## Assessment of VCSEL thermal rollover mechanisms from measurements and empirical modeling |

Optics Express, Vol. 19, Issue 16, pp. 15490-15505 (2011)

http://dx.doi.org/10.1364/OE.19.015490

Acrobat PDF (3263 KB)

### Abstract

We use an empirical model together with experimental measurements for studying mechanisms contributing to thermal rollover in vertical-cavity surface-emitting lasers (VCSELs). The model is based on extraction of the temperature dependence of threshold current, internal quantum efficiency, internal optical loss, series resistance and thermal impedance from measurements of output power, voltage and lasing wavelength as a function of bias current over an ambient temperature range of 15–100°C. We apply the model to an oxide-confined, 850-nm VCSEL, fabricated with a 9-*μ*m inner-aperture diameter and optimized for high-speed operation, and show for this specific device that power dissipation due to linear power dissipation (sum total of optical absorption, carrier thermalization, carrier leakage and spontaneous carrier recombination) exceeds power dissipation across the series resistance (quadratic power dissipation) at any ambient temperature and bias current. We further show that the dominant contributors to self-heating for this particular VCSEL are quadratic power dissipation, internal optical loss, and carrier leakage. A rapid reduction of the internal quantum efficiency at high bias currents (resulting in high temperatures) is identified as being the major cause of thermal rollover. Our method is applicable to any VCSEL and is useful for identifying the mechanisms limiting the thermal performance of the device and to formulate design strategies to ameliorate them.

© 2011 OSA

## 1. Introduction

1. W. Hofmann, “High-speed buried tunnel junction vertical-cavity surface-emitting lasers,” IEEE Photon. J. **2**, 802–815 (2010). [CrossRef]

3. P. Westbergh, J. Gustavsson, Å. Haglund, M. Skold, A. Joel, and A. Larsson, “High speed, low-current-density 850 nm VCSELs,” IEEE J. Sel. Top. Quantum Electron. **15**, 694–703 (2009). [CrossRef]

3. P. Westbergh, J. Gustavsson, Å. Haglund, M. Skold, A. Joel, and A. Larsson, “High speed, low-current-density 850 nm VCSELs,” IEEE J. Sel. Top. Quantum Electron. **15**, 694–703 (2009). [CrossRef]

6. I. A. Young, E. M. Mohammed, J. T. S. Liao, A. M. Kern, S. Palermo, B. A. Block, M. R. Reshotko, and P. L. D. Chang, “Optical technology for energy efficient I/O in high performance computing,” IEEE Commun. Mag. **48**, 184–191 (2010). [CrossRef]

7. Y. Ding, W. J. Fan, D. W. Xu, C. Z. Tong, Y. Liu, and L. J. Zha, “Low threshold current density, low resistance oxide-confined VCSEL fabricated by a dielectric-free approach,” Appl. Phys. B **98**, 773–778 (2010). [CrossRef]

8. Å. Haglund, J. S. Gustavsson, J. Vukušsić, P. Modh, and A. Larsson, “Single fundamental-mode output power exceeding 6 mW from VCSELs with a shallow surface relief,”IEEE Photon. Technol. Lett. **16**, 368–370 (2004). [CrossRef]

3. P. Westbergh, J. Gustavsson, Å. Haglund, M. Skold, A. Joel, and A. Larsson, “High speed, low-current-density 850 nm VCSELs,” IEEE J. Sel. Top. Quantum Electron. **15**, 694–703 (2009). [CrossRef]

9. C. Ji, J. Wang, D. Söderström, and L. Giovane, “20-Gb/s 850-nm oxide VCSEL operating at 25°C–70°C,” IEEE Photon. Technol. Lett. **22**, 670–672 (2010). [CrossRef]

11. A. N. Al-Omari and K. L. Lear, “VCSELs with a self-aligned contact and copper-plated heatsink,” IEEE Photon. Technol. Lett. **17**, 1225–1227 (2005). [CrossRef]

15. S. B. Healy, E. P. O’Reilly, J. S. Gustavsson, P. Westbergh, Å. Haglund, A. Larsson, and A. Joel, “Active region design for high-speed 850-nm VCSELs,” IEEE J. Quantum Electron. **46**, 506–512 (2010). [CrossRef]

15. S. B. Healy, E. P. O’Reilly, J. S. Gustavsson, P. Westbergh, Å. Haglund, A. Larsson, and A. Joel, “Active region design for high-speed 850-nm VCSELs,” IEEE J. Quantum Electron. **46**, 506–512 (2010). [CrossRef]

21. P. Debernardi, A. Kroner, F. Rinaldi, and R. Michalzik, “Surface relief versus standard VCSELs: A comparison between experimental and hot-cavity model results,” IEEE J. Sel. Top. Quantum Electron. **15**, 828–837 (2009). [CrossRef]

**15**, 694–703 (2009). [CrossRef]

12. Y. Ou, J. S. Gustavsson, P. Westbergh, Å. Haglund, A. Larsson, and A. Joel, “Impedance characteristics and parasitic speed limitations of high-speed 850-nm VCSELs,” IEEE Photon. Technol. Lett. **21**, 1840–1842 (2009). [CrossRef]

14. A. N. Al-Omari and K. L. Lear, “Polyimide-planarized vertical-cavity surface-emitting lasers with 17.0-GHz bandwidth,” IEEE Photon. Technol. Lett. **16**, 969–971 (2004). [CrossRef]

11. A. N. Al-Omari and K. L. Lear, “VCSELs with a self-aligned contact and copper-plated heatsink,” IEEE Photon. Technol. Lett. **17**, 1225–1227 (2005). [CrossRef]

16. Y. Liu, W.-C. Ng, K. D. Choquette, and K. Hess, “Numerical investigation of self-heating effects of oxide-confined vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. **41**, 15–25 (2005). [CrossRef]

20. W. Nakwaski and M. Osinski, “On the thermal resistance of vertical-cavity surface-emitting lasers,” Opt. Quantum Electron. **29**, 883–892 (1997). [CrossRef]

21. P. Debernardi, A. Kroner, F. Rinaldi, and R. Michalzik, “Surface relief versus standard VCSELs: A comparison between experimental and hot-cavity model results,” IEEE J. Sel. Top. Quantum Electron. **15**, 828–837 (2009). [CrossRef]

17. P. V. Mena, J. J. Morikuni, S.-M. Kang, A. V. Harton, and K. W. Wyatt, “A simple rate-equation-based thermal VCSEL model,” J. Lightwave Technol. **17**, 865–872 (1999). [CrossRef]

18. J. W. Scott, R. S. Geels, S. W. Corzine, and L. A. Coldren, “Modeling temperature effects and spatial hole burning to optimize vertical-cavity surface-emitting laser performance,” IEEE J. Quantum Electron. **29**, 1295–1308 (1993). [CrossRef]

