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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 18 — Aug. 29, 2011
  • pp: 17267–17282
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Comprehensive analysis of electrically-pumped GaSb-based VCSELs

S. Arafin, A. Bachmann, K. Vizbaras, A. Hangauer, J. Gustavsson, J. Bengtsson, A. Larsson, and M.-C. Amann  »View Author Affiliations


Optics Express, Vol. 19, Issue 18, pp. 17267-17282 (2011)
http://dx.doi.org/10.1364/OE.19.017267


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Abstract

This paper discusses several performance-related aspects of electrically-pumped GaSb-based buried tunnel junction VCSELs with an emission wavelength of 2.6 μm based on theoretical and experimental results. These results allow a deeper insight into the internal device physics, such as radial diffusion of carriers, maximum continuous-wave operating temperature, diffraction loss, internal temperature, gain and loss parameters, internal quantum efficiency of the active region etc. These parameters can be taken into account while designing mid-infrared lasers which leads to an improved device performance. A simple thermal model of the devices based on the two-dimensional (2-D) finite element method using the material data from the literature is also presented. In addition, an application-based result utilizing these lasers for the measurement of absolute water vapor concentration by wavelength modulation spectroscopy (WMS) method are also described, hinting that devices are well-suited for the targeted sensing applications.

© 2011 OSA

1. Introduction

Over the last couple of years, significant progress has been made towards the development of mid-infrared (MIR) GaSb-based semiconductor lasers in the wavelength range 2–3.5 μm. In fact, there are strong absorption lines of numerous trace gases like CO, H2S, H2O, HF, CH4, CO2 etc. in this spectral regime [1

1. L. S. Rothman, D. Jacquemart, A. Barbe, D. C. Benner, M. Birk, L. R. Brown, M. R. Carleer, C. Chackerian Jr., K. Chance, L. H. Coudert, V. Dana, V. M. Devi, J.-M. Flaud, R. R. Gamache, A. Goldman, J.-M. Hartmann, K. W. Jucks, A. G. Maki, J.-Y. Mandin, S. T. Massie, J. Orphal, A. Perrin, C. P. Rinsland, M. A. H. Smith, J. Tennyson, R. N. Tolchenov, R. A. Toth, J. Vander Auwera, P. Varanasi, and G. Wagner, “The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139–204 (2005). [CrossRef]

]. In the family of semiconductor lasers, vertical-cavity surface-emitting lasers (VCSELs) are the most promising light sources which are being currently used in lots of significant applications. Several groups worldwide are currently involved in realizing GaSb-based surface-emitting lasers. Bewley et al. [2

2. W. W. Bewley, C. L. Felix, I. Vurgaftman, E. H. Aifer, J. R. Meyer, L. Goldberg, J. R. Lindle, D. H. Chow, and E. Selvig, “Continuous-wave mid-infrared VCSELs,” IEEE Photon. Technol. Lett. 10, 660–662 (1998). [CrossRef]

], Rattunde et al. [3

3. N. Schulz, J.-M. Hopkins, M. Rattunde, D. Burns, and J. Wagner, “High-brightness long-wavelength semiconductor disk lasers,” Laser & Photon. Rev. 2, 160–181 (2008). [CrossRef] [PubMed]

] and Genty et al. [4

4. F. Genty, A. Garnache, and L. Cerutti, “VCSELs emitting in the 2–3 μm wavelength range,” in Mid-infrared Semiconductor Optoelectronics, A. Krier, ed. Springer Series in Optical Sciences (Springer, 2006), Vol. 118, pp. 159–188. [CrossRef]

] have already reported optically-pumped Sb-based VCSELs in the range of 2–3 μm for sensing applications. However, optical pumping significantly increases the complexity and the cost of the overall system due to the use of an additional pump laser which itself requires much more electrical power. The realization of a compact design seems to be difficult in this way. Recently, monolithic electrically-pumped (EP) GaSb-based VCSELs in pulse operation emitting at 2.63 μm have been achieved which is the longest wavelength ever reported for any EP-VCSELs [5

5. A. Ducanchez, L. Cerutti, P. Grech, F. Genty, and E. Tournie, “Mid-infrared GaSb-based EP-VCSEL emitting at 2.63 μm,” Electron. Lett. 45, 265–267 (2009). [CrossRef]

]. But such devices without any current aperture exhibit multimode operation. Thus devices lose its usability in gas sensing applications since lasers with single-mode emission are required in gas sensing applications by tunable diode laser absorption spectroscopy (TD-LAS) [6

6. R. S. Inman and J. J. F. McAndrew, “Application of tunable diode laser absorption spectroscopy to trace moisture measurements in gases,” Anal. Chem. 66, 2471–2479 (1994). [CrossRef]

]. EP and CW-operating GaSb-based single-mode VCSELs emitting at 2.3–2.6 μm [7

7. A. Bachmann, K. Kashani-Shirazi, and M.-C. Amann, “GaSb-based electrically pumped VCSEL with buried tunnel junction operating continuous wave up to 50°C,” in Proceedings of IEEE Conference on Semiconductor Laser (Institute of Electrical and Electronic Engineers, Italy, 2008), paper TuA1, pp. 39–40. [CrossRef]

, 8

8. S. Arafin, A. Bachmann, K. Kashani-Shirazi, and M.-C. Amann, “Electrically-pumped continuous-wave vertical-cavity surface-emitting lasers at 2.6 μm,” Appl. Phys. Lett. 95, 131120 (2009). [CrossRef]

] have also been demonstrated recently and proven to be application-suited [9

9. J. Chen, A. Hangauer, A. Bachmann, T. Lim, K. Kashani-Shirazi, R. Strzoda, and M.-C. Amann, “CO and CH4 sensing with single mode 2.3 μm GaSb-based VCSEL,” in Conference on Lasers and Electro-Optics (Optical Society of America, Baltimore, MD, 2009), paper CThI.

]. Note that wavelengths higher than 2.3 μm are only accessible with the GaSb material system, because this seems to be the wavelength limit where TDLS suitable VCSELs on the InP material system are available [10

10. A. Hangauer, J. Chen, R. Strzoda, M. Ortsiefer, and M.-C. Amann, “Wavelength modulation spectroscopy with a widely tunable InP-based 2.3 μm vertical-cavity surface-emitting laser,” Opt. Lett. 33, 1566–1568 (2008). [CrossRef] [PubMed]

]. Furthermore, the maximum tuning speed for the 2.3 μm GaSb based is significantly higher and the FM response is more flat than for the 2.3 μm InP based VCSEL which enhances the applicability of GaSb-based VCSELs [11

11. A. Hangauer, J. Chen, R. Strzoda, and M.-C. Amann, “The frequency modulation response of vertical-cavity surface-emitting lasers: experiment and theory,” IEEE J. Sel. Top. Quantum Electron. 17, 1–10 (2011).

