Chapter 5a

Chapter 5: Semiconductor Laser

Resonant Cavity
• A radio-frequency oscillator consists of an amplifier, a
tuned circuit and a feedback mechanism.
– The feedback connects the amplifier output to its input, causing
the signal to increase as it periodically passes through the
amplifier.
– A steady state is reached when the system losses are exactly
made up by the gain through the amplifier.
– System losses constitute of power extracted from the oscillator
as useful output & heating loss.
– The tuned circuit determines the oscillation frequency.

Optical resonant cavity
• A laser is a Very-High-Frequency oscillator
– Also refer to an optic oscillator
• The laser consists of a cylindrically shaped medium with
mirrors attached at each end.
– The medium provides the amplification
– Properties of the medium determine the output frequency and
spectral width of the laser
• Mirrors provide feedback for the light oscillator,
reflecting the light back & forth through the amplification
medium.
• Power exits the laser through one of the mirrors, which is
partially transmitting.

Fig.A: A laser cavity consists of an amplifying
medium and optical cavity

Fabry-Perot resonator
• The two mirrors form a cavity called Fabry-Perot resonator
– In which two wave exist, one moving to the right and one moving
to the left
– The total field in the cavity is the sum of the two moving waves.
– This results in the standing-wave pattern
• To produce standing-wave pattern, the cavity must be an
integral number of half wavelength long, that is L = ml/2.
– where l is the wavelength as measured in the material within the
cavity and m is a positive integer.

Fig. B: Stationary Standing-wave
pattern
L = l/2
L = 2l/2
L = 3l/2
L = 4l/2
L = 4l/2

Cavity resonant frequencies
• Only wavelengths satisfying l=2L/m can exist inside the
cavity in a steady state.
– Any wave of another length interferes destructively with itself &
attenuates very quickly
– We say that the cavity is resonant at wavelength satisfying
l=2L/m.
• The resonant frequencies are found as
f = mc/2nL
• The longitudinal modes of the cavity is shown in Fig. C
– The spacing between adjacent cavity longitudinal mode is
D f = c/2nL

Fig. C: Allowed modes and their frequency due to stationary EM waves
within the optical cavity.
f
Allowed Oscillations (Cavity Modes)
L
Stationary EM oscillations
Mirror
Mirror
Dfc =c/2nL
fm–1 fm fm+1 fm+2 …
… fm+3

Stimulated emission and photon amplification
• An electron in an atom can be excited from an energy
level E1 to a higher energy level E2 by the absorption of
a photon energy
hu= E2 – E1
• When an electron at a higher energy level transits
down in energy to an unoccupied energy level, it emit a
photon
• There are two possibilities for the emission process
1. The electron undergo the downward transition by itself
spontaneously
2. It can be induced to do so by another photon

Spontaneous emission
• The electron falls down in energy from level
E2 to E1
– emits a photon of energy hu = E2–E1 in a random
direction as shown in Fig.1
– A random photon is emitted
• The transition is spontaneous provided that
the state with energy E1 is not occupied
• The emission process during the transition of
electron from E2 to E1 can be thought of as if
the electron is oscillating with a frequency u.

E1
E2
hu
(a) Absorption
hu
(b) Spontaneous emission
hu
(c) Stimulated emission
In
hu
Out
hu
E2
E2
E1 E1
Absorption, spontaneous (random photon) emission and stimulated
emission.
© 1999 S.O. Kasap,Optoelectronics(Prentice Hall)
Fig.1 : Stimulated emission and
photon amplification

Stimulated emission
• An incoming photon of energy hu = E2 – E1
stimulates the whole emission process by
inducing the electron at E2 to transit down to E1
as shown in Fig.1
– The emitted photon is in phase with the incoming
photon
– It is in the same direction, it has the same
polarization and it has the same energy since hu =
E2–E1

