4.
SEMICONDUCTOR DEVICES II
PREVIOUS LECTURE
Introduced some basic semiconductor devices.
pn junction
Formed by combining p-type and n-type doped
semiconductors.
Ec
EF
Ev
n-type
p-type
Considered effect of applying external bias Vext.

rectifying I-V behaviour
I
V
INTRODUCTION TO LIGHT-EMITTING DEVICES
Many semiconductor devices are based on pn junction.
These include devices that involve emission or
absorption of electromagnetic radiation e.g. light
emitting diodes, solar cells, …
Absorption
solar panel
Emission
LED
In order to understand such devices, need to consider
how electromagnetic radiation interacts with
semiconducting material.
Visible (and near-visible) wavelengths.
(photon energies ph  g)
4.1 ABSORPTION
Band diagram of semiconductor (in real space).

c

Eg
Eph
v
x
i.e. plotted over extent of semiconductor
Earlier, saw how thermal energy can excite an electron
out of valence band across Eg into conduction band.
Can also do this by shining light onto the semiconductor.
Absorption of photon and Excitation of electrons across
Eg occurs if
Eph  Eg
[Eph = energy of incident photons = (hc/)]
Can also plot band diagram as function of wavevector k
(Unit 3) i.e. in reciprocal space
In case of direct gap semiconductors:
minimum in conduction band lies directly above
maximum in valence band in -k diagram

conduction
band
g
ph
valence
band
k
Incident photon, energy ph
If ph < g, photon does not have enough energy to
promote an electron from valence to conduction band.
If ph  g, photon can promote an electron across gap
from valence to conduction band. i.e. absorption of a
photon
If ph > Eg, electron excited into conduction band (and
hole in valence band) will have some excess energy (and
momentum).
Can find these using conservation of energy and
momentum.
E
Eph
E=0
k=0
k
Before: electron in VB + incoming photon
After:
electron in CB
Momentum:
Energy:
k ph  k v  k c
 2 k v2
 2 k c2
E 
E 
ph 2mv
g 2mc
Wavevector in conduction band - kc
Wavevector in valence band - kv
Wavevector of incident photon - kph
mc*, mv* - effective masses in conduction and valence
bands
2 simultaneous eq’ns for kv and kh. Can solve!
Can also simplify since for optical (and near-optical)
photons:
k ph  kc , kv
so can usually neglect momentum of photon.
i.e. k  0 . Vertical transition.
ph
[See Workshop Q.5]
4.2 EMISSION OF ELECTROMAGNETIC
RADIATION
Essentially the reverse of the absorption process.
Recombination of electron in conduction band with hole
in valence band; energy released emitted as photon of
well-defined frequency.
For process to occur, semiconductor must have direct
gap.



E
g
g
k
Fig.1
ph
k
Fig.2
Electrons excited into conduction band by some process
e.g. forward biasing of material
Holes excited in valence band.
These rapidly thermalise to occupy states near band
edges. i.e. energy transferred to lattice vibrations [Fig.1]
Probablility of recombination greatest for states near
band edges.
Energy released in recombination event is g i.e. ph = g
[Fig.2]
Both energy and momentum conserved (  k  0)
4.3 LIGHT EMITTING DIODES -
LEDs
LEDs make use of emission process in semiconductors.
Consist of pn junction of a direct gap semiconductor,
operated in forward bias.
Basic operation
1. Electrons from n-region diffuse across depletion layer
into narrow region just inside p-side.
2. Here, they recombine with holes, emitting photons.
3. Wavelength  of light determined by energy gap g.
Eg 
hc

III-V compounds
Many of these are direct gap semiconductors
For GaAs: g = 1.42 eV   = 870 nm (near infrared)
For GaP: g = 2.24 eV   = 550 nm (red region)
Ternary III-V compounds
Alloys between Gp III elements (Al, Ga , In)
and Gp V elements (P, As, Sb), containing 3
elements
e.g. GaAsxP1-x
0x1
g
2.24 eV
1.42 eV

x = 0
x
x=1
(GaAs)
(GaP)


