CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES 2015-6-9Fundamentals of Photonics 1 Chapter 5 Semiconductor Photon Sources

CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES

23/4/18Fundamentals of Photonics 1

Chapter 5 Chapter 5 Semiconductor Photon SourcesSemiconductor 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.



Semiconductor Photon Sources

• Advantages:readily modulated by controlling the injected currentefficiencyhigh 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



16.1 LIGHT-EMITTING DIODES

A. Injection ElectroluminescenceElectroluminescence 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.



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



• 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 (16.1-1)




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 ir

V n V nRV

(16.1-2)




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 indirect-gap semiconductors (e.g., ηi = 0.5 for GaAs, whereasηi = 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.



• 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

1( ) ( ) ( )sp e

r

r f

(16.1-3)




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

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

3/ 21/ 2

2

(2 )( ) ( )r

g

mh E

2 1( ) ( )[1 ( )]e c vf f E f E (16.1-4)




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.

2 ( )rc g

c

mE E h E

m (16.1-5)

1 2E E h (16.1-6)



K

Ec

Ev

Eg

E2

h

E1

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.




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),

The densities of states near the conduction- and valence-band edges are, respectively, as per (15.1-4) and (15.1-5),

0 0( ) ( ) ; ( )[1 ( )]v

c

E

c c v vEE f E dE n n n E f E dE p p n

(16.1-7)

3/ 21/ 2

2 3

(2 )( ) ( ) ,

2c

c c c

mE E E E E

3/ 21/ 2

2 3

(2 )( ) ( ) ,

2v

v v c

mE E E E E




Increasing the pumping level R causes ∆n to increase, which, in turn, moves Efc toward (or further into) the conduction band, and E fv 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).



• EXERCISE 16.1- 1Quasi-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

22 2/3 2/3(3 ) ( )

2fc cc

E E nm

(16.1-8a)

22 2/3 2/3(3 ) ( )

2fv vv

E E nm

(16.1-8b)



K

Efc Fc(E)

Efv

E

Fv(E)

E

K

Efc Fc(E)

Efv

E

Fv(E)

E

(a) (b)

Figure 16.1-3 Energy bands and Fermi functions for a semiconductor in quasi-equilibrium (a) at T=0K, and (b) T>0K.



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).

22 2/3 2/3(3 ) ( )

2fc fv gr

E E E nm

(16.1-8c)



• EXERCISE 16.1-2Spectral 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.

1/ 2( ) ( ) exp( ),gsp g g

B

h Er D h E h E

k T

(16.1-9a)

3/ 2

2

(2 )exp( )fc fv gr

r B

E E EmD

k T

(16.1-9b)



• EXERCISE 16.1-3Electroluminescence 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

2B

p g

k Th E (16.1-10)

1.8 Bk T

h (16.1-11)



(c) Show that this width corresponds to a wavelength spread ∆λ = 1.8λp

2kBT/hc, where λp = c/vp. For kBT expressed in eV and the wavelength expressed in um, show that

(d) Calculate ∆v and ∆λ at T = 300 K, for λp = 0.8 um and λp = 1.6 um.

21.45 p Bk T (16.1-12)



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.



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).

E

p n+V 0

Efc

Efv

eVh

Position

Ele

ctro

n

ener

gy



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

/i eR

V (16.1-13)

Equation (16.1-l) provides that ∆n = Rτ, which results in a steady-state carrier concentration



Internal Photon Flux

In accordance with (16.1-2), the generated photon flux Φ is then ηiRV, which, using (16.1-13), gives

( / )i en

V

(16.1-14)

i

i

e (16.1-15)

The internal quantum efficiency ηi is therefore simply the ratio of the generated photon flux to the injected electron flux.



Output Photon Flux and Efficiency

The output photon flux Φ0 is related to the internal photon flux by

0 e e i

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,

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.




ex e i (16.1-20)

The output photon flux in (16.1-19) can therefore be written as

0 ex

i

e (16.1-21)

The LED output optical power P0 is related to the output photon flux. Each photon has energy hv, so that

0 0 ex

iP h h

e (16.1-22)




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 wall-plug efficiency), which is defined at the ratio of the emitted optical power P0 to the applied electrical power,




0ex

P h

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.



