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Study on the effects of well number on temperature characteristics in 1.3-μm InGaAsP–InP quantum-well lasers
Infrared Physics & Technology 45 (2004) 209–215 www.elsevier.com/locate/infrared
Study on the effects of well number on temperature characteristics in 1.3-lm InGaAsP–InP quantum-well lasers Jinyan Jin b
a,*
, Decheng Tian
a,b
, Jing Shi
a,b
, Tongning Li
c
a Department of Physics, Wuhan University, Hubei 430072, People’s Republic of China International Center for Material Physics, Chinese Academy of Sciences, Shenyang 110016, People’s Republic of China c Inphenix Inc., Livermore, CA 94551, USA
Received 7 March 2003
Abstract Effects of well number on temperature characteristics in 1.3-lm InGaAsP–InP multi-quantum-well lasers have been investigated. A smaller well number is suitable for lower threshold current and higher differential quantum efficiency at 25 C, while larger well number produces better performances at 85 C. Furthermore, lasers with a larger well number can achieve a less output power penalty at high temperature. For the first time, a theoretical model has been established to precisely explain the relationship between the characteristic temperature of threshold current and that of external differential efficiency. 2003 Elsevier B.V. All rights reserved. Keywords: MOVPE; InGaAsP/InGaAsP SL-MQW; Well number; Characteristic temperature; Semiconductor lasers
1. Introduction Low-cost uncooled laser diodes, emitting at a wavelength of 1.3-lm with high-temperature and high-speed performances over a wide temperature range of )20–85 C, are highly desirable in both enterprise and public networks. Such advanced performances have been obtained in 1.3-lm InGaAsP–InP strained-layer multi-quantum-well (SL-MQW) lasers with 10 quantum-wells (QWÕs)
*
Corresponding author. Tel.: +86-27-87645613; fax: +86-2787654569. E-mail address: [email protected] (J. Jin).
[1,2]. A large well number are expected to maintain advanced performances at high temperatures, due to the reduction of gain saturation, threshold carrier density, and the electron leakage. All these advantages are beneficial for advanced high-temperature, and high-speed performances. However, a large well number would bring about increased internal loss and enlarged beam divergence in the transverse direction. The study of well number can provide a guideline for the uncooled operation in 1.3-lm InGaAsP–InP SL-MQW lasers. The effects of well number on the temperature characteristics of 1.3-lm InGaAsP–InP SL-MQW lasers have been investigated intensively [3–5], but these research activities have not explored the
1350-4495/$ - see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.infrared.2003.10.001
210
J. Jin et al. / Infrared Physics & Technology 45 (2004) 209–215
effect of external differential efficiency on the characteristic temperature of threshold current, and the relationship of their characteristic temperatures. In this paper, we have investigated the effects of well number on the temperature characteristics of threshold current as well as external differential efficiency. A reduced output power penalty at elevated temperatures has been obtained for the laser with a larger well number. Additionally, we have established an analytical expression of characteristic temperature of threshold current (T0 ðIth Þ), which describes the relationship between T0 ðIth Þ, and T0 ðgd Þ, the characteristic temperature of external differential efficiency. The theory shows that T0 ðIth Þ is directly determined by T0 ðgd Þ, and predicts T0 ðIth Þ with relative high accuracy compared to the experimental results in the temperature range of our interest.
2. Device structure and fabrication Fig. 1 shows the schematic band diagram of 1.3lm InGaAsP–InP SL-MQW active region. The MQW region is sandwiched by symmetric 2-step grad-index separate-confinement-heterostructure waveguide layers, lattice matched to InP substrate, with a band gap wavelength of 1.05-lm (60-nm thick) and 0.95-lm (40-nm thick). The undoped
0.9 0.95
1.05
1.4
Wavelength (µm)
MQW region is composed of 5-nm-thick compressively strained InGaAsP (Da=a ¼ 0:7%) well layers and 10-nm-thick InGaAsP (wavelength k ¼ 1:05 lm) barrier layers. Three wafers were grown, with 6, 8, and 10 quantum-wells in the active region on (100) n-InP substrates using lowpressure metalorganic vapor phase epitaxy (LPMOVPE). The p-InP cladding layer (P ¼ 5 1017 cm3 , 1.6-lm thick), and n-InP cladding layer (N ¼ 1 1018 cm3 , 1-lm thick) were grown on both sides of the MQW–SCH waveguide structure. The heavily p-doped lattice-matched InGaAs layer (P ¼ 2 1019 cm3 , 0.3-lm thick) grown above the p-cladding layer was used as the ohmic contact layer. Ridge waveguide (RWG) Fabry–Perot lasers with ridge width of 2.5-lm and cavity length of 300-lm were fabricated from these wafers. The as-cleaved devices were mounted on Cu heatsinks with the junction-up configuration for the investigation of their temperature-dependent performances. Before RWG process, photoluminescence (PL) measurement was carried out for three SL-MQW wafers at room temperature. The PL peak wavelengths of 1306-nm is independent on the well number, however, the full width at the half maximum (FWHM) of PL spectrum slightly increases from 28 to 32 meV when the well number increases from six to ten. The intensities of PL spectra are comparable among three wafers. No strain relaxation haze in 10-well MQW structure was found by Nomaski interference contrast microscopy observation; it could be attributed to the smaller compressive strain of 0.7%.
