Comparison of 1300 nm quantum well lasers
using different material systems
G . L I N * A N D C . P . L E E
Department of Electronics Engineering, National Chiao Tung University, Hsinchu, Taiwan, Republic of China
(*author for correspondence: E-mail: [email protected])
Abstract. The band structure and material gain are calculated for 1300-nm band quantum well lasers of GaInNAs, AlGaInAs and GaInAsPmaterial systems. The material compositions for each system are carefully chosen for comparison. The calculated results show that the peak gain is around the same in spite of the difference in band structures for the three systems.
Key words: band offset ratio, band structure, material gain, 1300-nm band, quaternary material system
1. Introduction
The optical communications market has seen a great expansion due to the strong demand for subscriber-loop applications such as fiber-in-the-loop (FITL) and fiber-to-the-home (FTTH). 1300-nm band quantum well lasers are the key components in these optical fiber communication systems. The emitters should be temperature insensitive for uncooled system and low-cost for common subscribers. Nevertheless, the GaInAsPsystem on InPsubstrate suffers from poor temperature characteristics due to electron overflow over the rather small conduction band offset. Although AlGaInAs system has been proposed for better high-temperature operation, the theoretical and experimental comparison does not seem to be based on the same basis.
Recently, GaInNAs system on GaAs substrates has been successfully demonstrated for 1300 nm lasers. The large band gap bowing makes the long-wavelength lasing possible for devices made with such material system based on low-cost GaAs substrates. The huge conduction band offset also contributes to the superior high-temperature characteristics (Kondow et al. 1997).
In this paper, we present theoretical comparison for the quantum well lasers based on GaInAsP, AlGaInAs and GaInNAs systems emitting at 1300 nm. The material parameters and the relevant models for different material systems are described. The criterion for choosing the material
composition is also given. Finally, the material gain is calculated and com-pared. In this way the lasers are compared in the equal footing.
2. Theoretical background
2.1. BAND STRUCTURE CALCULATION
The valence band structure (Ev ) kt) is calculated by using the
block-dia-gonalized 3· 3 strained Luttinger–Kohn Hamiltonian (Chuang 1995) and is given by H33U ;L¼ P þ Q jRkj i Sj jk ffiffiffi 2 p Rk j j iffiffi 2 p j jSk Rk j j i Sj jk P Q ffiffiffi 2 p Q i ffiffi 3 2 q Sk j j ffiffiffi 2 p Rk j j iffiffi 2 p j jSk pffiffiffi2Q i ffiffi 3 2 q Sk j j P þ D 2 6 6 6 4 3 7 7 7 5þ Vv ð1Þ where P ¼ Pkþ Pe Q¼ Qkþ Qe Pk ¼ h2 2m0 c1k2t o ozc1 o oz Qk ¼ h2 2m0 c2k2t þ 2 o ozc2 o oz Rk j j h 2 2m0 ffiffiffi 3 p 2 ðc2þ c3Þk 2 t j j ¼ iSk h2 2m0 ffiffiffi 3 p kt o ozc3þ c3 o oz Pe ¼ avðexxþ eyyþ ezzÞ Qe ¼ b 2ðexxþ eyy 2ezzÞ exx ¼ eyy ¼ a0 a a ezz ¼ 2C12 C11 exx exy¼ eyz¼ ezx¼ 0 ð2Þ
Here, the strain components, exx, eyy, and ezz, are related to the lattice
con-stant of the active layer and the substrate (a and a0, respectively), and the
elastic constant C11and C12. For calculating the conduction band structure,
the single-band effective mass equation is used. With strain included, the Hamiltonian is given by Hc¼ h2 2 k2t mct o oz 1 mcz o oz þ Vcþ acðexxþ eyyþ ezzÞ ð3Þ
The band offset, Vvin Equation (1) and Vcin Equation (3), will be treated in
2.2. CALCULATION OF STRAINED BULK BAND GAP
Setting the unstrained valence band-edge of the active region material as the reference energy of zero. The strained bulk valence band-edge, determined from Equation (1) with k¼ 0, is shifted by
dEhh¼ Pe Qe ðcompressiveÞ
dElh ¼ Peþ Qe ðtensileÞ
ð4Þ
and the strained bulk conduction band-edge, determined from Equation (3) with k = 0, is shifted by
dEc ¼ acðexxþ eyyþ ezzÞ ð5Þ
The strained band gap, Egs, can therefore be expressed as
Egs ¼
Eguþ dEc dEhh (compressive)
Eguþ dEc dElh (tensile)
ð6Þ
2.3. CALCULATION OF BAND OFFSET
The relative band alignment of band-edges between the quantum well and the barrier is very important, nevertheless controversial, for modeling semicon-ductor quantum well structures. This is rather complicated for the strained case. Two models regarding the band alignment are reviewed and chosen for the relevant quaternary systems.
