V. G. Garcia and M. Farzaneh
Citation: Journal of Applied Physics 119 , 045105 (2016); doi: 10.1063/1.4940710
View online: http://dx.doi.org/10.1063/1.4940710
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/119/4?ver=pdfcov
Published by the AIP Publishing
Articles you may be interested in
Thermal effects in 2.x μm vertical-external-cavity-surface-emitting lasers
J. Appl. Phys. 111 , 053107 (2012); 10.1063/1.3691228
Cross-plane thermal diffusivity measurement of an operating vertical cavity surface emitting laser using thermoreflectance
J. Appl. Phys. 109 , 096101 (2011); 10.1063/1.3581089
Reverse-bias emission sheds light on the failure mechanism of degraded vertical-cavity surface-emitting lasers
J. Appl. Phys. 99 , 123113 (2006); 10.1063/1.2206852
Reverse-bias electroluminescence imaging to diagnose failures of vertical-cavity surface-emitting lasers
Appl. Phys. Lett. 86 , 221108 (2005); 10.1063/1.1943496
Smart pixel using a vertical cavity surface-emitting laser
Appl. Phys. Lett. 71 , 3561 (1997); 10.1063/1.120391
[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:
143.236.90.85 On: Wed, 27 Jan 2016 16:47:31

JOURNAL OF APPLIED PHYSICS 119 , 045105 (2016)
V. G.
Garcia
1,2 and M.
Farzaneh
1,
a)
1
Department of Physics and Astronomy, University of Wisconsin Stevens Point, Stevens Point,
Wisconsin 54481, USA
2
Department of Physics, Federal University of Technology Paran a, Curitiba, Paran a 3165, Brazil
(Received 25 November 2015; accepted 12 January 2016; published online 27 January 2016)
Thermal transient response at the surface of a Vertical Cavity Surface-emitting Laser (VCSEL) is measured under operating conditions using a thermoreflectance imaging technique. From the transient curve, a thermal time constant of (9.7
6 0.5) l s is obtained for the device surface in response to a 40 l s heating pulse. A cross-plane thermal diffusivity of the order of 2 10
6 m
2
/s has been deduced from both the experimental data and heat transfer modeling. This reduced thermal diffusivity compared to the bulk is attributed to the enhanced phonon scattering at the boundaries of the VCSEL’s multi-layered structure.
V
2016 AIP Publishing LLC .
[ http://dx.doi.org/10.1063/1.4940710
]
INTRODUCTION
Thermal effects on the operation of Vertical Cavity
Surface-emitting Lasers (VCSELs) are well documented and can range from optical power reduction and variations in threshold current
1 to polarization switching,
2
local gain com-
pression,
3
and self-focusing due to thermal lensing.
4
Studies of thermal effects in VCSELs in the past have been extensive and include spatially resolved spontaneous electroluminescence wavelength shift ( l -EL) measurement
5
thermal microscopy (SThM).
6
and scanning
In the latter method, the measurement was done on the cross section of the VCSEL and not on the light emitting surface to avoid the absorption of the laser light by the SThM temperature sensor.
Thermal distribution, thermal resistance, and thermal lensing in VCSELs have also been measured using high resolution, all optical technique of thermoreflectance microscopy.
7
The same technique is also used for measuring ther-
mal cross-talk in VCSEL arrays
8 diffusivity of a VCSEL
9
and cross-plane thermal under operating conditions.
In all of the previous thermoreflectance measurements of a
VCSEL, the thermal distribution has been determined in the frequency domain and in steady-state conditions. Since in many applications, the VCSEL has to be pulsed at high rates, it is important to understand the thermal response of the laser as a function of time (thermal transients). In this paper, we present the results of transient thermal imaging of a VCSEL using charge-coupled device (CCD)-based thermoreflectance microscopy. In addition to measuring the thermal time constants on the surface of the VCSEL, we compare our results with a timedependent heat transfer model which confirms the reduction of thermal diffusivity in the multi-layered structure of a VCSEL.
EXPERIMENTAL METHOD
Transient thermal images reported in this paper are
obtained using a thermoreflectance imaging technique.
10
a)
Author to whom correspondence should be addressed. Electronic mail: mfarzane@uwsp.edu
Thermoreflectance is based on the fact that the relative change in the reflectivity ( D R / R ) of the device under test
(DUT) is directly proportional to the change in temperature
( D T )
D R
¼ C th
D T ;
R
(1) where C th is the material and wavelength dependent thermoreflectance calibration coefficient. The value of C th typically of the order of 10
2
–10
5
K
1 is and can be obtained by performing an independent calibration experiment.
