1 EE232 Lecture 14-1 Prof. Ming Wu EE 232 Lightwave Devices Lecture 14: Quantum Well and Strained Quantum Well Laser Reading: Chuang, Sec. 10.310.4 (There is also a good discussion in Coldren, Appendix 11) Instructor: Ming C. Wu University of California, Berkeley Electrical Engineering and Computer Sciences Dept. EE232 Lecture 14-2 Prof. Ming Wu Quantum Well Gain 1.4 1.6 1.8 2 2.2 2.4 2.6 1 − 10 6 × 0 1 10 6 × xi eV QW Material Gain: g (!ω ) = C 0 e ! ⋅ P !" cv 2 ρ r 2d (!ω ) f g (!ω ) C 0 = π e 2 n r c ε 0 m 0 2 ω e ! ⋅ P !" cv 2 ≈ m 0 6 E p ρ r 2d ( E ) = m r * π ! 2 L z H ( E − E en ) n=1 ∞ ∑
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
1
EE232 Lecture 14-1 Prof. Ming Wu
EE 232 Lightwave DevicesLecture 14: Quantum Well andStrained Quantum Well Laser
Reading: Chuang, Sec. 10.3-10.4(There is also a good discussion in Coldren, Appendix 11)
Instructor: Ming C. Wu
University of California, BerkeleyElectrical Engineering and Computer Sciences Dept.
EE232 Lecture 14-2 Prof. Ming Wu
Quantum Well Gain1.4 1.6 1.8 2 2.2 2.4 2.61−
0.5−
0
0.5
1
f_g xi 0.05eV, ( )f_g xi 0.1eV, ( )f_g xi 0.15eV, ( )f_g xi 0.2eV, ( )f_g xi 0.25eV, ( )f_g xi 0.3eV, ( )f_g xi 0.35eV, ( )f_g xi 0.4eV, ( )f_g xi 0.45eV, ( )
xieV
1.4 1.6 1.8 2 2.2 2.4 2.6
1− 106×
0
1 106×g xi 0.05eV, ( )g xi 0.1eV, ( )g xi 0.15eV, ( )g xi 0.2eV, ( )g xi 0.25eV, ( )g xi 0.3eV, ( )g xi 0.35eV, ( )g xi 0.4eV, ( )g xi 0.45eV, ( )
xieV
QW Material Gain:
g(!ω) =C0 e! ⋅P!"cv
2
ρr2d (!ω) fg (!ω)
C0 =πe2
nrcε0m02ω
e! ⋅P!"cv
2
≈m0
6Ep
ρr2d (E) =
mr*
π!2LzH (E − Een )
n=1
∞
∑
2
EE232 Lecture 14-3 Prof. Ming Wu
Advantages of Quantum Well Lasers(1) Low threshold current density:Compare fundamental material property
Transparency current density
10 nmSince ~100 nm
10%(
bulkbulk trtr active
QWQW trtr z
QWbulk QW tr ztr tr bulk
tr active
qNJ d
qNJ L
J LN NJ d
τ
τ
→
=
=
≈ ⇒ =
2) Higher differential gain Larger bandwidth:
Resonance frequency:
(3) Lower chirp:Smaller wavelength shift when the laser is directly modulated
Reduction of Lasing Threshold Current Density by Lowering Valence Band Effective Mass
• Yablonovitch, E.;; Kane, E., "Reduction of lasing threshold current density by the lowering of valence band effective mass," Lightwave Technology, Journal of , vol.4, no.5, pp. 504-506, May 1986
• Yablonovitch, E.;; Kane, E.O., "Band structure engineering of semiconductor lasers for optical communications," Lightwave Technology, Journal of , vol.6, no.8, pp.1292-1299, Aug 1988
1 1
Bernard-Duraffourg Condition:
C V e hF F E Eω− ≥ ≥ −h
* *
Ordinary Semiconductor6
High transparency carrier concentration
h em m≈ * *
Ideal Semiconductor
Low transparency carrier concentration
h em m≈
4
EE232 Lecture 14-7 Prof. Ming Wu
Bernard-Duraffourg Condition in Quantum Well
Bernard-Duraffourg Condition:FC − FV = E − Eh1(a) mh
* >me* (as in most semiconductors)
FV > Eh1FC ≫ Ee1
Ntr = ρe2d (FC − Ee1) =
me*
π!2Lz(FC − Ee1)
Large Ntr → High threshold current
(b) mh* =me
* (Ideal semiconductor)
FV = Eh1FC = Ee1
Ntr =me
*
π!2LzfC (E)dE
Ee1
∞
∫ is low
EE232 Lecture 14-8 Prof. Ming Wu
Transparency Carrier Concentration for Ordinary Semiconductor
( )
1
1
* *1 1
*
2
*
20
*
2 0
*
2
*0
17 3
(b) Ideal Semiconductor
=
1
11
1
ln(1 )
ln 2
For =0.067
4.6 10
e
e B
h e V h C e
etr E E
z E k T
B ex
z
xB e
z
B e
z
e
tr
m m F E F E
mN dEL
ek Tm dx
L e
k Tm eL
k TmL
m m
N cm
π
π
π
π
∞
−
∞
∞−
−
= ⇒ =
=+
=+
= − +
=
≈ ×
∫
∫
h
h
h
h1 1
Transparency Condition:
C V e hF F E E− = −
5
EE232 Lecture 14-9 Prof. Ming Wu
Transparency Carrier Concentration for Ordinary Semiconductor
1 1
Transparency Condition:
C V e hF F E E− = −
*2
1 2
*2
2
*
*
* *
*
(a) Ordinary Semiconductor
( )
To estimate , note that
For 6 (in 1.55 m laser), 1.43
1.43
B B
B
d etr e C e
z
k T k Td B hV
z
k T e
B h
h e
B
B etr
mN F ELN P
k TmP N e eL
mN P ek T m
m mk Tk TmN
ρπ
π
µ
π
−Δ −Δ
−Δ
= − = Δ
Δ =
= =
Δ= ⇒ =
≈Δ =
=
h
h
h2zL
EE232 Lecture 14-10 Prof. Ming Wu
Effective Mass Asymmetry Penalty
2 3 2 3
1.43 2ln 2
Threshold current density reduction is more than a factor of 2: