Optical Gain Spectra in InGaN/GaN Quantum Wells with the Compositional Fluctuations
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The compositional fluctuations of the In content were found in InGaN/GaN quantum wells and it caused the localized states by the potential fluctuation. We have evaluated the optical gain of GaN based quantum well structures with localized states. The localized states are treated as the subband states of the quantum disk-like dots in the well. It was found that the inhomogeneous broadening played an important role in the optical gain and that it should be reduced to use the benefit of the localized states for laser oscillations. Introduction A short wave length is one of the essential requirements of laser diodes (LDs) for highdensity storage devices. Recently, continuous-wave operation of the InGaN multi-quantum-well LDs with a life time of more than thousand hours has been achieved [1]. However, there is a key issue, such as high threshold carrier density, to lead them to commercial production. So far, we evaluated the optical gain of the wurzite GaN/AIGaN quantum well lasers and derived that the threshold current density of the GaN/AIGaN LDs would be estimated very high compared to conventional GaAs/AIGaAs quantum well LDs. It is caused by the large density of states due to the strong electronegativity and the weak spin-orbit coupling of the N atom in group-Ill nitrides. To overcome the problem, we proposed the strain effects [2] and the incorporation of the GaAs or GaP in the well layer to reduced the density of states. On the other hand, the well layer of InGaN/GaN quantum wells has the compositional fluctuations of the In contents. These fluctuations would induce the localized states due to the random potentials. Since the radiative recombination attributed to the localized excitons by the alloy fluctuation in InGaN/GaN quantum wells were measured recently [3,4], it becomes important to study the relation between the localized states and the optical gain. We evaluated the optical gain coefficient, including the broadening in the spectra by the transitions between the localized states.
G 2.9 Mat> Res, Soc. Symp. Proc. Vol. 537 0 1999 Materials Research Society
Formalism Let us describe the localized states caused by the compositional fluctuations. We assume that the potential fluctuations in the well are written by the quantum-disk like potentials and that they are randomly distributed without any correlation among them, as shown in Fig. 1. The Hamiltonians H' for the electronic states for the electron (i=e), the heavy hole (i=hh) and the light hole (i=lh) is given by H' = h'(z) + U (r, z), 2mi where
2
h d92 hm ,3•2 + Vý,w(z), (i = e, hh,lIh), 2
h'(z)
m, tZ
F
if z >-L2
0 v(r-rj,Rj,uj)
U(r,z)=-
otherwise
v(r - r,, R., uj) are the potentials by the compositional fluctuations at rj in the two dimensional system, where RJ and uJ are the radius and the potential depth of the quantum-disk, respectively, Then, the eingenfunctions of the localized state can be approximated as as shown in Fig.2. n(r, z) = i' ( ) ,( j,..... where
h
2mi
c-•R~u L2 +
))2j,(r)=
P
in j
)
E',m,n I (z).
hi(Z),m(n)(z ý'Jn(r
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