].

Despite the promising performance of GaSb-based VCSELs, their development towards large scale applications has been greatly hindered by the immature and complicated growth technique of this material system and insufficient knowledge on material data for the device design. Finding the optimum design by device modeling numerically or analytically sometimes does not give the real device picture due to a lot of unknown issues. This paper provides a clear insight into the physics of already realized VCSELs at 2.6 μm which can be utilized as guidelines for realistic modeling of future devices. As a result, the device performance is likely to be improved in future.

A thorough experimental and theoretical analysis of index-guided GaSb-VCSELs is addressed in this study. This index guiding in the device is obtained by an effective refractive index step due to the presence of a buried tunnel junction (BTJ) concept. This paper is organized as follows. Section 2 presents the device schematics and a detailed discussion of the thermal properties of such devices. We then demonstrate the various experimental results on device size dependent threshold current yielding carrier diffusion length, diffraction loss, internal temperature and extraction of laser parameters and then determine the optimum number of quantum wells (QWs). The applicability of 2.6 μm VCSELs is also demonstrated for the first time by wavelength modulation spectroscopy (WMS) of H2O. Finally, Section IV concludes the paper.

2. Device Design

A schematic illustration of the MBE-grown GaSb-based BTJ VCSELs is shown in Fig.1, where D BTJ denotes the aperture diameter of the device. The electric current injected around the dielectric mirror is effectively confined by the structured tunnel junction. Details of the electrical and optical design and all fabrication steps required to realize the device are mentioned in [12

12. A. Bachmann, S. Arafin, and K. Kashani-Shirazi, “Single-mode electrically pumped GaSb-based VCSELs emitting continuous-wave at 2.4 and 2.6 μm,” N. J. Phys. 11, 125014 (2009). [CrossRef]

, 13

13. A. Bachmann, K. Kashani-Shirazi, S. Arafin, and M.-C. Amann, “GaSb-based VCSEL with buried tunnel junction for emission around 2.3 μm,” IEEE J. Sel. Top. Quantum Electron. 15, 933–940 (2009). [CrossRef]

]. As a part of the device design, this section will focus only on the thermal design of such devices.

Fig. 1 Schematic cross-sectional view of the GaSb-based VCSEL structure with BTJ. The current path is shown. The upper right corner is the SEM photograph of the top-emitting device after fabrication.

2.1. Thermal Design

Thermal modeling is one of the key design issues for devices utilizing the low bandgap material system, GaSb. Generally the device performance, i.e., optical output power and threshold current is limited by thermal effects. To gain a deep insight into GaSb-based BTJ VCSELs, at first the theoretical and systematic thermal analysis using a heat dissipation model will be presented here. The device thermal parameters, such as internal temperature distribution, heat flux, and thermal resistance can be extracted out of the model based on the two-dimensional (2-D) rotationally symmetric, steady-state heat transfer model. The analysis was done by using COMSOL Multiphysics finite element analysis simulation software [14]. The thermal conductivities of the individual layers in GaSb-based BTJ VCSELs are taken from the literature [15

15. S. Adachi, “Lattice thermal conductivity of group-IV and III–V semiconductor alloys,” J. Appl. Phys. 102, 063502 (2007). [CrossRef]

, 16

16. T. Borca-Tasciuca, D. W. Song, J. R. Meyer, I. Vurgaftman, M.-J. Yang, B. Z. Noshob, L. J. Whitman, and G. Chen, “Thermal conductivity of AlAs0.07Sb0.93 and Al0.9Ga0.1As0.07Sb0.93 alloys and (AlAs)1/(AlSb)11 digital-alloy superlattices,” J. Appl. Phys. 92, 4994–4998 (2002). [CrossRef]

] and summarized in Table 1 along with brief details and the thickness of that corresponding layer. In this analysis, the effective thermal conductivities with anisotropy were used for thin multilayers, e.g. active region. The effective thermal conductivities in lateral and vertical directions are given by [17

17. M. Osinski and W. Nakwaski, “Effective thermal conductivity analysis of 1.55 μm InGaAsP/InP vertical-cavity top-surface-emitting microlasers,” Electron. Lett. 29, 1015–1016 (1993). [CrossRef]

]
kl=d1k1+d2k2d1+d2,kv=d1+d2d1/k1+d2/k2
(1)
where k 1/k 2 and d 1/d 2 are the thermal conductivity and thickness for layer 1/layer 2, respectively. For the active region and bottom epitaxial Bragg mirror, the effective thermal conductivity value is used defined by Eq. (1). Here, reduced values are expected that are caused by phonon mean free path restrictions in thin layers.

Table 1. Thermal Conductivity for Different Layers in GaSb-Based BTJ VCSELs

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As shown in Fig. 2 b), a large amount of heat from the active region flow laterally and vertically downward toward the GaSb substrate through bottom epitaxial DBR and also laterally toward the top p-side Au-contact. This has been indicated by long white arrows, showing the heat rapidly spreads out over a wide area in the radial direction. The heat source is sandwiched by top and bottom GaSb heat spreading layer which also contributes to dissipate the heat. The active region diameter, D BTJ + 2r diff = 5.5 μm + 3.4 μm = 8.9 μm has been considered in this simulation by taking the effective pumped area of the device into account, where r diff is the carrier diffusion length discussed in Sect. 3.1. Since the wallplug efficiency is nearly zero at threshold, all input electrical power is assumed to be dissipated in the form of heat. Thus, the volumetric heat source density, Q can be determined from experimental threshold parameters by
Q=IthVacV=IthVacπ4(DBTJ+2rdiff)2h
(2)
where, V ac and I th are the voltage drop across the active region and threshold current, respectively, V and h are the volume and thickness of the active region, respectively. The voltage drop across the active region is obtained by subtracting ohmic drop arising from the laser series resistance from the measured threshold voltage, V th
Vac=VthIthRs
(3)
where, R s is the series resistance. The measured threshold current, threshold voltage and series resistance of the device with D BTJ = 5.5 μm are 3.2 mA, 0.62 V, and 33 Ω, respectively. So, V ac can be calculated to ≈ 0.51 V. Thus the total dissipated heat power in the active region is 1.6 mW. The rest of the power ≈ 0.4 mW is assumed to be dissipated as joule heating in the other layers whose effect to rise in active region temperature is almost negligible. Using these values in the simulation, the maximum heating of ΔT = 4 K in the active region with respect to the heatsink temperature is obtained which corresponds to a thermal resistance of ≈ 1995 K/W, showing a good agreement with the experimental value mentioned in Sect. 3.2.

Fig. 2 a) Two-dimensional (2-D) GaSb-based top emitting VCSEL structure employing a rotational structural symmetry along the z-axis used in the simulation. The contribution of different layers of the device in dissipating the heat is shown in percentage as well. b) 2-D steady state heat flux and temperature distribution. The black rectangle represents the QW region which has been assumed to be the main heat source in this simulation. The bottom epitaxial Bragg mirror on top of 500 μm thick GaSb substrate and top dielectric Bragg mirror have been marked with yellow border lines. White arrows represent the magnitude and the direction of the heat flow.