Nw = 6,8,10
P-InP clad, 5E17 cm-3 InGaAsP SCH (40nm) InGaAsP SCH (60 nm) In InGaAsP well (0.7%, 5 nm) InGaAsP barrier (matched, 10 nm) InGaAsP SCH (40 nm) InGaAsP SCH (60 nm) N-InP clad, 1E18 cm-3 Fig. 1. Schematic band diagram of 1.3-lm InGaAsP–InP GRIN-SCH SL-MQW active region.
3. Device temperature characteristics The light-current characteristics of the lasers were measured for several cavity lengths under CW current excitation condition at 25 and 85 C. By plotting the inverse of external differential efficiency 1=gd as a function of the cavity length L, the internal quantum efficiency (gi ), and the internal loss (ai ) can be determined. As shown in Fig. 2, gi at 25 C is found to be a constant of 81.5%, independent of the number of QWÕs Nw , while ai linearly increases from 20 to 25 cm1 as Nw
J. Jin et al. / Infrared Physics & Technology 45 (2004) 209–215
3.5
45
Nw=10 Nw=8
3.0
Nw=6
2.5
1/ηd
Threshold Current (mA)
25°C, as-cleaved facets
2.0
1.5
85° C 40
Lc= 300 µm, as-cleaved
35 30 25 20
25° C
15 5
0.02
0.04
0.06
6
7
Cavity Length (cm) Fig. 2. Reciprocal external differential efficiency is plotted as a function of cavity length with Nw as a parameter, from which the internal quantum efficiency and internal loss can be determined.
increases from six to ten. The variation of the internal loss ai with Nw comes from the difference of optical absorption volume in the wells; the relationship between ai and Nw can be extracted as ai ¼ 12:5 þ 1:25Nw , in the unit of cm1 . The Nw independent part in the internal loss (12.5 cm1 ) represents the optical loss in all other regions except the MQW region. There are two possible mechanisms pertaining to the optical loss outside MQW region. One is the optical absorption loss in the p-cladding region of the ridge; another is the optical scattering loss near the bottom of the ridge, where the optical field distribution would be strongly scattered out of the waveguide if the fabrication process and the structure were not optimized. The temperature effect on ai was investigated on the MQW lasers with Nw ¼ 6, ai changed from 20 cm1 at 25 C to 23 cm1 at 85 C, corresponding to a variation rate with temperature T of 0.05 cm1 K1 . Fig. 3 shows the threshold currents (Ith ) for 300 lm-long lasers at 25 and 85 C as a function of well number Nw . Ith increases monotonically from 14.3 to 18 mA at 25 C when Nw increases from six to ten. On the contrary, it decreases from 43.4 to 38.6 mA at 85 C when Nw increases from six to ten. The higher threshold current at 25 C with Nw
8
9
10
11
Number of Wells
0.08
Fig. 3. Threshold currents at 25 and 85 C are plotted as a function of well number Nw , the lasers have 300-lm long length and as-cleaved facets.
larger than 6 is attributed to the approximately saturated threshold current density and the increase of active volume. The improvement of temperature characteristic with increased quantum-well number is due to the reduction of threshold carrier density, hence the reduction of thermal ionic emission and carrier leakage from quantum-well to SCH region, especially at elevated temperatures. Fig. 4 shows the temperature characteristic of the single facet slope efficiency gext . The external differential efficiency gd is calculated by the expression of gd ¼ 2gext hm=q, where hm is the photon energy, q is the charge of a free Single Facet Slope Efficiency(mW/mA)
1.0 0.00
211
0.26 0.24
25°C
0.22
Lc= 300 µm, as-cleaved
0.20 0.18 0.16 85°C
0.14 0.12
5
6
7 8 9 Number of Wells
10
11
Fig. 4. External slope efficiencies per facet at 25 and 85 C vary with well number Nw .
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J. Jin et al. / Infrared Physics & Technology 45 (2004) 209–215
electron. At 25 C, gext decreases from 0.257 to 0.233 mW/mA as Nw increases from six to ten. Since the internal quantum efficiency is independent on well number Nw , the reduction of gext results from the increase of internal loss ai . On the other hand, gext increases with Nw at 85 C. Combining the results as shown in Figs. 3 and 4, improved high-temperature performances have been reached in the lasers with a larger Nw . The reduced
T0 ðX Þ ¼ 60=ðlnðX ð25 CÞ=X ð85 CÞÞÞ
ð2Þ
The experimental characteristic temperatures of threshold current and those of external differential efficiency T0 ðgd Þ obtained by (2) are summarized in the following table, together with the experimental values of Ith and gd . Summary of performances in 1.3-lm InGaAsP– InP MQW lasers
Nw
Ith (25 C) (mA)
Ith (85 C) (mA)
gd (25 C)
gd (85 C)
T0 ðgd Þ (K)
T0 ðIth Þ (K)
6 8 10
14.3 16 18
43.4 40 38.6
0.541 0.516 0.490
0.269 0.297 0.337
86 106 159
54 65 78
temperature sensitivities of threshold current Ith and external slope efficiency gext in the lasers with larger Nw are considered to be the result of a reduced electron leakage across the heterostructure between MQW region and p-cladding layer. The electrons escaping from n-side wells by thermal ionic emission have a chance of being recaptured by the p-side wells if Nw is larger. The electron leakage from MQW region to p-side cladding layer contributes not only to higher threshold current, but also to lower internal quantum efficiency, therefore it implies the characteristic temperature of threshold current, to some extent, is related to that of internal quantum efficiency.