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

0 0ex

P h hR

i i e

(16.1-24)

The responsivity in W/A, when λ0 is expressed in um, is then

0

1.24( / )

( )exR W Am

(16.1-25)



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.



Spectral Distribution

2( ) 1.45 p Bm k T (16.1-26)

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.

where kBT is expressed in eV, the wavelength is expressed in um, and λp = c/vp.



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 ternaryAlxGa1-xAs (0.75 to 0.87 um) and quaternary In1-xGaxAs1-yPy (1.1 to 1.6 um).



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

( )1

RH

j

(16.1-27)



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).

internal quantum efficiency-bandwidth product ηiB = 1/2πτr

1/τ = 1/τr + 1/τnr

Typical rise times of LEDs fall in the range 1 to 50 ns, correspondingto bandwidths as large as hundreds of MHz.



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.



(a) (b)

Figure 16.1-10 (a) Surface-emitting LED. (b) Edge-emitting LED



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



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.



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



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.



Ec

Ev

Eg

E2

h

E1

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.

K

h

K

h

h

Absorption Stimulated emission

(a) (b)



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

2 1 2( ),rc g

c

mE E h E E E h

m (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)]

3/ 21/ 2

2

(2 )( ) ( ) ,r

g g

mh E h E

(16.2-2)



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)]

2 1( ) ( ) ( ) ( ) ( )g e a c vf f f f E f E (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).



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 ( ) ( ) ( )8 g

r

f

(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.



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.



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

g fc fvE E E

h 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( ) 1,

( ) 1,

g fc fv

g

f h E E

f otherwise

(16.2-6)



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).

Dependence of the Gain Coefficient on Pumping Level



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.)



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.



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

( 1)pT

n

n

(16.2-7)



The parameters α and ∆nT, are chosen to satisfy thefollowing 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.

Approximate Peak Gain Coefficient



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.



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)

K

Output signal photons

Input signal photon

Pump photon

Figure 16.2-5 Optical pumping of a semiconductor laser amplifier



★ 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.



Input photons

Output photons

+ -

l

p n

Aera A

W

d

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.

i



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 i JelA el

(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.,

( 1)pT

J

J (16.2-9)



The transparency current density J, is given by

T Ti r

elJ n

(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).



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.



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.



1 2 3p p n+ -

Input photons

Output photons

eV Eg2 Eg3

Eg1Barrier

E

n1

n2

n3

n

Figure 16.2-8 Energy-band diagram and refractive index as functions of position for double-heterostructure semiconductor laser amplifier.

V



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).

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.



16.3 Semiconductor Injection Lasers

Amplification, Feedback, and OscillationPowerSpectral DistributionSpatial DistributionMode SelectionCharacteristics of Typical Lasers＊ Quantum-Well Lasers



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 anLD arises from

stimulated emission

The light emitted form anLED is generated by

spontaneous emission

Amplification, Feedback, and Oscillation



AmplificationThe 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.

OscillationWhen provided with sufficient gain, the feedback converts the optical amplifier into an optical oscillator (or a laser diode).




+ -

l

p n

Aera A

W

d

Figure 16.3-1 An injection laser is a forward-biased p-n junction with two parallel surfaces that act as reflectors.

i

Cleaved surface

Cleaved surface



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




Laser Amplification

p

( 1),p T TT i r

J elJ n

J

0 ( )

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.

r /i r l

Tn TJ

The gain coefficient of a semiconductor laser amplifier has a peakvalue that is approximately proportional to the injected carrier Concentration which, in turn, is proportional to the injected current density .J

(16.3-1)




FeedbackThe 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.

21( )

1

nR

n

(16.3-2)




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.

1 21 2

1 1ln

2m m m d R R

r s m

1 2 (1/ ) ln(1/ )m d

s

(16.3-3)

(16.3-4)




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.




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

1( )r 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.




