Chapter 5 Semiconductor Photon Sources

1
Chapter 5 Semiconductor Photon Sources
2
Semiconductor Photon Sources

• injection electroluminescence
• A light-emitting diode (LED) a
  forward-biased p-n junction fabricated from a
  direct-gap semiconductor material that emits
  light via injection electroluminescence
• forward voltage increased beyond a certain
  value population inversion
• The junction may then be used as
• a diode laser amplifier
• or, with appropriate feedback, as an injection
  laser diode.

3
Semiconductor Photon Sources

• Advantages
• readily modulated by controlling the injected
  current
• efficiency
• high reliability
• compatibility with electronic systems
• Applications
• lamp indicators display devices scanning,
  reading, and printing systems fiber-optic
  communication systems and optical data storage
  systems such as compact-disc players

4
16.1 LIGHT-EMITTING DIODES

• Injection Electroluminescence
• Electroluminescence in Thermal Equilibrium
• At room temperature the concentration of
  thermally excited electrons and holes is so small
  that the generated photon flux is very small.

5

• Electroluminescence in the Presence of
  Carrier Injection
• The photon emission rate may be calculated from
  the electron-hole pair injection rate R
  (pairs/cm3-s), where R plays the role of the
  laser pumping rate.
• Assume that the excess electron-hole pairs
  recombine at the rate 1/t, where t is the overall
  (radiative and nonradiative) electron-hole
  recombination time

6

• Electroluminescence in the Presence of Carrier
  Injection
• Under steady-state conditions, the generation
  (pumping) rate must precisely balance the
  recombination (decay) rate, so that
• R ?n/t.
• Thus the steady-state excess carrier
  concentration is proportional to the pumping
  rate, i.e.,

(16.1-1)
7

• Electroluminescence in the Presence of Carrier
  Injection
• Only radiative recombinations generate photons,
  however, and the internal quantum efficiency ?i
  t/tr, accounts for the fact that only a fraction
  of the recombinations are radiative in nature.
  The injection of RV carrier pairs per second
  therefore leads to the generation of a photon
  flux Q ?iRV photons/s, i.e.,

(16.1-2)
8

• Electroluminescence in the Presence of Carrier
  Injection
• The internal quantum efficiency ?i plays a
  crucial role in determining the performance of
  this electron-to-photon transducer.
• Direct-gap semiconductors are usually used to
  make LEDs (and injection lasers) because ?i is
  substantially larger than for indirect-gap
  semiconductors (e.g., ?i 0.5 for GaAs, whereas
• ?i 10-5 for Si, as shown in Table 15.1-5).
• The internal quantum efficiency ?i depends on
  the doping, temperature, and defect concentration
  of the material.

9

• Spectral Density of Electroluminescence Photons
• The spectral density of injection
  electroluminescence light may be determined by
  using the direct band-to-band emission theory
  developed in Sec. 15.2. The rate of spontaneous
  emission rsp(v) (number of photons per second per
  hertz per unit volume), as provided in (15.2-16),
  is

(16.1-3)
10

• Spectral Density of Electroluminescence Photons
• where tr, is the radiative electron-hole
  recombination lifetime. The optical joint density
  of states for interaction with photons of
  frequency v, as given in (15.2-9), is
• where mr, is related to the effective
  masses of the holes and electrons by 1/ mr 1/mv
  1/mc, as given in (15.2-5), and Eg is the
  bandgap energy. The emission condition as given
  in (15.2-10) provides

(16.1-4)
11

• Spectral Density of Electroluminescence Photons
• which is the probability that a conduction-band
  state of energy
• is filled and a valence-band state of energy
• is empty, as provided in (15.26) and (15.2-7)
  and illustrated in Fig. 16.1-2. Equations
  (16.1-5) and (16.1-6) guarantee that energy and
  momentum are conserved.

(16.1-5)
(16.1-6)
12
E2
Ec
Eg
Ev
E1
K
Figure 16.1-2 The spontaneous emission of a
photon resulting from the recombination of an
electron of energy E2, with a hole of energy
E1E2-hv. The transition is represented by a
vertical arrow because the momentum carried away
by the photon, hv/c, is negligible on the scale
of the figure.
13

• Spectral Density of Electroluminescence Photons
• The semiconductor parameters Eg, tr, mv and mc,
  and the temperature T determine the spectral
  distribution rsp(v), given the quasi-Fermi levels
  Efc and Efv. These, in turn, are determined from
  the concentrations of electrons and holes given
  in (15.1-7) and (15.1-8),
• The densities of states near the conduction- and
  valence-band edges are, respectively, as per
  (15.1-4) and (15.1-5),

(16.1-7)
14

• Spectral Density of Electroluminescence Photons
• Increasing the pumping level R causes ?n to
  increase, which, in turn, moves Efc toward (or
  further into) the conduction band, and Efv toward
  (or further into) the valence band. This results
  in an increase in the probability fc(E2) of
  finding the conduction-band state of energy E2
  filled with an electron, and the probability 1 -
  fv(E1) of finding the valence-band state of
  energy E1 empty (filled with a hole). The net
  result is that the emission-condition probability
  fe(v) fc(E2) 1 - fv(E1) increases with R,
  thereby enhancing the spontaneous emission rate
  given in (16.1-3).

