Transcript Document

CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
Chapter 5
Semiconductor Photon Sources
Fundamentals of Photonics
2015/7/7
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
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.
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
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
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
16.1 LIGHT-EMITTING DIODES
A. 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.
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
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/τ, where τ is the overall (radiative and
nonradiative) electron-hole recombination time
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
•
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/τ.
Thus the steady-state excess carrier concentration is proportional
to the pumping rate, i.e.,
n  R
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(16.1-1)
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
•
Electroluminescence in the Presence of Carrier
Injection
Only radiative recombinations generate photons, however, and
the internal quantum efficiency ηi = τ/τr, 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 = ηiRV photons/s, i.e.,
  i RV  i
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V n

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
V n
r
(16.1-2)
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
•
Electroluminescence in the Presence of Carrier
Injection
The internal quantum efficiency ηi 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 ηi is substantially larger than for indirectgap semiconductors (e.g., ηi = 0.5 for GaAs, whereas
ηi = 10-5 for Si, as shown in Table 15.1-5).
The internal quantum efficiency ηi depends on the doping,
temperature, and defect concentration of the material.
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
•
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
rsp ( ) 
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1
r
 ( ) f e ( )
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(16.1-3)
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
•
Spectral Density of Electroluminescence Photons
where τr, 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
 ( ) 
(2mr )3/ 2

2
(h  Eg )1/ 2
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
fe ( )  fc ( E2 )[1  fv ( E1 )]
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
•
Spectral Density of Electroluminescence Photons
which is the probability that a conduction-band state of energy
E2  Ec 
mr
(h  Eg )
mc
(16.1-5)
is filled and a valence-band state of energy
E1  E2  h
(16.1-6)
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.
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E2
Ec
h
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 E1=E2-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.
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•
Spectral Density of Electroluminescence Photons
The semiconductor parameters Eg, τr, 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),


Ec
Ev
c ( E) fc ( E)dE  n  n0  n;  v ( E)[1  fv ( E)]dE  p  p0  n

(16.1-7)
The densities of states near the conduction- and valence-band edges
are, respectively, as per (15.1-4) and (15.1-5),
(2mc )3/ 2
c ( E ) 
( E  Ec )1/ 2 , E  Ec
2 3
2
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(2mv )3/ 2
v ( E ) 
( Ev  E )1/ 2 , E  Ec
2 3
2
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
•
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).
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
•
EXERCISE 16.1- 1
Quasi-Fermi Levels of a Pumped Semiconductor.
(a) Under ideal conditions at T = 0 K, when there is no thermal electronhole 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
E fc  Ec  (3 2 )2/ 3
E fv  Ev  (3 2 )2/ 3
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2
2mc
2
2mv
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(n)2/ 3
(16.1-8a)
(n)2/ 3
(16.1-8b)
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
E
E
E
Efc
Fc(E)
E
Efc
Fc(E)
Efv
Fv(E)
Efv
Fv(E)
K
K
(b)
(a)
Figure 16.1-3 Energy bands and Fermi functions for a
semiconductor in quasi-equilibrium (a) at T=0K, and (b) T>0K.
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
so that
E fc  E fv  Eg  (3 2 )2/ 3
2
2mr
(n)2/ 3
(16.1-8c)
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).
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
•
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
h  Eg
1/ 2
rsp ( )  D(h  Eg ) exp(
), h  Eg (16.1-9a)
kT
B
where
D
(2mr )3/ 2
 2 r
exp(
E fc  E fv  Eg
kBT
)
(16.1-9b)
is an exponentially increasing function of the separation between the
quasi-Fermi levels Efc - Efv.
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
•
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
k BT
h p  Eg 
2
(16.1-10)
(b) Show that the full width at half-maximum (FWHM) of the
spectral density is
1.8k BT
 
