Improvement of Thermal Resistance of Surface-emitting Quantum

Cascade Laser using Structural Function and 3D Thermal Flow

Simulation

Shigeyuki Takagi

, Hirotaka Tanimura

, Tsutomu Kakuno

, Rei Hashimoto

, Kei Kaneko

and Shinji Saito

Department of Electrical and Electronics Engineering, School of Engineering, Tokyo University of Technology,

1404-1 Katakura, Hachioji, Tokyo, Japan

Corporate Manufacturing Engineering Center, Toshiba Corporation,

8 Shinisogo, Isogo, Yokohama, Kanagawa, Japan

Keywords: Quantum Cascade Lasers, QCLs, Surface-emitting QCL, Photonic Crystal, PhC, Static Method, Structure

Function, Thermal Resistance, Thermal Flow Analysis, Diamond Submount.

Abstract: We have evaluated the thermal resistance of the surface-emitting QCL, which is expected to increase the

output and improve the beam quality, based on the structure function and 3D heat flow resolution. From the

structure function, the thermal resistance of the surface emitting QCL was divided into the mesa for laser

excitation, the InP substrate, and the CuW mount, and the total thermal resistance of 8.0 K/W was obtained.

The thermal resistance obtained by the 3D thermal analysis simulation was estimated to be 8.3 K/W, which

was in good agreement with that obtained from the structure function. Furthermore, the effect of the diamond

submount was evaluated and it was shown that the thermal resistance was reduced to 5.2 K/W. It is considered

that the thermal resistance is reduced by the horizontal transfer of heat in the diamond submount.

1 INTRODUCTION

A quantum cascade laser (QCL) is an n-type

semiconductor laser that can obtain laser light in the

infrared region (Faist et al., 1994). Since the

oscillation wavelength of the QCL is in the infrared

region called the fingerprint region of the molecule,

many gases can be measured with high sensitivity.

From the advantages, it is expected to be applied to

trace substance detection and distant gas detection. In

the detection of trace substances, the amount of laser

light absorbed is measured, and it is necessary to

propagate a long optical path length, and high output

is desired. Further, in the distant gas detection, since

the reflected light at the time of laser light

propagation is detected, a high-power laser is

required as a high-power laser, watt-class laser

oscillation has been obtained by A. Evans et al.

(Evans et al., 2007). This laser is an end face emitting

type laser in which the directions of the laser

https://orcid.org/0000-0002-7653-4602

https://orcid.org/0000-0002-1829-6482

excitation and the laser emission coincide with each

other. The laser beam is excited by concentrating the

current in a narrow current path called a ridge.

Therefore, the heat dissipation is low, and the laser

beam is emitted from the narrow ridge into a wide

space, so that there is a problem that the beam quality

) is low.

On the other hand, a surface-emitting QCL that

emits laser light in the vertical direction of the device

using a photonic crystal (PhC) has been proposed

(Colombelli, R., et al., 2003). By increasing the area

of the excited part called a mesa, improvements in

beam quality and heat dissipation can be expected. In

the surface-emitting QCL using PhC, laser oscillation

was reported by Colombelli et al. (Colombelli et al.,

2003), and laser oscillation of 5 W was reported by

Wang et al. (Wang et al., 2019).

One way to increase the output of the surface-

emitting QCL is to improve heat dissipation. We

determined the thermal resistance of the Au-

128

Takagi, S., Tanimura, H., Kakuno, T., Hashimoto, R., Kaneko, K. and Saito, S.

Improvement of Thermal Resistance of Surface-emitting Quantum Cascade Laser using Structural Function and 3D Thermal Flow Simulation.

DOI: 10.5220/0010896700003121

In Proceedings of the 10th International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS 2022), pages 128-133

ISBN: 978-989-758-554-8; ISSN: 2184-4364

embedded type surface-emitting QCL from the

structurer functions obtained by the static method and

the 3D thermal analysis simulation (Takagi et al.,

2021). In this study, the thermal resistance of the InP-

embedded surface-emitting QCL was estimated using

these methods. Furthermore, as a method of

increasing heat dissipation, we have proposed a

method using a diamond submount. As a result of

evaluation using 3D thermal analysis simulation, it

was shown that the heat spreads horizontally in the

diamond submount and the temperature rise of the

mesa that excites the laser can be reduced to about

2/3.