15

• EXERCISE 16.1- 1
• Quasi-Fermi Levels of a Pumped Semiconductor.
• (a) Under ideal conditions at T 0 K, when
  there is no thermal electron-hole pair generation
  see Fig. 16.1-3(a), show that the quasi-Fermi
  levels are related to the concentrations of
  injected electron-hole pairs ?n by

(16.1-8a)
(16.1-8b)
16
E
E
E
E
Efc
Fc(E)
Efc
Fc(E)
Efv
Fv(E)
Efv
Fv(E)
K
K
(a)
(b)
Figure 16.1-3 Energy bands and Fermi functions
for a semiconductor in quasi-equilibrium (a) at
T0K, and (b) Tgt0K.
17

• so that
• where ?n n0,p0. Under these conditions all ?n
  electrons occupy the lowest allowed energy levels
  in the conduction band, and all ?p holes occupy
  the highest allowed levels in the valence band.
  Compare with the results of Exercise 15.1-2.
• (b) Sketch the functions fe(v) and rsp(v) for two
  values of ?n. Given the effect of
• temperature on the Fermi functions, as
  illustrated in Fig. 16.1-3(b), determine the
  effect of increasing the temperature on rsp(v).

(16.1-8c)
18

• EXERCISE 16.1-2
• Spectral Density of Injection Electroluminescence
  Under Weak Injection.
• For sufficiently weak injection, such that Ec -
  Efc kBT and
• Efv - Ev kBT, the Fermi functions may be
  approximated by their exponential tails. Show
  that the luminescence rate can then be expressed
  as
• where
• is an exponentially increasing function of the
  separation between the quasi-Fermi levels Efc -
  Efv.

(16.1-9a)
(16.1-9b)
19

• EXERCISE 16.1-3
• Electroluminescence Spectral Linewidth.
• (a) Show that the spectral density of the
  emitted light described by
• (16.1-9) attains its peak value at a frequency
  vp determined by
• (b) Show that the full width at
  half-maximum (FWHM) of the spectral density is

(16.1-10)
(16.1-11)
20

• (c) Show that this width corresponds to a
  wavelength spread ?? 1.8?p2kBT/hc, where ?p
  c/vp. For kBT expressed in eV and the wavelength
  expressed in um, show that
• (d) Calculate ?v and ?? at T 300 K, for
  ?p 0.8 um and ?p 1.6 um.

(16.1-12)
21

• LED Characteristics
• Forward-Biased P-N Junction with a large
  radiative recombination rate arising from
  injected minority carriers.
• Direct-Gap Semiconductor Material to ensure high
  quantum efficiency.
• As shown in Fig. 16.1-5, forward biasing causes
  holes from the p side and electrons from the n
  side to be forced into the common junction region
  by the process of minority carrier injection,
  where they recombine and emit photons.

22
0
V
p
n
E
Electron energy
Efc
hn
eV
Efv
Position
Figure 16.1-5 Energy diagram of a heavily doped
p-n junction that is strongly forward biased by
an applied voltage V. The dashed lines represent
the quasi-Fermi levels, which are separated as a
result of the bias. The simultaneous abundance of
electrons and holes within the junction region
results in strong electron-hole radiative
recombination (injection electroluminescence).
23

• Internal Photon Flux
• An injected dc current i leads to an increase in
  the steady-state carrier concentrations ?n,
  which, in turn, result in radiative recombination
  in the active-region volume V.
• the carrier injection (pumping) rate (carriers
  per second per cm3) is simply

(16.1-13)
Equation (16.1-l) provides that ?n Rt, which
results in a steady-state carrier concentration
24

• Internal Photon Flux
• In accordance with (16.1-2), the generated
  photon flux F is then ?iRV, which, using
  (16.1-13), gives

(16.1-14)
(16.1-15)
The internal quantum efficiency ?i is therefore
simply the ratio of the generated photon flux to
the injected electron flux.
25

• Output Photon Flux and Efficiency

The photon flux generated in the junction is
radiated uniformly in all directions however,
the flux that emerges from the device depends on
the direction of emission.
The output photon flux F0 is related to the
internal photon flux by
(16.1-19)
where ?e is the overall transmission efficiency
with which the internal photons can be extracted
from the LED structure, and ?i relates the
internal photon flux to the injected electron
flux. A single quantum efficiency that
accommodates both kinds of losses is the external
quantum efficiency ?ex,
26