Therefore, in the CCD-based thermoreflectance microscopy, a spatial profile of D T on the surface of the device can be obtained by measuring the spatially resolved maps of D R / R .
Although the thermoreflectance measurements reported in this paper are not calibrated, a value of C th
¼ 2.3
10
4
K
1
(Ref.
7 ) has been previously reported for the similar VCSEL
under similar illumination wavelength of 470 nm. This will yield the order of magnitude of the calibration coefficient and thus D T in the present case.
The schematic of the experimental set up for measuring
D R / R is shown in Fig.
1 . The VCSEL is under a 100
,
NA ¼ 0.75 objective of an optical microscope and is actively cooled at 20 C by a thermoelectric cooler. The surface of the device is illuminated by a 470 nm blue light emitting diode (LED), and a blue band-pass filter (Chroma) is used to attenuate the laser light while allowing 80% transmission of the LED light. The changes in VCSEL’s temperature are achieved by pulsing its bias current. The back reflected light is then detected by a 12-bit, 60 Hz CCD camera.
The VCSEL under test is a commercially manufactured,
850 nm, multimode, oxide confined laser with a threshold current of 1.4 mA (Thorlabs-VCSEL850). In order to ensure that the changes in the refractive index and thus the reflectivity are only due to thermal effects and not the changes in the carrier density, the VCSEL is biased above the threshold.
This is achieved by adding a DC offset bias to the heating
0021-8979/2016/119(4)/045105/5/$30.00
119 , 045105-1 2016 AIP Publishing LLC
[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:
143.236.90.85 On: Wed, 27 Jan 2016 16:47:31

045105-2 V. G. Garcia and M. Farzaneh
FIG. 1. Schematic diagram of the transient thermoreflectance imaging set up. The inset shows the optical image of the VCSEL under 50 magnification.
pulse. In this way, the VCSEL’s current is pulsed from
2.5 mA to 9.5 mA, with a 25% duty cycle.
In order to obtain the time domain thermoreflectance images, we use the “pulsed-box car averaging technique.”
11 – 14
In this technique, the illumination source
(LED) is pulsed in short durations. Fig.
2
shows the relationship between the VCSEL’s heating pulse, LED pulse, and the camera trigger schematically. In each frame of the camera, many heating and cooling events occur. The duty cycle of the VCSEL’s heating pulse is kept at around 25% or lower to allow for the complete cooling of the device between heating cycles. The LED acts as a strobe and is pulsed at a very low duty cycle (about 1%).
Decreasing the LED pulse width would improve the temporal resolution of the technique. The LED pulse is also given a controlled time delay with respect to the heating pulse. By sweeping this time delay over the entire width of the heating pulse, different points on the thermal transient curve of the device are sampled.
The thermoreflectance signal at each pixel is then measured as the relative difference between the “ON” image (where the heating pulse is on) and the “reference” image (where the heating pulse is off and time delay is zero). In other words
D R
R
¼
R
ON
R
Ref :
R
Ref :
: (2)
Different “ON” images are obtained by changing the delay time ( s ) between the LED and the VCSEL’s heating pulse.
J. Appl. Phys.
119 , 045105 (2016)
Since the thermally induced changes in pixel brightness are typically far smaller than the random fluctuations caused by the shot noise inside the CCD, averaging over many cycles is necessary to improve the signal to noise ratio for each image. This allows for resolving the thermoreflectance signal well beyond the inherent dynamic range of the CCD because of "stochastic resonance."
15
In order to quantitatively validate the purity of the thermal signal and ensure that no optical emission from the
VCSEL has reached the CCD, an experiment was performed with continuous LED illumination. Thermal images were then taken at the VCSEL bias “off” and “on” positions. After averaging over 50 000 CCD frames (the same as the actual experiment), no thermal signal ( D R / R ) was detected, suggesting that the optical emission of the VCSEL was attenuated significantly by the band-pass filter.
RESULTS
Fig.
3
shows the normalized transient response of the surface of the VCSEL aperture to a 30 l s (red diamonds) and a 40 l s (black squares) heating pulse as a function of the delay time. The thermoreflectance signal is averaged over the entire VCSEL lasing aperture. Although the thermoreflectance signal in these experiments is not calibrated to yield the value of temperature change, it should be noted that
D T is proportional to the thermoreflectance signal D R / R via
Eq.