18. J. W. Scott, R. S. Geels, S. W. Corzine, and L. A. Coldren, “Modeling temperature effects and spatial hole burning to optimize vertical-cavity surface-emitting laser performance,” IEEE J. Quantum Electron. **29**, 1295–1308 (1993). [CrossRef]

*P*

_{opt}, bias voltage

*V*, and emission wavelength

_{b}*λ*of the fundamental mode as a function of bias current

*I*over an ambient temperature range of 15–100°C and calculate various contributions to self-heating responsible for an increase in the device temperature. The parameters are extracted by performing reliable single-parameter numerical fits to the measurements. We apply this model to an oxide-confined 850-nm VCSEL, fabricated with a 9-

_{b}*μ*m inner-aperture diameter and optimized for high speed operation. At room temperature (25°C), as the bias current is increased from threshold to thermal rollover, the saturation of the output power is caused by a 70°C rise in the internal device temperature, which causes the threshold current and internal optical loss to increase by 85% and 43%, respectively, and the internal quantum efficiency to decrease by 20%. Further, for this particular device, at any ambient temperature and bias current, linear power dissipation exceeds the quadratic power dissipation. In addition to quadratic power dissipation, internal optical loss and carrier leakage are the main factors limiting the thermal performance. Our method can potentially be applied to any VCSEL design to pin-point the factors limiting the thermal performance and assess the impact of steps taken to ameliorate them.

## 2. Theoretical Model

### 2.1. Modeling Thermal Effects

21. P. Debernardi, A. Kroner, F. Rinaldi, and R. Michalzik, “Surface relief versus standard VCSELs: A comparison between experimental and hot-cavity model results,” IEEE J. Sel. Top. Quantum Electron. **15**, 828–837 (2009). [CrossRef]

*R*

_{s}causes resistive or Joule heating. We refer to this mechanism as quadratic power dissipation (QPD), as its dependence on bias current is quadratic, and include it in our model using where

*I*is the bias current and

_{b}*T*is the ambient temperature. We have included a direct dependence of series resistance on current caused by charge accumulation at the hetero-interfaces in the distributed Bragg reflectors (DBRs); it leads to a reduction in resistance with bias current [19

_{a}19. G. Hasnain, K. Tai, L. Yang, Y. H. Wang, R. J. Fischer, J. D. Wynn, B. Weir, N. K. Dutta, and A. Y. Cho, “Performance of gain-guided surface emitting lasers with semiconductor distributed bragg reflectors,” IEEE J. Quantum Electron. **27**, 1377–1385 (1991). [CrossRef]

23. C. J. Chang-Hasnain, C. E. Zah, G. Hasnain, J. P. Harbison, L. T. Florez, N. G. Stoffel, and T. P. Lee, “Effect of operating electric power on the dynamic behavior of quantum well vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. **58**, 1247–1249 (1991). [CrossRef]

*I*, both below and above the threshold. We refer to the the sum of these mechanisms as linear power dissipation (LPD) and include it through where

_{b}*K*(

*T*) is the LPD coefficient whose value also depends on the device temperature, and therefore on both ambient temperature and current. In these equations,

*T*=

*T*+ Δ

_{a}*T*is the sum of the ambient temperature

*T*and the increase in temperature Δ

_{a}*T*caused by bias current induced self-heating. Henceforth, we define the value of a particular device parameter at a fixed

*T*and

_{a}*I*unless specified otherwise.

_{b}*P*

_{LPD}, it is important to understand the physical process behind each of the constituent LPD mechanisms. Figure 1 schematically depicts the capture and leakage of carriers injected into the active region of a VCSEL. Our model assumes that a fraction

*η*

_{i}(the internal quantum efficiency) of charge carriers carried by the bias current

*I*is captured by the quantum wells; remaining carriers, which constitute carrier leakage, recombine in the barriers and the separate-confinement hetero-structure surrounding the quantum wells to generate heat proportional to the dissipated power

_{b}*P*

_{leak}. Carriers captured by the quantum wells lose energy through various scattering mechanisms [24

24. W. H. Knox, D. S. Chemla, G. Livescu, J. E. Cunningham, and J. E. Henry, “Femtosecond carrier thermalization in dense fermi seas,” Phys. Rev. Lett. **61**, 1290–1293 (1988). [CrossRef] [PubMed]

*P*

_{therm}. Upon losing energy through thermalization, carriers recombine spontaneously through radiative and non-radiative mechanisms. Since only a small fraction of spontaneously emitted photons couple to the cavity modes, or escape the laser cavity by other means, it is therefore assumed that all spontaneous recombination events produce heat with the dissipated power

*P*

_{rec}[25]. Above threshold, a certain fraction of photons generated by stimulated emission are absorbed within the two DBRs forming the VCSEL cavity (internal optical loss). This absorption also produces heat with a dissipated power

*P*

_{abs}. Taking all these mechanisms into account, the current dependence of the various power dissipation mechanisms can be written as: We assume

*P*

_{abs}= 0 for

*I*<

_{b}*I*

_{th}as not many photons exist inside the VCSEL cavity below threshold. In these equations,

*E*

_{B}(

*T*) and

*E*

_{L}(

*T*) are the temperature-dependent barrier-bandgap energy and laser-photon energy (in eV), respectively,

*q*is the electron charge,

*I*

_{th}is the threshold current,

*α*

_{i}(

*T*) is the internal optical loss rate. Equation (5) takes into account clamping of the spontaneous recombination rate at the lasing threshold, and Eq. (6) assumes that light emitted through the bottom DBR is also absorbed and therefore produces heat. Note the temperature dependence, and consequently the bias current dependence, of most parameters in Eqs. (3)–(6).

*E*

_{B}(

*T*) is determined from the Varshini equations [26

26. Y.-A. Chang, J.-R. Chen, H.-C. Kuo, Y.-K. Kuo, and S.-C. Wang, “Theoretical and experimental analysis on InAlGaAs/AlGaAs active region of 850-nm vertical-cavity surface-emitting lasers,” J. Lightwave Technol. **24**, 536–543 (2006). [CrossRef]

27. I. Vurgaftman, J. R. Meyer, and L.-R. Ram-Mohan, “Band parameters for III–V compound semiconductors and their alloys,” Appl. Phys. Rev. **89**, 5815–5875 (2001). [CrossRef]

*T*

_{k}is the device temperature in Kelvin. The interpolation formula for the barrier bandgap of Al

*Ga*

_{x}_{1–}

*As is known to be [27*

_{x}27. I. Vurgaftman, J. R. Meyer, and L.-R. Ram-Mohan, “Band parameters for III–V compound semiconductors and their alloys,” Appl. Phys. Rev. **89**, 5815–5875 (2001). [CrossRef]

*E*

_{L}is estimated from temperature dependence of the lasing wavelength of the fundamental

*LP*

_{01}mode.

