EE529 Semiconductor Optoelectronics Semiconductor Lasers 1. Optical - - PowerPoint PPT Presentation

Lih Y. Lin EE 529 Semiconductor Optoelectronics – Semiconductor Lasers

EE529 Semiconductor Optoelectronics

Semiconductor Lasers

• 1. Optical gain spectrum
• 2. Laser threshold, power and efficiency
• 3. Modulation characteristics
• 4. Advanced laser structures

Reading: Liu, Sec. 13.3-13.4, 13.9-13.10 Ref: Bhattacharya, Sec. 6.7, 7.2, 7.13; Liu, Sec. 4.3, 5.1

Lih Y. Lin EE 529 Semiconductor Optoelectronics – Semiconductor Lasers 2

Laser Operation

Lasing process in a ruby laser

Process: 1. Population inversion ― Through optical pumping or carrier injection. 2. Seed photons ― From spontaneous emission and initiate the stimulated emission process. 3. Optical cavity ― Resonant enhancement and define the output wavelength. 4. Gain saturation – Population inversion decreases as stimulated emission increases. → Steady state. 5. Output coupling ― Let some of the photons out at each round trip.

Lih Y. Lin EE 529 Semiconductor Optoelectronics – Semiconductor Lasers 3

Basic Semiconductor Laser Structure

p+ n+

EFn (a) Eg Ev Ec Ev

Holes in V B Electrons in C B

Junction

Electrons

Ec

p+

Eg

V n+

(b) EFn eV EFp

Inversion region

EFp Ec Ec eV o

L

Electrode Current

G aA s G aA s n+ p+

Cleaved surface m irror Electrode Active region (stim ulated em issio n region) L

Photograph of an edge emitting laser diode 500 µm

Lih Y. Lin EE 529 Semiconductor Optoelectronics – Semiconductor Lasers 4

Different Regimes of Operation

hυ Eg O p tic a l g ain EFn − EFp O p tic a l ab so rp tio n E n e r g y Ec Ev

C B V B

D e n sity

• f sta

te s

E le c tron s in C B H

• le

s in V B = E m pty s ta tes

EFn EFp e V

A t T > A t T =

λ L ase r λ L ase r

Optical Power Optical Power

I

λ L E D

Optical Power

Ith

S ponta ne

• us

e m issio n S tim ulate d e m issio n O ptic a l P

• w

e r

Pumped electrically or

• ptically until population

inversion happened. → Emission > Absorption.

Lih Y. Lin EE 529 Semiconductor Optoelectronics – Semiconductor Lasers 5

Optical Gain Spectrum

Optical gain coefficient g: Fractional change in the light power (or intensity) per unit distance

( )

* 3/2 2 1/2 2 1 2 2 2

2( ) g( ) [ ( ) ( )]

r g c v sp

m c h E f E f E n h ν = ν − − ν τ

F

E ∆

Lih Y. Lin EE 529 Semiconductor Optoelectronics – Semiconductor Lasers 6

Threshold Gain gth

L Pi Pf R1 R2 S te a d y sta te E M

• sc

illa tio n s R e f le c tin g su rf a c e R e f le c tin g su rf a c e C a v ity a x is x 1 2 Ef Ei

Shown on the right is a typical output power-Injection current characteristics of a laser diode. When does lasing happen?

PO I Lasing Ith → gth

Steady-state condition: Laser power is constant → Round-trip gain = Round-trip loss Where does the loss come from? Reflection loss at the mirrors. Losses in the cavity medium (scattering at defects, absorption by impurities, absorption by free carriers …)

1 2 exp[ (2 )]exp[

(2 )] : Loss coefficient of the laser medium

f i

P PR R g L L = −α α

1 2

1 1 ln 2

f i th

P P g L R R   = → = α +    

Lih Y. Lin EE 529 Semiconductor Optoelectronics – Semiconductor Lasers 7

Threshold Current and Efficiency

Laser diode active layer thickness = d Determine Nth from the gain spectrum Above threshold, under steady state,

I

Ith nth n n

Threshold population inversion

Po

Po = Lasing output pow er ∝ Nph Slope represents efficiency

th th inj s

edN J = η τ

External quantum efficiency

( )

sp th th inj i

edR N J = η η

• r

1 2 1 2

(1/ 2 )ln(1/ ) ( ) (1/ 2 )ln(1/ )

ut i inj th

L R R h P I I e L R R ν = η η − α +

( )