The table clearly shows that both T0 ðIth Þ and T0 ðgd Þ increase with well number Nw . In the following section, we carried out theoretical analysis to the relationship between T0 ðIth Þ and T0 ðgd Þ. Taking the effect of internal quantum efficiency gi into account, the material gain per well in the quantum-well structure can be expressed as G ¼ G0 lnðgi J =Jtr Þ ð3Þ where Jtr is the transparency current density per well, J is the injected current density per well, and G0 is the gain coefficient when G=J is maximum at gi J ¼ eJtr , where e is the base of natural logarithm. At threshold, the threshold gain Gth can be obtained by
4. Results and analysis
Nw Cw Gth ¼ ai þ am
We quantify the characteristic of measurable laser parameter X (such as Ith , and gd ) in terms of the normalized change with respect to temperature T [6] as
and
1 dX 1 ¼ X dT T0 ðX Þ
ð1Þ
where T0 ðX Þ is the characteristic temperature of parameter X and a +()) sign is used when the value of X increases (decreases) with temperature. Accordingly, the averaged characteristic temperature of parameter X in temperature range of 25 and 85 C is specified as
am ¼ lnð1=ðR1 R2 ÞÞ=2L
ð4Þ ð5Þ
where ai is the internal, am is the mirror loss, Nw is the number of QWÕs, Cw is the optical confinement factor per well, R1 and R2 are the power reflectivities at two facets, and L is the cavity length. Combining (3) with (4), the threshold current of QW LDs can be written as WLJtr ai þ am Ith ¼ Nw exp ð6Þ gi Nw Cw G0 where W is the active region width.
J. Jin et al. / Infrared Physics & Technology 45 (2004) 209–215
The differential quantum efficiency is given by gd ¼ g
i
am ai þ a m
ð7Þ
Substituting Eqs. (6) and (7) into Eq. (1), the characteristic temperature of threshold current T0 ðIth Þ is derived as 1 1 1 1 ¼ þ þ T0 ðIth Þ T0 ðgd Þ T0 ðJtr Þ Nw Cw G0 1 oai ai þ am 1 þ ð8Þ ai þ am oT Nw Cw G0 T0 ðG0 Þ The transparency current density Jtr is written as Jtr ¼ qLz BNtr2 þ CNtr3 ð9Þ where q is the elementary charge, Lz is the well width, B is the spontaneous emission coefficient, and C is the Auger recombination coefficient. Assuming B is inversely proportional to temperaDE ture T , and C is proportional to eKT [7], T0 ðJtr Þ is deduced as 1 3 2r ¼ T0 ðJtr Þ T
ð10Þ
where r ¼ 1=ð1 þ CNtr =BÞ. To my best knowledge, there are limited experimental results for spontaneous radiative recombination coefficient B and Auger recombination coefficient C for 1.3-lm InGaAsP–InP MQW lasers, the newly obtained experimental results in [8] are used: B ¼ ð0:698–0:737Þ 1010 cm3 s1 , C ¼ ð3:95–6:8Þ 1029 cm6 s1 at room temperature. Assuming the activation energy of Auger recombination coefficient DE to be 60 meV [5], and using the expression for Ntr and effective masses for electrons and heavy holes in [9], Ntr is calculated to be 7.46 · 1017 cm3 at 85 C, therefore the ratio of spontaneous radiative current to total recombination current is in the range of 0.443–0.591, resulting in an range of 169– 197 K for the characteristic temperature of transparency current T0 ðJtr Þ at 85 C. The third term of (8) has been experimentally proved to be negligible [3,10], meantime it can be estimated theoretically. For 300-lm-long InP-based lasers with as-cleaved facet, the mirror loss am ¼ lnð1=RÞ=L ¼ lnð1=0:3Þ=0:03 ¼ 40 cm1 , the above-mentioned experimental results of internal loss ai is in the range of 20–25 cm1 , depending on the number of
213
quantum-well. Thus the total loss ai þ am lies in 60–65 cm1 . The third term caused by total loss is calculated to be 8 · 104 K1 with the experimental result of 0.05 cm1 K1 for oai =oT . The curve of gain versus current density shows the optimized operation point satisfies the expression: Nw Cw G0 ¼ ai þ am [11]. For practical laser operation, Nw Cw G0 is generally very near to (ai þ am ). Both experiment and theory prove the neglected effect of the third term on the right of Eq. (8). According to another experimental result in [10], T0 ðG0 Þ is assumed to be infinity, Eq.(8) is simplified into the following forms: 1 T0max ðIth Þ 1 T0min ðIth Þ
¼
1 1 þ T0 ðgd Þ 169
ð11:1Þ
¼
1 1 þ T0 ðgd Þ 197
ð11:2Þ
Applying the experiment results of T0 ðgd Þ to Eq. (11), the averaged characteristic temperatures of threshold current T0 ðIth Þ in the temperature range of 25 and 85 C are calculated to be 57–59.9, 65.1– 68.9, 81.9–87.9 K for 6-well, 8-well and 10-well lasers, respectively. The variation of Auger recombination coefficient due to the uncertainty of design structure and interface between QWÕs [8] causes 3–6 K to the characteristic temperatures of threshold current for MQW lasers with different well number. The theoretical values are on some extent larger by a largest discrepancy amount of 9.9 K than the experimental results, the discrepancy between theory and experiment may be attributed to the underestimated effective mass of heavy hole in the QWÕs. If a more reasonable effective mass of heavy hole of 0:2m0 is adopted [12], the characteristic temperature of transparency current density T0 ðJtr Þ shifts to the range of 153.6– 175 K, the characteristic temperature of threshold current for MQW lasers with Nw ¼ 6, 8, 10 is calculated to be 55–57.7, 62.7–66, 78.1–83 K, depending on different Auger recombination coefficient. After choosing reasonable effective mass of heavy hole, the discrepancy of characteristic temperature of threshold current between experiment and theory is thus reduced to be less than 5 K. In the temperature range of 25– 85 C, Auger recombination together with the