*P*

_{LPD}can be written as

*P*

_{tot}) is thus given by where the series resistance has been replaced by the differential resistance (

*R*=

_{s}*dV*/

_{b}*dI*) at the given bias point and

_{b}*V*denotes the applied voltage. The device temperature

_{b}*T*, is subsequently obtained using the thermal impedance

*R*

_{th}which relates the change in device temperature to the dissipated power and can be written as [3

**15**, 694–703 (2009). [CrossRef]

17. P. V. Mena, J. J. Morikuni, S.-M. Kang, A. V. Harton, and K. W. Wyatt, “A simple rate-equation-based thermal VCSEL model,” J. Lightwave Technol. **17**, 865–872 (1999). [CrossRef]

*R*

_{th}also depends on temperature through temperature dependence of the thermal conductivities of various materials in the VCSEL structure [20

20. W. Nakwaski and M. Osinski, “On the thermal resistance of vertical-cavity surface-emitting lasers,” Opt. Quantum Electron. **29**, 883–892 (1997). [CrossRef]

*P*

_{QPD}and

*P*

_{LPD}, respectively, on the bias current for the VCSELs operating under continuous bias current.

*λ*(

*T*) is the emission wavelength of the fundamental mode,

*c*is the speed of light and

*h*is the Planck constant.

### 2.2. Extraction of parameters from measurements

*P*

_{tot}, device temperature

*T*, and output power

*P*

_{opt}to the bias current. These equations contain a number of parameters whose temperature dependence needs to be quantified. To achieve this, we measure the output power, voltage and emission wavelength as a function of the bias current over a range of

*T*(15–100°C). The measurements are performed under continuous or low-duty-cycle pulsed operation.

_{a}*T*, depends on the ambient temperature

*T*owing to the temperature dependence of thermal impedance [Eq. (11)] and the increasing difficulty faced in stabilizing high stage temperatures against room temperature. At low ambient temperatures (

_{a}*T*≤ 50°C), the error in the extracted parameter values corresponds to a bias current induced increase in the device temperature (Δ

_{a}*T*≤ 2°C). As discussed in the next section, this corresponds to the resolution limit of the device thermometer [3

**15**, 694–703 (2009). [CrossRef]

*T*increases. The corresponding errors in the reported parameter values at room temperature (

*T*= 25°C) are summarized in Tables 1 and 2, assuming a worst-case value of 5°C uncertainty at

_{a}*T*= 100°C.

_{a}*λ*(

*T*), is found by measuring the wavelength of the fundamental mode (LP

_{01}) as a function of ambient temperature [3

**15**, 694–703 (2009). [CrossRef]

*λ*/Δ

*T*is typically around 0.06 nm/°C. This quantity is also used to estimate the device temperature at various values of

*T*and

_{a}*I*.

_{b}*I*

_{th}(

*T*), is extracted from power versus current (P

_{opt}–I

*) measurements recorded at different ambient temperatures [3*

_{b}**15**, 694–703 (2009). [CrossRef]

*α*(

_{i}*T*), is extracted from the measured dependence of output power on bias current just above threshold for VCSELs with different top-DBR reflectivities. This reflectivity is varied by changing the thickness of the top layer (using dry etching), which controls the phase of the surface reflection. The method is described in [10]. By performing these measurements at different ambient temperatures, the temperature dependence of

*α*(

_{i}*T*) is obtained. Other methods for carrying out these measurements for any VCSEL have been previously reported [28

28. D. V. Kuksenkov, H. Temkin, and S. Swirhun, “Measurement of internal quantum efficiency and losses in vertical cavity surface emitting lasers,” Appl. Phys. Lett. **66**, 1720–1722 (1995). [CrossRef]

*η*(

_{i}*T*), is also extracted from the measured P

_{opt}–I

*curves. The slope efficiency (SE) is extracted from the P*

_{b}_{opt}–I

*curves at different ambient temperatures by averaging the slope*

_{b}*dP*

_{opt}

*/dI*over optical powers in the range of

_{b}*P*

_{1}and

*P*

_{2}. The choice of

*P*

_{1}and

*P*

_{2}is constrained such that the increase in the device temperature over this range should be negligible (Δ

*T*≤ 5°

*C*). Therefore,

*P*

_{1}is chosen as emitted power at the lasing threshold at a particular ambient temperature and

*P*

_{2}is chosen as 10% of the maximum emitted power at room temperature. The external differential quantum efficiency is then calculated using [22, 25] We then calculate

*η*(

_{i}*T*) using the relation Here, the temperature dependence of the transmission loss rates through the top and bottom DBRs is accurately calculated using an effective index model that takes into account the temperature dependence of the refractive index of the constituent layers of the DBRs [10, 29

29. G. R. Hadley, “Effective index model for vertical-cavity surface-emitting lasers,” Opt. Lett. **20**, 1483–1485 (1995). [CrossRef] [PubMed]

*R*

_{th}(

*T*), is estimated by measuring the change in the emission wavelength, and therefore the increase in the device temperature, with increasing dissipated power in the current range

*I*< 2

_{b}*I*

_{th}at different ambient temperatures [11

11. A. N. Al-Omari and K. L. Lear, “VCSELs with a self-aligned contact and copper-plated heatsink,” IEEE Photon. Technol. Lett. **17**, 1225–1227 (2005). [CrossRef]

20. W. Nakwaski and M. Osinski, “On the thermal resistance of vertical-cavity surface-emitting lasers,” Opt. Quantum Electron. **29**, 883–892 (1997). [CrossRef]

## 3. Measurements on the Device Under Test

### 3.1. Device Under Test

30. A. Larsson, P. Westbergh, J. Gustavsson, Å. Haglund, and B. Kögel, “High-speed VCSELs for short reach communication,” Semicond. Sci. Technol. **26**, 014017 (2011). [CrossRef]

**15**, 694–703 (2009). [CrossRef]

15. S. B. Healy, E. P. O’Reilly, J. S. Gustavsson, P. Westbergh, Å. Haglund, A. Larsson, and A. Joel, “Active region design for high-speed 850-nm VCSELs,” IEEE J. Quantum Electron. **46**, 506–512 (2010). [CrossRef]

30. A. Larsson, P. Westbergh, J. Gustavsson, Å. Haglund, and B. Kögel, “High-speed VCSELs for short reach communication,” Semicond. Sci. Technol. **26**, 014017 (2011). [CrossRef]