Stimulated emission, cont
• During stimulate emission, the E-field of
incoming photon couples to the electron and
drives it with the same frequency as the photon
– The forced oscillation of the electron at a frequency
u = (E2–E1)/h causes it to emit EM radiation whose
E-field is in total phase with that of stimulating
photon.
– When the incoming photon leaves the site, the
electron return to E1because it has emitted a photon
of energy hu = E2–E1

Population Inversion
• Stimulated emission is the basis for obtaining
photon amplification
– since one incoming photon results in two
outgoing photons which are in phase.
– The incoming photon should not be absorbed by
another atom at E1.
• When we are considering a collection of atoms
to amplify the light, we must have the majority
of the atoms at the energy level E2
– When there are more atoms at E2 than at E1, we
then have what is called a population inversion

Optical pumping and stimulated
emission
• For three energy level system
– An external excitation causes the atoms in this system to be
excited to E3, which is called optical pumping
– From E3, the atoms decay rapidly to an energy level E2
• The state E2 is a long-lived state
– Since the atoms cannot decay rapidly from E2 to E1, they
accumulate at this energy level causing a population inversion
between E2 and E1
– When one atom at E2 decays spontaneously, it emits a photon
which can go on to a neighboring atom and cause that to execute
stimulated emission
– The photons from the latter can go on to the next atom at E2 and
cause that to emit by stimulated emission & so on.
– The result is an avalanche effect of stimulated emission
processes with all the photons in phase.

E1
hu13
E2
Metastable
state
E1
E3
E2
hu32
E1
E3
E2
E1
E3
E2
hu21
hu21
Coherent photons
OUT
(a) (b) (c) (d)
E3
The principle of the LASER. (a) Atoms in the ground state are pumped up to the energy levelE3 by
incoming photons of energyhu13 = E3–E1. (b) Atoms at E3 rapidly decay to the metastable state at
energy level E2 by emitting photons or emitting lattice vibrations;hu32 = E3–E2. (c) As the states atE2
are long-lived, they quickly become populated and there is a population inversion between
E2 and E1.
(d) A randomphoton (from a spontaneous decay) of energy
hu21 = E2–E1 can initiate stimulated
emission. Photons fromthis stimulated emission can themselves further stimulate emissions leading to an
avalanche of stimulated emissions and coherent photons being emitted.
© 1999 S.O. Kasap, Optoelectronics(Prentice Hall)
IN
Fig.2 : Principle of the LASER

Light Amplification by Stimulated Emission of
Radiation
• At the end of the avalanche of stimulated
emission processes, the atoms at E2 would
have dropped to E1
– It can be pumped again to repeat the stimulated
emission cycle again
• The emission from E2 to E1 is called the lasing
emission
– The system we have just described for photon
amplification is a LASER, an acronym for
“Light Amplification by Stimulated Emission of
Radiation”

Upward transition rate
• Consider a medium as in Fig 1
– N1 atoms per unit volume with energy E1
– N2 atoms per unit volume with energy E2
• The rate of upward transition from E1 to E2by photon
absorption will be proportional to
– The number of atoms N1
– The number of photon per unit volume with energy hu = E2–E1.
Upward transition rate: R12 = B12 N1 r (hu) (1)
where B12 is a proportionality constant (Einstein coefficient)
r (hu) is the photon energy density per unit frequency
which represents the number of photon per unit volume with
an energy hu

Downward transition rate
• The rate of downward transitions from E2 to E1 involved
spontaneous and stimulated emission depends on
– The concentration of N2 of atoms at E2
– Both N2 and the photon concentration r (hu) with energy hu (=
E2–E1)
Downward transition rate:
R21 = A21 N2 + B21 N2 r (hu) (2)
– First term is due to spontaneous emission (no need
photon to drive it)
– Second term is due to stimulated emission which
requires photons to drive it.
where A21 & B12 are the Einstein coefficients for spontaneous
and stimulated emission respectively