• Output Photon Flux and Efficiency

(16.1-20)
The output photon flux in (16.1-19) can therefore
be written as
(16.1-21)
The LED output optical power P0 is related to the
output photon flux. Each photon has energy hv, so
that
(16.1-22)
27

• Output Photon Flux and Efficiency

Although ?i can be near unity for certain LEDs,
?ex generally falls well below unity, principally
because of reabsorption of the light in the
device and internal reflection at its boundaries.
As a consequence, the external quantum efficiency
of commonly encountered LEDs, such as those used
in pocket calculators, is typically less than 1.
Another measure of performance is the overall
quantum efficiency ? (also called the
power-conversion efficiency or wall-plug
efficiency), which is defined at the ratio of the
emitted optical power P0 to the applied
electrical power,
28

• Output Photon Flux and Efficiency

(16.1-23)
where V is the voltage drop across the device.
For hv eV, as is the case for commonly
encountered LEDs, it follows that ? ?ex.
29

• Responsivity

The responsivity R of an LED is defined as the
ratio of the emitted optical power P0 to the
injected current i, i.e., R P0/i. Using
(16.1-22), we obtain
(16.1-24)
The responsivity in W/A, when ?0 is expressed in
um, is then
(16.1-25)
30

• Responsibility

As indicated above, typical values of ?ex for
LEDs are in the range of 1 to 5, so that LED
responsivities are in the vicinity of 10 to 50
uW/mA.
In accordance with (16.1-22), the LED output
power P0 should be proportional to the injected
current i. In practice, however, this
relationship is valid only over a restricted
range. For larger drive currents, saturation
causes the proportionality to fail the
responsivity is then no longer constant but
rather declines with increasing drive current.
31

• Spectral Distribution

Under conditions of weak pumping, such that the
quasi-Fermi levels lie within the bandgap and are
at least a few kBT away from the band edges, the
width expressed in terms of the wavelength does
depend on ?.
(16.1-26)
where kBT is expressed in eV, the wavelength is
expressed in um, and ?p c/vp.
32

• Materials

LEDs have been operated from the near ultraviolet
to the infrared. In the near infrared, many
binary semiconductor materials serve as highly
efficient LED materials because of their
direct-band gap nature. Examples of III-V binary
materials include GaAs (?g 0.87 um), GaSb (1.7
um), InP (0.92 um), InAs (3.5 um), and InSb (7.3
um). Ternary and quaternary compounds are also
direct-gap over a wide range of compositions (see
Fig. 15.1-5). These materials have the advantage
that their emission wavelength can be
compositionally tuned. Particularly important
among the III-V compounds is ternary AlxGa1-xAs
(0.75 to 0.87 um) and quaternary In1-xGaxAs1-yPy
(1.1 to 1.6 um).
33

• Response Time

The response time of an LED is limited
principally by the lifetime t of the injected
minority carriers that are responsible for
radiative recombination. If the injected current
assumes the form i i0 i1 cos(Ot), where i1 is
sufficiently small so that the emitted optical
power P varies linearly with the injected
current, the emitted optical power behaves as P
P0 P1 cos(Ot f). The associated transfer
function, which is defined as H(O) (P1/i1)exp(i
f), assumes the form
(16.1-27)
34

• Response Time

which is characteristic of a resistor-capacitor
circuit. The rise time of the LED is t (seconds)
and its 3-dB bandwidth is B 1/2pt (Hz).
1/t 1/tr 1/tnr
internal quantum efficiency-bandwidth product ?iB
1/2ptr
Typical rise times of LEDs fall in the range 1 to
50 ns, corresponding to bandwidths as large as
hundreds of MHz.
35

• Device Structures

LEDs may be constructed either in
surface-emitting or edge-emitting configurations
(Fig. 16.1-10)
Surface emitting LEDs are generally more
efficient than edge-emitting LEDs.
36
(a)
(b)
Figure 16.1-10 (a) Surface-emitting LED. (b)
Edge-emitting LED
37

• Spatial Pattern of Emitted Light

The far-field radiation pattern from a
surface-emitting LED is similar to that from a
Lambertian radiator.
Electronic Circuitry
38
16.2 SEMICONDUCTOR LASER AMPLIFIERS

• ?The theory of the semiconductor laser amplifier
  is somewhat more complex than that presented in
  Chap. 13 for other laser amplifiers, inasmuch as
  the transitions take place between bands of
  closely spaced energy levels rather than
  well-separated discrete levels.
• ? Most semiconductor laser amplifiers fabricated
  to date are designed to operate in 1.3- to 1.55um
  lightwave communication systems as
  nonregenerative repeaters, optical preamplifiers,
  or narrowband electrically tunable amplifiers.