31. L. F. Lester, S. S. O’Keefe, W. J. Schaff, and L. F. Eastman, “Multiquantum well strained-layer lasers with improved low frequency response and very low damping,” Electron. Lett. **28**, 383–385 (1992). [CrossRef]

*μ*m diameter) for current and optical confinement and a larger oxide aperture (18

*μ*m diameter) for reducing device capacitance [10, 13]. In a second dry-etching process, the bottom contact layer is reached and the n-contact layer is evaporated. The etched mesas are embedded in a low-k dielectric (benzo-cyclo-butene or BCB) to further reduce the parasitic capacitance [1

1. W. Hofmann, “High-speed buried tunnel junction vertical-cavity surface-emitting lasers,” IEEE Photon. J. **2**, 802–815 (2010). [CrossRef]

**15**, 694–703 (2009). [CrossRef]

12. Y. Ou, J. S. Gustavsson, P. Westbergh, Å. Haglund, A. Larsson, and A. Joel, “Impedance characteristics and parasitic speed limitations of high-speed 850-nm VCSELs,” IEEE Photon. Technol. Lett. **21**, 1840–1842 (2009). [CrossRef]

### 3.2. Experimental setup and measurements

*I*under CW operation at different ambient temperatures

_{b}*T*. Clearly, the slope efficiency decreases and the threshold current

_{a}*I*

_{th}increases with increasing

*T*. The corresponding dependence of voltage

_{a}*V*on

_{b}*I*at different

_{b}*T*is shown in part (b). At a given

_{a}*I*,

_{b}*V*decreases with increasing

_{b}*T*due to a reduction of the bandgap and improved carrier transport through the DBRs at higher temperatures. The inset Fig. shows the dependence of differential resistance (

_{a}*R*

_{s}) on

*I*at different

_{b}*T*. It can be seen that

_{a}*R*

_{s}decreases much more rapidly with increasing

*I*, as opposed to increasing

_{b}*T*. This can be attributed to an increase in charge accumulation at DBR interfaces with increasing bias current [19

_{a}19. G. Hasnain, K. Tai, L. Yang, Y. H. Wang, R. J. Fischer, J. D. Wynn, B. Weir, N. K. Dutta, and A. Y. Cho, “Performance of gain-guided surface emitting lasers with semiconductor distributed bragg reflectors,” IEEE J. Quantum Electron. **27**, 1377–1385 (1991). [CrossRef]

23. C. J. Chang-Hasnain, C. E. Zah, G. Hasnain, J. P. Harbison, L. T. Florez, N. G. Stoffel, and T. P. Lee, “Effect of operating electric power on the dynamic behavior of quantum well vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. **58**, 1247–1249 (1991). [CrossRef]

*R*

_{s}on

*I*and

_{b}*T*is used to calculated

_{a}*P*

_{QPD}at any combination of current and

*T*. Figure 3(c) shows the emission wavelength of the fundamental LP

_{a}_{01}mode at different

*T*, measured close to lasing threshold to avoid self-heating. The deduced linear dependence of wavelength on temperature is subsequently used to find the device temperature at any combination of

_{a}*T*and

_{a}*I*under CW operation.

_{b}### 3.3. Extraction of VCSEL Parameters

*I*

_{th}on device temperature, with minimum

*I*

_{th}occurring at the temperature for which the gain peak is spectrally aligned with the cavity resonance (30°C for the device under test) [22]. Here we use a two-segment line-fit to calculate threshold current at any ambient temperature from the corresponding P

_{opt}–I

*curve. This method is relatively insensitive to changes in slope efficiency [25]. A parabolic numerical fit is used to model the dependence of*

_{b}*I*

_{th}on

*T*. The maximum error in the calculated value of

_{a}*I*

_{th}is less than 2% at any

*T*. Part (e) shows the dependence of dissipated power,

_{a}*P*

_{tot}=

*I*–

_{b}V_{b}*P*

_{opt}, on

*I*at different ambient temperatures. At any bias current, a slight increase in dissipated power with increasing

_{b}*T*is observed. The reason behind this will be discussed in detail in Section 5. Part (f) shows the dependence of slope efficiency on output power at different

_{a}*T*. Following the procedure outlined in Section 2.2 and using Eqs. (13) and (14), the dependence of the internal quantum efficiency (

_{a}*η*) on the device temperature is deduced and plotted in the inset of Fig. 3(f). The

_{i}*η*is nearly constant and close to 88% at low device temperatures, but it decreases quite rapidly as the device temperature is increased beyond 50°C. A polynomial fit is used to represent

_{i}*η*(

_{i}*T*). The maximum calculated error in the extracted value of

*η*

_{i}is less than 1 % at any

*T*. To enable the calculation of

_{a}*η*(

_{i}*T*) from Eq. (14), we use values for the internal optical loss obtained using the method outlined in [10] and briefly described in Section 2. The internal optical loss was found to increase linearly with ambient temperature, from 0.070 ps

^{−1}at 25°C, to 0.097 ps

^{−1}at 85°C. This is consistent with the linear dependence of the free-carrier absorption coefficient on temperature [10].

**15**, 694–703 (2009). [CrossRef]

**29**, 883–892 (1997). [CrossRef]

29. G. R. Hadley, “Effective index model for vertical-cavity surface-emitting lasers,” Opt. Lett. **20**, 1483–1485 (1995). [CrossRef] [PubMed]

## 4. Predictions from the Thermal Model

*I*at three ambient temperatures (

_{b}*T*= 25, 55 and 85°C). The theoretical predictions based on Eqs. (10)–(12) are found to be in good agreement with the measured data for all values of

_{a}*I*. This agreement depicts the optical, electrical, and thermal consistency of our thermal model as well as underlying accuracy of the extracted temperature dependence of various VCSEL parameters.