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J. Jin et al. / Infrared Physics & Technology 45 (2004) 209–215
temperature characteristic of external differential efficiency determines the temperature characteristic of threshold current. The improved T0 ðgd Þ in 1.3-lm InGaAsP–InP MQW laser with a larger well number directly creates the improvement of T0 ðIth Þ, the variation of internal loss with temperature and the temperature dependence of G0 play negligible roles in determining the temperature sensitivity of threshold current in InGaAsP–InP material system. However, in InGaAlAs-InP material system, these two effects must be included to account for T0 ðIth Þ due to the strong electron confinement and very high T0 ðgd Þ [6]. From the viewpoint of practical application, a less temperature dependent output power at a fixed drive current is more important than the reduced temperature sensitivity of threshold current if 1.3-lm InGaAsP–InP MQW lasers are required to work over a wide temperature range without cooling [13]. The temperature dependence of output power in terms of power penalty DPout from 25 to 85 C is described as gd ð25 CÞ Id Ith ð25 CÞ DPout ¼ 10 log ð12Þ gd ð85 CÞ Id Ith ð85 CÞ
Power Penalty at 85°C (dB)
The drive current Id is set to 60 mA. As shown in Fig. 5, DPout greatly decreases as Nw increases from six to ten. In order to get a smaller power penalty
7.0 6.5
at a high temperature, both gd and Ith are required to be less temperature dependent, while the threshold current at room temperature is also required to be smaller. There is as much as 50% of the injected current escaping out of the active region in RWG structure at threshold [14]. For a lower threshold current, a buried-heterostructure (BH) should be used to eliminate the lateral spreading current occurred in the RWG structure. All these results indicate that it is very necessary to increase T0 ðIth Þ, and T0 ðgd Þ by using a larger well number, such as 10, and to decrease Ith by using a BH structure for a lower power penalty in 1.3-lm InGaAsP–InP MQW lasers.
5. Conclusion The effects of well number on temperature performance in 1.3-lm InGaAsP–InP strainedlayer multi-quantum-well lasers have been investigated. A smaller well number is helpful to get a lower threshold current and a higher external differential efficiency at room temperature, while a larger number of QWÕs is beneficial for an advanced high-temperature characteristics such as a lower power penalty. A theoretical model explaining the effect of T0 ðgd Þ on T0 ðIth Þ has been established. The discrepancy of characteristic temperature of threshold current between theory and experiment is less than 5 K after reasonable effective mass of heavy hole in the WQs is adopted.
6.0
Acknowledgement 5.5
This work is supported in part by National Scientific Foundation of China under grant no. 10174056.
5.0 4.5 6
8
10
Number of Wells Fig. 5. The effect of well number on the output power penalty at 85 C with a CW drive current of 60 mA indicates that output power penalty decreases with the increasing of well number.
References [1] M. Silver, W.E. Booij, S. Malik, A. Galbraith, S. Uppal, P.E. Mcbrien, G.M. Berry, P.D. Ryder, S.J. Chamdle, D.M. Atkin, S. Chan, R. Harding, R.M. Ash, Wide temperature ()20–95 C) operation of an uncooled 2.5 Gb/s
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1300-nm DFB laser, IEEE Photon. Technol. Lett. 14 (2002) 741–743. D. Bang, J. Shim, J. Kang, M. Um, S. Park, S. Lee, D. Jang, Y. Eo, High-temperature and high-speed operation of 1.3-lm uncooled InGaAsP–InP DFB laser, IEEE Photon. Technol. Lett. 14 (2002) 1240–1242. T. Namegaya, N. Matsumoto, N. Yamanaka, N. Iwai, H. Nakayama, A. Kasukawa, Effects of well number in 1.3lm InGaAsP/InP GRIN-SCH strained-layer quantum well lasers, IEEE J. Quantum Electron. 30 (1994) 578– 584. H. Lu, C. Blaauw, T. Makino, Single-mode operation over a wide temperature range in 1.3-lm InGaAsP/InP distributed feedback lasers, IEEE J. Lightwave Technol. 14 (1996) 851–895. S. Seki, H. Oohashi, H. Sugiura, T. Hirono, K. Yokoyama, Study on the dominant mechanisms for the temperature sensitivity of threshold current in 1.3-lm InP-based strained-layer quantum-well lasers, IEEE J. Quantum Electron. 32 (1996) 1478–1486. C.E. Zah, R.B. Bhat, B. Pathak, F. Favire, W. Lin, M.C. Wang, N.C. Andreadakis, D.M. Hwang, M.A. Koza, T.P. Lee, Z. Wang, D. Darby, D.C. Flanders, J.J. Hsieh, Highperformance uncooled 1.3 lm Alx Gay In1xy As/InPstrained-layer quantum well lasers for subscriber loop application, IEEE J. Quantum Electron. 30 (1994) 511– 523. P.J.A. Thijs, L.F. Tiemeijer, J.J.M. Binsma, T.V. Dongen, Progress in long-wavelength strained-layer InGaAs (P) quantum-well semiconductor lasers and amplifiers, IEEE J. Quantum Electron. 30 (1994) 477–499.