(1) , and so, the transient behavior is the same. As can be
seen from the figure, it takes about 30 l s for the temperature of the top diffracted Bragg reflector (DBR) layer of the
VCSEL to reach its saturation value.
Fig.
4
shows the thermal images for the case of the 40 l s heating pulse, at 10 l s time intervals. Each image is the average of 50 000 CCD frames.
One common feature of the transient response of the
VCSEL surface is the slow rise of the temperature in the first
4 to 5 l s of heating as can be observed from Fig.
3
. Instead of a sharp increase at the onset of the heating pulse, the transient response shows a slow rise. This behavior can be explained by considering the fact that in thermoreflectance the thermal signal is measured at the surface of the top DBR layer of the VCSEL. However, the main heat sources in the
VCSEL are buried underneath this layer, in particular, in the active region. Unfortunately, the exact dimensions of our
VCSEL’s layered structure are not known. However, according to the manufacturer, the top DBR layers are about 3.5
l m thick. Therefore, one can estimate the distance from the active region to the top surface of the VCSEL to be of the
FIG. 2. Schematic timing diagram for transient thermoreflectance imaging of the VCSEL.
[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:
143.236.90.85 On: Wed, 27 Jan 2016 16:47:31

045105-3 V. G. Garcia and M. Farzaneh
FIG. 3. Transient thermal response of the VCSEL top DBR mirror to 30 l s
(red diamonds) and 40 l s (black squares) heating pulses. It takes about 30 l s for the thermoreflectance signal to reach its saturation value.
order of 4 l m. In the active region, heat is created by nonradiative recombination and absorption of spontaneous emission. The thermal transient curves of Fig.
3
suggest that it takes about 4 l s for the heat wave to reach the surface.
Assuming a one dimensional heat flow and ignoring the
Joule heating in the top DBR layers, the thermal penetration depth, l th
, is given by l th
¼ p ffiffiffiffiffiffiffiffiffiffi
2 a
?
t ; (3) where a
?
is the cross-plane thermal diffusivity and t is time.
At t ¼ 4 l s and l th of 2 10
6 m
2
¼ 4 l m, a thermal diffusivity of the order
/s can be obtained. This is in good agreement with the previous results both in an un-biased VCSEL struc-
ture
16
and in a biased VCSEL
9
with a similar structure to the one discussed here. This value is smaller than the bulk value for AlGaAs alloys by almost an order of magnitude
16
because of the decrease in thermal conductivity in multilayered structures due to increased phonon scattering at layer boundaries.
After the first 4 to 5 l s, the thermal relaxation on the surface of the VCSEL can be described by
J. Appl. Phys.
119 , 045105 (2016)
D
R
R
¼
D
R
R max
"
1 exp t s th
!
#
; (4) where
D R
R max is the maximum value of the thermoreflectance signal at the surface of the VCSEL and s
ð s Þ th is the thermal time constant of the surface. After the heating pulse is turned off, the thermal signal decreases exponentially as
D
R
R
¼
D
R
R max exp t s th
!
: (5)
Fig.
5
shows the results of fitting these two equations to the data of Fig.
3
for the 40 l s heating pulse (solid red lines).
From these fits, a value of s
ð s Þ th
¼ (9.7
6 0.5) l s for the surface thermal time constant can be obtained. Similar results are achieved by fitting the above equations to the 30 l s heating pulse curve of Fig.
3 .
DISCUSSION
In order to verify that the slow rise of temperature at the start of the heating pulse application is, indeed, due to thermal wave diffusion through the layers above the active region, we explored a time-dependent heat transfer model in a VCSEL using finite element method. Since the VCSEL used in these experiments is a commercially purchased device, the details of its structure are not known. However, we selected an oxide confined VCSEL structure discussed in detail in Ref.
17
as our model structure. Using MATLAB
PDE Toolbox, we first checked our model at the steady state condition with the same parameters as in Ref.
17
and successfully reproduced their results. Ignoring radiation and convection, the parabolic (time-dependent) heat transfer equation (due to conduction) can be written as q c
@ T
r ð k r T Þ ¼ q ;
@ t
(6) where q , c , and k are the density, specific heat, and thermal conductivity of the material, respectively.
T is the
FIG.
