Enhanced longitudinal mode spacing in blue-violet InGaN semiconductor laser

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by  Igor V. Smetanin

Enhanced longitudinal mode spacing in blue-violet InGaN semiconductor laser
Enhanced longitudinal mode spacing in blue-violet InGaN semiconductor laser
I.V. Smetanin1,a) and P. P. Vasil’ev1,2
1)P. N. Lebedev Physical Institute, Leninskii prospect 53, Moscow 119991, Russia
2)Centre for Photonic Systems, University of Cambridge, 9 J.J. Thomson Avenue, Cambridge CB3 0AF,
UK
(Dated: 16 January 2012)
AnovelexplanationofobservedenhancedlongitudinalmodespacinginInGaNsemiconductorlasershasbeen
proposed. It has been demonstrated that e-h plasma oscillations, which can exist in the laser active layer at
certain driving conditions, are responsible for mode clustering effect. The resonant excitation of the plasma
oscillationsoccursduetolongitudinalmode beating. Theseparationofmode clustersistypicallybyanorder
2 of magnitude larger that the individual mode spacing.
1
0
2
Blue-violet GaN-based diode lasers have attracted a Eg

n great deal of attention over the last decade because AlGaN
a of their growing applications in optoelectronics, optical AlGaN
J
storage systems, medicine, and some other field of mod-

3
ernscienceandtechnology. Atthesametime,manyfun-
1
damental properties of this type of semiconductor lasers