(1) Model-solid theory (Van der Walle 1989): The valence band position is given by Ev¼ Ev;avþD3þ dEhh for hh Ev;avþD3þ dElh for lh ð7Þ
where Ev,av is the average valence band-edge energy and D is the spin-orbit
split-off energy. The conduction band position can be calculated by simply adding the strained band gap energy, Egs, to the valence band position. The
conduction band offset ratio is given by DEc DEg ¼ 1 E w v Ebv Eb gs Ewgs ð8Þ
where Ewgs and Ebgs are the strained band gaps for the well and the barrier, respectively.
(2) Harrison’s model (Harrison 1977): The band-edge positions of the con-duction band and the valence band are given by
EHv ¼ EvHþ dEhh for hh EvHþ dElh for lh
EHc ¼ EcHþ dEc
ð9Þ
where EvH and EcHare Harrison’s band-edge energy. The conduction band
offset ratio is then given by DEc DEg ¼ E H;b c EcH;w ðEH;bc EH;wc Þ þ ðEH;wv EH;bv Þ ð10Þ
where the superscript ÔwÕ and ÔbÕ refer to the well and the barrier, respectively.
2.4. CALCULATION OF MATERIAL GAIN
The optical gain is calculated based on the Fermi’s Golden Rule and Lo-rentzian lineshape function with an intraband relaxation time of 0.1 ps. Only TE modal gain is calculated for compressive strain that we are concerned here. The momentum matrix elements for the quaternary active layer are interpolated from their binary constituents. The material and band param-eters used in the calculation are listed in Table 1.
3. Simulation details
Unless otherwise specified, the material parameters P for quaternary GaIn-AsP, AlGaInAs and GaInNAs systems are interpolated from their respective binary or ternary constituents and are given as,
PðGaxIn1xAsyP1yÞ ¼ xyPðGaAsÞ þ ð1 xÞð1 yÞPðInPÞ
þ ð1 xÞyP ðInAsÞ þ xð1 yÞP ðGaPÞ
PðGaxAlyIn1xyAsÞ ¼ xP ðGaAsÞ þ yP ðAlAsÞ þ ð1 x yÞP ðInAsÞ
PðGaxIn1xNyAs1yÞ ¼ P ðGaxIn1xAsÞ þ P ðGaNyAs1yÞ P ðGaAsÞ
ð11Þ
The material parameters of the binary semiconductors are listed in Table 1. For GaInNAs system, the material parameters of GaInAs is used because the N content is rather small ( 1%) in quantum well lasers.
One exception to above interpolation formula is the unstrained band gap. For GaInAsP, AlGaInAs systems, and GaInAs/GaNAs in the GaInNAs system, the unstrained band gap is given as,
EguðGaxIn1xAsyP1yÞ ¼ 1:35 þ 0:668x 1:068y þ 0:758x2þ 0:078y2
0:069xy 0:322x2yþ 0:03xy2ðeVÞ
EguðAlxGayIn1xyAsÞ ¼ 0:36 þ 2:093x þ 0:629y þ 0:577x2þ 0:436y2
þ 1:013xy 2:0xyð1 x yÞðeVÞ EguðGaxIn1xAsÞ ¼ 0:36 þ 0:509x þ 0:555x2ðeVÞ
EguðGaNyAs1yÞ ¼ 1:424 14:024y þ 18y2ðeVÞ
ð12Þ
All the band gap data are taken from (Chuang 1995) except that for ternary GaNAs which is taken from (Takeuchi et al. 1998).
Regarding to the band offsets, different model is chosen for different ma-terial systems. For GaInAsPand AlGaInAs systems on InPsubstrate, Harrison’s model, instead of model-solid theory, is used because it has a better agreement with the empirical results (Minch et al. 1999). For the GaInNAs system on GaAs substrate, the model-solid theory is used as in the case for strained GaInAs materials.
Table 1. Material parameters for the calculation for GaInAsPand AlGaInAs and GaInNAs material systems
Materials GaAs AlAs InAs InPGaPGaN
Parameters
a0(A˚) 5.6533 5.6600 6.0584 5.8688 5.4505 4.503
Eg(eV) at RT 1.424 3.03 0.354 1.344 2.78 3.40
D (eV) 0.34 0.28 0.38 0.11 0.08 –
MME (eV) 25.7 21.1 22.2 20.7 22.2 –
Deformation potential (eV)
ac(eV) 7.17 5.64 5.08 5.04 7.14 –
av(eV) 1.16 2.47 1.00 1.27 1.70 –
b(eV) 1.7 1.5 1.8 1.7 1.8 –
C11(1011dyne/cm2) 11.879 12.5 8.329 10.11 14.05 –
C12(1011dyne/cm2) 5.376 5.34 4.526 5.61 6.203 –
Effective mass (in unit of h2/2m
0)
c1 6.8 3.45 20.4 4.95 4.05 –
c2 1.9 0.68 8.3 1.65 0.49 –
c3 2.73 1.29 9.1 2.35 1.25 –
Model-solid theory (average valence-band-edge energy)
Ev,av(eV) –6.92 –7.49 –6.67 –7.04 –7.40 –
Harrison’s Model (valence-band-edge energy in reference scale)
EvH(eV) 0.111 –0.4245 0.441 0 –0.388 –
As a first-order approximation, we use the momentum matrix element of GaInAs for the GaInNAs system. However, due to the interaction between the conduction band and the nitrogen states, a more accurate calculation should include a correction factor, fCc (Lindsay and O’Reilly 1999).