1 2 1 2

( / ) (1/ 2 )ln(1/ ) / (1/ 2 )ln(1/ )

• ut

e i inj th

d P h L R R d I I e L R R ν η = = η η − α +

Slope efficiency

• ut

s e

dP h VdI eV ν η = = η

Power conversion efficiency

1

• ut

th c e

P I h VI eV I ν   η = = η −    

Lih Y. Lin EE 529 Semiconductor Optoelectronics – Semiconductor Lasers

Exercise: Threshold Current Density of a GaAs Laser

8

Calculate the threshold current of a GaAs laser with an undoped active region of width d = 0.2 µm starting from g(E) and Rsp(E): Assuming the following parameters for the laser: L = 400 µm, R1 = R2 = 0.9, α = 103 cm-1, Γ = 0.95, ηi = 0.9, ηinj=1 . Along your calculation, verify that you obtain the following results:

( )

1/2 4 1 2 1

g( ) 3 10 [ ( ) ( )] cm

g c v

E E E f E f E E

−

− = × −

( )

1/2 29 1 3 1 2 1

( ) 1.15 10 ( )[1 ( )] s cm (eV)

sp g c v

R E E E E f E f E

− − −

= × − −

Lih Y. Lin EE 529 Semiconductor Optoelectronics – Semiconductor Lasers

Exercise: Efficiencies of an InP Laser

9

An InP Fabry-Perot laser emits at wavelength ~ 920 λ =

• nm. It has an

injection efficiency 90%

inj

η = and an internal quantum efficiency 95%

i

η = . The voltage applied to the device is 2.5V. The reflectivity

• f both cavity ends are

1

100% R = and

2

70% R = . The loss coefficient of the laser medium is 1 α = cm-1. Its threshold current is characterized to be 1

th

I = mA. (a) The semiconductor laser has a cavity length L = 400 µm. Assume the refractive index n = 3.3. What should be the exact emission wavelength? At which longitudinal mode does lasing

• ccur?

(b) Calculate the photon extraction efficiency, external quantum efficiency, and slope efficiency of the device. (c) If the laser is operated at an injection level twice the threshold, find its power conversion efficiency and output power.

Lih Y. Lin EE 529 Semiconductor Optoelectronics – Semiconductor Lasers

Transient Response

10

Transient phenomena occur because of the time required for the electron and photon populations to come into equilibrium. As the photon population builds up rapidly, the carrier density is depleted until it falls below transparency condition.  Photon population

• decreases.  Carrier population starts to build up again, this time from a higher initial

value, and so does the photon population.

Lih Y. Lin EE 529 Semiconductor Optoelectronics – Semiconductor Lasers

Frequency Response under Small-signal Modulation

11

As the initial oscillations cease, the situation becomes periodic small-signal modulation

• f a laser.

2 2

( ) | |

i c n r r

m r r e i

ϕ

γ γ Ω = = Ω − Ω + Ωγ

Complex response function:

2 2 2 2 4 2 2 2 2 2 2

( ) ( ) 16 ( ) 4

c n r r

m R f r f f f f γ γ = = π − + π γ Modulation power spectrum: Resonance peak:

1/2 2 2 2

8

r pk r

f f   γ = −   π   3-dB modulation bandwidth:

1/2 2 1/2 2 3 2

(1 2) 8 2

r dB r

f f   γ = + −   π  

Lih Y. Lin EE 529 Semiconductor Optoelectronics – Semiconductor Lasers

Exercise: Modulation Characteristics

12

A GaAs QW VCSEL has the following parameters: Emission wavelength = 850 nm, refractive index 3.52 n = , gain overlap factor 0.2 Γ = , threshold gain coefficient

4 1

8.16 10 m

th

g

−

= × , excess carrier spontaneous lifetime 3.02 ns

s

τ = , gain cross-section

19 2

2.2 10 m

−

σ = × . (a) Find the values of spontaneous carrier relaxation rate

s

γ and cavity decay rate

c

γ . What is the photon lifetime

c

τ ? (b) If the laser output power 60.6 W

• ut

P = µ , the mode volume

18 3 mode

4.74 10 m V

−

= × , the emitted and photon extraction efficiency 89%

t

η = . Find the intracavity photon density S . (c) Find the values of differential gain parameter

n

g . Assume the nonlinear gain parameter

p n

g g = − , find the values of differential carrier relaxation rate

n

γ and nonlinear carrier relaxation rate

p

γ . (d) Find the values of relaxation resonance frequency

r

f and total carrier relaxation rate

r

γ . (e) Find the resonance peak of the modulation spectrum

pk

f . What is the 3-dB modulation bandwidth

3dB

f ?