h
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
(c) Show that this width corresponds to a wavelength spread ∆λ =
1.8λp2kBT/hc, where λp = c/vp. For kBT expressed in eV and the
wavelength expressed in um, show that
  1.45 k T
2
p B
(16.1-12)
(d) Calculate ∆v and ∆λ at T = 300 K, for λp = 0.8 um and λp = 1.6
um.
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
B. 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.
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
+V
0
p
n
Electron energy
E
Efc
h
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 quasiFermi 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).
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
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
R
i/e
V
(16.1-13)
Equation (16.1-l) provides that ∆n = Rτ, which results in a
steady-state carrier concentration
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
Internal Photon Flux
In accordance with (16.1-2), the generated photon flux Φ is then
ηiRV, which, using (16.1-13), gives
(i / e)
n 
V
i
  i
e
(16.1-14)
(16.1-15)
The internal quantum efficiency ηi is therefore simply the ratio
of the generated photon flux to the injected electron flux.
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
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 Φ0 is related to the internal photon flux by
i
 0  e   ei
e
(16.1-19)
where ηe is the overall transmission efficiency with which the internal
photons can be extracted from the LED structure, and ηi 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 ηex,
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Output Photon Flux and Efficiency
ex  ei
(16.1-20)
The output photon flux in (16.1-19) can therefore be written as
i
 0   ex
e
(16.1-21)
The LED output optical power P0 is related to the output photon flux.
Each photon has energy hv, so that
i
P0  h 0  ex h
e
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
Output Photon Flux and Efficiency
Although ηi can be near unity for certain LEDs, ηex 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 η (also called the power-conversion efficiency or wallplug efficiency), which is defined at the ratio of the emitted
optical power P0 to the applied electrical power,
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
Output Photon Flux and Efficiency
P0
h

  ex
iV
eV
(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 η ≈ηex.
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
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
P0 h 0
h
R

 ex
i
i
e
(16.1-24)
The responsivity in W/A, when λ0 is expressed in um, is then
1.24
R(W / A)  ex
0 (  m)
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
Responsibility
As indicated above, typical values of ηex 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.
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
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 λ.
 (m)  1.45 k T
2
p B
(16.1-26)
where kBT is expressed in eV, the wavelength
is expressed in um, and λp = c/vp.
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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 (λg =
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).
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
Response Time
The response time of an LED is limited principally by the lifetime
τ of the injected minority carriers that are responsible for radiative
recombination.
If the injected current assumes the form i = i0 + i1 cos(Ωt), 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(Ωt + φ).
The associated transfer function, which is defined as H(Ω) =
(P1/i1)exp(i φ), assumes the form
R
H () 
1  j
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Response Time
which is characteristic of a resistor-capacitor circuit.
The rise time of the LED is τ (seconds) and its 3-dB
bandwidth is B = 1/2πτ (Hz).
1/τ = 1/τr + 1/τnr
internal quantum efficiency-bandwidth product ηiB = 1/2πτr
Typical rise times of LEDs fall in the range 1 to 50 ns, corresponding
to bandwidths as large as hundreds of MHz.
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
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.
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
(a)
(b)
Figure 16.1-10 (a) Surface-emitting
LED. (b) Edge-emitting LED
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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
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
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.
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
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
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
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.
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
Absorption
Stimulated emission
E2
Ec
Eg
h
h
h
h
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.
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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
mr
E2  Ec 
(h  Eg ), E1  E2  h
mc
(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)]
 ( ) 
(2mr )3/ 2
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
2
(h  Eg )1/ 2 , h  Eg
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(16.2-2)
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
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)]
f g ( )  fe ( )  fa ( )  fc (E2 )  fv (E1 ) (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).
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
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, γ0(v) = [rst(v) - rab(v)]/φv
2
 0 ( ) 
 ( ) f g ( )
8 r
(16.2-4)
Comparing (16.2-4) with (13.1-4), it is apparent that the quantity
ρ(v)fg(v) in the semiconductor laser amplifier plays the role of Ng(v)
in other laser amplifiers.
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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) > fv(E1).
External pumping is required to separate the Fermi levels of the
two bands in order to achieve amplification.
The condition fc(E2) > fv(E1) is equivalent to the requirement that
the photon energy be smaller than the separation between the
quasi-Fermi levels, i.e., hv < Efc - Efv, as demonstrated in
Exercise 15.2-1.
Of course, the photon energy must be larger than the bandgap
energy (hv > Eg) in order that laser amplification occur by means
of band-to-band transitions.
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
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
Eg
h
 
