Modelling and experimental study of heat deposition and transport in a semiconductor laser diode

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Mieroelectronics Journal 29 (1998) 171-179 © 1998 Published by Elsevier Science Limited

Printed in Great Britain. All rights reserved 0026-2692/98/$19.00

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Modelling and experimental study of heat deposition and transport in a semiconductor laser diode D. Lewis1, S. Dilhairel, T. Phanl, V. Quintard 1, V. Hornung 2. and W. Claeysl 1CPMOH-University of Bordeaux I, 33405 Talence Cedex, France 2Alcatel Alsthom Recherche, 91460 Marcoussis, France

An analytical model of heat transport in a laser diode is presented together with measurements of the temperature distribution by photothermal microscopy. Comparison between model and measurements shows the temperature distribution to be issued from a cylindrical heat source diffusing in the surrounding bulk material. Laser output facet heating by stimulated photon absorption is shown to be of negligible importance. © 1998 Published by Elsevier Science Ltd. All rights reserved.

1. In t roduct ion

I n recent years, the development of high performance InGaAsP/InP laser diodes has

received considerable attention. They are used as the light source in optical communication systems to take advantage o f the low dispersion and low losses in silica fibres occurring around 1.3 and 1.5/am.

*Author to whom all correspondence should be addressed.

Temperature rise in the semiconductor laser diode active region is known to have a critical influence on laser characteristics, e.g. the light output power. Heat generation in a laser is mainly due to the materials used, the ohmic contacts and the confinement layers, etc. but also to laser stripe morphology and technology. The analysis of the thermal dependencies of the electrooptical characteristics o f the laser gives the general behaviour o f the component with temperature. There is, however, a need for better understanding o f the thermal behaviour related to laser technology in order to optimize the performances.

In this respect, the purpose o f this contribution is to present an analytical model of heat transport in a laser diode and to compare these results with measurements o f temperature distributions

171

D. Lewis et al./Semiconductor laser diode

obtained with photothermal reflectance microscopy upon the laser facet. The experimental method provides micrometric spatially resolved measurements of the facet temperature distribution and the agreement with the model gives a good understanding of heat generation and transport inside laser diodes. Similar measurements have already been carried out [1] but with the purpose of measuring the laser facet output temperature. Our aim is to localize the different heat sources and to provide a better insight into the heat exchange.

In this work, we have experimentally studied, with photothermal reflectance microscopy [2], the InGaAsP/InP laser diode temperature behaviour near the active region. Measurements were carried out on laser output facet and on the ridge on the top of the laser diode. First, the laser is operated with a sine wave current above a dc component. As a consequence, the different heat sources are time modulated and generate thermal waves that propagate in the entire medium around the active region. This allows one to study thermal propagation along the laser facet. Comparison with a three-dimensional numerical simulation, where the active region is taken as a cy~ndrical bulk heat source, shows that measurements upon the laser facet give good information about the heat transport. Second, the laser is operated with a square wave current. This allows one to measure steady-state temperatures in the laser diode. We have measured the facet temperature variation versus the current amplitude above and below the threshold of laser operation. From the experimental results we show that facet heating by photons from stimulated emission is negligible compared to active region heating.

2. Experimental method for temperature measurements

To measure local temperatures on electronic devices, we have developed an optical laser probe, which has been described in detail in earlier work [3]. The experimental method is

based upon reflectance change of the surface under test due to a variation of its temperature. This technique is called photothermal reflectance microscopy [2, 4]; the measured signal is a direct function of the surface temperature.

In fact, the relative reflectance change &R/R is related to the temperature variation AT by the following relation:

Al~(t) [1OR] - AT(t) = KAT(t) (1)

where /c is the relative reflectance temperature coefficient of the probed material. If the reflected light intensity is measured by a photodiode producing a signal S, then:

AR(t) _ AS(t) _ ~:AT(t) =~ AT(t) - - 1 AS(t) R S lc S

(2)

For measurements on the InP laser facet we take the relative reflectance temperature coefficient of the InP from Ref. [1]: /qnp=3.4X 10 -5 K -1.