39

• In comparison with Er3 silica fiber amplifiers
• Advantages
• smaller in size
• readily incorporated into optoelectronic
  integrated circuits
• bandwidths can be as large as 10 THz
• Disadvantages
• greater insertion losses (typically 3
  to 5 dB per facet)
• temperature instability
• polarization sensitivity

40

• A. Gain
• The incident photons may be absorbed resulting
  in the generation of electron-hole pairs, or they
  may produce additional photons through stimulated
  electron-hole recombination radiation (see Fig.
  16.2-1).
• When emission is more likely than absorption,
  net optical gain ensues and the material can
  serve as a coherent optical amplifier.

41
Absorption
Stimulated emission
E2
Ec
Eg
Ev
E1
K
K
(a)
(b)
Figure 16.2-1 (a) The absorption of a photon
results in the generation of an electron-hole
pair. (b) Electron-hole recombination can be
induced by a photon the result is the stimualted
emission of an identical photon.
42

• With the help of the parabolic approximation for
  the E-k relations near the conduction- and
  valence-band edges, it was shown in (15.2-6) and
  (15.2-7) that the energies of the electron and
  hole that interact with a photon of energy hv are

(16.2-1)
The resulting optical joint density of states
that interacts with a photon of energy hv was
determined to be see (15.2-9)
(16.2-2)
43

• The occupancy probabilities fe(v) and fa(v) are
  determined by the pumping rate through the
  quasi-Fermi levels Efc and Efv. fe(v) is the
  probability that a conduction-band state of
  energy E2 is filled with an electron and a
  valence-band state of energy E1 is filled with a
  hole. fa(v), on the other hand, is the
  probability that a conduction-band state of
  energy E2 is empty and a valence-band state of
  energy E1 is filled with an electron. The Fermi
  inversion factor see (15.2-24)

(16.2-3)
represents the degree of population inversion.
fg(v) depends on both the Fermi function for the
conduction band, fc(E) 1/exp(E - Efc)/kBT
1, and the Fermi function for the valence band,
fv(E) 1/exp(E - Efv)/kBT 1).
44

• Expressions for the rate of photon absorption
  rab(v), and the rate of stimulated emission
  rst(v) were provided in (15.2-18) and (15.2-17).

The results provided above were combined in
(15.2-23) to give an expression for the net gain
coefficient, ?0(v) rst(v) - rab(v)/fv
(16.2-4)
Comparing (16.2-4) with (13.1-4), it is apparent
that the quantity ?(v)fg(v) in the semiconductor
laser amplifier plays the role of Ng(v) in other
laser amplifiers.
45

• Amplifier Bandwidth

In accordance with (16.2-3) and (16.2-4), a
semiconductor medium provides net optical gain at
the frequency v when fc(E2) gt fv(E1). External
pumping is required to separate the Fermi levels
of the two bands in order to achieve
amplification. The condition fc(E2) gt fv(E1) is
equivalent to the requirement that the photon
energy be smaller than the separation between the
quasi-Fermi levels, i.e., hv lt Efc - Efv, as
demonstrated in Exercise 15.2-1. Of course, the
photon energy must be larger than the bandgap
energy (hv gt Eg) in order that laser
amplification occur by means of band-to-band
transitions.
46

• Amplifier Bandwidth

Thus if the pumping rate is sufficiently large
that the separation between the two quasi-Fermi
levels exceeds the bandgap energy Eg, the medium
can act as an amplifier for optical frequencies
in the band
(16.2-5)
For hv lt Eg the medium is transparent, whereas
for hv gt Efc - Efv it is an attenuator instead of
an amplifier.
At T 0 K
(16.2-6)
47
Dependence of the Gain Coefficient on Pumping
Level
The gain coefficient ?0(v) increases both in its
width and in its magnitude as the pumping rate R
is elevated. As provided in (16.1-1), a constant
pumping rate R establishes a steady-state
concentration of injected electron-hole pairs.
Knowledge of the steady-steady total
concentrations of electrons and holes, permits
the Fermi levels Efc and Efv to be determined via
(16.1-7). Once the Fermi levels are known, the
computation of the gain coefficient can proceed
using (16.2-4).
48
Figure 16.2-3 (a) Calculated gain coefficient
?0(v) for an InGaAsP laser amplifier
versus photon energy hv, with the
injected-carrier concentration ?n as a parameter
(T 300 K). The band of frequencies over which
amplification occurs (centered near 1.3 um)
increases with increasing ?n. At the largest
value of ?n shown, the full amplifier bandwidth
is 15THz, corresponding to 0.06 eV in energy, and
75 nm in wavelength. (Adapted from N. K. Dutta,
Calculated Absorption, Emission, and Gain in
In0.72Ga0.28AS0.6P0.4, Journal of Applied
Physics, vol. 51, pp. 6095-6100, 1980.)
49
Figure 16.2-3(b) Calculated peak gain coefficient
?p as a function of ?n. At the largest value of
?n, the peak gain coefficient 270 cm-1.
(Adapted from N. K. Dutta and R. J. Nelson, The
Case for Auger Recombination in In1-xGaxAsyP1-y,
Journal of Applied Physics, vol. 53, pp. 74-92,
1982.
50