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[8] J.M. Pikal, C.S. Menoni, H. Temkin, P. Thiagarajan, G.Y. Robinson, Carrier lifetime and recombination in longwavelength quantum-well lasers, IEEE J. Select. Top. Quantum Electron. 5 (1999) 613–619. [9] P.J.A. Thijs, L.F. Tiemeijer, P.I. Kuindersma, J.J.M. Binsma, T.V. Dongen, High-performance strained 1.5 lm wavelength InGaAs–InGaAsP quantum well lasers and amplifiers, IEEE J. Quantum Electron. 27 (1991) 1426– 1439. [10] T. Higashi, T. Yamamoto, S. Ogita, M. Kobayashi, Experimental analysis of characteristic temperature in quantum-well semiconductor lasers, IEEE J. Select. Top. Quantum Electron. 3 (1997) 513–521. [11] P.W.A. Mcllory, A. Kurobe, Y. Uematsu, Analysis and application of theoretical gain curves to the design of multi-quantum-well lasers, IEEE J. Quantum Electron. 21 (1985) 1958–1963. [12] S. Seki, T. Yamanaka, W. Lui, Y. Yoshikumi, Yokoyama, Theoretical analysis of pure effects of strain and quantum confinement on differential gain in InGaAsP/InP strainedlayer quantum-well lasers, IEEE J. Quantum Electron. 30 (1994) 500–510. [13] N. Yamamoto, S. Seki, Y. Nogushi, S. Kondo, Design criteria of 1.3-lm multiple-quantum-well lasers for hightemperature operation, IEEE Photon. Technol. Lett. 12 (2000) 137–139. [14] G.J. Letal, J.G. Simmons, J.D. Evans, G.P. Li, Determination of active-region leakage currents in ridge-waveguide strained-layer quantum-well lasers by varying the ridge width, IEEE J. Quantum Electron. 34 (1998) 512– 518.
Study on the effects of well number on temperature characteristics in 1.3-lm InGaAsP–InP quantum-well lasers Jinyan Jin b
a,*
, Decheng Tian
a,b
, Jing Shi
a,b
, Tongning Li
c
a Department of Physics, Wuhan University, Hubei 430072, People’s Republic of China International Center for Material Physics, Chinese Academy of Sciences, Shenyang 110016, People’s Republic of China c Inphenix Inc., Livermore, CA 94551, USA
Received 7 March 2003
Abstract Effects of well number on temperature characteristics in 1.3-lm InGaAsP–InP multi-quantum-well lasers have been investigated. A smaller well number is suitable for lower threshold current and higher differential quantum efficiency at 25 C, while larger well number produces better performances at 85 C. Furthermore, lasers with a larger well number can achieve a less output power penalty at high temperature. For the first time, a theoretical model has been established to precisely explain the relationship between the characteristic temperature of threshold current and that of external differential efficiency. 2003 Elsevier B.V. All rights reserved. Keywords: MOVPE; InGaAsP/InGaAsP SL-MQW; Well number; Characteristic temperature; Semiconductor lasers
1. Introduction Low-cost uncooled laser diodes, emitting at a wavelength of 1.3-lm with high-temperature and high-speed performances over a wide temperature range of )20–85 C, are highly desirable in both enterprise and public networks. Such advanced performances have been obtained in 1.3-lm InGaAsP–InP strained-layer multi-quantum-well (SL-MQW) lasers with 10 quantum-wells (QWÕs)
*
Corresponding author. Tel.: +86-27-87645613; fax: +86-2787654569. E-mail address: [email protected] (J. Jin).
[1,2]. A large well number are expected to maintain advanced performances at high temperatures, due to the reduction of gain saturation, threshold carrier density, and the electron leakage. All these advantages are beneficial for advanced high-temperature, and high-speed performances. However, a large well number would bring about increased internal loss and enlarged beam divergence in the transverse direction. The study of well number can provide a guideline for the uncooled operation in 1.3-lm InGaAsP–InP SL-MQW lasers. The effects of well number on the temperature characteristics of 1.3-lm InGaAsP–InP SL-MQW lasers have been investigated intensively [3–5], but these research activities have not explored the
1350-4495/$ - see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.infrared.2003.10.001
210
J. Jin et al. / Infrared Physics & Technology 45 (2004) 209–215
effect of external differential efficiency on the characteristic temperature of threshold current, and the relationship of their characteristic temperatures. In this paper, we have investigated the effects of well number on the temperature characteristics of threshold current as well as external differential efficiency. A reduced output power penalty at elevated temperatures has been obtained for the laser with a larger well number. Additionally, we have established an analytical expression of characteristic temperature of threshold current (T0 ðIth Þ), which describes the relationship between T0 ðIth Þ, and T0 ðgd Þ, the characteristic temperature of external differential efficiency. The theory shows that T0 ðIth Þ is directly determined by T0 ðgd Þ, and predicts T0 ðIth Þ with relative high accuracy compared to the experimental results in the temperature range of our interest.