The sample is mounted on an x-y translation stage with a minimum step size of 0.05 #m. The lateral resolution limited by the laser probe spot diameter is less than 1 #m.

For a sine wave current excitation the signal S is detected with a lock-in amplifier and for a time square current excitation with a numerical oscil- loscope. Translation stages, generator and detection instruments are monitored remotely by a micro computer.

3. Heat loss mechanisms in semiconductor laser diodes

Heat generation produced in the active region of a laser diode can be separated into different contributions. First, a bulk contribution produced by Joule heating and non-radiative recombinations of carriers from current injection

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Microelectronics Journal, Vol. 29, Nos 4-5

and from Auger absorption. Second, a surface contribution, especirdly at laser facets, as non- radiative recombinations of injected carriers and of carriers photogenerated by absorption of stimulated photons. :['he facet heating accelerates mirror degradation, induces dislocations and therefore limits the lifetime and the maximum output power through the formation of a rapid positive feedback cycle, resulting in thermal runaway or catastrophic optical damage (COD) [5, 6].

3.1. Bulk mechanisms A current driven through a conductor or semiconductor produces heat by the Joule effect, which depends on the local resistivity and the current density. The laser operating conditions imply an important electric confinement in the active region where most Joule losses are produced. Joule heating due to the ohmic contact and the contact layers occurring close to the active region should also be taken into account.

Carrier injection in the active region induces electron-hole recombinations. The corresponding deposited power density is distributed into two contributions: one is light emitted by stimulated photons, the remainder is trans- formed into heat by non-radiative recombinations.

Absorption ofstimul~Lted photons by free carriers or by photogenerated carriers could also give a temperature increase. It is important to note that the cladding medium absorption increases the second contribution [7].

3.2. Surface mechanisms The surface of a semiconductor can be the source of different light and heat thermal mechanisms. Surface state energy levels are discretely or discontinuously distributed within the energy gap and can act as traps, as recombination centres or as both. The result is a change in electrical and optical properties of the cleaved

uncoated mirror that increase the rate of stimulated photon absorption and of non-radiative recombinations at laser output on the facets. The influence of the surface state on the Joule effect is negligible [8].

The surface stimulated photon absorption is a direct function of the free carrier concentra- tion and the surface recombination velocity [6].

3.3. Qualitative evaluation of the contributions The Joule effect is the relevant mechanism below the laser threshold. Above the threshold heat generation is mainly governed by non- radiative recombination and absorption processes.

4. Experimental results

4.1. Sine wave current excitation

E l e c t r i c a l e x c i t a t i o n

The laser is operated with a time varying current: 1(0=1o+11 cos(2nfi) with I0=100mA, I1=31 mA and fE[5kHz, 50kHz]. These values were chosen as they provide reliable data for the analysis of thermal propagation inside the laser diode.

4.2. Detection In the active region both heat loss mechanisms are separated in two contributions, a pure linear current dependent contribution L(t) due to recombinations in the active region, and a pure quadratic current-dependent contribution Q(t) due to the Joule effect.

P(t) = L(t) + Q(t) = VoI(t) + Ro[I(t)] 2

Vo and R0 are proportionality constants and can be determined from the electrical and optical characteristics of the laser diode.

By including the current time dependence, the two contributions can be written:

173


L(t) = VoI(t) = Volo + VoIlCOS(2rcfi) (3)

Q(t) = Ro[I(t)] 2 = R0[I 0 + IlCOS(2gfi)] 2 = (4)

Ro + + 2Rolollcos(2rcfi) + ---~-cosu+Ut )

The corresponding temperature rise detected as a surface reflectance change is analysed with a lock-in amplifier.