4. Thermal images of the
VCSEL’s top DBR layer pulsed at
40 l s. Each image is the average of
50 000 CCD frames. Heating of the laser aperture up to 40 l s and the subsequent cool down is observable from these images.
[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:
143.236.90.85 On: Wed, 27 Jan 2016 16:47:31

045105-4 V. G. Garcia and M. Farzaneh J. Appl. Phys.
119 , 045105 (2016)
FIG. 5. Transient thermal response of the VCSEL top DBR layer to a 40 l s heating pulse (black squares). The solid red lines are the result of the fit to
Eqs.
(4)
and
(5)
. From this fit, a value of (9.7
6 0.5) l s for the surface thermal time constant has been obtained.
temperature, and q is the heat source density. In a VCSEL, with cylindrical symmetry, Eq.
(6)
reduces to a 2D equation in cylindrical coordinates which only depends on r and z .
We used Neumann boundary conditions for all boundaries except for the bottom substrate surface which was kept at a constant 20 C, similar to the experimental conditions. For simplicity, we ignored the Joule heat sources in the DBR layers. The only heat source was located at the multi-quantum-well (MQW) active region. The values of density ( q ) and specific heat ( c ) for Al
1 x
Ga x
As layers were calculated using the linear interpolations of the values for GaAs and
AlAs.
18
For the DBR layers, these values were taken as the average for each period, weighted by the thickness of each corresponding layer in the period. We used the same thermal conductivity values for different layers as the ones used in
Ref.
17 , with the exception of the top and bottom DBR
layers and the MQW active region. For these layers, we used isotropic values for k , such that the thermal diffusivity a
?
¼ k q c would be in the order of 10
6 m
2
/s, which is justified based on previous measurements.
9 , 16
This resulted in thermal conductivity of 3 W/m K for the DBR layers and
1.8 W/m K for the active region.
The variation of the thermal signal as a function of time on the top surface of the model VCSEL is shown in Fig.
6
(solid red line), along with our experimental data of Fig.
3
for the first 40 l s (solid squares). Since the two structures could be different in details such as layer thicknesses and compositions, the overall discrepancy between the experiment and the model is expected. However, with the choice of the above-mentioned thermal conductivities for the DBR layers and the active region, the slow rise of surface temperature in the first few microseconds after the onset of heating is observable in the model. This slow rise is not observed if the aforementioned thermal conductivities are kept as large as the bulk values. For a VCSEL with known structural details, the combination of thermal transient imaging experiment and finite element modeling can, in principle, yield physical parameters such as thermal conductivity and thermal diffusivity.
FIG. 6. Results of the finite element heat transfer modeling on a model
VCSEL structure (red solid lines) compared with the transient thermal imaging result of Fig.
3
(black solid squares) for the first 40 l s. The overall discrepancy between the model and the experimental values is expected due to the differences in the model VCSLE structure and the VCSEL studied in this work. The slow rise of the thermal signal at the onset of heating is evident in both model and experiment. This can only be achieved if the thermal conductivities of the DBR and active region layers are significantly (an order of magnitude) smaller than the bulk values.
CONCLUSION
Thermal transient response at the top DBR layer of an active VCSEL is measured from the thermal images in a thermoreflectance microscopy setup. The transient curve shows a slow rise at the onset of heating, consistent with the thermal wave diffusion from the active region to the surface of the device. The slow rise time results in a cross-plane thermal diffusivity of the order of 2 10
6 m
2
/s which is an order of magnitude smaller than the bulk values. This fact is also verified using a finite element heat transfer model for a model VCSEL structure. This reduction of thermal diffusivity is due to the enhanced phonon scattering at the boundaries of the multi-layered structure of the VCSEL. A surface thermal time constant of (9.7
6 0.5) l s is also measured for the VCSEL.
ACKNOWLEDGMENTS
This work is supported by the Department of Physics and
Astronomy, and College of Letters and Science, University of Wisconsin-Stevens Point and by the CAPES Foundation
(Coordenac¸ ~
Superior) on behalf of the Ministry of Education of Brazil.
1
B. Lu, P. Zhou, J. Cheng, K. J. Malloy, and J. C. Zolper, “High temperature pulsed and continuous-wave operation and thermally stable threshold characteristics of VCSELs grown by metalorganic chemical vapor deposi-
2 tion,” Appl. Phys. Lett.
65 , 1337–1339 (1994).
