1. Introduction

Reliable laser diodes (LDs) are required for applications such as materials processing,solid-state laser pumping,optical communications,and printing machines^[1]. In recent years,major research efforts have been made to improve the performance of LDs and analyze their reliability. The thermal behavior of LD packaging has been related to the ambient temperature,the base materials,the cooling conditions and the gravity direction^[2]. The temperature distribution over the facet of a working device was determined by simulations^[3] and spatially resolved thermo-reflectance measurements^[4]. Graphene-oxide deposits on the top of p-down-mounted chips have been used to reduce the thermal resistance of high power LDs and improve their upper heat flux removal efficiency^[5]. The thermal resistance is the most useful indicator of the thermal performance of LDs^[6]. Reduction of the thermal resistance leads to a reduced bulk temperature rise in the LD chip,and the thermal resistance could be reduced by up to 40% by appropriate design of the laser chip and the use of epi-down bonding^[7]. The electrically-based transient measurement technique is a popular way to obtain the thermal resistance of LDs and is based on a temperature sensitive parameter^[8]. As mentioned above,accurate and reliable characterization of LD thermal behavior has a critical effect on device performance.

In this work,thermal analysis was performed via the electrical transient method and infrared thermography. The electrical method is based on the linear relationship between the junction temperature and the forward voltage. Infrared thermography is a process where original data is calibrated on the basis of emissivity and reference data. Using these two methods,we investigated the thermal resistance and the temperature rise in LDs at various input currents.

2. Sample description and experimental details

Figure 1(a) shows a schematic of the 808 nm GaAs-based LD. The LD mainly consists of the LD chip,indium solder,and a copper heat sink. The LD chip consists of a Zn-doped GaAs cap,a Zn-doped AlGaAs p-cladding layer,an AlGaAs p-guide layer,an AlGaInAs single quantum well (SQW) active area,an AlGaAs n-guide layer,and a Si-doped AlGaAs n-cladding layer. The edge-emitting structure is processed and cleaved to form mirror facets. The facets are coated with anti-reflection (AR)/high-reflectivity (HR) coatings. The cavity length is 2~mm,and the stripe width is 100 $\mu$m. The typical lasing wavelength and threshold current are 808 nm and 410 mA,respectively. The power--current--voltage ($P$--$I$--$V$) characteristics during continuous-wave (CW) operation are shown in Figure 1(b).

The thermal resistance directly indicates the amount of heat that is generated under specific input power levels in a p--n junction and is the most useful indicator of the thermal performance of LDs^[2]. According to JEDEC standard No. 51-1^[9],the thermal resistance is defined as

$${R_{{\rm{th}}}} = \frac{{\Delta T}}{{{P_{\rm{t}}}}} = \frac{{{T_{\rm{j}}} - {T_{\rm{a}}}}}{{{P_{\rm{t}}}}}.$$

(1)

Here,$P_{\rm t}$ is the heat dissipated power,$T_{\rm j}$ is the junction temperature,and $T_{\rm a}$ is the ambient temperature.

When the laser is operating,the electrical input power will be dissipated as heat and optical power,and thus the apparent thermal resistance is introduced to specify the thermal characteristics. The apparent thermal resistance is defined by the following relation:

$${R_{{\rm{tha}}}} = \frac{{\Delta T}}{{{P_{\rm{e}}}}} = \frac{{\Delta T}}{{{P_{\rm{t}}} + {P_{\rm{o}}}}} = \frac{{\Delta T/{P_{\rm{t}}}}}{{1 + {P_{\rm{o}}}/({P_{\rm{e}}} - {P_{\rm{o}}})}} = {R_{{\rm{th}}}}\left( {1 - \frac{{{P_{\rm{o}}}}}{{{P_{\rm{e}}}}}} \right) = {R_{{\rm{th}}}}(1 - \eta ).$$

(2)

Here,$P_{\rm e}$ is the electrical input power,$P_{\rm o}$ is the optical power,and $\eta$ is the power conversion efficiency,which is defined as:

$$\eta = \frac{{{P_{\rm{o}}}}}{{{P_{\rm{e}}}}}.$$

(3)