E fc  E fv
h
(16.2-5)
For hv < Eg the medium is transparent, whereas for hv > Efc - Efv it
is an attenuator instead of an amplifier.
At T = 0 K
f g ( )  1, h  E fc  E fv
f g ( )  1, otherwise
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Dependence of the Gain Coefficient on
Pumping Level
The gain coefficient γ0(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).
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Figure 16.2-3 (a) Calculated gain coefficient γ0(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.)
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Figure 16.2-3(b) Calculated peak gain
coefficient γp 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.
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Approximate Peak Gain Coefficient
It is customary to adopt an empirical approach in which the peak
gain coefficient γp 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 γp is large. The
dependence of the peak gain coefficient γp on ∆n may then be
modeled by the linear equation
n
 p  (
 1)
nT
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Approximate Peak Gain Coefficient
The parameters α and ∆nT, are chosen to satisfy the
following limits:
• When ∆n = 0, γp = -α, where α represents the absorption
coefficient of the semiconductor in the absence of current
injection.
• When ∆n = ∆nT, γp = 0. Thus ∆nT is the injected-carrier
concentration at which emission and absorption just balance so
that the medium is transparent.
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EXAMPLE 16.2-2. InGaAsP Laser Amplifier.
The peak gain coefficient γp 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 α = 600 cm-1. For ∆n = 1.4 ∆nT
= 1.75 X 1018 cm-3, the linear model yields a peak gain γp =
240 cm-1. For an InGaAsP crystal of length d = 350 um,
this corresponds to a total gain of exp(γpd) = 4447 or 36.5
dB. It must be kept in mind, however, that coupling losses
are typically 3 to 5 dB per facet.
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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 (> Eg)
Pump
photon
Input signal
photon
Output signal
photons
K
Figure 16.2-5 Optical pumping of a semiconductor laser amplifier
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★ Electric-Current Pumping
A more practical scheme for pumping a semiconductor is by
means of electron-hole injection in a heavily doped p-n
junction—a 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.
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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.
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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
n   R 

elA
i

el
J
(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.,
J
 p   (  1)
JT
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The transparency current density J, is given by
JT 
el
i r
nT
(16.2-10)
where ηi = τ/τr, 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).
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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.
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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.
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Output photons
1
p
V
+
2
p
3
n
-
Input photons
E
Barrier
Eg1
eV
Eg2
Eg3
n2
n
n3
n1
Figure 16.2-8 Energy-band diagram and refractive index as functions
of position for double-heterostructure semiconductor laser amplifier.
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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 γp. 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 < Eg1, Eg3).
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16.3 Semiconductor Injection Lasers







Amplification, Feedback, and Oscillation
Power
Spectral Distribution
Spatial Distribution
Mode Selection
Characteristics of Typical Lasers
＊Quantum-Well Lasers
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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
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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).
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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.
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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
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Amplification, Feedback, and Oscillation
 Laser Amplification
The gain coefficient  0 ( ) of a semiconductor laser amplifier has a peak
value  p that is approximately proportional to the injected carrier
Concentration which, in turn, is proportional to the injected current density J .
J
el
 p   (  1), JT 
nT
JT
i r
(16.3-1)
where  r is the radiative electron-hole recombination lifetime,  i   /  r
is the internal quantum efficiency, l is the thickness of the active region,
 is the thermal equilibrium absorption coefficient, and nT and JT are the
injected-carrier concentration and current density required to just make
The semiconductor transparent.
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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
n 1 2
R(
)
n 1
(16.3-2)
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.
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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
 m   m1   m 2
1
1

ln
2d R1R2
(16.3-3)
If the two surfaces have the same reflectance 1   2   , then
. The total loss coefficient is
 m  (1/ d ) ln(1/ )
r  s  m
(16.3-4)
 where  s represents other sources of loss, including free carrier absorption
in semiconductor material and scattering from optical inhomogeneities.
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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.
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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
r 
1
( s   m )

(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.
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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  r . If we set  p   r and
J  Jt in (16.3-1) corresponds to a threshold injected current
density J t given by
Jt 
r  
JT