The first and second harmonic amplitude response H1, 82 can be written as:

H~ = k(VoI1 + 2Rolllo) (5)

H2= k ' ( - ~ ) (6)

where k and k' are proportionality factors taking the power to surface temperature transform into account.

It is important to note that the first harmonic signal contains two heat loss contributions, the non-radiative recombination processes and the Joule effect, while the second harmonic includes only the Joule effect. It shows the diffi- culty of separating the Joule effect heating from other heating mechanisms with a simple first harmonic analysis.

4.3. Laser samples The laser samples we have studied are of the Inl_xGaxAsyPl_r/InP multi-quantum-well (MQW) standard ridge waveguide type. Figure 1 shows a schematic view of the sample while Fig. 2 shows a scheme of the laser facet. The laser cavity is 520 pm long, made of quantum wells. The ridge waveguide is 2 #m wide and 2/~m thick. The laser is obtained by cleaving in air. The device is soldered p side up on a copper heat sink. No coating is applied on the laser facet.

Active r e g i ] ~

Fig. 1. Schematic representation of a ridge laser diode.

Ohmic contact

Si3N 4 ~ Metal

I . ' . . . . . . . ( ( . . . , . . . r r r . . . . . r r t r , . / r (

Mp// " " - - - - ~ n-InP Active region

I InP

Fig. 2. Sketch of laser facet.

The operating wavelength is 1.55#m and the maximum optical output power is typically 20mW; the threshold current is between 30 and 40mA at 25°C.

4.4. Temperature response for a sine wave excitation

Thermal mode/ Figure 3 shows a schematic representation of the geometrical configuration of a laser diode and illustrates the coordinate system. The electrical current and the heat sources are assumed to be uniformly distributed along the laser active region of radius r0. Therefore, we assume the active region to be a bulk cylindrical heat source modulated at f and 2f In this work, we present an analysis of the first harmonic response of a thermal wave generated in the active region and propagating in a homogeneous InP medium.

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Microelectronics Journal, Vol. 2& Nos 4-5

Active region Emission facet

X Z

L st I*,

InP O ? M

Y w,

Fig. 3. Schematic representation of the geometrical configuration of a laser diode.

The distribution of temperature variation is obtained by solving the Fourier heat equation:

1 0 T AT -- 0 (7)

a 0 t

With a as the thermal diffusivity, for numerical calculations we take the InP thermal diffusivity value: a=0.46 cm2/sec [1].

In a cylindrical coordinate system, the first harmonic of the complex temperature variation is:

T1 (r, 0, z , t) = T(r, O, z)4 ~t (8)

= IT ( r , O, z)l For the frequencies we have explored 0e>5 kHz), we consider the heat source as a cylindrical heat source with a small radius compared to the thermal diffusion leni~h .,/(aft'). In addition, the thermal diffusion length is'small compared to the dimensions of the bulk InP medium, therefore we can consider our approach as a semi-infinite thermal model.

For fc[5kHz, 50kHz], we can take the following boundary conditions:

T(oo, O,z) = 0 a n d - 2th-~ fro, O,z) = OB

where ~t3 is the first harmonic heat flux leaving the source and ~th is the thermal conductivity of the InP.

The initial conditions and boundary conditions are independent of the coordinates 0 and z, and the flow of heat is radial, therefore the amplitude of the temperature will be a function of r only.

The solution of the Fourier heat equation [9] gives the absolute temperature increase:

OB K°(jl/2v~ar) (9)

T(r) =).th~aK1(jl/2v~aro )

where Ko(x) and Kl(x) are the zero- and the first-order modified Bessel functions.

For our excitation frequencies, ro<<x/(a/w ) and eq. (9) can be simplified:

T(r) = -~th Ko r

Numerical calculation using an asymptotic development for complex arguments with the Kelvin functions [10] of the temperature distribution (modulus and phase) is performed. By comparing the result of this simple model with a Cartesian thermal model developed by Berto- lotti [11, 12], good agreement is found.