As displayed in Fig. 2 a) most of the heat (78%) generated in the active region flow downward mainly to the copper heatsink by conduction through the GaSb substrate (43%) and epitaxial bottom DBR (35%). The rest of the heat is mainly transferred to the air by radiation and natural convection through the top p-side Au contact. The top dielectric DBR hardly conducts any heat due to the low thermal conductivities of dielectric materials. Since the presented devices with upside up concept already show good thermal properties, the upside-down concept would even improve the thermal management in such devices.

3. Experimental Details

3.1. Carrier Diffusion Length

The threshold current density in any aperture VCSELs is mainly scaled by the current spreading and the lateral carrier diffusion in the active region. Current spreading takes place in the region between the current aperture and the active region. In our BTJ VCSELs, the vertical distance between the BTJ aperture and the active region is roughly 100 nm, so the influence of the current-spreading phenomenon on the threshold current is negligible. Also, if one assumes the thin region below the aperture is low-doped, then the assumption is valid. Hence the threshold current density of the devices under study is mainly governed by the radial carrier diffusion in the active region. That means that the carrier diffusion length needs to be experimentally measured in order to determine the threshold current density accurately. The threshold current, I th in VCSELs can be expressed with the threshold current density, J th by the following equation:
Ith=π4(DBTJ+2rdiff)2Jth(DBTJ+2rdiff)2
(4)
where, r diff is the lateral carrier diffusion length. It is evident that I th is proportional to the square of the BTJ aperture diameter plus an extension caused by the carrier diffusion on both sides of the BTJ. Clearly, this is the area of the active region which is being effective pumped during device operation. Figure 3 shows the measured CW threshold current against BTJ aperture diameter for 2.3 μm and 2.6 μm VCSELs at a constant device internal temperature. In fact, devices with different aperture diameters have different internal heating at constant heatsink temperature. So, it is important to measure the threshold current of VCSELs at constant internal temperature which is simply the sum of the heatsink temperature and the temperature rise, ΔT in the active region of the device at threshold. ΔT value can be obtained by measuring the thermal resistance, R th and the applied threshold power, P th for each device.
ΔT=RthΔPth
(5)

Fig. 3 Square root of the measured CW threshold current at constant internal temperature against BTJ diameter of VCSELs emitting at a) 2.35 μm and b) 2.6 μm. Extracting the carrier diffusion length from these figures and taking that into account, the threshold current densities in such devices have been calculated shown as displayed in inset. The increase of the threshold current in devices with small aperture diameters is due to the high diffraction losses.

Note that the proportionality behavior indicated in Eq. (4) is valid up to the device with a certain BTJ diameter since J th starts to increase at small aperture diameters which can be attributed by the diffraction loss present in such devices. By plotting the square root of the threshold current against BTJ diameter, one can calculate the diffusion length from the intercept of the x-axis. A diffusion length of r diff ≈1.7 μm on each side of the BTJ is evaluated in Fig. 3 for both 2.3 μm and 2.6 μm VCSELs, being in good accordance with values determined for other BTJ-VCSELs [18

18. M. Ortsiefer, “Langwellige Vertikalresonator-Laserdioden im Materialsystem InGaAlAs/InP,” PhD thesis (Technische Universität München, 2000).

]. Once the diffusion length is experimentally determined, the effective threshold current density can be calculated as shown in inset of Fig. 3. Interestingly, both 2.3 μm and 2.6 μm VCSELs show the minimum of the threshold current at the device size of approximately 4 μm diameter, hinting that these devices are strongly index guided. If the device would be weakly index guided, e.g. implanted VCSELs, the minimum of the threshold current would shift to device with larger aperture diameter where the diffraction loss would start to dominate earlier with decreasing device size [19

19. K. L. Lear, R. P. Schneider Jr., K. D. Choquette, and S. P. Kilcoyne, “Index guiding dependent effects in implant and oxide confined vertical-cavity lasers,” IEEE Photon. Technol. Lett. 8, 740–742 (1996). [CrossRef]

]. As a matter of fact, the strong index guiding in GaSb-based BTJ VCSELs is achieved by an high effective refractive index step due to the presence of a laterally structured BTJ in the cavity [20

20. S. Arafin, A. Bachmann, and M.-C. Amann, “Transverse-mode characteristics of GaSb-based VCSELs with buried-tunnel junctions,” IEEE J. Sel. Top. Quantum Electron. 9, 1–8 (2011).

].

3.2. Maximum CW operating temperature

Figure 4 a) shows the maximum CW operating temperature, T max against BTJ diameter ranging from 3.5 μm to 20 μm. It is seen that T max decreases with the increase of the BTJ diameter except D BTJ ≤ 4 μm. In other words, the smaller devices are suitable for higher temperature operation in cw mode. In order to identify the reason of this behavior, we measured the thermal resistance of each device as displayed in Fig. 4 b). The decrease of the thermal resistance with device diameter does not follow 1/D BTJ behavior as expected for top emitting VCSELs. Therefore, the heat removal in such BTJ VCSELs is not one-dimensional, three-dimensional instead. The thermal resistance can be measured or extracted from the shift of emission wavelength to longer wavelength with increasing temperature and with increasing current which can be mathematically written as follows:
Rth=ΔλΔPel|T=const.ΔλΔT|Pel=const.
(6)
Here, ΔλΔPel|T=const. is the power tuning coefficient at a constant heatsink temperature and ΔλΔT|Pel=const. is the thermal tuning coefficient at a constant applied electrical power. At this point, Table 2 can be introduced in order to demonstrate a comparison of thermal resistance among VCSELs with active region diameter between 5 μm and 13 μm based on different material system. Thus one can have a better feeling about the thermal performance in devices under study. In particular, the thermal resistance value of the InP-based BTJ VCSEL mentioned in Table 2 is for the structure mounted epi-side-down onto an integrated Au-heatsink. Since the presented top-emitting GaSb-based devices without any integrated heatsink show a reasonably good thermal properties, this proves a good thermal design.

Fig. 4 The dependence of a) maximum CW lasing temperature (T max) and b) thermal resistance at 20°C as a function of BTJ diameter of 2.6 μm VCSELs. The measured thermal resistance points are obtained by Eq. (6), whereas, the simulated (red-marked) points are by the finite element method (FEM) simulation, showing a good agreement. The curve fitting was done to the measured data. c) The consumed threshold power at a constant internal temperature and the temperature rise of the active region with respect to the heatsink temperature against BTJ diameter of 2.6 μm VCSELs. The continuously increasing temperature rise of the devices with BTJ diameters indicates that the device performance can be further improved by a better thermal design.