_{b}*T*= 25, 55, and 85°C. Part (a) shows variation of

_{a}*η*

_{i}with

*I*. At 25°C ambient temperature,

_{b}*η*

_{i}is reduced from 88% at threshold to 70% at thermal rollover where the device temperature is close to 100°C as shown in Fig. 4(c). The reduction in

*η*becomes more severe at higher ambient temperatures. For example, when

_{i}*T*= 85°C,

_{a}*η*is reduced to less than 50% at thermal rollover. Figure 5(b) shows the evolution of

_{i}*I*

_{th}with

*I*. As expected, the threshold current increases with bias current because of current-induced self-heating. The inset plots the derivative

_{b}*dI*

_{th}/

*dI*as a function of

_{b}*I*and shows that this derivative becomes so large near thermal rollover that the rate of increase of

_{b}*I*

_{th}is 0.2 times the change in

*I*. Ideally, an

_{b}*I*

_{th}insensitive to

*I*over a wide range of device temperatures is desired, from the standpoint of improving the device thermal performance. This can be achieved by optimizing wavelength detuning between the gain-peak and the cavity resonance at which the VCSEL operates [1

_{b}1. W. Hofmann, “High-speed buried tunnel junction vertical-cavity surface-emitting lasers,” IEEE Photon. J. **2**, 802–815 (2010). [CrossRef]

*T*, as

_{a}*I*increases, the power dissipated within the VCSEL increases [Eq. (10)]. The corresponding increase in temperature [Eq. (11)] reduces

_{b}*η*and increases

_{i}*I*

_{th}and

*α*, which eventually causes the thermal rollover. To delay the onset of thermal rollover, the rate of increase of

_{i}*T*with respect to

*I*must be reduced. Traditionally, this has been achieved by reducing series resistance

_{b}*R*

_{s}[3

**15**, 694–703 (2009). [CrossRef]

12. Y. Ou, J. S. Gustavsson, P. Westbergh, Å. Haglund, A. Larsson, and A. Joel, “Impedance characteristics and parasitic speed limitations of high-speed 850-nm VCSELs,” IEEE Photon. Technol. Lett. **21**, 1840–1842 (2009). [CrossRef]

14. A. N. Al-Omari and K. L. Lear, “Polyimide-planarized vertical-cavity surface-emitting lasers with 17.0-GHz bandwidth,” IEEE Photon. Technol. Lett. **16**, 969–971 (2004). [CrossRef]

*R*

_{th}[11

**17**, 1225–1227 (2005). [CrossRef]

**29**, 883–892 (1997). [CrossRef]

*P*

_{LPD}) in our device with an aim to formulate design strategies to reduce them. For this purpose, we plot the LPD coefficient

*K*introduced in Eq. (2). The three curves in Fig. 5(c) show the total

*K*representing the sum of four individual contributions at three ambient temperatures [

*T*= 25, 55, and 85°C]. As seen there,

_{a}*K*initially decreases with increasing

*I*, reaches a minimum value, and then starts increasing as

_{b}*I*approaches the bias current corresponding to thermal rollover. It is this increase of

_{b}*K*with current that causes a rapid increase in internal temperature of our VCSEL, which in turn causes the thermal rollover behavior.

*K*(

*I*), we decompose the LPD coefficient into individual coefficients for the four constituent LPD mechanisms. We attach a subscript to

_{b}*K*and introduce

*K*

_{d}=

*P*

_{d}/

*I*, where

_{b}*d*is the subscript label used in Eqs. (3)–(7) that identifies the specific LPD mechanism in question. Four individual

*K*parameters are calculated from Eqs. (3)–(7) by simply dividing the four equations with

*I*. In Fig. 5(d) we plot these individual LPD coefficients as a function of bias current at

_{b}*T*= 25°C. The total

_{a}*K*is also plotted for comparison.

*I*but the other two change considerably. Consider first heating due to the carrier recombination governed by

_{b}*K*

_{rec}. This parameter is large at low bias currents and decreases as

*I*increases. This can be understood by noting that heating due to spontaneous recombination is high below laser threshold as most injected carriers recombine spontaneously to produce heat. It is reduced near and beyond the laser threshold because of a clamping of the carrier density. Consider next heating due to internal optical loss (absorption of photons produced by stimulated emission) governed by

_{b}*K*

_{abs}. This heating mechanism starts at laser threshold and its contribution increases with

*I*due to an increase in the number of stimulated photons generated inside the laser cavity. The net effect of

_{b}*K*

_{rec}and

*K*

_{abs}is an initial reduction of

*K*(

*I*) with increasing

_{b}*I*around threshold.

_{b}*K*takes its relatively low values. In this region, the coefficients representing thermalization and absorption heating are nearly constant while the coefficients representing spontaneous recombination and carrier leakage are slowly decreasing and increasing, respectively. The net effect is a nearly constant

*K*in this region, implying a linear increase of

*P*

_{LPD}with current [Eq. (2)]. Beyond the second dotted line, the coefficient representing carrier leakage increases, causing an increase of

*K*and a corresponding super-linear increase of

*P*

_{LPD}with increasing bias current. This is due to a rapid reduction of

*η*at high bias currents [Fig. 5(a)] corresponding to an internal device temperature increase in excess of 70°C [Fig. 4(b)]. Furthermore, the coefficient representing internal optical loss saturates at the thermal rollover current, which is consistent with the saturation of the photon density in the laser cavity.

_{i}*P*

_{leak}, is the dominant contributor to the thermal rollover.

## 5. Thermal Analysis

*P*

_{LPD}and

*P*

_{QPD}to

*P*

_{tot}at

*T*= 25, 55, and 85°C. At any

_{a}*T*,

_{a}*P*

_{LPD}exceeds

*P*

_{QPD}. This may seem counterintuitive. However, the proportionality constants (

*R*

_{s}and

*K*, respectively) in Eqs. (1) and (2) themselves depend on temperature, and therefore on

*I*, as seen in the inset of Figs. 3(b) and 5(c), respectively. Further, with increasing

_{b}*T*,

_{a}*P*

_{QPD}is slightly reduced while

*P*

_{LPD}increases progressively at any bias current.

*P*

_{leak},

*P*

_{therm},

*P*

_{rec}, and

*P*

_{abs}to

*P*

_{LPD}as a function of

*I*are shown in Fig. 6(b) at

_{b}*T*= 25, 55, and 85°C. At a low ambient temperature (25°C), internal optical loss (optical absorption) and carrier leakage are the two dominant power dissipation mechanisms. With increasing

_{a}*I*, power dissipation due to optical absorption saturates and eventually rolls over, whereas power dissipation due to carrier leakage is enhanced significantly. The rollover of the absorption heating is consistent with the rollover of the photon density while the significant increase of the leakage heating is consistent with the rapid reduction of the internal quantum efficiency at high temperatures. The reduction in

_{b}*η*also causes a saturation and subsequent rollover of the power dissipation due to carrier thermalization. Finally, the slight increase of recombination heating with

_{i}*I*is consistent with the increase of

_{b}*I*

_{th}, and therefore of the carrier density in the quantum wells, with increasing

*I*. However, its overall contribution is negligible at any

_{b}*T*and

_{a}*I*. This analysis points to carrier leakage (reduction of

_{b}*η*with increasing device temperature) as being the single most dominant contributor to

_{i}*P*

_{LPD}limiting the VCSEL thermal performance, especially at high ambient temperatures.