The thermal resistance and the temperature rise in the LD are measured using an electrical transient measurement technique^[10] and infrared thermography^[11],respectively. The electrical method is based on the linear relationship between junction temperature rise and forward voltage,which is given as follows^[12]:

$$\Delta T = \frac{{\Delta {V_{{\rm{pn}}}}}}{k}.$$

(4)

Here,$k$ is a temperature coefficient,and $\Delta V_{\rm pn}$ is the difference between the forward voltages before and during operation. We first measured the value of $k$. The forward voltage is measured at a constant sensor current of 5 mA under various temperatures ranging from 30 to 80 $^\circ C$. We then obtain a proportional constant,as shown in Figure 2(a). The temperature coefficient $k$ is thus $-1.7$ mV/$^\circ C$. The results clearly show a linear relationship between the temperature and the forward voltage^[13].

3. Results and discussion

The transient thermal resistance is monitored at various input currents over a working current range from 0.1 to 1.3 A. The device is set on a thermoelectric cooler (TEC) and operated at a stabilized temperature of 25 $^\circ C$ during the thermal transient measurements. The LD is operated at each working current for 100 s,which is chosen to be sufficiently long to reach a steady state,and is then switched from the working state to a measurement state to measure the forward voltage under a sensor current of 5 mA. The switching process is fast enough and the switch delay time is less than 1 $\mu$s. Using Equations (2) and (4),we can obtain both the transient cooling curve and the thermal resistance curve. The transient temperature rise curve is obtained via a mathematical inversion of the transient cooling curve^[12].

We have investigated the temperature rise and thermal resistance of the LDs at various input currents. Figure 2(b) shows the LD thermal characteristics,including the junction temperature rise and the apparent thermal resistance of the LD as a function of input power. The temperature rise tends to increase with increasing input power^[14]. The apparent thermal resistance falls from 20 to 16.5 $^\circ C$/W over the input power range from 0.15 to 2.3 W,which is in accordance with the characteristic of increasing power conversion efficiency with increasing power,as shown in Figure 2(b). The temperature rise that occurs below the threshold current is caused by Joule heating from the drive current,while significant power-dependent heating caused by absorption of the laser radiation is added to the temperature rise above the threshold current^[15]. From Equations (2) and (3),when the input current is beyond the threshold current,the device begins to emit light and the input electrical power is transformed into optical power,and thus the power conversion efficiency begins to increase. When more power is converted into optical power,less is transformed into heat,and thus the apparent thermal resistance begins to decrease. Because of the limitations of the fabrication process,the power conversion efficiency reaches a maximum value after a temperature rise process. In this experiment,we simply consider the case below the maximum power conversion efficiency.

To obtain more information about the heat conduction process,we have analyzed the thermal resistance composition from the transient temperature rise curve using structure functions^[16]. Figure 3(a) shows the differential structure function of the LD at a driving current of 0.6 A and the total thermal resistance of the LD is 19 $^\circ C$/W. There are four peaks that correspond to the thermal resistances of the LD chip,the indium solder layer,and the copper sub-mount,and the resistance from the sub-mount to the TEC^[12]. From the differential structure function at various currents ranging from 0.4 to 1.3 A,we then abstract the component thermal resistance. The results shown here demonstrate that the total thermal resistance is mainly controlled by the packaging design rather than by the chip structure itself^{[14, 17]},and the decrease in thermal resistance is mainly caused by the decrease in the thermal resistance of the sub-mount.