2 SURFACE-EMITTING QCL

The structure of the surface-emitting QCL is shown

in Fig. 1, where (a) is a cross-sectional view, (b) is a

top view, and (c) is a bottom view. A mesa area where

the input power is supplied and a dummy ridge are

formed on an InP substrate with a thickness of 600

µm. In the mesa area, a photonic crystal (PhC) is

formed on the active layer that excites the laser and

PhC is embedded with InP. An Au electrode for

current supply is formed on the opposite side of the

InP substrate.

Figure 1: Surface emitting QCL, (a) Cross-sectional view,

(b) top view, and (c) bottom view.

The surface-emitting device has an epi-side-down

structure in which the mesa and dummy ridge sides

are mounted on a CuW mount with AuSn solder.

Figure 2 is an external photograph of the surface-

emitting QCL used for the measurement, in which

mesas and dummy ridges are observed to be formed

on the InP substrate.

Figure 2: Photograph of surface-emitting QCL.

3 MEASUREMENT OF

STRUCTURE FUNCTION

3.1 K-factor Measurement

We reported on a method for measuring the thermal

resistance of end-face emitting QCLs using the static

method (Takagi et al., 2019). In this paper, the static

method was applied to the thermal resistance

measurement of InP-embedded QCL. A T3Ster

(Siemens AG) was used for the measurement. Since

the resistance of a semiconductor device changes with

temperature, the temperature change is proportional

to the voltage change at the end of the device when a

constant current is flowing. In the static method, this

voltage change ΔT

[mV] is measured, and the

device temperature change ΔT

[K] is obtained using

∆𝑇



=𝐾∙∆𝑇



(1)

where K is a coefficient called K-factor.

The K-factor is required to measure the

temperature of a surface-emitting QCL in the static

method. Therefore, a surface-emitting QCL was

installed in the thermostat of the T3Ster, the

thermostat temperature was changed from 20 ° C to

70 ° C, and the K-factor was measured. The K-factor

was determined to be -0.022772.

3.2 Structure Function

T3Ster was used to measure the structure function by

the static method. The mounting part of the QCL

mount was cooled to 20 ° C, and the QCL device was

heated by supplying about 1.6 W of electric power.

After stopping the heating power supply, the QCL

temperature during cooling was measured and the

cooling curve was obtained. Assuming that the

thermal resistances of each element constituting the

Improvement of Thermal Resistance of Surface-emitting Quantum Cascade Laser using Structural Function and 3D Thermal Flow

Simulation

129

QCL is R

and the heat capacity is C

, the time

constant τ during cooling is expressed by

𝜏= 𝐶



∙𝑅



. (2)

The time constant τ was extracted from the

inflection point of the cooling curve, and C

and R

were obtained from τ using Eq. (4). In the structure

function, R

is plotted on the horizontal axis and C

is plotted on the vertical axis (Székely, 1997).

Fig. 3 shows the structure function of the surface

emitting QCL. As shown in Fig. 1, the surface

emitting QCL is divided into the mount, the InP

substrate, and the mesa area. From the thermal

conductivity and component size, it is estimated that

the structure function divided by the inflection point

corresponds to the three QCL components. In

addition, the flat region with a thermal resistance over

8.5 K/W or more changes depending on whether the

QCL is attached to a cooling plate. It is considered to

be the thermal resistance between the surface emitting

QCL and the T3Ster cooler, and the total thermal

resistance of the surface emitting QCL is estimated to

be about 8.0 K/W.

Figure 3: Structure function of surface emitting QCL.