*I*at

_{b}*T*= 25, 55, and 85°C. At a low

_{a}*T*of 25°C, temperature increase due to

_{a}*P*

_{QPD}(Joule heating) exceeds that due to heating from optical absorption and carrier leakage. However, at high ambient temperatures (85°C), increase in device temperature due to carrier leakage exceeds that due to other mechanisms. Also, at any

*T*, heating due to carrier leakage increases most rapidly at high bias currents. This again shows that the reduction of internal quantum efficiency with increasing device temperature sets the ultimate limit for the thermal performance of this device.

_{a}*P*

_{QPD}and

*P*

_{abs}must be minimized. In a conventional VCSEL with current injection through doped DBRs, this involves a trade-off since higher doping levels lead to reduced resistance and increased free-carrier absorption [14

14. A. N. Al-Omari and K. L. Lear, “Polyimide-planarized vertical-cavity surface-emitting lasers with 17.0-GHz bandwidth,” IEEE Photon. Technol. Lett. **16**, 969–971 (2004). [CrossRef]

32. K. L. Lear and R. P. Schneider Jr., “Uniparabolic mirror grading for vertical cavity surface emitting lasers,” Appl. Phys. Lett. **68**, 605–607 (1996). [CrossRef]

4. J. S. Harris, T. O’Sullivan, T. Sarmiento, M. M. Lee, and S. Vo, “Emerging applications for vertical cavity surface emitting lasers,” Semicond. Sci. Technol. **26**, 014010 (2011). [CrossRef]

8. Å. Haglund, J. S. Gustavsson, J. Vukušsić, P. Modh, and A. Larsson, “Single fundamental-mode output power exceeding 6 mW from VCSELs with a shallow surface relief,”IEEE Photon. Technol. Lett. **16**, 368–370 (2004). [CrossRef]

**15**, 828–837 (2009). [CrossRef]

**17**, 1225–1227 (2005). [CrossRef]

**15**, 694–703 (2009). [CrossRef]

31. L. F. Lester, S. S. O’Keefe, W. J. Schaff, and L. F. Eastman, “Multiquantum well strained-layer lasers with improved low frequency response and very low damping,” Electron. Lett. **28**, 383–385 (1992). [CrossRef]

26. Y.-A. Chang, J.-R. Chen, H.-C. Kuo, Y.-K. Kuo, and S.-C. Wang, “Theoretical and experimental analysis on InAlGaAs/AlGaAs active region of 850-nm vertical-cavity surface-emitting lasers,” J. Lightwave Technol. **24**, 536–543 (2006). [CrossRef]

33. Y.-A. Chang, T.-S. Ko, J.-R. Chen, F.-I Lai, C.-L. Yu, I.-T. Wu, H.-C. Kuo, Y.-K. Kuo, L.-W. Laih, L.-H. Laih, T.-C. Lu, and S.-C. Wang, “The carrier blocking effect on 850 nm In-AlGaAs/AlGaAs vertical-cavity surface-emitting lasers,” Semicond. Sci. Technol. **21**, 1488–1494 (2006). [CrossRef]

## 6. Concluding Remarks

*μ*m inner aperture diameter and optimized for high-speed operation. The model shows that the thermal saturation behavior is caused by a rapid increase of device temperature with bias current, which causes a reduction in the internal quantum efficiency, an increase in the threshold current and increase in the internal optical loss.

*R*

_{s}and

*K*, respectively) depend themselves on the internal device temperature, and change in opposite directions as the bias current is increased close to thermal rollover. Still, quadratic power dissipation is a major source of device heating, having a significant impact on the thermal performance of the VCSEL.

## Acknowledgments

## References and links

1. | W. Hofmann, “High-speed buried tunnel junction vertical-cavity surface-emitting lasers,” IEEE Photon. J. |

2. | R. Safaisini, J. R. Joseph, and K. L. Lear, “Scalable high-CW-power high-speed 980-nm VCSEL arrays,” IEEE J. Quantum Electron. |

3. | P. Westbergh, J. Gustavsson, Å. Haglund, M. Skold, A. Joel, and A. Larsson, “High speed, low-current-density 850 nm VCSELs,” IEEE J. Sel. Top. Quantum Electron. |

4. | J. S. Harris, T. O’Sullivan, T. Sarmiento, M. M. Lee, and S. Vo, “Emerging applications for vertical cavity surface emitting lasers,” Semicond. Sci. Technol. |

5. | B. Ciftcioglu, R. Berman, J. Zhang, Z. Darling, S. Wang, J. Hu, J. Xue, A. Garg, M. Jain, I. Savidis, D. Moore, M. Huang, E. G. Friedman, G. Wicks, and H. Wu, “A 3-D integrated intrachip free-space optical interconnect for many-core chips,” IEEE Photon. Technol. Lett. |

6. | I. A. Young, E. M. Mohammed, J. T. S. Liao, A. M. Kern, S. Palermo, B. A. Block, M. R. Reshotko, and P. L. D. Chang, “Optical technology for energy efficient I/O in high performance computing,” IEEE Commun. Mag. |

7. | Y. Ding, W. J. Fan, D. W. Xu, C. Z. Tong, Y. Liu, and L. J. Zha, “Low threshold current density, low resistance oxide-confined VCSEL fabricated by a dielectric-free approach,” Appl. Phys. B |

8. | Å. Haglund, J. S. Gustavsson, J. Vukušsić, P. Modh, and A. Larsson, “Single fundamental-mode output power exceeding 6 mW from VCSELs with a shallow surface relief,”IEEE Photon. Technol. Lett. |

9. | C. Ji, J. Wang, D. Söderström, and L. Giovane, “20-Gb/s 850-nm oxide VCSEL operating at 25°C–70°C,” IEEE Photon. Technol. Lett. |

10. | P. Westbergh, J. S. Gustavsson, B. Kögel, Å. Haglund, and A. Larsson, “Impact of photon life-time on high speed VCSEL performance,” IEEE J. Sel. Top. Quantum Electron. (accepted for publication). |

11. | A. N. Al-Omari and K. L. Lear, “VCSELs with a self-aligned contact and copper-plated heatsink,” IEEE Photon. Technol. Lett. |

12. | Y. Ou, J. S. Gustavsson, P. Westbergh, Å. Haglund, A. Larsson, and A. Joel, “Impedance characteristics and parasitic speed limitations of high-speed 850-nm VCSELs,” IEEE Photon. Technol. Lett. |

13. | Y.-C. Chang and L. A. Coldren, “Efficient, high-data-rate, tapered oxide-aperture, vertical-cavity surface-emitting lasers,” IEEE J. Sel. Top. Quantum Electron. |

14. | A. N. Al-Omari and K. L. Lear, “Polyimide-planarized vertical-cavity surface-emitting lasers with 17.0-GHz bandwidth,” IEEE Photon. Technol. Lett. |