K. D. Choquette, D. Richie, and R. E. Leibenguth, “Temperature dependence of gain-guided VCSEL polarization,” Appl. Phys. Lett.
64 ,
3
2062–2064 (1994).
C. Degan, I. Fischer, and W. Elsaber, “Thermally induced local gain sup-
4 presion in VCSELs,” Appl. Phys. Lett.
76 , 3352–3354 (2000).
M. Brunner, K. Gulden, R. Hovel, M. Moser, and M. Ilegems, “Thermal lensing effects in small oxide confined VCSELs,” Appl. Phys. Lett.
76 ,
7–9 (2000).
5
M. Dabbicco, V. Spagnolo, M. Ferrara, and G. Scamarcio, “Experimental determination of the temperature distribution in trench-confined oxide
VCSELs,” IEEE J. Quantum Electron.
39 , 701–707 (2003).
[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:
143.236.90.85 On: Wed, 27 Jan 2016 16:47:31

045105-5 V. G. Garcia and M. Farzaneh
6
K. Luo, R. W. Herrick, A. Majumdar, and P. Petroff, “Scanning thermal microscopy of a VCSEL,” Appl. Phys. Lett.
71 , 1604–1606
7
(1997).
M. Farzaneh, R. Amatya, D. L € and J. A. Hudgings, “Temperature profiling of VCSELs by thermoreflec-
8 tance microscopy,” IEEE Photonics Technol. Lett.
19 , 601 (2007).
K. Greenberg, J. Summers, and J. Hudgings, “Thermal coupling in vertical-cavity surface-emitting laser arrays,” IEEE Photonics Technol.
Lett.
22 , 655–657 (2010).
9
M. Farzaneh, A. F. Harris, and A. Lebovitz, “Cross-plane thermal diffusivity measurement of an operating vertical cavity surface emitting laser using thermoreflectance,” J. Appl. Phys.
109 , 096101 (2011).
10
M. Farzaneh, K. Maize, D. L uerßen, J. A. Summers, P. M. Mayer, P. E.
Raad, K. P. Pipe, A. Shakouri, R. J. Ram, and J. A. Hudgings, “CCD-based thermoreflectance microscopy: Principles and applications,” J. Phys. D:
Appl. Phys.
42 , 143001 (2009).
11
K. Maize, J. Christofferson, and A. Shakouri, “Transient thermal imaging using thermoreflectance,” in Proceedings of the 24th IEEE SEMI-THERM
12
Symposium, San Jose, CA, 2008.
J. Christofferson, Y. Ezzahri, K. Maize, and A. Shakouri, “Transient thermal imaging of pulsed-operation superlattice micro-refrigerators,” in
J. Appl. Phys.
119 , 045105 (2016)
Proceedings of the 25th IEEE SEMI-THERM Symposium, San Jose, CA,
13
2009.
B. Vermeersch, J. Christofferson, K. Maize, A. Shakouri, and G. De Mey,
“Time and frequency domain CCD-based thermoreflectance technique for high-resolution transient thermal imaging,” in Proceedings of the 26th
IEEE SEMI-THERM Symposium, Santa Clara, CA, 2010.
14
B. Vermeersch, J.-H. Bahk, J. Christofferson, and A. Shakouri,
“Thermoreflectance imaging of sub 100 ns pulsed cooling in high-speed thermoelectric microcoolers,” J. Appl. Phys.
113 , 104502 (2013).
15
P. M. Mayer, D. L uerßen, R. J. Ram, and J. A. Hudgings, “Theoretical and experimental investigation of the thermal resolution and dynamic range of
CCD-based thermoreflectance imaging,” J. Opt. Soc. Am. A 24 ,
1156–1163 (2007).
16
G. Chen, C. L. Tien, X. Wu, and J. S. Smith, “Thermal diffusivity measurement of GaAs/AlGaAs thin-film structures,” J. Heat Transfer 116 , 325
(1994).
17
H. K. Lee, Y. M. Song, Y. T. Lee, and J. S. Yu, “Thermal analysis of asymmetric intracavity-contacted oxide-aperture VCSELs for efficient
18 heat dissipation,” Solid-State Electron.
53 , 1086 (2009).
S. Adachi, “GaAs, AlAs, and AlGa1-xAsx: Material parameters for use in research and device applications,” J. Appl. Phys.
58 , R1–R29 (1985).
[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:
143.236.90.85 On: Wed, 27 Jan 2016 16:47:31