• Approximate Peak Gain Coefficient

It is customary to adopt an empirical approach in
which the peak gain coefficient ?p is assumed to
be linearly related to ?n for values of ?n near
the operating point. As the example in Fig.
16.2-3(b) illustrates, this approximation is
reasonable when ?p is large. The dependence of
the peak gain coefficient ?p on ?n may then be
modeled by the linear equation
(16.2-7)
51
Approximate Peak Gain Coefficient

• The parameters a and ?nT, are chosen to satisfy
  the
• following limits
• When ?n 0, ?p -a, where a represents the
  absorption coefficient of the semiconductor in
  the absence of current injection.
• When ?n ?nT, ?p 0. Thus ?nT is the
  injected-carrier concentration at which emission
  and absorption just balance so that the medium is
  transparent.

52

• EXAMPLE 16.2-2. InGaAsP Laser Amplifier.
• The peak gain coefficient ?p versus ?n for
  InGaAsP presented in Fig. 16.2-3(b) may be
  approximately fit by a linear relation in the
  form of (16.2-7) with the parameters ?nT 1.25 X
  1018 cm-3 and a 600 cm-1. For ?n 1.4 ?nT
  1.75 X 1018 cm-3, the linear model yields a peak
  gain ?p 240 cm-1. For an InGaAsP crystal of
  length d 350 um, this corresponds to a total
  gain of exp(?pd) 4447 or 36.5 dB. It must be
  kept in mind, however, that coupling losses are
  typically 3 to 5 dB per facet.

53

• B. Pumping

?Optical Pumping Pumping may be achieved by the
use of external light, as depicted in Fig.
16.2-5, provided that its photon energy is
sufficiently large (gt Eg)
Pump photon
Output signal photons
Input signal photon
K
Figure 16.2-5 Optical pumping of a semiconductor
laser amplifier
54

• ? Electric-Current Pumping

A more practical scheme for pumping a
semiconductor is by means of electron-hole
injection in a heavily doped p-n junctiona
diode. The thickness l of the active region is
an important parameter of the diode that is
determined principally by the diffusion lengths
of the minority carriers at both sides of the
junction. Typical values of I for InGaAsP are 1
to 3 um.
55
Output photons
W
l
d
i
-

p
n
Input photons
Aera A
Figure 16.2-6 Geometry of a simple laser
amplifier. Charge carriers travel perpendicularly
to the p-n junction, whereas photons travel in
the plane of the junction.
56

• the steady-state carrier injection rate is R
  i/elA J/el per second per unit volume, where J
  i/A is the injected current density. The
  resulting injected carrier concentration is then

(16.2-8)
The injected carrier concentration is therefore
directly proportional to the injected current
density. In particular, it follows from (16.2-7)
and (16.2-8) that within the linear approximation
implicit in (16.2-7), the peak gain coefficient
is linearly related to the injected current
density J, i.e.,
(16.2-9)
57

• The transparency current density J, is given by

(16.2-10)
where ?i t/tr, again represents the internal
quantum efficiency.
Note that JT is directly proportional to the
junction thickness I so that a lower transparency
current density JT is achieved by using a
narrower active-region thickness. This is an
important consideration in the design of
semiconductor amplifiers (and lasers).
58

• Motivation for Heterostructures

If the thickness I of the active region in
Example 16.2-3 were able to be reduced from 2 um
to, say, 0.1 um, the current density J, would be
reduced by a factor of 20, to the more reasonable
value 1600 A/cm2. Reducing the thickness of the
active region poses a problem, however, because
the diffusion lengths of the electrons and holes
in InGaAsP are several um the carriers would
therefore tend to diffuse out of this smaller
region. These carriers can be confined to an
active region whose thickness is smaller than
their diffusion lengths by using a
heterostructure device.
59

• C. Heterostructures

The double-heterostructure design therefore calls
for three layers of different lattice-matched
materials (see Fig. 16.2-8) Layer 1 p-type,
energy gap Eg1 refractive index n1. Layer 2
p-type, energy gap Eg2 refractive index n2. Layer
3 n-type, energy gap Eg3 refractive index n3.
60
Output photons
1
2
3
V
-

p
p
n
Input photons
E
Barrier
Eg1
eV
Eg2
Eg3
n2
n
n1
n3
Figure 16.2-8 Energy-band diagram and refractive
index as functions of position for
double-heterostructure semiconductor laser
amplifier.
61
The materials are selected such that Eg1 and Eg3
are greater than Eg2 to achieve carrier
confinement, while n2 is greater than n1 and n3
to achieve light confinement. The active layer
(layer 2) is made quite thin (0.1 to 0.2 um) to
minimize thetransparency current density JT and
maximize the peak gain coefficient ?p. Stimulated
emission takes place in the p-n junction region
between layers 2 and 3.
Advantages of the double-heterostructure
design 1.Increased amplifier gain, for a given
injected current density, resulting from a
decreased active-layer thickness 2.Increased
amplifier gain resulting from the confinement of
light within the active layer caused by its
larger refractive index 3.Reduced loss,
resulting from the inability of layers 1 and 3 to
absorb the guided photons because their bandgaps
Eg1 and Eg3 are larger than the photon energy
(i.e., hv Eg2 lt Eg1, Eg3).
62
16.3 Semiconductor Injection Lasers