Table 2. Thermal Conductivity for VCSELs with Active Diameter, 5 μm ≤ D a ≤ 13 μm (D aD BTJ) on Different Material System

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3.3. Diffraction loss

In most VCSELs, the cavity propagation loss is mainly due to outcoupling through the Bragg mirrors and optical absorption in the semiconductor material. In addition to these two loss types, there is the diffraction loss, which is the excess loss caused by the fact that light does not propagate only in the longitudinal direction. Like all beams of light, the cavity field has a tendency to spread, i.e. to propagate also in the radial direction, which causes a radial leakage of radiation along the entire length of the cavity. For most VCSELs, this leakage - the diffraction loss - is small, since the typical VCSEL cavity is short in the longitudinal direction and relatively wide in the lateral direction. So this type of loss can be neglected in most VCSELs. However, because of the BTJ and the resulting change in the topology of all layers above it, the intracavity field in the GaSb-based BTJ VCSEL experiences a strongly varying refractive index also in the lateral direction. This lateral disturbance results in an enhanced spreading of the light, thus considerably increasing the diffraction loss.

A direct measurement of the diffraction loss is very difficult; on the other hand, since diffraction is caused by the spatially varying real part of the refractive index, without being much influenced by, e.g., the QW gain or material absorption, it can be estimated with fair accuracy by numerical simulation, provided that the numerical model of the complicated VCSEL structure does not overwhelm the computer resources. Therefore we implemented a numerical method for calculating the intracavity field, and the radial field leakage, that is efficient in terms of computer memory. It is a hybrid method using a 3D transfer matrix method (TMM) [23

23. D. I. Babic, Y. Chung, N. Dagli, and J. E. Bowers, “Modal reflection of quarter-wave mirrors in vertical-cavity lasers,” IEEE J. Quantum Electron. 29, 1950–1962 (1993). [CrossRef]

] for the VCSEL structure beneath the BTJ, where there is no lateral variation in the refractive index, and a beam propagation method (BPM) [24

24. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

] for the BTJ and the structure above it. As a result we obtained the diffraction loss as a function of the BTJ diameter as shown in Fig. 5 a). As expected the diffraction loss increases when the BTJ diameter is decreased, and for D BTJ ≤ 8 μm the diffraction loss is of the same order of magnitude as the outcoupling loss through the mirrors; this can lead to an increased threshold current for VCSELs with a small BTJ.

Fig. 5 a) Simulated diffraction loss as a function of the BTJ diameter. Two different cavities are analyzed, the 2.3 μm VCSEL and the 2.6 μm VCSEL, the latter with a smaller BTJ-induced step in the cavity structure, thereby reducing the diffraction loss. For each cavity the diffraction loss for the fundamental mode field (LP01) and for the first higher order mode field (LP11) is calculated. b) Calculation of loss budget for 2.6 μm VCSELs with D BTJ = 8 μm.

Also the other loss mechanisms in VCSELs, such as outcoupling loss for both top and bottom mirrors obtained by the calculation is listed in Fig. 5 b). The total cavity loss has been measured to be as high as 23.2 cm−1. The experimental procedure involved in obtaining the total loss value will be described in Sect. 3.5. So, the remaining loss of 13 cm−1 can be attributed to the free-carrier absorption (FCA) losses in the epitaxial mirror, QW active region and the 3λ thick GaSb cavity. Out of those remaining losses, the average FCA loss in the epitaxial mirror can be calculated by the following relation
α¯mFCA=nLαH+nHαLnH+nL
(7)
where α¯mFCA is the average absorption coefficient in the epitaxial mirror, n L and n H are the low and high refractive indices of the mirror material and the absorption coefficient in the high and low index material are denoted with α H and α L. For the emission wavelength of 2.6 μm, we have, n AlAsSb = 3.19, n GaSb = 3.83, α AlAsSb = 13.2 cm−1 and α GaSb = 10.1 cm−1 which yields α¯mFCA=11.7cm1, whereas the optical absorption losses in such DBRs were measured to be 5–10 cm−1 at 2.3 μm [25

25. A. Perona, A. Garnache, L. Cerutti, A. Ducanchez, S. Mihindou, P. Grech, G. Boissier, and F. Genty, “AlAsSb/GaSb doped distributed Bragg reflectors for electrically pumped VCSELs emitting around 2.3 μm,” Semicond. Sci. Technol. 22, 1140–1144 (2007). [CrossRef]

].

3.4. Internal Temperature

Neither the direct measurement nor the analytical analysis or modeling can accurately tell the internal temperature of VCSELs. This is just because of the device self-heating as well as the presence of several unknown effects, e.g. QW Auger recombination in the device above threshold. Such heat-generating unknown effects introduces the non-linearity in the device PI characteristics measured at constant T hs. By removing only the self-heating effect from other effects, it is possible to obtain the PI characteristics with a reduced non-linearity. For devices under study, we follow the wavelength method from [26

26. A. Hangauer, J. Chen, and M.-C. Amann, “Vertical-cavity surface-emitting laser light-current characteristic at constant internal temperature,” IEEE Photon. Technol. Lett. available online,(2011). [CrossRef]

] to obtain the PI characteristics at constant internal temperature. Figure 6 a) illustrates the contour curves of the device lasing wavelengths at different driving currents and heatsink temperature. Each constant emission wavelength curve indicates a constant internal temperature of the device which can be extracted by extrapolating those curves to I = 0. From Fig. 6 a), the internal temperature at which the laser turns off can be determined to be approximately 77°C which is the highest temperature the laser would work in pulsed mode. In order to verify this, the laser internal rollover temperature and turn off temperature defined by Eq. (8) and Eq. (9), respectively are plotted against the heatsink temperature as shown in Fig. 6 b).
Tro=Ths+ProRth
(8)
Toff=Ths+PoffRth
(9)

Fig. 6 a) Curves of constant laser emission wavelength at different driving current and heatsink temperature. Each constant wavelength curve represents the constant internal temperature of the device which can be extracted by extrapolating them to I = 0. The laser turn-off temperature can be determined to ≈ 77 ° C which is independent of T hs. Temperature dependent PI characteristics of the device with D BTJ = 9 μm is shown in inset. The maximum CW operating heatsink temperature of the device is approximately 59°C. b) Internal rollover temperature (T ro) and laser turn off temperatures (T off) as a function a T hs.