Temperature distribution images of the entire output facets of working LDs were obtained using an FLIR System SC5700 camera working in the 3.7--4.8-$\mu$m range,and a temperature resolution of 20 mK. The thermal infrared camera recorded these images with a frequency of 115 Hz and a spatial resolution of approximately 3.0 $\mu$m per pixel. The LD was placed on a TEC that stabilized the heat-sink temperature at 25 $^\circ C$,unless stated otherwise. The LD radiation from the inter-band quantum well transitions was rejected using a Ge wafer as a filter to avoid any additional heating of the lens and the detector during the operation. The system described above is capable of mapping the heat distributions of the facets of LDs during operation. However,the emissivity differences between the elements in the LD,the parasitic reflections of the thermal radiation inside the LD,and the signal interference caused by thermal radiation reflected from surrounding objects are all factors that may cause additional measurement errors and should thus be taken into account^[11]. Therefore,to obtain quantitative temperature data,the total thermal measurement system requires a thorough calibration procedure.

The initial calibration process was carried out when the nonoperational LDs were heated by an external heat source in the range from 25 to 55 $^\circ C$ in 5 $^\circ C$ steps. The temperature was measured using a thermocouple placed in the vicinity of the LDs. For each temperature setting,a thermal image of the device located under a Ge wafer was captured. The calibration characteristics for the typical image regions,i.e.,from the LD facet region and from the heat sink,are shown in Figure 4. The second calibration process includes a reference image of the nonoperational LD acquired at ambient temperature. Subsequently,the LD is switched on and when it is stabilized,the thermal image is captured. The resulting map corresponds to the temperature difference between the reference temperature and the stabilized temperature,as shown in Figure 5(a).

Thermal maps of the LD under various currents ranging from 0.1 to 1.5 A were acquired by following the procedure described above. Figure 5(a) shows the thermal image of an LD operating at a working current of 1.5 A during the second calibration step. Figure 5(b) shows its horizontal profile,taken at line b shown in Figure 5(a),and Figure 5(c) shows its vertical profile,taken at line c in Figure 5(a). Both temperature profiles were measured through the active region after two calibration steps. The width of the active region is approximately 100 $\mu$m and the width between the two cladding layers is 1.9 $\mu$m,as indicated by the dotted rectangular lines in Figure s 5(b) and 5(c),respectively. We found that the temperature rise in the active region is higher than that which occurs outside the active region^{[17, 18]}. Because the temperature distribution is captured when the device has been stabilized,the temperature of the output facet is almost at its average and the temperature of the active region is only 1--2 $^\circ C$ higher than that beyond the active region. The temperature distribution maps of the front output facet were recorded at different driving currents ranging from 0.1 to 1.5 A. The junction temperature difference before and after operation was also acquired. The results shown in Figure 6 demonstrate that the temperature rise at the front facet increased with increasing output power^[19] and show the temperature rise characteristics measured by the electrical transient measurement technique and by infrared thermography. The temperature rise value measured by infrared thermography is smaller than that of the transient measurement technique^{[20, 21]}. There are two reasons for this: first,the spatial resolution of the thermographic method is 3 $\mu$m,which is far beyond the size of the active region,and thus the thermal images are spatially smoothed. Second,the temperature distribution that was acquired was mainly from the facet rather than the junction and the facet temperature is quite different to that of the junction. In addition,because the material under test,which was AlGaAs or GaAs,is transparent to infrared light,these effects can be caused by residual thermal radiation^[11]. Thus,the temperature rise measured by infrared thermography is lower than that obtained by the transient measurement technique. The advantage of infrared thermography is that the temperature rise is measured directly and rapidly,compared with by using a temperature sensitive parameter.

4. Conclusion

The thermal characteristics of 808 nm AlGaAs/GaAs LDs were investigated via electrical transient measurements and infrared thermography. The temperature rise and thermal resistance values of the LDs were measured. The results of the electrical transient measurements demonstrated that the thermal resistance decreases with increasing input power because of the device power conversion efficiency. The structural function was used to analyze the components of the thermal resistance. The results demonstrated that the total thermal resistance is dominated by the sub-mount component rather than that of the LD chip and the thermal resistance of the sub-mount increased with increasing current. The temperature rise that was measured by infrared thermography was smaller than that obtained by the electrical thermal transient,which occurred because of the limited spatial resolution of the measurements and because the signal was captured from the facet rather than from the junction of the LD.