15. | S. B. Healy, E. P. O’Reilly, J. S. Gustavsson, P. Westbergh, Å. Haglund, A. Larsson, and A. Joel, “Active region design for high-speed 850-nm VCSELs,” IEEE J. Quantum Electron. |

16. | Y. Liu, W.-C. Ng, K. D. Choquette, and K. Hess, “Numerical investigation of self-heating effects of oxide-confined vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. |

17. | P. V. Mena, J. J. Morikuni, S.-M. Kang, A. V. Harton, and K. W. Wyatt, “A simple rate-equation-based thermal VCSEL model,” J. Lightwave Technol. |

18. | J. W. Scott, R. S. Geels, S. W. Corzine, and L. A. Coldren, “Modeling temperature effects and spatial hole burning to optimize vertical-cavity surface-emitting laser performance,” IEEE J. Quantum Electron. |

19. | G. Hasnain, K. Tai, L. Yang, Y. H. Wang, R. J. Fischer, J. D. Wynn, B. Weir, N. K. Dutta, and A. Y. Cho, “Performance of gain-guided surface emitting lasers with semiconductor distributed bragg reflectors,” IEEE J. Quantum Electron. |

20. | W. Nakwaski and M. Osinski, “On the thermal resistance of vertical-cavity surface-emitting lasers,” Opt. Quantum Electron. |

21. | P. Debernardi, A. Kroner, F. Rinaldi, and R. Michalzik, “Surface relief versus standard VCSELs: A comparison between experimental and hot-cavity model results,” IEEE J. Sel. Top. Quantum Electron. |

22. | C. Wilmsen, H. Temkin, and L. Coldren, |

23. | C. J. Chang-Hasnain, C. E. Zah, G. Hasnain, J. P. Harbison, L. T. Florez, N. G. Stoffel, and T. P. Lee, “Effect of operating electric power on the dynamic behavior of quantum well vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. |

24. | W. H. Knox, D. S. Chemla, G. Livescu, J. E. Cunningham, and J. E. Henry, “Femtosecond carrier thermalization in dense fermi seas,” Phys. Rev. Lett. |

25. | L. A. Coldren and S. W. Corzine, |

26. | Y.-A. Chang, J.-R. Chen, H.-C. Kuo, Y.-K. Kuo, and S.-C. Wang, “Theoretical and experimental analysis on InAlGaAs/AlGaAs active region of 850-nm vertical-cavity surface-emitting lasers,” J. Lightwave Technol. |

27. | I. Vurgaftman, J. R. Meyer, and L.-R. Ram-Mohan, “Band parameters for III–V compound semiconductors and their alloys,” Appl. Phys. Rev. |

28. | D. V. Kuksenkov, H. Temkin, and S. Swirhun, “Measurement of internal quantum efficiency and losses in vertical cavity surface emitting lasers,” Appl. Phys. Lett. |

29. | G. R. Hadley, “Effective index model for vertical-cavity surface-emitting lasers,” Opt. Lett. |

30. | A. Larsson, P. Westbergh, J. Gustavsson, Å. Haglund, and B. Kögel, “High-speed VCSELs for short reach communication,” Semicond. Sci. Technol. |

31. | L. F. Lester, S. S. O’Keefe, W. J. Schaff, and L. F. Eastman, “Multiquantum well strained-layer lasers with improved low frequency response and very low damping,” Electron. Lett. |

32. | K. L. Lear and R. P. Schneider Jr., “Uniparabolic mirror grading for vertical cavity surface emitting lasers,” Appl. Phys. Lett. |

33. | Y.-A. Chang, T.-S. Ko, J.-R. Chen, F.-I Lai, C.-L. Yu, I.-T. Wu, H.-C. Kuo, Y.-K. Kuo, L.-W. Laih, L.-H. Laih, T.-C. Lu, and S.-C. Wang, “The carrier blocking effect on 850 nm In-AlGaAs/AlGaAs vertical-cavity surface-emitting lasers,” Semicond. Sci. Technol. |

**OCIS Codes**

(060.4510) Fiber optics and optical communications : Optical communications

(140.6810) Lasers and laser optics : Thermal effects

(200.4650) Optics in computing : Optical interconnects

(230.1150) Optical devices : All-optical devices

(250.7260) Optoelectronics : Vertical cavity surface emitting lasers

**ToC Category:**

Optoelectronics

**History**

Original Manuscript: May 23, 2011

Revised Manuscript: July 4, 2011

Manuscript Accepted: July 11, 2011

Published: July 28, 2011

**Citation**

Prashant P. Baveja, Benjamin Kögel, Petter Westbergh, Johan S. Gustavsson, Åsa Haglund, Drew N. Maywar, Govind P. Agrawal, and Anders Larsson, "Assessment of VCSEL thermal rollover mechanisms from measurements and empirical modeling," Opt. Express **19**, 15490-15505 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-16-15490