2. Device structure and fabrication Fig. 1 shows the schematic band diagram of 1.3lm InGaAsP–InP SL-MQW active region. The MQW region is sandwiched by symmetric 2-step grad-index separate-confinement-heterostructure waveguide layers, lattice matched to InP substrate, with a band gap wavelength of 1.05-lm (60-nm thick) and 0.95-lm (40-nm thick). The undoped
0.9 0.95
1.05
1.4
Wavelength (µm)
MQW region is composed of 5-nm-thick compressively strained InGaAsP (Da=a ¼ 0:7%) well layers and 10-nm-thick InGaAsP (wavelength k ¼ 1:05 lm) barrier layers. Three wafers were grown, with 6, 8, and 10 quantum-wells in the active region on (100) n-InP substrates using lowpressure metalorganic vapor phase epitaxy (LPMOVPE). The p-InP cladding layer (P ¼ 5 1017 cm3 , 1.6-lm thick), and n-InP cladding layer (N ¼ 1 1018 cm3 , 1-lm thick) were grown on both sides of the MQW–SCH waveguide structure. The heavily p-doped lattice-matched InGaAs layer (P ¼ 2 1019 cm3 , 0.3-lm thick) grown above the p-cladding layer was used as the ohmic contact layer. Ridge waveguide (RWG) Fabry–Perot lasers with ridge width of 2.5-lm and cavity length of 300-lm were fabricated from these wafers. The as-cleaved devices were mounted on Cu heatsinks with the junction-up configuration for the investigation of their temperature-dependent performances. Before RWG process, photoluminescence (PL) measurement was carried out for three SL-MQW wafers at room temperature. The PL peak wavelengths of 1306-nm is independent on the well number, however, the full width at the half maximum (FWHM) of PL spectrum slightly increases from 28 to 32 meV when the well number increases from six to ten. The intensities of PL spectra are comparable among three wafers. No strain relaxation haze in 10-well MQW structure was found by Nomaski interference contrast microscopy observation; it could be attributed to the smaller compressive strain of 0.7%.
Nw = 6,8,10
P-InP clad, 5E17 cm-3 InGaAsP SCH (40nm) InGaAsP SCH (60 nm) In InGaAsP well (0.7%, 5 nm) InGaAsP barrier (matched, 10 nm) InGaAsP SCH (40 nm) InGaAsP SCH (60 nm) N-InP clad, 1E18 cm-3 Fig. 1. Schematic band diagram of 1.3-lm InGaAsP–InP GRIN-SCH SL-MQW active region.
3. Device temperature characteristics The light-current characteristics of the lasers were measured for several cavity lengths under CW current excitation condition at 25 and 85 C. By plotting the inverse of external differential efficiency 1=gd as a function of the cavity length L, the internal quantum efficiency (gi ), and the internal loss (ai ) can be determined. As shown in Fig. 2, gi at 25 C is found to be a constant of 81.5%, independent of the number of QWÕs Nw , while ai linearly increases from 20 to 25 cm1 as Nw
J. Jin et al. / Infrared Physics & Technology 45 (2004) 209–215
3.5
45
Nw=10 Nw=8
3.0
Nw=6
2.5
1/ηd
Threshold Current (mA)
25°C, as-cleaved facets
2.0
1.5
85° C 40
Lc= 300 µm, as-cleaved
35 30 25 20
25° C
15 5
0.02
0.04
0.06
6
7
Cavity Length (cm) Fig. 2. Reciprocal external differential efficiency is plotted as a function of cavity length with Nw as a parameter, from which the internal quantum efficiency and internal loss can be determined.
increases from six to ten. The variation of the internal loss ai with Nw comes from the difference of optical absorption volume in the wells; the relationship between ai and Nw can be extracted as ai ¼ 12:5 þ 1:25Nw , in the unit of cm1 . The Nw independent part in the internal loss (12.5 cm1 ) represents the optical loss in all other regions except the MQW region. There are two possible mechanisms pertaining to the optical loss outside MQW region. One is the optical absorption loss in the p-cladding region of the ridge; another is the optical scattering loss near the bottom of the ridge, where the optical field distribution would be strongly scattered out of the waveguide if the fabrication process and the structure were not optimized. The temperature effect on ai was investigated on the MQW lasers with Nw ¼ 6, ai changed from 20 cm1 at 25 C to 23 cm1 at 85 C, corresponding to a variation rate with temperature T of 0.05 cm1 K1 . Fig. 3 shows the threshold currents (Ith ) for 300 lm-long lasers at 25 and 85 C as a function of well number Nw . Ith increases monotonically from 14.3 to 18 mA at 25 C when Nw increases from six to ten. On the contrary, it decreases from 43.4 to 38.6 mA at 85 C when Nw increases from six to ten. The higher threshold current at 25 C with Nw
8
9
10
11
Number of Wells
0.08
Fig. 3. Threshold currents at 25 and 85 C are plotted as a function of well number Nw , the lasers have 300-lm long length and as-cleaved facets.
larger than 6 is attributed to the approximately saturated threshold current density and the increase of active volume. The improvement of temperature characteristic with increased quantum-well number is due to the reduction of threshold carrier density, hence the reduction of thermal ionic emission and carrier leakage from quantum-well to SCH region, especially at elevated temperatures. Fig. 4 shows the temperature characteristic of the single facet slope efficiency gext . The external differential efficiency gd is calculated by the expression of gd ¼ 2gext hm=q, where hm is the photon energy, q is the charge of a free Single Facet Slope Efficiency(mW/mA)
1.0 0.00
211
0.26 0.24
25°C
0.22
Lc= 300 µm, as-cleaved
0.20 0.18 0.16 85°C
0.14 0.12
5
6
7 8 9 Number of Wells
10
11
Fig. 4. External slope efficiencies per facet at 25 and 85 C vary with well number Nw .