• Amplification, Feedback, and Oscillation
• Power
• Spectral Distribution
• Spatial Distribution
• Mode Selection
• Characteristics of Typical Lasers
• Quantum-Well Lasers

63
Amplification, Feedback, and Oscillation

• Laser diode (LD) Vs Light-emitting diode (LED)

In both devices, the sources of energy is an
electric current injected into a p-n junction.
The light emitted form an LED is generated by
spontaneous emission
The light emitted form an LD arises from
stimulated emission
64
Amplification, Feedback, and Oscillation

• Amplification
• The amplification (optical gain) of a laser
  diode is provided by a forward-biased p-n
  junction fabricated from a direct-gap
  semiconductor material which is usually heavily
  doped .
• Feedback
• The optical feedback is provided by mirrors
  which are usually obtained by cleaving the
  semiconductor material along its crystal planes
  in semiconductor laser diodes.
• Oscillation
• When provided with sufficient gain, the feedback
  converts the optical amplifier into an optical
  oscillator (or a laser diode).

65
Cleaved surface
W
l
-

p
n
i
d
Cleaved surface
Aera A
Figure 16.3-1 An injection laser is a
forward-biased p-n junction with two parallel
surfaces that act as reflectors.
66
Amplification, Feedback, and Oscillation

• Advantages
• Small size
• High efficiency
• Integrability with electronic components
• Ease of pumping and modulation by electric
  current injection
• Disadvantages
• Spectral linewidth is typically larger than that
  of other lasers
• The light emitted from LD have a larger
  divergence angle
• Temperature has much influence on the performance
  of LD

67
Amplification, Feedback, and Oscillation

• Laser Amplification

The gain coefficient of a semiconductor
laser amplifier has a peak value that is
approximately proportional to the injected
carrier Concentration which, in turn, is
proportional to the injected current density .
(16.3-1)
where is the radiative electron-hole
recombination lifetime, is the
internal quantum efficiency, is the thickness
of the active region, is the thermal
equilibrium absorption coefficient, and and
are the injected-carrier concentration
and current density required to just make The
semiconductor transparent.
68
Amplification, Feedback, and Oscillation

• Feedback
• The feedback is usually obtained by cleaving the
  crystal planes normal to the plane of the
  junction, or by polishing two parallel surface of
  the crystal.
• The power reflectance at the semiconductor-air
  interface
• Semiconductor materials typically have large
  refractive indices, if the gain of the medium is
  sufficiently large, the refractive index
  discontinuity itself can serve as an adequate
  reflective surface and no external mirrors are
  necessary.

(16.3-2)
69
Amplification, Feedback, and Oscillation

• Resonator Losses
• Principal resonator loss arise from the partial
  reflection at the surfaces of the crystal. This
  loss constitutes the transmitted useful laser
  light. For a resonator of length d the reflection
  loss coefficient is
• If the two surfaces have the same reflectance
  , then
  . The total loss coefficient is
  
• where represents other sources of loss,
  including free carrier absorption in
  semiconductor material and scattering from
  optical inhomogeneities.

(16.3-3)
(16.3-4)
70
Amplification, Feedback, and Oscillation

• The spread of optical energy outside the active
  layer of the amplifier (in the direction
  perpendicular to the junction plane) cause
  another important contribution to the loss.

Figure 16.3-2 Spatial spread of the laser light
in the direction perpendicular to the plane of
the junction for (a) homostructure, (b)
heterostructure lasers.
71
Amplification, Feedback, and Oscillation

• By defining a confinement factor , we can
  represent the fraction of the optical energy
  lying within the active region. Then equation
  (16.3-4) must therefore be modified to reflect
  this increase

(16.3-5)
Based on the different mechanism used for
confining the carriers or light in the lateral
direction, there are basically three types of LD
structure Broad-area no mechanism for lateral
confinement is used Gain-guided lateral
variations of gain are used for
confinement Index-guided lateral refractive
index variations are used for confinement.
72
Amplification, Feedback, and Oscillation

• Gain Condition Laser Threshold
• The laser oscillation condition is that the gain
  exceed the loss. The threshold gain coefficient
  is therefore . If we set and
• in (16.3-1) corresponds to a
  threshold injected current density given by
• where the transparency current density,
• is the current density that just makes the
  medium transparent.

(16.3-6)
(16.3-7)
73
Amplification, Feedback, and Oscillation

• The threshold current density is a key
  parameter in characterizing the diode-laser
  performance smaller value of indicate
  superior performance. According to (16.3-6) and
  (16.3-7), we can improve the performance of the
  laser in lots of ways.

Figure 16.3-3 Dependence of the threshold current
density on the thickness of the active layer .
The double-heterostructure laser exhibits a lower
value of than the homostructure laser, and
therefore superior performance.
74
Power

• Internal Photon Flux
• Steady state As the photon flux in the laser
  becomes larger and the population difference
  becomes depleted, the gain coefficient decreases
  until it equal to the loss coefficient.
• The steady-state internal photon flux is
  proportional to the difference between the
  pumping rate and the threshold pumping rate
  .
• The steady-state internal photon flux
• according to (16.2-8) and .

(16.3-8)
75
Power

• The internal laser power above threshold is
  simply related to the internal photon flux by
  , and so we have
• is expressed in m, in amperes, and
  in Watts.

(16.3-9)
76
Power

• Output Photon Flux and Efficiency
• The output photon flux the product of the
  internal photon flux and the emission efficiency
  
• emission efficiency is the ratio of the loss
  associated with the useful light transmitted
  through the mirrors to the total resonator loss
  .
• For example if only the light transmitted
  through mirror 1 is used, then .

(16.3-10)
77
Power

• The proportionality between the laser output
  photon flux and the injected electron flux above
  threshold is governed by external differential
  quantum efficiency
• External differential quantum efficiency
  represents the rate of change of the output
  photon flux with respect to the injected electron
  flux above threshold
• The laser output power above threshold is

(16.3-11)
(16.3-12)
(16.3-13)
78
Power
The light-current curve Ideal (straight line)
and actual (solid curve). This is a light-current
curve for a strongly Index-guided
buried-heterostructure InGaAsP Injection laser
operated at 1.3 . The nonlinearities which
can cause the output power to saturate for
currents greater than 75mA is not considered here.
79
Power

• The differential responsivity
• The slope of the light-current curve above
  threshold
• The overall efficiency
• the ratio of the emitted laser light power to
  the electrical input power

(16.3-14)
(16.3-15)
80
Spectral Distribution

• The three factors that govern the spectral
  distribution
• In the spectral width the active medium
  small-signal gain coefficient is greater than the
  loss coefficient .
• The line-broadening mechanism.
• The resonator longitudinal modes .
• Semiconductor lasers are characterized by the
  following features
• Spectral width is relatively large.
• Spatial hole burning permits the simultaneous
  oscillation of many longitudinal modes.
• The frequency spacing of adjacent resonator modes
  is relatively large.

81
Spectral Distribution

• Transverse and longitudinal modes
• In semiconductor lasers, the laser beam extends
  outside the active layer. So the transverse modes
  are modes of the dielectric waveguide created by
  the different layers of the semiconductor
  diode.

• The transverse modes characterize the spatial
  distribution in the transverse direction.
• The longitudinal modes characterize the variation
  along the direction of wave propagation.

82
Spectral Distribution

• Transverse modes
• Go back the theory presented in Sec.7.3 for an
  optical waveguide with rectangular cross section
  of dimensions l and w.
• is usually small, the waveguide admit
  only a single mode in the transverse direction
  perpendicular to the junction plane.
• However, is larger than , so that the
  waveguide will support several modes in the
  direction parallel to the junction (lateral
  modes).

Figure 16.3-6 Schematic illustration Of spatial
distributions of the optical Intensity for the
laser waveguide Modes (l, m) (1,1), (1,2), and
(1,3).
83
Spectral Distribution

• Example
• A design using a laterally confined active layer
  is ( buried-heterostructure laser) illustrated in
  Fig.16.3-7. The lower-index material on either
  side of the active region produces lateral
  confinement in this index-guided lasers.

Figure 16.3-7 Schematic diagram of an AlGaAs/GaAs
buried-heterostructure Semiconductor injection
laser. The junction width w is typically 1 to 3
, so that the device is strongly index
guided.
84
Spectral Distribution

• Longitude modes
• The allowed longitude modes of the laser cavity
  are those where the mirror separation distance L
  is equal to an exact multiple of half the
  wavelength.
• where q is an integer known as the mode order.
• The frequency separation between any two adjacent
  longitude modes q and q1 are given (for an empty
  linear resonator of length L) by
• where c is the speed of light in vacuum.