The turn off temperature, T off has been found to be 78°C, showing a good agreement with the value determined by the method mentioned earlier. As expected, the laser turn off temperature, T off is independent of heatsink temperature while the thermal rollover temperature, T ro increases linearly with heatsink temperature. This is not surprising since the thermal rollover point is determined by not only the heatsink temperature and the amount of self heating caused by the applied electrical power but also with the applied driving current. Evidently, the device operated at lower heatsink temperature will be driven by more current to reach the thermal rollover than it would be for higher heatsink temperature. Then the slope (equivalent to the differential quantum efficiency) of the PI characteristics measured indirectly at constant internal temperature is plotted as a function of device internal temperature, T in. As shown in Fig. 7 a) where we can see that the slope decreases with increasing T in. This is not surprising either since several unknown effects, for instance, QW leakage current, QW Auger recombination and leakage current through the region outside of BTJ can take place in the QW region with increasing temperature which has not been taken into account so far. The latter can be excluded from this discussion since the current confinement efficiency does not degrade in our devices with increasing temperature as demonstrated in Fig. 7 b). Here we measured the IV characteristics of a point contact test structure with diameter, D pc = 23 μm in the region with BTJ and without BTJ. It was found that the ratio of the current in the region of BTJ to the region outside BTJ at a particular voltage of 0.8 is approximately 25,000 and this value remains almost constant with increasing temperature.

Fig. 7 a) The slope of the PI characteristics calculated at constant internal temperature as a function of internal temperature, T in, b) Temperature dependent IV characteristics of the test structures with D pc = 23 μm representing device central part with BTJ and outer part without BTJ in order to show the current confinement efficiency in VCSELs as a function of temperature.

3.5. Internal quantum efficiency and losses

With only 4 pair SiO2/a-Si dielectric DBR and by depositing additional 80 nm, 104 nm, 128 nm and 141 nm a-Si on top of that mirror which corresponds to a power reflectivity of 99.8%, 99.7%, 99.6%, 99.5% and 99.2%, respectively, the differential quantum efficiencies are measured from the LI-characteristics of single-mode VCSELs emitting at 2.6 μm at a heatsink temperature of 10° C and 0° C. Plotting 1/η d against the calculated 1/α m and using a linear fit according to Eq. (10), η i = 40% and α i = 23.2–26 cm−1 are obtained as illustrated in Fig. 8 a).

Fig. 8 a) Inverse differential quantum efficiency ( ηd1) against the inverse of mirror loss αm1 in order to extract the internal parameters, η i and α i, Using a linear fit. b) Band diagram of the active region, consisting of quaternary InGaAsSb embedded in GaSb barriers, used in 2.6 μm VCSELs.

The reduced internal quantum efficiency in such laser could be attributed to several issues, such as hole confinement of the QWs, hole leakage by thermionic emission or inhomogeneous filling of the QWs by the carriers. The latter is rather unlikely since the conduction and valence band offsets are as low as ΔEcQW212meV and ΔEhhQW48meV, respectively as shown in Fig. 8 b). Electrons remain very well confined in such QWs due to its moderately large conduction band offset, whereas EhhQW value is just less than twice of the thermal energy at room temperature (k B T). Therefore, hole leakage by thermionic emission could be the most probable reason of the low η i. Even the separate confinement layer Al0.15GaAsSb does not help so much in confining the carriers into the active region since the valence band offset at the separate confinement layer EhhSCH is approximately twice as low as K B T. The low η i could also be due to the presence of well-known strong non-radiative Auger recombination effect at the long wavelength MIR lasers.

The extracted loss parameter, α i contains all types of losses in the laser resonator. It includes out-coupling mirror losses, free carrier absorption in the cavity, the active region and epitaxial bottom Bragg mirror and diffraction loss. It should be noted that the deviation in α i value as indicated in Fig. 8 a) is resulting from the measurement carried out at two different temperatures and partly due to the different current injection magnitude. This clearly indicates the presence of temperature dependent loss mechanisms, e.g. Auger recombination, in the resonator. As expected, at 10°C the value of α i is higher than at 0°C since α i and η i are both function of temperature.

3.6. Gain constant and transparency current

Fig. 9 a) Quantum well threshold gain against threshold current density for 2.6 μm VCSELs with D BTJ = 8 μm at 0° C and 10° C. The measured points are fitted using Eq. (12). b) Gain-current density curve for 2.6 μm VCSELs based on threshold gain variation with aperture diameter of the device. c) Calculated CW threshold current density as a function of number of QWs in the device.

In fact, J tr sensitively depends on the sample quality and fabrication process and g 0 value obtained here is in a range and the measurement also involves some experimental inaccuracies. So, we recalculated these two laser parameters by an alternative experimental method.

Thus we obtain a pair of numbers (g th, J th) where g th is calculated using Eq. (14). As expected, both the threshold current and threshold current density will vary with the change of devices with different aperture diameters. As shown in Fig. 9 b), g o = 1580 cm−1 and J tr = 240 A/cm2 per QW can be extracted by plotting these measured data and then fitting with logarithmic gain-current relation. Compared to GaAs-based material system, the higher gain coefficient value indicates that this material system exhibits excellent gain properties of the active region material [28

28. C. Bückers, A. Thränhardt, S. W. Koch, M. Rattunde, N. Schulz, J. Wagner, J. Hader, and J. V. Moloney, “Microscopic calculation and measurement of the laser gain in a (GaIn)Sb quantum well structure,” Appl. Phys. Lett. 92, 071107 (2008). [CrossRef]

].

With the known gJ relationship we are in position to determine the optimum number of QWs for devices under study. Note that the round trip loss, δ is given by
δ=2NQWLQWΓr(NQW)gth(JthNQW)
(15)
Jth=NQWJtrηiexp(δ2NQWLQWΓrg0)
(16)

For two different round trip cavity losses, the calculated CW threshold current density is plotted as a function of number of QWs as indicated in Fig. 9 c). An exemplary numerical calculation of the threshold current density, J th for the device with D BTJ = 5 μm is mentioned here which has been marked by a red dot in Fig. 9 c). Using Eq. (15) and N QW = 7, L QW = 10 nm, Γr = 1.8 and g th = 638 cm−1, one obtains the round trip loss, δ =1.6%. The value of g th can be calculated by Eq. (12) using J th = 5.2 kA/cm2, η i = 0.4, J tr = 0.19 kA/cm2 and g o = 1450 cm−1. The round trip loss value δ can also be calculated by the right side of Eq. (14) and using measured η d = 7%, η i = 0.4 and calculated T OC = 0.0024. Finally one calculates CW threshold current density J th ≈ 5.2 kA/cm2 using Eq. (16) and in good agreement with the measured value.

As can be seen in Fig. 9 c), with 1.6% round trip loss, the optimum number of well is 3, whereas 7 QW was used in presented devices. Therefore, reducing the number of QWs from 7 to 3, J th will decrease and thus the device performance will be improved.