4.5. T h e r m a l m e a s u r e m e n t s

Temperature increases for different excitation conditions First we measured the first and the second harmonic temperature increase on the emission facet, near the active region, for different excita- tions.

175


Modulus o f t e m p e r a t u r e rise (rms)

= t t ! t i t = = = " i I + I I , i i

H~=k(Voh+2~1~Xo)=O.4S/~ t t i ! ! 10 , i , , , ,, _ . . ~ , - 7 - ~ T + l

l i i i ~ I i , i ! i i + L..P.~ I il i [ii,.

" i ": t I i | , k--'i'-i 1 I i l t i -. l-~ i-,,.., 1 .......... ! - - [ ~ ~ - T - - ~ i . . . . . Y r , r

i i i1+I i .,,,"I. i l i iz i _i H i l t i j / i i ± i i

0.1 " - - "-" i - - " i " " . i""---- ' i . , ...... ! '--;"-I,", ~ : !'T

F ] i [ I i f " ~ 2 " T k " f ~ ; T i "O- O0126/~ 0.(: t " I ~ z ~

10 100 I 1 in mA (rms)

• First harmonic • Second harmonic

Fig. 4. First and second harmonic amplitude of the temperature rise versus I1.

Figure 4 shows the first and the second harmonic amplitude of the temperature rise versus 11 for a given value of I 0. Pure linear and quadratic responses are observed.

Figure 5 shows the first harmonic amplitude of the temperature increase versus I0 for a given value ofI1. A pure linear response of the type of eq. (5) is observed.

These measurements show the temperature first and second harmonic to behave has expected from eqs. (5) and (6). Thus, the heat loss mechanisms in a laser diode could be separated into two contributions.

4.6. T e m p e r a t u r e d i s t r i b u t i o n on e m i s s i o n f a c e t We have measured temperature increase on the laser diode output facet at different locations with our thermoreflectance laser probe [2, 3].

Figures 6 and 7 present, respectively, the modulus and the phase of the temperature distribution as a function of radius r for different 0 directions starting from the centre of the active region, which is the laser output point on the diode laser facet. The excitation frequency is 10 kHz.

Modulus o f f i rst harmonic t e m p e r a t u r e dse 8 1 I , , , 1 . 2 " 7 ~" Hi =k(Voll+2Ro/tlo) = L34+0.06/o ~:~'~"--'-- 6 ] i i ) . ~ | . . . .

o F$_-::i , F .......... . . . .

L.._~.~L_L--_I__--~ ..... r-- .... [" I i i i =

I I- . . . . . . . I" =" . . . . . . f ................... i . . . . . ~ . . . . . . . . o [ [ I i i i

0 20 40 60 80 100 120 /oin mA (rms)

Fig. 5. First harmonic amplitude of the temperature rise versus Io.

10

0.1

0.01 0 5 10 15 20 25 30 35 40

radius in /am

Fig. 6. Amplitude of the reflectivity variation for different directions as a function of the distance r from the source.

We observe the results to be independent of the angle 0. In agreement with our thermal model, a cyhndrical symmetry is observed. Figures 8 and 9 show, respectively, the modulus and the phase of the-absolute temperature distribution along the Ox direction. Dots show the measured results (absolute values) for three frequencies, full lines show the results from the numerical simulation. To derive the measured absolute temperatures, the value o f 3 .4×10-SK -1 was used for/¢.

Measurements and calculations show the same behaviour except close to the heat source

176


T7 phases (degrees) 0 !

! l I ', an~ te -75 ° I

I • an= te-45 ° i + su~i I¢ 0°oi

• ~m~ ¢ +75 °,,

-I00, =,,, . . . . I~- -~! - - - - i I T

0 5 10 15 20 25 30 35 40 radius pm

Fig. 7. Phase of the reflectivity variation for different directions as a function of the distance r from the source.