have not been completely investigated and are not yet
]
s well understood. One of the notable features of InGaN
c
lasersisthatmodespacingoftenexperimentallyobserved
i GaN Ev
t in optical spectra of lasing emission can be 8-10 times
p
o larger as compared to that calculated from the cavity
. length1–4. A few physical mechanisms have been pro- 1
s h
c posed for explaining this effect. Irregular longitudinal
y
si mode spectra can be caused either by variation of the sit 0.8
y imaginarypartoftherefractiveindexorbyamodulation en e
h of the real part of the refractive index along the active d 0.6
y
[p rceaguisoend.byIrrsecgauttlearriintyg fmroamy braendaottmrilbyudteisdtrtibouitnetdersfceartetnecre- bilit 0.4
a
1 ing centers along the waveguide. In InGaN semiconduc- ob
v tor lasers an inhomogeneous distribution of threading Pr 0.2
4 dislocations may cause inhomogeneous strain and local
0 scattering centers. 0
8 Meyer et al have recently demonstrated5 that optical 0 02.02 0.440 06.06 080.8 110.00
2
gainfluctuations canbe responsible for anadditionalfil- Distance (a.u.)
.
1 tering effect of longitudinal modes. Indeed, there are
0 severalmechanismsthatcancauseadecreaseorincrease FIG. 1. Schematic of the band diagram (top) and spatial
2
or of the gain for some longitudinal modes. Spatial distribution of the e-h probability densities in GaN quantum
1
fluctuations of the quantum well depth have been pro- well.
:
v posed as one of the reasons. The gain of an individual
Xi longitudinal mode is then given by the overlap of the
mode intensity distribution and the gain profile along anism explaining the mode spacing irregularity in GaN-
r
a the waveguide5. As a result, variations of modal gain in based diode lasers, which is based on the resonant ex-
the laser cavity can amplify certain longitudinal modes citation of plasma oscillations in the coupled 2D layers
moreefficientlythananother. Thismechanismexplained of electrons and holes. A characteristic feature of GaN-
reasonablywellopticalspectraofInGaNlasersgrownon based lasers (as compared to, say, GaAs/AlGaAs lasers)
SiCsubstrates,butfailedtodothesameforlasersgrown is the presence of an internal electric field caused by
on GaN substrates. On the other hand, at appropriate piezoelectric polarization existing in the structure6. As
conditions temporal variations of the optical gain may a result, the potential profile of the quantum well (QW)
also be responsible for irregular amplification of longitu- is distortedand the wavefunctions of electrons and holes
dinal modes. localize at the opposite sides of the QW, see Fig. 1. On
In this letter, we have proposed a new physical mech- other words, an effective capacitor is formed inside the
active layer, whose electrical field tends to compensate
the strong intrinsic electric field. One has the two layers
with the opposite charge of 2D electron and hole plas-
a)Electronicmail: [email protected] mas separated in space by a gap ∆. The value of ∆
Enhanced longitudinal mode spacing in blue-violet InGaN semiconductor laser 2
dependsontheinternalfieldstrength7,beingaroundthe At the conditions of the problem at hand, one can
QW width when the field is strong and vanishing when neglect the internal pressure terms9 in Eqs.(1) and in-
internal field disappears (i.e., becomes compensated by troduce the 2D plasma frequencies of electrons Ω2 =
pe
thespace-chargefield). Separationofchargedlayerspro- (2πn e2/εm )k and holes Ω2 = (2πn e2/εm )k. In
0e e ph 0h h
vides the low-frequencyplasma eigenmode insucha sys- the first order of perturbation theory, one can find the
tem of coupled oscillators, which vanishes for complete response functions f (ω,k) = n (ω,k)/S for elec-
e,h e,h nm
separation ∆ or merging of layers ∆ 0. The tron and hole plasma layers,
→ ∞ →
eigenfrequency for this mode in GaN is in sub-THz do-
main which provides the above experimentally observed
D (ω+iγ ) (ω+iγ )Ω2 e−k∆
modulation of lasing spectrum. f (ω,k)=i h e − h pe ,
Plasma oscillations in the active layer of InGaN lasers e D D Ω2 Ω2 e−2k∆
e h− pe ph
can be excited by the slow traveling wave of photoin- D (ω+iγ ) (ω+iγ )Ω2 e−k∆
duced modulation of plasma density8. Indeed, two lon- f (ω,k)=i e h − e ph . (3)
gitudinal modes with intensities Pn and Pm , frequen- h DeDh−Ω2peΩ2phe−2k∆
cies ω and ω , and wave numbers k and k form
n m n m
the low-frequency beating wave with the wave number where De = (ω+iγR)(ω+iγe)−Ω2pe and Dh =(ω+
k = kn +km and frequency ω = ωn+ωm. The rate of iγR)(ω +iγh)−Ω2ph determine the single-layer electron
photoinduced electron - hole generation is then modu- and hole plasma oscillation spectrum, respectively.
lated as S = σ√P P exp(i[kx ωt])+c.c., the co- Theresonantfrequenciesofplasmaresponsearedeter-
nm n m
efficient σ is proportional to the p−air photo-production mined by the denominator in Eq. (3). In the relaxation-
cross-section, and x is the co-ordinate along the active free case, it yields the following dispersion equation10,11
layer.
(ω2 Ω2 )(ω2 Ω2 ) Ω2 Ω2 e−2k∆ =0 (4)
Within the hydrodynamic approach, plasma oscilla- − pe − ph − pe ph
tions in the system of two separated 2D layers of elec-
In the limit of k∆ 1 there is no bound between the
trons and holes are described by the following system of ≫
layers, and 2D electron and hole liquids oscillate sepa-
equations8,9
rately with their own plasma frequencies. When layers
∂n ∂n v coincide, the eigenfrequency is (Ω2 + Ω2 )1/2 and the
e + e e = γ (n n )+S , pe ph
∂t ∂x − R e− 0e nm second root of Eq.(4) vanishes. In the case of our in-
∂n ∂n v terest, when the layer separation is small but not equal
h h h
+ = γ (n n )+S , (1)
R h 0h nm to 0, i.e. k∆ 1, two solutions exist: 1) the high fre-
∂t ∂x − −
≪
∂ve +v ∂ve = s2e ∂ne e (E +E ) γ v , qfrueeqnuceyncbyrabnrcahncωhh2igh ≈(Ω2pe+Ω2ph)−ωl2ow and2)thelow
e 11 21 e e
∂t ∂x −n ∂x − m −
0e e
∂v ∂v s2 ∂n e Ω2 Ω2
∂te +ve ∂xe =−n0hh ∂xh + mh(E22+E12)−γhvh. ωl2ow ≈2k∆Ω2pepe+Ωph2ph (5)
Here, n , v are the density and velocity of electron
e,h e,h With∆ 0,the low-frequencymodedegeneratesto the
and hole 2D liquids, n0e and n0h are their steady-state zero solu→tion.
densities, γ are the characteristic rates of momentum
e,h The plasma oscillations result in modulation of the
relaxationof electrons and holes, γ is the radiativelife-
R optical gain and consequently to an additional filtering
time of the carriers, s is the speed of sound in 2D
e,h of the longitudinal modes. The mode filtering mecha-
liquids. The first two equations are just the continuity
nism here is exactly the same as for the effect of gain
equations of 2D e-h densities with the source term being ?
fluctuations ,whenvariationsofmodalgaininthelaser
S . The second pair of the equations is the equations
nm cavityamplifycertainlongitudinalmodesmoreefficiently
ofmotionofelectronsandholesinself-consistentelectric
thananother. Nowthequestioniswhetherthepredicted
field. The 2Dlayerofelectronsis affectedbyits intrinsic
modulation of the laser spectrum can describe observed
electric field E and inter-layer electric field from the
11 enhancedmodespacing. AccordingtoEq. (5),assuming
holelayerE . Likewise,the layerofholesisaffectedby
21 the equal densities of electrons and holes n n =
E22 and the field from the electrons E12. Fourier com- n and taking into account that kc = (ω +0eω≈ )√0hε
ponents of the intra-layer self-consistent fields are9 2D n m ≈
2√εω , for the GaN diode parameters m 0.2m ,
n e 0
≈
2πe 2πe mh 0.8m0, and the radiation wavelength λ=425 nm,
E11(ω,k)=i ne(ω,k), E22(ω,k)= i nh(ω,k) we h≈ave the estimate for the low-bandplasma frequency
ε − ε
(2) ωlow 2π 0.84THz p∆[nm]n2D[cm−2]/1012 and
≈ × ×
heren (ω,k)andn (ω,k)arethedensitycomponentsof for the modulation of laser diode spectrum ∆λ/λ
electroens and holeshand ε is the dielectric permeability ω /ω 1.19 10−3p∆[nm]n [cm−2]/1012. ∼
low 2D
≈ ×
of the medium. For the inter-layer components one has Figure 2 illustrates the dependence of the nonlinear
the following relations9: E (ω,k) = E (ω,k)e−k∆ and response of the plasma double layer n (ω)/S on the
12 11 e nm
E (ω,k)=E (ω,k)e−k∆. oscillationfrequencyωwhichisdescri|bedbyEq. |(3). We
21 22
Enhanced longitudinal mode spacing in blue-violet InGaN semiconductor laser 3
sity depends on the cavity length, internal absorption,
carrier lifetime and some other parameters.
1.2 Inconclusion,wepresenthereanewexplanationofthe
a b mode clustering effect which is generally observed in In-
c
1.0 d GaNlasers. Theinternalpiezoelectricfieldintheselasers
)|
resultsinaslightseparationofwavefunctionsofelectrons
(
e |fe 0.8 athnadthinoleasbinoutnhdetawcoti-vlaeyreergedione.-hWsyestheamvepdlaesmmoansotsrcaitllead-
s
pon 0.6 tionscanexist. Theplasmaoscillationsleadtothe mod-
s ulationoftheopticalgaininthecavityandconsequently
e
ma r 0.4 taotiaonnsadofdimtioondaallfiglatienriningtohfethleasleorngciatvuidtyinaamlmpolidfyesc.eVrtaariin-
s
a longitudinalmodesmoreefficientlythananother. Thees-
l
p 0.2 timationofthe separationbetweenthe clusters ofmodes
fits well to the previously observed experimental values.
0.0 This research is supported by the EC Seventh Frame-
0 2 4 6 8 10
workProgrammeFP7/2007-2013undertheGrantAgree-
12 -1
frequency /10 s
ment N 238556(FEMTOBLUE).
0.0 0.2 0.4 0.6 0.8