85
Spectral Distribution

• Far-Field Radiation Pattern

Figure 16.3-8 Angular distribution of the optical
beam emitted from a laser diode.
86
Mode Selection

• Single-Frequency Operation
• By reducing the dimensions of the active-layer
  cross section can make a injection laser operate
  on a single-transverse mode.
• By reducing the length of the resonator so that
  the frequency spacing between adjacent
  longitudinal modes exceeds the spectral width of
  the amplifying medium. So that the laser operate
  on single longitudinal mode.
• A cleaved-coupled-cavity (C3) laser provide a
  more stringent restriction that can be satisfied
  only at a single frequency.
• Use frequency-selective reflectors as mirrors.
  Such as gratings parallel to the junction plane
  (Distributed Bragg Reflectors, DFB).
• Place the grating directly adjacent to the active
  layer by using a spatially corrugated waveguide.
  This is known as a distributed-feedback (DFB)

87
Mode Selection
Figure 16.3-9 Cleaved-coupled-cavity (C3) laser
Figure 16.3-10 (a) DBR laser (b) DFB laser
88
Characteristics of Typical Lasers
Semiconductor lasers can operate At wavelengths
from the near ultraviolet to the far infrared.
Output power can reach 100mW, and Laser-diode
arrays offer narrow Coherent beams with powers
in excess of 10W.
Figure 16.3-11 Compound materials used for
semiconductor lasers. The range of wavelengths
reaches from the near ultraviolet to the far
infrared.
89
Quantum-Well Lasers

• Quantum well
• In a double heterostructure, the active layer
  has a bandgap energy smaller than the surrounding
  layers, the structure then acts as a quantum well
  and the laser is called a single-quantum well
  laser (SQW).

The interactions of photons with electrons and
holes in a quantum well take the form of energy
and momentum conserving transitions between the
conduction and valence bands. The transitions
must also conserve the quantum Number q.
Review the knowledge about quantum theory.
90
Quantum-Well Lasers
Figure 16.3-12 (b) optical joint density of
states for a quantum-well structure (staircase
curve) And for a bulk semiconductor (dashed
curve).
91
Quantum-Well Lasers

• Gain Coefficient
• The gain coefficient of the laser is given by
  the usual expression
• The Fermi inversion factor depends on the
  quasi-Fermi levels and temperature, so it is the
  same for bulk and quantum-well lasers.
• The density of states differs in the two cases as
  we have shown in figure 16.3-12.

(16.3-17)
92
Quantum-Well Lasers
The frequency dependences of ,
, and their product are illustrated in the
figure. The quantum-well laser has a Smaller
peak gain and a narrower gain profile.
If only a single step of the staircase function
occurs at an energy smaller than The
maximum gain
(16.3-18)
93
Quantum-Well Lasers

• Relation Between Gain Coefficient and Current
  Density

The gain coefficient undergo some jumps during
the increasing of the injected current J. The
steps correspond to different energy gaps ,
and so on.
94
Quantum-Well Lasers

• The threshold current density for QW laser
  oscillation is considerably smaller than that for
  bulk (DH) laser oscillation because of the
  reduction in active-layer thickness.
• Advantages of QW lasers
• narrower spectrum of the gain coefficient
• smaller linewidth of the laser modes
• the possibility of achieving higher Modulation
  frequencies
• the reduce temperature dependence

95
Quantum-Well Lasers

• Multiquantum-well Lasers
• The gain coefficient may be increased by using a
  parallel stack of quantum wells which is known as
  a multiquantum-well (MQW) laser.

Make a comparison of the SQW and MQW lasers they
both be injected by the same current. Low current
densities, the SQW is superior High current
densities, the MQW is superior
Figure 16.3-15 AlGaAs/GaAs multiquantum- well
laser with .
96
Quantum-Well Lasers

• Strained-Layer Lasers
• Rather than being lattice-matched to the
  confining layers, the active layer of a
  strained-layer laser is purposely chosen to have
  a different lattice constant.
• If the active layer is sufficiently thin, it can
  accommodate its atomic spacing to those of the
  surrounding layers, and in the process become
  strained.
• The compressive strain alters the band structure
  in three significant ways
• Increases the bandgap Eg.
• Removes the degeneracy at K0 between the heavy
  and light hole bands.
• Makes the valence bands anisotropic so that in
  the direction parallel to the plane of the layer
  the highest band has a light effective mass,
  whereas in the perpendicular direction the
  highest band has a heavy effective mass.

97
Quantum-Well Lasers

• The improved performance of Strained-Layer Lasers
• The laser wavelength is altered by virtue of the
  dependence of Eg on the strain.
• The laser threshold current density can be
  reduced by the presence of the strain.
• The reduced hole mass more readily allows Efv to
  descend into the valence band, thereby permitting
  the population inversion condition (Efc Efv gt
  Eg) to be satisfied at a lower injection current.

98
Quantum-Well Lasers

• Surface-Emitting Quantum-well Laser-Diode Arrays
• SELDs are of increasing interest, and offer the
  advantages of high packing densities on a wafer
  scale.

Scanning electron micrograph of a small portion
of an array of vertical- cavity quantum-well
lasers with diameters between 1 and 5 .