3.7. Measurement of water vapor concentration

An emission wavelength of 2.6 μm is of significant interest for gas detection by TDLAS. In fact, emission wavelengths of the presented lasers are obtained at 2.605, 2.596 and 2.594 μm where the strongest water vapor absorption lines are located. Such application-suited VCSELs open the way for gas measurements and isotopic ratio studies [29

29. E. R. T. Kerstel, R. Q. Iannone, M. Chenevier, S. Kassi, H.-J. Jost, and D. Romanini, “A water isotope (2H, 17O, and 18O) spectrometer based on optical feedback cavity-enhanced absorption for in situ airborne applications,” Appl. Phys. B: Lasers Opt. 85, 397–406 (2006). [CrossRef]

] by realizing absorption spectrometers with significant sensitivity improvements.

To prove the applicability of the VCSEL, an experiment was carried out in which the emission wavelength or intensity of the laser was modulated across the atmospheric water absorption features. This will show the suitability of such lasers in terms of modulation speed and stability of single-mode emission. The modulation was done by changing the driving current with an additional sinusoidal signal of frequency 10 kHz. This wavelength modulation spectroscopy method [30

30. J. T. C. Liu, J. B. Jeffries, and R. K. Hanson, “Wavelength modulation absorption spectroscopy with 2f detection using multiplexed diode lasers for rapid temperature measurements in gaseous flows,” Appl. Phys. B: Lasers Opt. 78, 503–511 (2004). [CrossRef]

, 31

31. R. Arndt, “Analytical line shapes for Lorentzian signals broadened by modulation,” J. Appl. Phys. 36, 2522–2524 (1965). [CrossRef]

] typically has a higher sensitivity for detecting the trace gases than direct absorption spectroscopy. In addition to its sensitivity, WMS has several other benefits which make it desirable over direct absorption spectroscopy due to the low spectral background.

In order to measure the atmospheric water vapor concentration, the first and the second harmonic (2f) spectra were recorded with the help of a lock-in amplifier which receives the intensity-modulated signal from the detector. Using the model in [31

31. R. Arndt, “Analytical line shapes for Lorentzian signals broadened by modulation,” J. Appl. Phys. 36, 2522–2524 (1965). [CrossRef]

], the measured spectra are then fitted analytically as illustrated in Fig. 10 a). An absolute water vapor concentration of 1.5% in laboratory air was determined. The excellent fit proves that the laser exhibits single-mode operation and without mode-hops over the entire operating range (shown in Fig. 10 b) which is required for high resolution TDLS.

Fig. 10 a) Measured WMS first and second harmonic spectra of H2O absorption lines (black lines) and the fit using absorption line parameters from HITRAN database [1] (blue lines). The detected signal at the photodetector for VCSELs emitting at 2.6 μm and the fit extracted from corresponding first and second harmonic spectra as shown in inset. Due to the lack of the temperature stability in the measurement setup, a mismatch appears between these two signals. b) The driving current dependent emission spectra at T = 20°C, showing the single-mode emission and the range of tunability.

4. Conclusion

References and links

1.

L. S. Rothman, D. Jacquemart, A. Barbe, D. C. Benner, M. Birk, L. R. Brown, M. R. Carleer, C. Chackerian Jr., K. Chance, L. H. Coudert, V. Dana, V. M. Devi, J.-M. Flaud, R. R. Gamache, A. Goldman, J.-M. Hartmann, K. W. Jucks, A. G. Maki, J.-Y. Mandin, S. T. Massie, J. Orphal, A. Perrin, C. P. Rinsland, M. A. H. Smith, J. Tennyson, R. N. Tolchenov, R. A. Toth, J. Vander Auwera, P. Varanasi, and G. Wagner, “The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139–204 (2005). [CrossRef]

2.

W. W. Bewley, C. L. Felix, I. Vurgaftman, E. H. Aifer, J. R. Meyer, L. Goldberg, J. R. Lindle, D. H. Chow, and E. Selvig, “Continuous-wave mid-infrared VCSELs,” IEEE Photon. Technol. Lett. 10, 660–662 (1998). [CrossRef]

3.

N. Schulz, J.-M. Hopkins, M. Rattunde, D. Burns, and J. Wagner, “High-brightness long-wavelength semiconductor disk lasers,” Laser & Photon. Rev. 2, 160–181 (2008). [CrossRef] [PubMed]

4.

F. Genty, A. Garnache, and L. Cerutti, “VCSELs emitting in the 2–3 μm wavelength range,” in Mid-infrared Semiconductor Optoelectronics, A. Krier, ed. Springer Series in Optical Sciences (Springer, 2006), Vol. 118, pp. 159–188. [CrossRef]

5.

A. Ducanchez, L. Cerutti, P. Grech, F. Genty, and E. Tournie, “Mid-infrared GaSb-based EP-VCSEL emitting at 2.63 μm,” Electron. Lett. 45, 265–267 (2009). [CrossRef]

6.

R. S. Inman and J. J. F. McAndrew, “Application of tunable diode laser absorption spectroscopy to trace moisture measurements in gases,” Anal. Chem. 66, 2471–2479 (1994). [CrossRef]

7.

A. Bachmann, K. Kashani-Shirazi, and M.-C. Amann, “GaSb-based electrically pumped VCSEL with buried tunnel junction operating continuous wave up to 50°C,” in Proceedings of IEEE Conference on Semiconductor Laser (Institute of Electrical and Electronic Engineers, Italy, 2008), paper TuA1, pp. 39–40. [CrossRef]

8.

S. Arafin, A. Bachmann, K. Kashani-Shirazi, and M.-C. Amann, “Electrically-pumped continuous-wave vertical-cavity surface-emitting lasers at 2.6 μm,” Appl. Phys. Lett. 95, 131120 (2009). [CrossRef]

9.

J. Chen, A. Hangauer, A. Bachmann, T. Lim, K. Kashani-Shirazi, R. Strzoda, and M.-C. Amann, “CO and CH4 sensing with single mode 2.3 μm GaSb-based VCSEL,” in Conference on Lasers and Electro-Optics (Optical Society of America, Baltimore, MD, 2009), paper CThI.

10.

A. Hangauer, J. Chen, R. Strzoda, M. Ortsiefer, and M.-C. Amann, “Wavelength modulation spectroscopy with a widely tunable InP-based 2.3 μm vertical-cavity surface-emitting laser,” Opt. Lett. 33, 1566–1568 (2008). [CrossRef] [PubMed]

11.

A. Hangauer, J. Chen, R. Strzoda, and M.-C. Amann, “The frequency modulation response of vertical-cavity surface-emitting lasers: experiment and theory,” IEEE J. Sel. Top. Quantum Electron. 17, 1–10 (2011).

12.

A. Bachmann, S. Arafin, and K. Kashani-Shirazi, “Single-mode electrically pumped GaSb-based VCSELs emitting continuous-wave at 2.4 and 2.6 μm,” N. J. Phys. 11, 125014 (2009). [CrossRef]

13.

A. Bachmann, K. Kashani-Shirazi, S. Arafin, and M.-C. Amann, “GaSb-based VCSEL with buried tunnel junction for emission around 2.3 μm,” IEEE J. Sel. Top. Quantum Electron. 15, 933–940 (2009). [CrossRef]

14.

http://www.comsol.com/

15.