100

10

0,1

0.01 0 10 20 30 40 50

radius pm

Fig. 8. Measurements and simulations (full lines) of the amplitude of the temperature variation for two excitation

frequencies.

(r<5 #m). This difference has three causes. First, we have not yet solved the Fourier heat equation for small radii. Second, the dimensions o f the active region ~,re smaller than the probing laser spot, temperature measurements are therefore a spatial average of the real temperature with Gaussian weight factor. Third, the laser ridge and active region cannot be considered as cylindrical below a radius o f 5#m. It is also important to note that the active region is made of InP producing heat confinement in the

T I phases (rms)

, 5 k~az I

-50 -" I

-100 ,

. oo . . . . . . . , . . . . . . . . . .

i -250 l

0 10 20 30 40 .50 radius pm

Fig. 9. Measurements and simulations (full lines) of the phase of the temperature variation for two excitation

frequencies.

M Q W active region owing to thermal character- istic discontinuities [1]. We therefore limit the comparison of the data to values of r>5/~m.

5. D i s c u s s i o n

By comparing measurements and cyhndrical simulations with semi-infinite geometry good agreement is achieved concerning the slopes. This proves the active region to be a heat source propagating uniformly in the bulk medium. Figure 10 shows the results of the measurement of the modulus of the temperature profile on the top of the sample along the active region near the output facet (zE[0/~m, 50#m]). In the z direction the temperature distribution is mainly seen as uniform and no temperature increase is observed at the laser facet (z=0). This temperature behaviour shows an absence of significant heat released at the laser exit facets. In accordance with the small value of the surface recombination velocity of InP, this denotes the weak influence of the non-radiative processes at the facet of the studied laser sample.

In conclusion, this experimental study proves that the heat is uniformly distributed along the

177

D. Lewis e t al./Semiconductor laser diode

6 10"s Modulus o f &R/R (rms) ! ~ I

~,o- - - - - - I ~ . . . . . . . i . . . . . . . . . . . . . . . . . ! , i ! i ______L. __.l 410 s ~ , - ' - ' - - T i ~ ~ - , ;.,, . . + . . . . I l " i

3 , 0 , . . . . ~ r .......... t - . . . . . . . i- . . . . .

a 1 i i I i

2 1 o " 1 i i i I 0 10 20 30 40 50

posit ion in pm

Fig. 10. Modulus of the first harmonic relative reflectivity variation along the active region on top of the laser diode,

near the output facet.

active region of the laser sample. The absorption of the stimulated photons at the facets produces negligible heating.

5 . 1 . Q u a s i s t e a d y - s t a t e t e m p e r a t u r e o f l a s e r f a c e t The heating curve, for a step function current excitation, exhibits a plateau appearing after the chip-inside transients have been carried out and before the beginning of the thermal transients of the mount and the package. We consider this plateau temperature as a quasi steady state and perform measurements in this regime. We have measured the reflectance changes with our laser probe for square wave current pulses. Figure 11 shows the temperature evolution at laser output for a current pulse of amplitude 160mA and 80/~sec duration. We observe the temperature to reach its quasi steady-state value after a few microseconds. Relation (2) was used to transform the reflectance change into a temperature. We see the temperature increase to be of about 35°C.

We have also measured the steady-state temperature increase near the active region on the laser facet for different current amplitudes between 6 and 150mA. Figure 12 shows the result.

40

30

20

10

0

AT i n K

! ! i

t l

~ , = . . L L m ~ . . . . .

i

I I 50 1 O0 150 200

t ime (in ps)

Fig. 11. Temperature response on diode facet at laser output for a 160 mA and 80 #sec duration current pulse.

30 AT I l i

I J i • 2s . . . . r - - - " ~

I ! i . " 20 . . . . . . . . + . . . . ÷ t

I I " i = • l

15 . . . . . . $ . . . . . ~ . . . . . . ~ ................. 1' I ', ', = •

• t l = I J . , I Z

,-;.-:.-i-- I . . . . . . . . . i 0 = I I

0 Is 50 100 150 current amplitude in mA

Fig. 12. Temperature variation versus current amplitude.