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electron. At 25 C, gext decreases from 0.257 to 0.233 mW/mA as Nw increases from six to ten. Since the internal quantum efficiency is independent on well number Nw , the reduction of gext results from the increase of internal loss ai . On the other hand, gext increases with Nw at 85 C. Combining the results as shown in Figs. 3 and 4, improved high-temperature performances have been reached in the lasers with a larger Nw . The reduced
T0 ðX Þ ¼ 60=ðlnðX ð25 CÞ=X ð85 CÞÞÞ
ð2Þ
The experimental characteristic temperatures of threshold current and those of external differential efficiency T0 ðgd Þ obtained by (2) are summarized in the following table, together with the experimental values of Ith and gd . Summary of performances in 1.3-lm InGaAsP– InP MQW lasers
Nw
Ith (25 C) (mA)
Ith (85 C) (mA)
gd (25 C)
gd (85 C)
T0 ðgd Þ (K)
T0 ðIth Þ (K)
6 8 10
14.3 16 18
43.4 40 38.6
0.541 0.516 0.490
0.269 0.297 0.337
86 106 159
54 65 78
temperature sensitivities of threshold current Ith and external slope efficiency gext in the lasers with larger Nw are considered to be the result of a reduced electron leakage across the heterostructure between MQW region and p-cladding layer. The electrons escaping from n-side wells by thermal ionic emission have a chance of being recaptured by the p-side wells if Nw is larger. The electron leakage from MQW region to p-side cladding layer contributes not only to higher threshold current, but also to lower internal quantum efficiency, therefore it implies the characteristic temperature of threshold current, to some extent, is related to that of internal quantum efficiency.
The table clearly shows that both T0 ðIth Þ and T0 ðgd Þ increase with well number Nw . In the following section, we carried out theoretical analysis to the relationship between T0 ðIth Þ and T0 ðgd Þ. Taking the effect of internal quantum efficiency gi into account, the material gain per well in the quantum-well structure can be expressed as G ¼ G0 lnðgi J =Jtr Þ ð3Þ where Jtr is the transparency current density per well, J is the injected current density per well, and G0 is the gain coefficient when G=J is maximum at gi J ¼ eJtr , where e is the base of natural logarithm. At threshold, the threshold gain Gth can be obtained by
4. Results and analysis
Nw Cw Gth ¼ ai þ am
We quantify the characteristic of measurable laser parameter X (such as Ith , and gd ) in terms of the normalized change with respect to temperature T [6] as
and
1 dX 1 ¼ X dT T0 ðX Þ
ð1Þ
where T0 ðX Þ is the characteristic temperature of parameter X and a +()) sign is used when the value of X increases (decreases) with temperature. Accordingly, the averaged characteristic temperature of parameter X in temperature range of 25 and 85 C is specified as
am ¼ lnð1=ðR1 R2 ÞÞ=2L
ð4Þ ð5Þ
where ai is the internal, am is the mirror loss, Nw is the number of QWÕs, Cw is the optical confinement factor per well, R1 and R2 are the power reflectivities at two facets, and L is the cavity length. Combining (3) with (4), the threshold current of QW LDs can be written as WLJtr ai þ am Ith ¼ Nw exp ð6Þ gi Nw Cw G0 where W is the active region width.
J. Jin et al. / Infrared Physics & Technology 45 (2004) 209–215
The differential quantum efficiency is given by gd ¼ g
i
am ai þ a m
ð7Þ
Substituting Eqs. (6) and (7) into Eq. (1), the characteristic temperature of threshold current T0 ðIth Þ is derived as 1 1 1 1 ¼ þ þ T0 ðIth Þ T0 ðgd Þ T0 ðJtr Þ Nw Cw G0 1 oai ai þ am 1 þ ð8Þ ai þ am oT Nw Cw G0 T0 ðG0 Þ The transparency current density Jtr is written as Jtr ¼ qLz BNtr2 þ CNtr3 ð9Þ where q is the elementary charge, Lz is the well width, B is the spontaneous emission coefficient, and C is the Auger recombination coefficient. Assuming B is inversely proportional to temperaDE ture T , and C is proportional to eKT [7], T0 ðJtr Þ is deduced as 1 3 2r ¼ T0 ðJtr Þ T
ð10Þ
where r ¼ 1=ð1 þ CNtr =BÞ. To my best knowledge, there are limited experimental results for spontaneous radiative recombination coefficient B and Auger recombination coefficient C for 1.3-lm InGaAsP–InP MQW lasers, the newly obtained experimental results in [8] are used: B ¼ ð0:698–0:737Þ 1010 cm3 s1 , C ¼ ð3:95–6:8Þ 1029 cm6 s1 at room temperature. Assuming the activation energy of Auger recombination coefficient DE to be 60 meV [5], and using the expression for Ntr and effective masses for electrons and heavy holes in [9], Ntr is calculated to be 7.46 · 1017 cm3 at 85 C, therefore the ratio of spontaneous radiative current to total recombination current is in the range of 0.443–0.591, resulting in an range of 169– 197 K for the characteristic temperature of transparency current T0 ðJtr Þ at 85 C. The third term of (8) has been experimentally proved to be negligible [3,10], meantime it can be estimated theoretically. For 300-lm-long InP-based lasers with as-cleaved facet, the mirror loss am ¼ lnð1=RÞ=L ¼ lnð1=0:3Þ=0:03 ¼ 40 cm1 , the above-mentioned experimental results of internal loss ai is in the range of 20–25 cm1 , depending on the number of
213