S. Adachi, “Lattice thermal conductivity of group-IV and III–V semiconductor alloys,” J. Appl. Phys. 102, 063502 (2007). [CrossRef]

16.

T. Borca-Tasciuca, D. W. Song, J. R. Meyer, I. Vurgaftman, M.-J. Yang, B. Z. Noshob, L. J. Whitman, and G. Chen, “Thermal conductivity of AlAs0.07Sb0.93 and Al0.9Ga0.1As0.07Sb0.93 alloys and (AlAs)1/(AlSb)11 digital-alloy superlattices,” J. Appl. Phys. 92, 4994–4998 (2002). [CrossRef]

17.

M. Osinski and W. Nakwaski, “Effective thermal conductivity analysis of 1.55 μm InGaAsP/InP vertical-cavity top-surface-emitting microlasers,” Electron. Lett. 29, 1015–1016 (1993). [CrossRef]

18.

M. Ortsiefer, “Langwellige Vertikalresonator-Laserdioden im Materialsystem InGaAlAs/InP,” PhD thesis (Technische Universität München, 2000).

19.

K. L. Lear, R. P. Schneider Jr., K. D. Choquette, and S. P. Kilcoyne, “Index guiding dependent effects in implant and oxide confined vertical-cavity lasers,” IEEE Photon. Technol. Lett. 8, 740–742 (1996). [CrossRef]

20.

S. Arafin, A. Bachmann, and M.-C. Amann, “Transverse-mode characteristics of GaSb-based VCSELs with buried-tunnel junctions,” IEEE J. Sel. Top. Quantum Electron. 9, 1–8 (2011).

21.

A. N. Al-Omari and K. L. Lear, “VCSELs with a self-aligned contact and copper-plated heatsink,” IEEE Photon. Technol. Lett. 17, 1767–17697 (2005). [CrossRef]

22.

R. Michalzik, M. Grabherr, R. Jaeger, M. Miller, and K. J. Ebeling,“Progress in high-power VCSELs and arrays,” Proc. SPIE 3419, 187–195 (1998). [CrossRef]

23.

D. I. Babic, Y. Chung, N. Dagli, and J. E. Bowers, “Modal reflection of quarter-wave mirrors in vertical-cavity lasers,” IEEE J. Quantum Electron. 29, 1950–1962 (1993). [CrossRef]

24.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

25.

A. Perona, A. Garnache, L. Cerutti, A. Ducanchez, S. Mihindou, P. Grech, G. Boissier, and F. Genty, “AlAsSb/GaSb doped distributed Bragg reflectors for electrically pumped VCSELs emitting around 2.3 μm,” Semicond. Sci. Technol. 22, 1140–1144 (2007). [CrossRef]

26.

A. Hangauer, J. Chen, and M.-C. Amann, “Vertical-cavity surface-emitting laser light-current characteristic at constant internal temperature,” IEEE Photon. Technol. Lett. available online,(2011). [CrossRef]

27.

G. M. Yang, M. H. MacDougal, V. Pudikov, and P. D. Dapkus, “Influence of mirror reflectivity on laser performance of very-low-threshold vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 7, 1228–1230 (1995). [CrossRef]

28.

C. Bückers, A. Thränhardt, S. W. Koch, M. Rattunde, N. Schulz, J. Wagner, J. Hader, and J. V. Moloney, “Microscopic calculation and measurement of the laser gain in a (GaIn)Sb quantum well structure,” Appl. Phys. Lett. 92, 071107 (2008). [CrossRef]

29.

E. R. T. Kerstel, R. Q. Iannone, M. Chenevier, S. Kassi, H.-J. Jost, and D. Romanini, “A water isotope (2H, 17O, and 18O) spectrometer based on optical feedback cavity-enhanced absorption for in situ airborne applications,” Appl. Phys. B: Lasers Opt. 85, 397–406 (2006). [CrossRef]

30.

J. T. C. Liu, J. B. Jeffries, and R. K. Hanson, “Wavelength modulation absorption spectroscopy with 2f detection using multiplexed diode lasers for rapid temperature measurements in gaseous flows,” Appl. Phys. B: Lasers Opt. 78, 503–511 (2004). [CrossRef]

31.

R. Arndt, “Analytical line shapes for Lorentzian signals broadened by modulation,” J. Appl. Phys. 36, 2522–2524 (1965). [CrossRef]

OCIS Codes
(140.5960) Lasers and laser optics : Semiconductor lasers
(140.7260) Lasers and laser optics : Vertical cavity surface emitting lasers

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: May 23, 2011
Revised Manuscript: July 2, 2011
Manuscript Accepted: July 4, 2011
Published: August 18, 2011

Citation
S. Arafin, A. Bachmann, K. Vizbaras, A. Hangauer, J. Gustavsson, J. Bengtsson, A. Larsson, and M.-C. Amann, "Comprehensive analysis of electrically-pumped GaSb-based VCSELs," Opt. Express 19, 17267-17282 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-18-17267