Thermal Equilibrium
• To find the coefficients A21 , B12 , B21 , we consider the medium in
thermal equilibrium
• There is no net change with time in the populations at E1 and E2 which
means
R12 = R21 (3)
• In thermal equilibrium, Boltzmann statistics demands that
(4)
where kB is the Boltzmann constant & T is the absolute temperature
• In thermal equilibrium, radiation from the atom must give rise to an
equilibrium photon energy density that is given by Planck’s black body
radiation distribution law,
( )



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
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c
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eq
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Conclusion: stimulated emission
• There are two important conclusion
1. For stimulated photon emission to exceed photon
absorption, we need to achieve population
inversion, that is N2 > N1.
• According to Boltzmann statistics, N2 > N1 implies a
negative absolute temperature
• The laser principle is based on non-thermal equilibrium
2. For stimulated emission far exceed spontaneous
emission, we must have a large photon
concentration, which is achieved by building an
optical cavity to contain the photons

Principle of the Laser Diode
• Consider a degenerately doped direct band gap
semiconductor pn-junction whose band diagram is shown
in Fig.3
– Degenerate doping means that the Fermi level EFp in the p-side is
in the valence band (VB) and that EFn in the n-side is in the
conduction band (CB)
– All energy levels up to the Fermi level are occupied by electrons
• Without applied voltage, the Fermi level is continuous
across the diode, EFp= EFn.
– The depletion region is very narrow
– High potential energy barrier eVo (Vo is built-in voltage) that
prevents electrons in the n+-side diffusing into the p+-side
– Similar potential barrier also stop hole diffusion.

p+ n+
EFn
(a)
Eg
Ev
Ec
Ev
Holes in V B
Electrons in C B
Junction
Electrons
Ec
p+
Eg
V
n+
(b)
EFn
eV
EFp
The energy band diagramof a degenerately doped p-n with no bias. (b) Band
diagramwith a sufficiently large forward bias to cause populationinversion and
hence stimulated emission.
Inversion
region
EFp
Ec
Ec
eVo
Fig.3 : Energy Band Diagram

Forward bias
• When a voltage is applied, the separation
between EFp and EFn is due to electrical work
done by the applied voltage, DEF=eV.
• The applied voltage diminishes the built-in
potential barrier to almost zero
– Electrons flow into the Space Charge Layer (SCL)
and flow over to p+-side to constitute diode
current.
– Holes flow from p+-side to n+-side.

Active region:
population inversion
• From the energy band diagram with EFp – EFn =
eV >Eg as shown in Fig.3,
– there are more electrons in the CB at energies
near Ec than electrons in the VB near Ev.
– In other words, there is a population inversion
between energies near Ec and those near Ev
around the junction.
• This population inversion region is a layer
along the junction
– It is called the inversion layer or the active region

Stimulated emission & optical gain
• An incoming photon with an energy of (Ec – Ev) cannot
excite an electron from Ev to Ec as there are almost none
near Ev
– However, it stimulate an electron to fall down from Ec to Ev
– The incoming photon stimulates direct recombination
• The region where there is population inversion and hence
more stimulated emission than absorption
– The active region has an optical gain
• The optical gain depends on
– The photon energy as apparent by the energy distributions of
electrons and holes in the CB and VB in the active layer.

hu
Eg
Optical gain EFn  EFp
Optical absorption
0
Energy
Ec
Ev
CB
VB
(a) The density of states and energy distribution of electrons and holes in
the conduction and valence bands respectively at T  0 in the SCL
under forward bias such that EFn  EFp > Eg. Holes in the VB are empty
states. (b) Gain vs. photon energy.
Density of states
Electrons
in CB
Holes in VB
= Empty states
EFn
EFp
eV
At T > 0
At T = 0
(a) (b)
© 1999 S.O. Kasap,
Optoelectronics(Prentice Hall)
Fig.4: Density of state & optical gain

Optical Gain for T=0K & T>0K
• At T 0K, the states between Ec and EFn are filled with
electrons and those between EFp and Ev are empty.
– Photon with energy (Eg < hu < EFn – EFp) cause stimulated
emission
– whereas those photon with energy (EFn–EFp< hu) become
absorbed
• As T > 0K, the Fermi-Dirac function spreads the energy
distribution of electrons in the CB to above EFn and holes
below EFp in the VB
– The result is a reduction in optical gain as shown in Fig.4
– The optical gain depends on EFn–EFp (which depends on the
applied voltage and hence on the diode current)