4 HERMAL SIMULATION OF

SURFACE-EMITTING QCL

4.1 3D Thermal Flow Simulation

Model

As another method for analysing the thermal

characteristics of the surface emitting QCL, thermal

flow analysis using a 3D model was performed. A

simulation model was constructed by inputting the 3D

structure and physical property data of the surface

emitting QCL. The thermal flow analysis software

STEAM (MSC software) and FloTHERM (Mentor

Graphics Japan) were used as the simulator. The

thermal flow analysis is performed using a natural

convection model in which mesa area is overheated

and natural convection is generated. The equation for

gas flow is expressed by

𝜕𝜌

𝜕𝑡

∂



𝜌𝑣

𝑥



∂x

∂𝜌𝑣

𝑦



∂



𝜌𝑣

𝑧



∂z

=0 ,

(3)

where ρ is the density, t is the time, and v

, v

, and v

are the velocities in the x, y, and z directions,

respectively. The heat equation is determined as

𝜕𝑢

𝜕𝑡

𝐾

𝜎𝜌



𝜕

𝑢

𝜕𝑥

𝜕

𝑢

𝜕𝑦

𝜕

𝑢

𝜕𝑧



𝜎

𝐹



𝑥, 𝑦,𝑧, 𝑡



(4)

where u is the temperature and is a function of the

position and time. σ is the specific heat, and Κ is the

thermal conductivity. F is the external heating value

per time, and is a function of position and time.

The 3D structure of the surface-emitting QCL

shown in Fig. 1 were input, and a three-dimensional

model was constructed. Figure 4 (a) is a three-

dimensional model of a surface-emitting QCL. The

surface-emitting QCL has an epi-side-down structure

in which the mesa area and dummy ridge sides are

mounted on a CuW mount with AuSn solder. Fig. 4

(b) is a top view of the 3D model as in the photograph

of Fig. 2 The outline of the InP substrate, mesa,

dummy ridge, and Au electrode on the back surface

are shown.

In the 3D model, the physical property values

were as follows. The thermal conductivity of CuW

mount, AuSn solder, InP, SiO

, Ti, Au, Cu is 157, 59,

68, 1.38, 21, 296, 403 W/mK, respectively. For the

PhC part in which InP was embedded, the thermal

conductivity was calculated based on the volume ratio

of the PhC and the InP. In the active layer, thin films

of Al

0.638

0.362

As and Ga

0.331

0.669

As are alternately

laminated. The thermal conductivity of the active

layer was calculated by multiplying the film thickness

ratio with InAlAs of 10.0 W/mK (Kim et al., 2002)

and InGaAs of 5.6 W/mK (Adachi, 1985), and was

estimated to be 7.5 W/ mK. The temperature

boundary condition is fixed at 0 ° C on the mount with

a cooling Peltier, and the ambient temperature of the

surface emitting QCL is set at 25 ° C.

PHOTOPTICS 2022 - 10th International Conference on Photonics, Optics and Laser Technology

130

Figure 4: 3D simulation model of surface emitting QCL. (a)

perspective view and (b) top view.

5 SIMULATION RESULTS

5.1 Thermal Resistance of Surface

Emitting QCL

The temperature distribution of the surface emitting

QCL was calculated under the conditions of the of 10

W input power to the mesa area. Figure 5 shows the

temperature distribution of the surface-emitting QCL

in the central cross section. The CuW mount has high

thermal conductivity and the most of the mount is

kept at 0 ° C. The temperature around the mesa area

is higher than that in other parts. Since the

temperature rise at an input power of 10 W is 82.63 °

C, the thermal resistance of the surface emitting QCL

was calculated to be 8.3 K/W. This value was almost

the same as the thermal resistance of 8.0 K/W

obtained from the structure function. It shows the

validity of the 3D thermal analysis simulation.

Figure 5: Temperature distribution of surface emitting

QCL.

5.2 Effect of Diamond Submount

A diamond submount has a large value of 2000

W/mK, and it has been reported that the thermal

resistance of light emitting device is reduced

(Bezotosnyi et al., 2014). To reduce the thermal

resistance of the surface emitting QCL, the thermal

resistance of structure in which diamond was inserted

between the substrate and the mount was evaluated

by 3D thermal analysis simulation. Figure 6 is a 3D

simulation model of a surface emitting QCL using a

diamond submount. It is assumed that the lower

surface of the diamond submount is soldered to CuW

with AuSn having a thickness of 5 µm, and the InP

substrate is soldered to the upper surface with AuSn

having a thickness of 5 µm. The thermal conductivity

of the diamond submount and AuSn was set to be

2000 W/mK and 59 W/mK in the calculation,

respectively.

Figure 6: 3D simulation model of surface emitting QCL

with diamond submount.

We applied the input power of 10 W to the mesa

area of the QCL with diamond submount, and the

temperature rise of the mesa area was calculated.

Figure 7 (b) shows the simulation results. For

comparison, Fig. 7 (a) shows the calculation results

of the temperature distribution of the QCL without

diamond submount. In the QCL with diamond

submount (b), the temperature rise at an input power

of 10 W was 52.47 ° C, and the thermal resistance was

reduced to 5.2 K/W. Figure 8 shows the temperature

rise of the mesa area when the power input is changed

from 4 to 10 W. As the input power increases, the

temperature difference with and without the diamond

submount increases. It has been shown that the

diamond submount is more effective under high input

power operating conditions.

Improvement of Thermal Resistance of Surface-emitting Quantum Cascade Laser using Structural Function and 3D Thermal Flow

Simulation

131

Figure 7: Comparison of temperature distribution between

QCLs with and without diamond submount.

Figure 8: Relationship between input power and

temperature rise in the mesa area.

6 DISCUSSION

We discussed the factors that reduce the thermal

resistance by using the diamond submount. In the

QCL without submount (Fig. 7(a)), the isotherms of

the temperature distribution under the mesa are semi-

circular, and the heat generated with the input power

is transmitted concentrically around the mesa area.

On the other hand, in (b), due to the large thermal

conductivity of the diamond, the heat spreads

horizontally and is transmitted vertically in CuW. To

investigate the heat flow in more detail, the heat flux

of the surface emission QCL was calculated. Fig. 9(a)

shows the distribution of the heat flux vector without

submount, and Fig. 9 (b) shows the distribution of the

heat flux vector with submount. In Fig. 9(a), the heat

flux is mainly directed from the mesa area to the CuW

mount, while in (b) horizontal flux vector is generated

in the diamond submount. From the temperature

distribution in Fig. 7 and the heat flux distribution in

Fig. 9, it is estimated that the heat resistance is

reduced by the horizontal transfer of the heat by the

diamond submount.

Figure 9: Comparison of heat flux between QCLs with and

without diamond submount.

7 CONCLUSIONS

To evaluate the thermal resistance of the InP-

embedded surface-emitting QCL, the structure

function and 3D thermal analysis simulation were

adopted. Using the structure function, the thermal

resistance of the surface emitting QCL was divided

into the mesa area, the InP substrate, and the CuW

mount and the thermal resistance of 8.0 K W was

obtained. The temperature distribution of the surface

emission QCL at an input power of 10 W was

calculated by the 3D thermal analysis simulation. The

thermal resistance obtained from the temperature rise

in the mesa area was 8.3 K/W, which was in good

agreement with the thermal resistance obtained from

the structure function.

Furthermore, the effect of the diamond submount

was evaluated by 3D thermal analysis simulation, and

it was shown that the thermal resistance was reduced

to 5.2 K/W. From the calculation results of the

temperature distribution and the heat flux

distribution, it was estimated that the heat resistance

is reduced by the horizontal transfer of heat by the

diamond submount.

PHOTOPTICS 2022 - 10th International Conference on Photonics, Optics and Laser Technology

132

ACKNOWLEDGEMENTS

This work was supported by Innovative Science and

Technology Initiative for Security (Grant Number

JPJ004596), ATLA, Japan.

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Improvement of Thermal Resistance of Surface-emitting Quantum Cascade Laser using Structural Function and 3D Thermal Flow

Simulation

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