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References

  1. L. S. Rothman, D. Jacquemart, A. Barbe, D. C. Benner, M. Birk, L. R. Brown, M. R. Carleer, C. Chackerian, K. Chance, L. H. Coudert, V. Dana, V. M. Devi, J.-M. Flaud, R. R. Gamache, A. Goldman, J.-M. Hartmann, K. W. Jucks, A. G. Maki, J.-Y. Mandin, S. T. Massie, J. Orphal, A. Perrin, C. P. Rinsland, M. A. H. Smith, J. Tennyson, R. N. Tolchenov, R. A. Toth, J. Vander Auwera, P. Varanasi, and G. Wagner, “The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139–204 (2005). [CrossRef]
  2. W. W. Bewley, C. L. Felix, I. Vurgaftman, E. H. Aifer, J. R. Meyer, L. Goldberg, J. R. Lindle, D. H. Chow, and E. Selvig, “Continuous-wave mid-infrared VCSELs,” IEEE Photon. Technol. Lett. 10, 660–662 (1998). [CrossRef]
  3. N. Schulz, J.-M. Hopkins, M. Rattunde, D. Burns, and J. Wagner, “High-brightness long-wavelength semiconductor disk lasers,” Laser & Photon. Rev. 2, 160–181 (2008). [CrossRef] [PubMed]
  4. F. Genty, A. Garnache, and L. Cerutti, “VCSELs emitting in the 2–3 μm wavelength range,” in Mid-infrared Semiconductor Optoelectronics , A. Krier, ed. Springer Series in Optical Sciences (Springer, 2006), Vol. 118, pp. 159–188. [CrossRef]
  5. A. Ducanchez, L. Cerutti, P. Grech, F. Genty, and E. Tournie, “Mid-infrared GaSb-based EP-VCSEL emitting at 2.63 μm,” Electron. Lett. 45, 265–267 (2009). [CrossRef]
  6. R. S. Inman and J. J. F. McAndrew, “Application of tunable diode laser absorption spectroscopy to trace moisture measurements in gases,” Anal. Chem. 66, 2471–2479 (1994). [CrossRef]
  7. A. Bachmann, K. Kashani-Shirazi, and M.-C. Amann, “GaSb-based electrically pumped VCSEL with buried tunnel junction operating continuous wave up to 50°C,” in Proceedings of IEEE Conference on Semiconductor Laser (Institute of Electrical and Electronic Engineers, Italy, 2008), paper TuA1, pp. 39–40. [CrossRef]
  8. S. Arafin, A. Bachmann, K. Kashani-Shirazi, and M.-C. Amann, “Electrically-pumped continuous-wave vertical-cavity surface-emitting lasers at 2.6 μm,” Appl. Phys. Lett. 95, 131120 (2009). [CrossRef]
  9. J. Chen, A. Hangauer, A. Bachmann, T. Lim, K. Kashani-Shirazi, R. Strzoda, and M.-C. Amann, “CO and CH4 sensing with single mode 2.3 μm GaSb-based VCSEL,” in Conference on Lasers and Electro-Optics (Optical Society of America, Baltimore, MD, 2009), paper CThI.
  10. A. Hangauer, J. Chen, R. Strzoda, M. Ortsiefer, and M.-C. Amann, “Wavelength modulation spectroscopy with a widely tunable InP-based 2.3 μm vertical-cavity surface-emitting laser,” Opt. Lett. 33, 1566–1568 (2008). [CrossRef] [PubMed]
  11. A. Hangauer, J. Chen, R. Strzoda, and M.-C. Amann, “The frequency modulation response of vertical-cavity surface-emitting lasers: experiment and theory,” IEEE J. Sel. Top. Quantum Electron. 17, 1–10 (2011).
  12. A. Bachmann, S. Arafin, and K. Kashani-Shirazi, “Single-mode electrically pumped GaSb-based VCSELs emitting continuous-wave at 2.4 and 2.6 μm,” N. J. Phys. 11, 125014 (2009). [CrossRef]
  13. A. Bachmann, K. Kashani-Shirazi, S. Arafin, and M.-C. Amann, “GaSb-based VCSEL with buried tunnel junction for emission around 2.3 μm,” IEEE J. Sel. Top. Quantum Electron. 15, 933–940 (2009). [CrossRef]
  14. http://www.comsol.com/
  15. S. Adachi, “Lattice thermal conductivity of group-IV and III–V semiconductor alloys,” J. Appl. Phys. 102, 063502 (2007). [CrossRef]
  16. T. Borca-Tasciuca, D. W. Song, J. R. Meyer, I. Vurgaftman, M.-J. Yang, B. Z. Noshob, L. J. Whitman, and G. Chen, “Thermal conductivity of AlAs0.07Sb0.93 and Al0.9Ga0.1As0.07Sb0.93 alloys and (AlAs)1/(AlSb)11 digital-alloy superlattices,” J. Appl. Phys. 92, 4994–4998 (2002). [CrossRef]
  17. M. Osinski and W. Nakwaski, “Effective thermal conductivity analysis of 1.55 μm InGaAsP/InP vertical-cavity top-surface-emitting microlasers,” Electron. Lett. 29, 1015–1016 (1993). [CrossRef]
  18. M. Ortsiefer, “Langwellige Vertikalresonator-Laserdioden im Materialsystem InGaAlAs/InP,” PhD thesis (Technische Universität München, 2000).
  19. K. L. Lear, R. P. Schneider, K. D. Choquette, and S. P. Kilcoyne, “Index guiding dependent effects in implant and oxide confined vertical-cavity lasers,” IEEE Photon. Technol. Lett. 8, 740–742 (1996). [CrossRef]
  20. S. Arafin, A. Bachmann, and M.-C. Amann, “Transverse-mode characteristics of GaSb-based VCSELs with buried-tunnel junctions,” IEEE J. Sel. Top. Quantum Electron. 9, 1–8 (2011).
  21. A. N. Al-Omari and K. L. Lear, “VCSELs with a self-aligned contact and copper-plated heatsink,” IEEE Photon. Technol. Lett. 17, 1767–17697 (2005). [CrossRef]
  22. R. Michalzik, M. Grabherr, R. Jaeger, M. Miller, and K. J. Ebeling,“Progress in high-power VCSELs and arrays,” Proc. SPIE 3419, 187–195 (1998). [CrossRef]
  23. D. I. Babic, Y. Chung, N. Dagli, and J. E. Bowers, “Modal reflection of quarter-wave mirrors in vertical-cavity lasers,” IEEE J. Quantum Electron. 29, 1950–1962 (1993). [CrossRef]
  24. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  25. A. Perona, A. Garnache, L. Cerutti, A. Ducanchez, S. Mihindou, P. Grech, G. Boissier, and F. Genty, “AlAsSb/GaSb doped distributed Bragg reflectors for electrically pumped VCSELs emitting around 2.3 μm,” Semicond. Sci. Technol. 22, 1140–1144 (2007). [CrossRef]
  26. A. Hangauer, J. Chen, and M.-C. Amann, “Vertical-cavity surface-emitting laser light-current characteristic at constant internal temperature,” IEEE Photon. Technol. Lett. available online, (2011). [CrossRef]
  27. G. M. Yang, M. H. MacDougal, V. Pudikov, and P. D. Dapkus, “Influence of mirror reflectivity on laser performance of very-low-threshold vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 7, 1228–1230 (1995). [CrossRef]
  28. C. Bückers, A. Thränhardt, S. W. Koch, M. Rattunde, N. Schulz, J. Wagner, J. Hader, and J. V. Moloney, “Microscopic calculation and measurement of the laser gain in a (GaIn)Sb quantum well structure,” Appl. Phys. Lett. 92, 071107 (2008). [CrossRef]
  29. E. R. T. Kerstel, R. Q. Iannone, M. Chenevier, S. Kassi, H.-J. Jost, and D. Romanini, “A water isotope (2H, 17O, and 18O) spectrometer based on optical feedback cavity-enhanced absorption for in situ airborne applications,” Appl. Phys. B: Lasers Opt. 85, 397–406 (2006). [CrossRef]
  30. J. T. C. Liu, J. B. Jeffries, and R. K. Hanson, “Wavelength modulation absorption spectroscopy with 2f detection using multiplexed diode lasers for rapid temperature measurements in gaseous flows,” Appl. Phys. B: Lasers Opt. 78, 503–511 (2004). [CrossRef]
  31. R. Arndt, “Analytical line shapes for Lorentzian signals broadened by modulation,” J. Appl. Phys. 36, 2522–2524 (1965). [CrossRef]

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