Injection Pumping
• It is apparent that population inversion between
energies near Ec and those near Ev is achieved
– by the injection of carriers across the junction under a
sufficiently large forward bias.
• The pumping mechanism is therefore the forward
diode current
• The pumping energy is supplied by the external
battery
• This type of pumping is called injection pumping

Optical Cavity
• Optical cavity is also needed to implement a laser
oscillator
– to build up the intensity of stimulated emissions by
means of an optical resonator
– This would provide a continuous coherent radiation as
output
• Fig.5 shows schematically the structure of a homojunction
laser diode
– pn-junction with direct bandgap material like GaAs
– The ends of the crystal are cleaved to be flat and optically
polished to provide reflection and hence form optical
cavity

L Electrode
Current
GaAs
GaAs
n+
p+
Cleaved surface mirror
Electrode
Active region
(stimulated emission region)
A schematic illustration of a GaAs homojunction laser
diode. The cleaved surfaces act as reflecting mirrors.
L
© 1999 S.O. Kasap,
Optoelectronics(Prentice Hall)
Fig.5 : Homojunction laser diode

Mode of cavity
• The photons are reflected from the cleaved
surface stimulate more photons of the same
frequency
– This process builds up the intensity of the
radiation in the cavity
– The wavelength of the radiation is determined by
the cavity length L because only multiple of the
half-wavelength can exists
m (l/2n) = L
where m is an integer, n is the refractive index of the
semiconductor and l is free space wavelength

Resonant frequency
m (l/2n) = L
where l  c/u (u is laser frequency)
• Each radiation satisfying the above
relationship is essentially a resonant
frequency of the cavity
– that is a mode of the cavity
– The separation between possible modes (allowed
wavelength) of the cavity Dlm.

Output spectrum of laser diode
• The exact output spectrum from the laser
diode depends on
1. The nature of optical cavity
2. The optical gain vs wavelength characteristic
• dependant on the energy distribution of electrons in
the CB and holes in the VB around the junction

Diode current
• Two critical diode current
1. Transparency current Itrans:
• provides just sufficient injection to lead to stimulated
emission just balancing absorption
• Above Itrans, there is optical gain in the medium but
output is not yet a continuous wave coherent radiation
2. Threshold current Ith:
• the optical gain in the medium has overcome the
photon losses from the cavity
• Lasing radiation is only obtained above Ith

Threshold current
• Fig.6 shows the output light intensity as a
function of diode current
– Above Ith, the light intensity becomes coherent
radiation consisting of cavity wavelength (or
mode) and increases steeply with current
– The number of modes in the output spectrum and
their relative strengths depends on the diode
current

Typical output opticalpower vs. diode current ( I) characteristics and the corresponding
output spectrum of a laser diode.
l
Laser
l
Laser
Optical Power
Optical Power
I
0
l
LED
Optical Power
Ith
Spontaneous
emission
Stimulated
emission
Optical Power
Fig.6: Characteristics of laser output

Threshold current of homojunction
• The main problem of the homojunction laser
diode is that the threshold current density Jth is
too high for practical uses
– For GaAs at room temperature, Jth the order of 500
Amm-2
– GaAs laser can only operates continuously at very
low temperature.
• The reduction of Ith to a practical value requires
– Improvement in the rate of stimulated emission
– Improving the efficiency of the optical cavity

Reduction of the threshold current
1. Carrier confinement
– Confine the injected electrons and holes to a narrow
region around the junction
– Less current is needed to establish the necessary
concentration of carriers for population inversion
2. Photon confinement
– Build a dielectric waveguide around the optical gain region
to increase the photon concentration and the probability
of stimulated emission
– Can reduce the loss of photons traveling off the cavity axis

Chapter 5a

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Chapter 5a