g can be tailored by varying x to give required 
Quaternary III-V compounds
e.g. GaxIn1-xAsyP1-y
0x1
0y1
These types of semiconducting materials allow
fabrication of red , yellow and green LEDs.
I-V Characteristic
Can also estimate g from I-V characteristic.
Recall that in ideal case, can show that
I
V
In forward bias
I = I0[exp{eV/kT} – 1]
So for large V, we should get an exponential increase.
In practice, I increases linearly with V for large V.
Once I is high enough, the series resistance of the diode
limits the exponential increase and Ohmic behaviour is
observed.
[Could be due to contact resistance between metal and
semiconductor, resistivity of the semiconductor, or series
resistance of connecting wires].
So actually get something like:
I
Ohmic Region
V
g/e
Once pn junction is forward biased by value greater
than  Eg/e, large numbers of electrons injected from
n to p, and holes from p to n  I becomes large and
limited by series resistance.
Can extrapolate linear region back to I = 0 to obtain
estimate for g.
In terms of energy bands
c
zero bias
Eg
F
v
n
p
modest forward bias V
eV
large forward bias V
eV
large numbers of electrons flow from n to p
(and holes from p to n) when eV > g and I
is limited by series resistance
4.4 INJECTION LASER
Essentially a pn junction with very heavy doping levels
( 0.1%).
On n-side
concentration of electrons in conduction band
is very high  F effectively moves into bottom of
conduction band
Similarly, for p-side
F effectively moves into top of valence band
So in zero bias
F
n
p
Under forward bias
ph
n
p
If bias is high enough, large numbers of electrons are
injected into states near conduction band edge on p-side.
If enough electrons injected, can get population inversion
(more electrons near conduction band edge than near
valence band edge on p-side).

electron-hole recombination  photon emission

photon can cause recombination of electron in
conduction band, with associated stimulated
emission of second coherent photon
(consequence of population inversion)
Both stimulating and stimulated photons can cause
further stimulated emission
[Can enhance this by sandwiching active p-region
between mirrors]
So can build up narrow coherent beam of monochromatic
radiation [ph  g] . High energy density possible.
Light Amplification by Stimulated Emission of Radiation
4.5 QUANTUM WELL DEVICES
Single layer pn junction laser requires high threshold
current densities  reliability problems.
Alternative Approach
Could consider making laser from a stack of thin active
layers, separated by confining layers.
Each thin active layer can be regarded as quantum well,
in which electrons are confined in 2-D.
Example of a low dimensional structure.
Consider thin layer of GaAs sandwiched between 2
layers of AlxGa1-x As.
g(AlxGa1-xAs)
g(GaAs)
d
AlxGa1-xAs
GaAs
AlxGa1-xAs
z

g(GaAs) – 1.42 eV
1.42 eV < g(Al1-xGaxAs) < 2.16 eV
Assuming d << lateral (in-plane) dimensions:
electrons in GaAs layer confined in potential well

quantisation of electron motion in z-direction
If approximate the potential step to be infinite, can
compare with particle in 1-D box.
Solving Schrodinger eq’n for this gives [as in Unit 2]
h2n2
Ecz 
8me* d 2
n - integer
[Ecz - quantised energy of electrons in conduction band
of GaAs]
Including (unrestricted) in-plane motion of electron
 2 k //2
h2n2
Ec 

2me* 8me* d 2
[k// - in-plane component of wavevector k]
Similarly for quantised states in valence band:
 2 k //2
h2n2
 Eg 
Ev 
2mh*
8mh* d 2



D()  E1/2
z
k
(a)
D()
(b)
(c)
(a) quantised energy levels in quantum well
(b) -k curves, including in-plane motion
(c) Density of states D()
In 2-D
me*
D(E) = 2

[Unit 2]
So D() of 2D electrons within each bound state in well
is independent of 
 steps in D()
As potential well gets wider, energies of bound states
become more closely spaced  steps harder to see
 D() approaches parabolic 3-D form i.e. D()  E1/2
If quantum well structure is to form a light emitting
device e.g. laser , what is wavelength  of emitted light?
Photon emission occurs as result of electron-hole
recombination between bottom of conduction band and
top of valence band (direct gap material).
i.e. for k// =0, and n = 1
So
E ph
h2
h2

 Eg  * 2  * 2

8me d
8mh d
hc
Hence  can be tuned by altering well width d.
In practice, normally use sequence of wells in a
multiquantum well (MQW) structure, rather than a single
well.
AlxGa1-xAs
GaAs