quantum-well. Thus the total loss ai þ am lies in 60–65 cm1 . The third term caused by total loss is calculated to be 8 · 104 K1 with the experimental result of 0.05 cm1 K1 for oai =oT . The curve of gain versus current density shows the optimized operation point satisfies the expression: Nw Cw G0 ¼ ai þ am [11]. For practical laser operation, Nw Cw G0 is generally very near to (ai þ am ). Both experiment and theory prove the neglected effect of the third term on the right of Eq. (8). According to another experimental result in [10], T0 ðG0 Þ is assumed to be infinity, Eq.(8) is simplified into the following forms: 1 T0max ðIth Þ 1 T0min ðIth Þ
¼
1 1 þ T0 ðgd Þ 169
ð11:1Þ
¼
1 1 þ T0 ðgd Þ 197
ð11:2Þ
Applying the experiment results of T0 ðgd Þ to Eq. (11), the averaged characteristic temperatures of threshold current T0 ðIth Þ in the temperature range of 25 and 85 C are calculated to be 57–59.9, 65.1– 68.9, 81.9–87.9 K for 6-well, 8-well and 10-well lasers, respectively. The variation of Auger recombination coefficient due to the uncertainty of design structure and interface between QWÕs [8] causes 3–6 K to the characteristic temperatures of threshold current for MQW lasers with different well number. The theoretical values are on some extent larger by a largest discrepancy amount of 9.9 K than the experimental results, the discrepancy between theory and experiment may be attributed to the underestimated effective mass of heavy hole in the QWÕs. If a more reasonable effective mass of heavy hole of 0:2m0 is adopted [12], the characteristic temperature of transparency current density T0 ðJtr Þ shifts to the range of 153.6– 175 K, the characteristic temperature of threshold current for MQW lasers with Nw ¼ 6, 8, 10 is calculated to be 55–57.7, 62.7–66, 78.1–83 K, depending on different Auger recombination coefficient. After choosing reasonable effective mass of heavy hole, the discrepancy of characteristic temperature of threshold current between experiment and theory is thus reduced to be less than 5 K. In the temperature range of 25– 85 C, Auger recombination together with the
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J. Jin et al. / Infrared Physics & Technology 45 (2004) 209–215
temperature characteristic of external differential efficiency determines the temperature characteristic of threshold current. The improved T0 ðgd Þ in 1.3-lm InGaAsP–InP MQW laser with a larger well number directly creates the improvement of T0 ðIth Þ, the variation of internal loss with temperature and the temperature dependence of G0 play negligible roles in determining the temperature sensitivity of threshold current in InGaAsP–InP material system. However, in InGaAlAs-InP material system, these two effects must be included to account for T0 ðIth Þ due to the strong electron confinement and very high T0 ðgd Þ [6]. From the viewpoint of practical application, a less temperature dependent output power at a fixed drive current is more important than the reduced temperature sensitivity of threshold current if 1.3-lm InGaAsP–InP MQW lasers are required to work over a wide temperature range without cooling [13]. The temperature dependence of output power in terms of power penalty DPout from 25 to 85 C is described as gd ð25 CÞ Id Ith ð25 CÞ DPout ¼ 10 log ð12Þ gd ð85 CÞ Id Ith ð85 CÞ
Power Penalty at 85°C (dB)
The drive current Id is set to 60 mA. As shown in Fig. 5, DPout greatly decreases as Nw increases from six to ten. In order to get a smaller power penalty
7.0 6.5
at a high temperature, both gd and Ith are required to be less temperature dependent, while the threshold current at room temperature is also required to be smaller. There is as much as 50% of the injected current escaping out of the active region in RWG structure at threshold [14]. For a lower threshold current, a buried-heterostructure (BH) should be used to eliminate the lateral spreading current occurred in the RWG structure. All these results indicate that it is very necessary to increase T0 ðIth Þ, and T0 ðgd Þ by using a larger well number, such as 10, and to decrease Ith by using a BH structure for a lower power penalty in 1.3-lm InGaAsP–InP MQW lasers.
5. Conclusion The effects of well number on temperature performance in 1.3-lm InGaAsP–InP strainedlayer multi-quantum-well lasers have been investigated. A smaller well number is helpful to get a lower threshold current and a higher external differential efficiency at room temperature, while a larger number of QWÕs is beneficial for an advanced high-temperature characteristics such as a lower power penalty. A theoretical model explaining the effect of T0 ðgd Þ on T0 ðIth Þ has been established. The discrepancy of characteristic temperature of threshold current between theory and experiment is less than 5 K after reasonable effective mass of heavy hole in the WQs is adopted.
6.0
Acknowledgement 5.5
This work is supported in part by National Scientific Foundation of China under grant no. 10174056.
5.0 4.5 6
8
10
Number of Wells Fig. 5. The effect of well number on the output power penalty at 85 C with a CW drive current of 60 mA indicates that output power penalty decreases with the increasing of well number.
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