Gain Condition: Laser ThresholdThe 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.

r p r tJ J

tJ

rt TJ J

(16.3-6)

T Ti r

elJ n

(16.3-7)




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.

tJtJ

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.

ltJ




Power

Internal Photon FluxSteady 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 .

,

0,

ti t

t

i ii i

ei i

(16.3-8)

R tR

R i tR ti



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.

P h

0

1.24( )i tP i i

(16.3-9)

0 i P

Power



Output Photon Flux and EfficiencyThe 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 .

0t

e i

i i

e

(16.3-10)

e

r

1 /e m r

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:

d e i (16.3-11)

0

( / )d

d

d i e

(16.3-12)

00

1.24( )d tP i i

(16.3-13)

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 InGaAsPInjection laser operated at 1.3 .

The nonlinearities which can cause the output power to saturate for currents greater than 75mAis not considered here.

m

Power



The differential responsivityThe slope of the light-current curve above threshold

The overall efficiencythe ratio of the emitted laser light power to the electrical input power

0

0

( ) 1.24

( ) ( )d d

dP WR

di A m

(16.3-14)

(1 )td

i h

i eV

(16.3-15)

Power




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.

/ 2F c d



Transverse and longitudinal modesIn 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.




Transverse modesGo 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).

w

0/l

w 0

Figure 16.3-6 Schematic illustrationOf spatial distributions of the opticalIntensity for the laser waveguideModes (l, m)= (1,1), (1,2), and (1,3).




• 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-heterostructureSemiconductor injection laser. The junction width w is typically 1 to 3 , so that the device is strongly index guided.

m




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 q+1 are given (for an empty linear resonator of length L) by :

where c is the speed of light in vacuum.

2L q

3

c

L




• Far-Field Radiation Pattern

A laser diode with an active layer of dimensions and emits light with far-field angular divergence (radians) in the plane perpendicular to the junction and in the plane parallel to the junction.

0 / lw

0 / w

l

l

W

0

w

0

l

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




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)



Figure 16.3-9 Cleaved-coupled-cavity (C3) laser Figure 16.3-10 (a) DBR

laser (b) DFB laser

Mode Selection



Characteristics of Typical Lasers

Semiconductor lasers can operateAt wavelengths from the near ultraviolet to the far infrared. Output power can reach 100mW, and Laser-diode arrays offer narrow Coherent beams with powers inexcess 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.



＊ Quantum-Well LasersQuantum 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).

Review the knowledge about quantum theory.

The interactions of photons with electronsand holes in a quantum well take the formof energy and momentum conserving transitionsbetween the conduction and valence bands.The transitions must also conserve the quantumNumber q.



Density of StatesThe optical joint density of states is related to by

. It follows from (15.1-28) that

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.

( ) ( )c E( ) ( / ) ( ) ( / ) ( )c r c cdE d E hm m E

2

2, '

( )

0,

cr rg q q

c

mhm mh E E E

m l l

otherwise

(16.3-16)

( )

Figure 16.3-12 (b) optical joint density of states for a quantum-well structure (staircase curve) And for a bulk semiconductor (dashed curve).

＊ 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.

2

0 ( ) ( ) ( )8 g

r

f

(16.3-17)

( )gf




The frequency dependences of , , and their product are illustrated inthe figure. The quantum-well laser has a Smaller peak gain and a narrower gain profile.

( ) ( )gf

If only a single step of the staircase function occurs at an energy smaller than The maximum gain:

( ) fc fE E

2

2r

mr

m

hl

(16.3-18)




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.2gE1gE




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




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

Figure 16.3-15 AlGaAs/GaAs multiquantum-well laser with .10l nm

Make a comparison of the SQW and MQWlasers: they both be injected by the samecurrent.Low current densities, the SQW is superiorHigh current densities, the MQW is superior




Strained-Layer LasersRather 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.




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.




Surface-Emitting Quantum-well Laser-Diode ArraysSELDs 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 .m


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CHAPTER 5-2--- SEMICONDUCTOR PHOTON SOURCES 2015-6-9Fundamentals of Photonics 1 Chapter 5 Semiconductor Photon Sources