(16.3-6)
where the transparency current density,
JT 
el
i r
nT
(16.3-7)
is the current density that just makes the medium transparent.
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Amplification, Feedback, and Oscillation
The threshold current density Jt is a key parameter in characterizing
the diode-laser performance; smaller value of Jt 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 layerl . The double-heterostructure
laser exhibits a lower value of Jt than the
homostructure laser, and therefore superior
performance.
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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 R and the threshold pumping rate Rt .
The steady-state internal photon flux:
 i  it
, i  it
i

e
0, i  it
(16.3-8)
according to (16.2-8) R  i and Rt  it .
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Power
The internal laser power above threshold is simply related to the
internal photon flux by P  h , and so we have
P  i (i  it )
1.24
0
(16.3-9)
 0 is expressed in  m, i in amperes, and P in Watts.
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Power
 Output Photon Flux and Efficiency
The output photon flux the product of the internal photon flux and the
emission efficiency
: e
i  it
 0  ei
e
(16.3-10)
emission efficiency is the ratio of the loss associated with the useful
light transmitted through the mirrors to the total resonator loss r .
For example: if only the light transmitted through mirror 1 is used,
then  e   m1 /  r .
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Power
The proportionality between the laser output photon flux and the
injected electron flux above threshold is governed by external
differential quantum efficiency:
d  ei
(16.3-11)
External differential quantum efficiency represents the rate of
change of the output photon flux with respect to the injected electron
flux above threshold:
d 0
d (i / e)
The laser output power above threshold is:
d 
P0  d (i  it )
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1.24
0
2015/7/7
(16.3-12)
(16.3-13)
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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 m.
The nonlinearities which can cause the output
power to saturate for currents greater than 75mA
is not considered here.
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Power
 The differential responsivity
The slope of the light-current curve above threshold
dP0 (W )
1.24
Rd 
 d
di( A)
0 (  m)
(16.3-14)
 The overall efficiency
the ratio of the emitted laser light power to the electrical input power
i h
i eV
  d (1  t )
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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  F  c / 2d.
 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.
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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.
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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.
 l /  0 is usually small, the waveguide admit only a single mode in the
transverse direction perpendicular to the junction plane.
 However, w is larger than  0 , so that the waveguide will support
several modes in the direction parallel to the junction (lateral
modes).
w
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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).
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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES
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
m , so that
the device is strongly index guided.
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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.

Lq
2
where q is an integer known as the mode order.
 The frequency separation between any two adjacent longitude
modes q and q+1 are given (for an empty linear resonator of length
L) by :
c
 
3L
where c is the speed of light in vacuum.
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Spectral Distribution
0
l
• Far-Field Radiation Pattern
A laser diode with an active layer of dimensions
l and w emits light with far-field angular
divergence   0 /l (radians) in the plane
perpendicular to the junction and   0 / win the
plane parallel to the junction.
0
w
W
l
Figure 16.3-8 Angular distribution of the
optical beam emitted from a laser diode.
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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 distributedfeedback (DFB)
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Mode Selection
Figure 16.3-9 Cleavedcoupled-cavity (C3) laser
Fundamentals of Photonics
Figure 16.3-10 (a) DBR
laser (b) DFB laser
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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.
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＊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.
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＊Quantum-Well Lasers
 Density of States
The optical joint density of states  ( )is related to  c ( E ) by
 ( )  (dE / d )  c( E )  (hmr / mc)  c( E ) . It follows from (15.1-28) that
2mr
 hmr mc

, h  Eg  Eq  Eq '

2
l
 ( )   mc  l
0,
otherwise

(16.3-16)
Including transitions between all subbands, we arrive at a  ( ) that has a
staircase distribution with steps at the energy gaps between subbands of
the same quantum number.
Figure 16.3-12 (b) optical joint density of states
for a quantum-well structure (staircase curve)
And for a bulk semiconductor (dashed curve).
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＊Quantum-Well Lasers
 Gain Coefficient
The gain coefficient of the laser is given by the usual expression:
2
 0 ( ) 
 ( ) f g ( )
8 r
(16.3-17)
 The Fermi inversion factor f g ( )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.
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The frequency dependences of  ( ) ,
f g ( ) , 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 Efc  Ef 
The maximum gain:
 2 mr
m 
2 r hl
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 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 Eg 1, Eg 2 …and so on.
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 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
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 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 multiquantumwell laser with
.
l  10nm
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 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 K=0 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.
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 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 > Eg) to be satisfied at a lower injection current.
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 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 verticalcavity quantum-well lasers with
diameters between 1 and 5 m .
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