The dashed line shows the threshold current Is for lasing to occur. No significant discontinuities are observed below and above the lasing threshold. If absorption of photons plays a relevant role in the facet heating mechanisms, one would expect a significant difference in the temperature increase behaviour above and below the threshold current. No such difference is observed experimentally, which demonstrates once again that stimulated photon absorption plays a minor role in the facet heating of such laser devices.

1 7 8


6. Conclusions

In summary, we have determined the temperature distribution and heat transport properties o f an InGaAsP/InP rnul t i -quantum well ridge waveguide laser diode. By comparing the temperature distribution at laser facet operated wi th a sine wave current and a simple cylindrical simulation, we have demonstrated that the heat source can be approximated by a hot wire model in a semi-infinite InP bulk. Besides, measurements on top o f the laser diode along the ridge show the heat to be uniformly distributed along the active region. In addition, the analysis o f the steady-state temperature rise as a funct ion o f the current amplitude for square wave excitation confirms the negligible influence o f stimulated pho ton absorption at the laser facet.

References

[1] Mansanares, A.M., Roger, J.P., Fournier, D. and Boccara, A.C. Temperature field determination of InGaAsP/InP lasers by photothermal microscopy: evidence for weak nonradiative processes at the facets, Appl. Phys. Lett., 64 (1994) 4-6.

[2] Quintard, V., Deboy, G., Dilhaire, S., Lewis, D., Phan, T. and Claeys, W. Laser beam thermography of circuits in the particular case of passivated semiconductors, Microelectronic Eng., 31 (1994) 291-298.

[3] Claeys, W., Dilhaire, S., Quintard, V., Dom, J.P. and

Danto, Y. Thermoreflectance optical test probe for the measurement of current induced temperature change in microelectronic components, Quality Reliab. Eng. Int., 9 (1993) 303-308.

[4] Rosencwaig, A. in A. Mandelis (ed.), Photoacoustic and Thermal Wave Phenomena in Semiconductors, North- Holland, New York, 1987, pp. 97-135.

[5] Hakki, B.W. and Nash, F.R. Catastrophic failure in GaAs double-heterostructure injection laser, J. Appl. Phys., 45 (1974) 3907-3912.

[6] Henry, C.H., Petroff, P.M., Logan, R.A. and Merritt, F.R. Catastrophic damage of AlxGal_xAs double heterostructure laser material, J. Appl. Phys., 50 (1979) 3721-3732.

[7] Chen, G. and Tien, C.L. Facet heating of quantum well lasers,J. Appl. Phys., 74 (1993) 2167-2174.

[8] Tang, W.C., Rosen, H.J., Vettiger, P. and Webb, D.J. Evidence for current-density-induced heating of A1GaAs single-quantum-well laser facets, Appl. Phys. Lett., 59 (1991) 1005-1007.

[9] Carlslaw H.S. and Jaeger, J.C. Conduction of Heat Solids, Clarendon Press, Oxford, 1993, p. 193.

[10] Abramovitz, M. and Stegun, I.A. Handbook of Mathe- matical Functions, Dover Publication, I.N.C., New York, 1970, p. 379.

[11] Bertolotti, M., Liakhou, G., Li Voti, R., Wang, R.P. and Yakovlev, V.P. Mirror temperature of semiconductor diode laser studied with a photothermal deflection method, J. Appl. Phys., 74 (1993) 7054- 7060.

[12] Bertolotti, M., Liakhou, G., Li Voti, R., Sibilia, C., Syrbu, A. and Wang, R.P. New method for the study of mirror heating of a semiconductor laser diode and for the determination of thermal diffusivity of the entire structure, Appl. Phys. Lett., 65 (1994) 2266- 2268.

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Modelling and experimental study of heat deposition and transport in a semiconductor laser diode