4. Results
Fig. 1 shows the contour plot relating x and y to the strain and the strained bulk band gap of GaxIn1xAsyP , GaxAlyIn1xyAs, and GaxIn1xNyAs1y
systems. The solid lines are for strained bulk band gap and the short-dashed lines are for strain. The long-dashed line delimits the boundary between type-I and type-type-Itype-I heterojunctions. For lasing transition in 1300-nm band, we choose the strained bulk band gap around 0.9 eV in account of quantum confinement of 0.05 eV.
The conduction band offset ratio versus Ga composition for GaInAsP and AlGaInAs systems on InPare shown in Fig. 2. The solid line and dashed line are for the latticed-matched GaInAsPand AlGaInAs sys-tems, respectively, while the enclosed regions are for strained systems with strained bulk band gap of 0.9 ± 0.02 eV. It reveals that the conduction band offset is larger for lower Ga content or higher compressive strain. So, to increase the conduction band offset can be achieved by maximizing the compressive strain (or minimizing the Ga content). The quaternary compositions for GaInAsPand AlGaInAs are therefore determined for subsequent band structure calculation. For the GaInNAs system, the N content and the maximum allowable compressive strain should be practical otherwise the device performance may degrade. The quaternary composi-tions chosen for the active layers for these material systems are marked by ‘X’ in Fig. 1.
Fig. 3 shows calculated band structure for different material system com-binations. The zero energy is chosen to be the top of the unstrained valence band. The strained band-edge and the barrier band-edge are also determined and shown in the figure for comparison. The lowest transition wavelength is around 1300 nm. The well width chosen is 70 A˚ for all the material combi-nations and the value of the compressive strain chosen is for practical con-sideration. The barrier band gap wavelength is 1100 nm for both GaInAsP and AlGaInAs on InPsubstrates, while the barrier band gap for the GaIn-NAs lasers is that of GaAs. The strained band offset ratio (DEc:DEv) for the
three material combinations, InAsP/GaInAsP, AlInAs/AlGaInAs and GaInNAs/GaAs, are 0.48:0.52, 0.51:0.49 and 0.74:0.26, respectively. For InAsP/AlGaInAs, the strained band offset ration is 0.70:0.30. In terms of larger conduction band discontinuity, it is the best choice to have GaInAsP over AlGaInAs on InPsubstrate.
Fig. 4 shows the gain spectra versus carrier density (from 1 1018 to
5 1018 cm)3) for the above material systems. Only TE polarization gain
spectra are shown for compressively strained quantum well systems. The peak gain versus injected carrier concentration is shown in Fig. 5. The gain spectrum for GaInNAs is shown without the correction factor, fCc. If a factor
of 0.8 were used (multiply the calculated result by 0.8) for GaInNAs, the peak material gain for the three systems is around the same. Here, we may have under-estimated the conduction band effective mass for GaInNAs as the
Fig. 1. Strain and strained bulk band gap energy versus material composition for GaInAsP, AlGaInAs and GaInNAs material systems.
Fig. 3. Conduction and valence band structure for the four quantum well lasers. The solid horizontal lines are for unstrained well or barrier edges and the horizontal dashed lines are for strained well band-edges.
Fig. 2. Conduction band offset ratio versus Ga composition for lattice-matched and compressively strained GaInAsPand AlGaInAs systems on InP. The solid lines are for GaInAsPsystem, and the dashed lines are for AlGaInAs system.
strong interaction from the N impurity may increase its value (Lindsay and O’Reilly 1999).
For the four material combinations considered here, the material gain is around the same, however, GaInNAs/GaAs outperforms the other in terms of conduction band offset. Its large band discontinuity as well as large conduction band offset ratio would contribute to superior high-temperature characteristics for temperature insensitive applications.
5. Conclusion
We have theoretically calculated the band structure and material gain for quantum well lasers of GaInAsP, AlGaInAs and GaInNAs systems emitting in 1300-nm band. The quaternary compositions are carefully chosen to maximize the conduction band offset of each material system. Four hetero-structure combinations out of three material systems are compared. Despite the differences in the band structure, the material gain is around the same for all these systems. However, the GaInNAs/GaAs system should be a better
Fig. 4. Gain spectra versus injected carrier concentration for the four quantum well lasers. The injected carrier density increases from 1 1018to 5 1018cm)3.
choice because of its large conduction band offset would decrease the carrier leakage over the barrier and the device’s temperature sensitivity.
Acknowledgements
This work is supported by the National Science Council of the Republic of China under Contract NSC89-2218-E-009-055 and the LEE-MTI Founda-tion of the NaFounda-tional Chiao Tung University.
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