Lih Y. Lin EE 529 Semiconductor Optoelectronics – Semiconductor Lasers 13

Heterojunction Lasers

Ith for homostructure laser diode extremely high → Not practical for room temperature operation

R e fra c t iv e in d e x P h o to n d e n si ty

A c t iv e re g io n

∆n ~ 5 %

2 eV

H o l e s in V B E le c tro n s i n C B A l G a A s A l G a A s

1.4 eV

Ec Ev Ec Ev (a) (b) p n p ∆Ec

2 eV

(~ 0 .1 µm ) (c) (d) G a A s Oxide insulator Stripe electrode

Substrate

Electrode Active region where J > Jth. (Emission region) p-GaAs (Contacting layer) n-GaAs (Substrate) p-GaAs (Active layer)

Current paths

L W Cleaved reflecting surface

Elliptical laser beam

p-AlxGa1-xAs (Confining layer) n-AlxGa1-xAs (Confining layer)

1 2 3

Cleaved reflecting surface Substrate

Heterostructure laser: Enhance carrier confinement and photon confinement

Lih Y. Lin EE 529 Semiconductor Optoelectronics – Semiconductor Lasers 14

DBR Laser and DFB Laser

λ Laser

Optical Power

Output spectrum of a typical Fabry-Perot (F-P) laser

L

2L q = λ

→ Many wavelengths are possible, as long as they are within the gain spectrum How do we obtain single-frequency semiconductor lasers?

C

• r

r u g a t e d d ie l e c t r i c s t r u c t u r e D i s t r i b u t e d B r a g g r e f le c t

• r

(a) (b)

A B

Λ

q(λB/2n) = Λ

A c t i v e l a y e r

Distributed Bragg reflector (DBR) laser

Λ

A ct iv e la y e r C

• rr

u g at ed g ra ti n g G u id in g l ay e r

(a)

O p ti ca l p

• w

e r

λ ( n m )

.1 n m Id e al l as i n g em is s io n

λ λ B (b) (c)

Distributed feedback (DFB) laser

( ) 2

m B B

c m n l ν ≈ ν ± + µ

Lih Y. Lin EE 529 Semiconductor Optoelectronics – Semiconductor Lasers 15

Typical Grating Coupler Structure and Coupled-Mode Theory

Coherent coupling between forward- and backward-propagating waves results in selection of longitudinal modes.

( ) ( )

2 2 2 2 2

sinh | | 1 / cosh | | 1 / / L R L κ − δ κ = κ − δ κ − δ κ ( )

B

δ = β − β ω

Lih Y. Lin EE 529 Semiconductor Optoelectronics – Semiconductor Lasers

Exercise: DBR Laser

16

A DBR laser has gain section of length 400 l = µm and two identical DBRs as end mirrors, each of length 150 m

DBR

l = µ . The grating period of the DBR is 225 nm Λ = . The effective indices for the laser modes are 3.45 n N

β β

= = . The DBR coupling coefficient is

1

| | 50 cm− κ = . The gain spectrum peaks ~1550 nm. (a) Find the Bragg wavelength and frequency near the gain peak. (b) Find the peak reflectivity and the bandwidth of the two DBRs. (c) Find the effective phase length of the DBRs and that of the DBR laser to determine the longitudinal mode spacing of the laser. (d) Assume the gain bandwidth is much broader than the DBR frequency bandwidth, how many longitudinal modes can exist? (e) If the laser is pumped right at the threshold, only one mode can oscillate. What’s its wavelength? Calculate the DBR reflectivity at this lasing wavelength.

Lih Y. Lin EE 529 Semiconductor Optoelectronics – Semiconductor Lasers 17

Vertical Cavity Surface Emitting Laser (VCSEL)

Contact Surface emission Dielectric mirror Contact Substrate

λ/4n1

Active layer

λ/4n2

Dielectric mirror

Dielectric mirrors → Distributed Bragg reflector structures

SEM (Scanning electron micrograph) of a VCSEL array.

/ 2

B

n Λ = λ A 1st-order square grating of a 50% duty factor has the largest coupling coefficient

2 | | n ∆ κ = λ