstructure of alloys is difficult to calculate in
principle since alloys are not perfect crystals even if they
have a perfect lattice
This is because the atoms are placed randomly and not
in any periodic manner
In most alloys there is a bowing factor arising from the
disorder due to the alloying
One usually defines the bandgap by the relation
Eg (alloy) = a + bx + cx2
where c is the bowing parameter
Experimentally determined relations
Lattice constant vs composition
Energy Gap vs Lattice Constant
Important information
obtained from chart:
(1) determine which
semiconductors can
be alloyed
(2) determine suitable
substrate for an alloy
(3) the bandgap of a
particular alloy (and
dependence on
composition)
(4) direct or indirect
(solid or dash lines)
Example: GaAs-AlAs Alloy
Excellent lattice match of AlxGa1-xAs with GaAs for all Al mole fraction
(mismatch less than 0.13%)
Bandgap varies from 1.42 eV (GaAs) to 2.14 eV (AlAs)
AlxGa1-xAs changes from direct bandgap to indirect bandgap material
for x > 0.37
Wide applications in high speed heterojunction devices (HEMTs and
HBTs) and optoelectronic devices (LEDs and LDs)
Quarternary Alloys
Example: GaInAsN
Alloy of GaAsN and InAsN
Wide applications in optical communications: 1.3 m and 1.55 m
Materials for visible light emission