Sort: Year | Journal | Reset

### References

- W. Hofmann, “High-speed buried tunnel junction vertical-cavity surface-emitting lasers,” IEEE Photon. J. 2, 802–815 (2010). [CrossRef]
- R. Safaisini, J. R. Joseph, and K. L. Lear, “Scalable high-CW-power high-speed 980-nm VCSEL arrays,” IEEE J. Quantum Electron. 46, 1590–1596 (2010). [CrossRef]
- P. Westbergh, J. Gustavsson, Å. Haglund, M. Skold, A. Joel, and A. Larsson, “High speed, low-current-density 850 nm VCSELs,” IEEE J. Sel. Top. Quantum Electron. 15, 694–703 (2009). [CrossRef]
- J. S. Harris, T. O’Sullivan, T. Sarmiento, M. M. Lee, and S. Vo, “Emerging applications for vertical cavity surface emitting lasers,” Semicond. Sci. Technol. 26, 014010 (2011). [CrossRef]
- B. Ciftcioglu, R. Berman, J. Zhang, Z. Darling, S. Wang, J. Hu, J. Xue, A. Garg, M. Jain, I. Savidis, D. Moore, M. Huang, E. G. Friedman, G. Wicks, and H. Wu, “A 3-D integrated intrachip free-space optical interconnect for many-core chips,” IEEE Photon. Technol. Lett. 23, 164–166 (2011). [CrossRef]
- I. A. Young, E. M. Mohammed, J. T. S. Liao, A. M. Kern, S. Palermo, B. A. Block, M. R. Reshotko, and P. L. D. Chang, “Optical technology for energy efficient I/O in high performance computing,” IEEE Commun. Mag. 48, 184–191 (2010). [CrossRef]
- Y. Ding, W. J. Fan, D. W. Xu, C. Z. Tong, Y. Liu, and L. J. Zha, “Low threshold current density, low resistance oxide-confined VCSEL fabricated by a dielectric-free approach,” Appl. Phys. B 98, 773–778 (2010). [CrossRef]
- Å. Haglund, J. S. Gustavsson, J. Vukušsić, P. Modh, and A. Larsson, “Single fundamental-mode output power exceeding 6 mW from VCSELs with a shallow surface relief,”IEEE Photon. Technol. Lett. 16, 368–370 (2004). [CrossRef]
- C. Ji, J. Wang, D. Söderström, and L. Giovane, “20-Gb/s 850-nm oxide VCSEL operating at 25°C–70°C,” IEEE Photon. Technol. Lett. 22, 670–672 (2010). [CrossRef]
- P. Westbergh, J. S. Gustavsson, B. Kögel, Å. Haglund, and A. Larsson, “Impact of photon life-time on high speed VCSEL performance,” IEEE J. Sel. Top. Quantum Electron. (accepted for publication).
- A. N. Al-Omari and K. L. Lear, “VCSELs with a self-aligned contact and copper-plated heatsink,” IEEE Photon. Technol. Lett. 17, 1225–1227 (2005). [CrossRef]
- Y. Ou, J. S. Gustavsson, P. Westbergh, Å. Haglund, A. Larsson, and A. Joel, “Impedance characteristics and parasitic speed limitations of high-speed 850-nm VCSELs,” IEEE Photon. Technol. Lett. 21, 1840–1842 (2009). [CrossRef]
- Y.-C. Chang and L. A. Coldren, “Efficient, high-data-rate, tapered oxide-aperture, vertical-cavity surface-emitting lasers,” IEEE J. Sel. Top. Quantum Electron. 15, 1–12 (2009).
- A. N. Al-Omari and K. L. Lear, “Polyimide-planarized vertical-cavity surface-emitting lasers with 17.0-GHz bandwidth,” IEEE Photon. Technol. Lett. 16, 969–971 (2004). [CrossRef]
- S. B. Healy, E. P. O’Reilly, J. S. Gustavsson, P. Westbergh, Å. Haglund, A. Larsson, and A. Joel, “Active region design for high-speed 850-nm VCSELs,” IEEE J. Quantum Electron. 46, 506–512 (2010). [CrossRef]
- Y. Liu, W.-C. Ng, K. D. Choquette, and K. Hess, “Numerical investigation of self-heating effects of oxide-confined vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 41, 15–25 (2005). [CrossRef]
- P. V. Mena, J. J. Morikuni, S.-M. Kang, A. V. Harton, and K. W. Wyatt, “A simple rate-equation-based thermal VCSEL model,” J. Lightwave Technol. 17, 865–872 (1999). [CrossRef]
- J. W. Scott, R. S. Geels, S. W. Corzine, and L. A. Coldren, “Modeling temperature effects and spatial hole burning to optimize vertical-cavity surface-emitting laser performance,” IEEE J. Quantum Electron. 29, 1295–1308 (1993). [CrossRef]
- G. Hasnain, K. Tai, L. Yang, Y. H. Wang, R. J. Fischer, J. D. Wynn, B. Weir, N. K. Dutta, and A. Y. Cho, “Performance of gain-guided surface emitting lasers with semiconductor distributed bragg reflectors,” IEEE J. Quantum Electron. 27, 1377–1385 (1991). [CrossRef]
- W. Nakwaski and M. Osinski, “On the thermal resistance of vertical-cavity surface-emitting lasers,” Opt. Quantum Electron. 29, 883–892 (1997). [CrossRef]
- P. Debernardi, A. Kroner, F. Rinaldi, and R. Michalzik, “Surface relief versus standard VCSELs: A comparison between experimental and hot-cavity model results,” IEEE J. Sel. Top. Quantum Electron. 15, 828–837 (2009). [CrossRef]
- C. Wilmsen, H. Temkin, and L. Coldren, Vertical-Cavity Surface-Emitting Lasers: Design, Fabrication, Characterization, and Applications , (Cambridge Univ. Press, 1999).
- C. J. Chang-Hasnain, C. E. Zah, G. Hasnain, J. P. Harbison, L. T. Florez, N. G. Stoffel, and T. P. Lee, “Effect of operating electric power on the dynamic behavior of quantum well vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 58, 1247–1249 (1991). [CrossRef]
- W. H. Knox, D. S. Chemla, G. Livescu, J. E. Cunningham, and J. E. Henry, “Femtosecond carrier thermalization in dense fermi seas,” Phys. Rev. Lett. 61, 1290–1293 (1988). [CrossRef] [PubMed]
- L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Intergrated Circuits (Wiley, 1995).
- Y.-A. Chang, J.-R. Chen, H.-C. Kuo, Y.-K. Kuo, and S.-C. Wang, “Theoretical and experimental analysis on InAlGaAs/AlGaAs active region of 850-nm vertical-cavity surface-emitting lasers,” J. Lightwave Technol. 24, 536–543 (2006). [CrossRef]
- I. Vurgaftman, J. R. Meyer, and L.-R. Ram-Mohan, “Band parameters for III–V compound semiconductors and their alloys,” Appl. Phys. Rev. 89, 5815–5875 (2001). [CrossRef]
- D. V. Kuksenkov, H. Temkin, and S. Swirhun, “Measurement of internal quantum efficiency and losses in vertical cavity surface emitting lasers,” Appl. Phys. Lett. 66, 1720–1722 (1995). [CrossRef]
- G. R. Hadley, “Effective index model for vertical-cavity surface-emitting lasers,” Opt. Lett. 20, 1483–1485 (1995). [CrossRef] [PubMed]
- A. Larsson, P. Westbergh, J. Gustavsson, Å. Haglund, and B. Kögel, “High-speed VCSELs for short reach communication,” Semicond. Sci. Technol. 26, 014017 (2011). [CrossRef]
- L. F. Lester, S. S. O’Keefe, W. J. Schaff, and L. F. Eastman, “Multiquantum well strained-layer lasers with improved low frequency response and very low damping,” Electron. Lett. 28, 383–385 (1992). [CrossRef]
- K. L. Lear and R. P. Schneider, “Uniparabolic mirror grading for vertical cavity surface emitting lasers,” Appl. Phys. Lett. 68, 605–607 (1996). [CrossRef]
- Y.-A. Chang, T.-S. Ko, J.-R. Chen, F.-I Lai, C.-L. Yu, I.-T. Wu, H.-C. Kuo, Y.-K. Kuo, L.-W. Laih, L.-H. Laih, T.-C. Lu, and S.-C. Wang, “The carrier blocking effect on 850 nm In-AlGaAs/AlGaAs vertical-cavity surface-emitting lasers,” Semicond. Sci. Technol. 21, 1488–1494 (2006). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.