, nm 1S.Nakamura,M.Senoh, S.Nagahama, N.Iwasa,T.Yamada,T.
Matsushita,Y.Sugimoto,H.Kiyoku,Appl.Phys.Lett.,69,1568
(1996).
FIG. 2. Frequency response of the 2D plasma at 2S.Nakamura,M.Senoh, S.Nagahama, N.Iwasa,T.Yamada,T.
a)∆[nm]n2D[cm−2]/1012 =0.25, b) 0.5, c) 0.75, and d)1.0 Matsushita,Y.Sugimoto,H.Kiyoku,Appl.Phys.Lett.,70,616
(1997).
3G.Ropas,A.LeFloch,G.Agraval,Appl.Phys.lett.,89,241128
(2006).
usetheaboveGaNdiode parametersλ=425nm, m
e ≈ 4C. Eichler, S. Schad, F. Scholz, D. Hofstetter, S. Miller, A.
0.2m0, mh 0.8m0, as well as the radiative relaxation Weimar,A.Lell,V.Harle,IEEEPhoton.Tech. Letts.,17,1782
rate γ =1≈09 s−1 , and the momentum relaxation rates (2005).
R
γ =γ =1012s−1. 5T.Meyer,H.Braun,U.T.Schwarz,S.Tautz,M.Schillgalies,S.
e h Lutgen, U.Strauss,Opt.Express,16,6833(2008).
One can clearly see that the spectral modulation pe-
6S.-H.ParkandS.-L.Chuang,in: NitridesemiconductorDevices,
riod ∆λ fits well to the observed experimental data1,5.
ed. J. Piprek , Wiley VCH Verlag GmbH & Co K GaA, Wein-
Since the modulation period, which determines the ob- heim,(2007).
servedmode spacing,depends onthe carrierdensity and 7I.A.Fedorov,V.N.Sokolov,K.W.Kim,J.M.Zavada,J.Appl.
the charge layers separation in quantum well, different Phys.,98,063711 (2005).
8I.V.Smetanin, H.Han,J.RussianLaserRes.,22,403(2001).
devices exhibit different ∆λ. It is well-known that the
9A.Fetter,AnnalsPhys.,81,367(1973); ibid.,88,1(1974).
carrierdensityinsemiconductorlasersfixesatthethresh- 10M.V.Krasheninnikov,A.P.Chaplik,Sov.Phys.JETP,52,279
old density and does not go up with an increase of the (1980).
current above the lasing threshold. The threshold den- 11R.Z.Vitlina,A.V.Chaplik,Sov.Phys.JETP,54,536(1981).