Diode junction temperature in ultraviolet AlGaN quantum-disks-in-nanowires

The diode junction temperature (T j ) of light emitting devices is a key parameter affecting the efﬁciency, output power, and reliability. Herein, we present experimental measurements of the T j on ultraviolet (UV) AlGaN nanowire (NW) light emitting diodes (LEDs), grown on a thin metal-ﬁlm and silicon substrate using the diode forward voltage and electroluminescence peak-shift meth-ods. The forward-voltage vs temperature curves show temperature coefﬁcient dV F /dT values of (cid:2) 6.3 mV/ (cid:3) C and (cid:2) 5.2 mV/ (cid:3) C, respectively. The signiﬁcantly smaller T j of (cid:4) 61 (cid:3) C is measured for the sample on the metal substrate, as compared to that of the sample on silicon ( (cid:4) 105 (cid:3) C), at 50 mA, which results from the better electrical-to-optical energy conversion and the absence of the thermally insulating SiN x at the NWs/silicon interface. In contrast to the reported higher T j values for AlGaN planar LEDs exhibiting low lateral and vertical heat dissipation, we obtained a relatively lower T j at similar values of injection current. Lower temperatures are also achieved using an Infrared camera, conﬁrming that the T j reaches higher values than the overall device temperature. Furthermore, the heat source density is simulated and compared to experimental data. This work provides insight into addressing the high junction temperature limitations in light-emitters, by using a highly conductive thin metal substrate, and it aims to realize UV AlGaN NWs for high power and reliable emitting


I. INTRODUCTION
III-nitride light emitters have emerged as attractive ultraviolet (UV) light sources owing to their environmentally friendly (mercury-free) material properties, high reliability, and cost-effectiveness.In particular, Al x Ga 1-x N materials attracted attention due to their bandgap tunability throughout the UV range, hence allowing the use of this material in various electronic and optoelectronic applications. 1Although high power AlGaN-based light emitting diodes (LEDs) have been well demonstrated with emission wavelength ranging from UV-A-to UV-C regions, [2][3][4] the device efficiency suffers from the detrimental thermal heating associated with the high operating current.LEDs usually operate at high injection current and most of these devices show such a decrease in efficiencies for current injections as low as 10 A/cm 2 . 5While some part of the electrical input power is converted into photons yielding the illumination, most of it remains within the device as heat, which is lost in Joule heating.Such a drop in efficiency is dominantly related to the diode junction temperature (T j ) that can reach values higher than the ambient operating temperatures and the overall device temperature.The increment in T j not only affects the device efficiency, but also the operating voltage, emission wavelength, 6,7 power output, 8 chromaticity, and reliability. 9Specifically, prolonged current injection leads to higher T j which drastically degrades the LED performance, thereby causing catastrophic device failure.Various methods have been employed for measuring the junction temperature such as Raman spectroscopy, 10 thermal resistance, 11 photoluminescence, 12 nematic liquid crystals, 13 electroluminescence (EL) (band peak shift and high-energy slope of the spectrum), 14 and diode forward voltage. 15Among these, the forward voltage method is considered the most accurate, though a precise calibration is needed for each device under test.
III-nitride nanowires (NWs) have attracted much interest as they circumvent planar device problems such as straininduced polarization, threading dislocation, and cost-effective growth on various substrates.While NWs on a silicon substrate consist of a desirable platform for low-cost and scalable devices, the spontaneous formation of the insulating SiN x layer at the semiconductor/substrate interface limits their applicability, impeding heat dissipation and electrical conduction. 16][19][20][21] As many efforts have been made in the UV III-nitride NW community to bring NW technology to a practical application, it is of particular importance to study the diode T j of such devices to evaluate the best configuration for efficient heat dissipation through the heat sink substrate, prevent a) tienkhee.ng@kaust.edu.sab) boon.ooi@kaust.edu.sa0021-8979/2018/124(1)/015702/8 V C Author(s) 2018.124, 015702-1 overheating, short lifespan, and reduced light intensity.To date, there are no reports on UV AlGaN (and in general IIInitride) NWs LED T j measurements; therefore, this work consists of experimental findings that aim to enlighten the UV LED NW community for designing and optimizing the diode structures and substrate and to realize high power and reliable devices for eventual practical implementation.
We present T j measurements by employing the diode forward voltage and the energy peak-shift methods on UV Al x Ga 1-x N/Al y Ga 1-y N quantum disk (QD)/quantum barrier (x < y) NW LEDs grown on metal (Ti/TaN) and silicon substrates.Despite the lower thermal conductivity of the metal template, we observed lower T j of 61 C as compared to that of Si (105 C) at 50 mA.This reveals that the reduced T j is mainly due to the more efficient electrical-to-optical energy conversion of the sample grown on the metal substrate and therefore reduced Joule heating.We have reported recently that AlGaN NWs grown on metal thin films can achieve higher injection current due to the increased electrical conductivity and the absence of the above-mentioned SiN x barrier at the substrate/NW interface. 20We report a lower T j compared to planar UV GaN and AlGaN planar structures by using the same forward voltage method (compared to previous reports).Comparison of T j using the EL peak-shift method and infrared (IR) thermo-camera resulted in slightly lower values as previously reported in planar devices.

II. EXPERIMENTAL
The Al x Ga 1-x N/Al y Ga 1-y N NW devices are grown on Ti (80 nm)/TaN (20 nm)/Si (100) and on silicon substrates using the molecular beam epitaxy (MBE).The metal deposition, NW growth, and fabrication process details can be found in Refs.20 and 22.Briefly, for the sample on metal, the growth was initiated with $85 nm n-GaN followed by 50 nm n-AlGaN.The active region is composed of 10 stacked Al x Ga 1-x N quantum disks (3 nm)/Al y Ga 1-y N quantum barriers (4 nm), x < y. p þ -AlGaN contact layer is then grown above a p-AlGaN layer with a total thickness of 20 nm.For the sample on the silicon substrate, $150 nm n-GaN is grown, followed by 75 nm n-AlGaN.15 stacked Al x Ga 1-x N/ Al y Ga 1-y N quantum disks/quantum barriers are then grown atop the n-doped layer.The p-contact layer is formed growing 10 nm p-GaN.The samples are fabricated using the contact lithography technique.Ni (5 nm)/Au (5 nm) was evaporated and annealed to form an ohmic contact with p-AlGaN and subsequent Ni (10 nm)/Au (400 nm) and Ti (10 nm)/Au (150 nm) are deposited as p-and n-contacts, respectively.
For the calibration of the diode forward voltage method, a semi-automated probe system (Cascade Microtech Summit 11000 AP) was incorporated with a pulsed source meter (Keithley 2611B, 1% duty cycle, 25 ms pulses).The measurement of the instant voltage and the voltage at the equilibrium was performed using a direct-current (DC) source meter (Keithley 2400).The EL spectrum was collected using a 15Â objective lens (Thorlabs LMU-15X-UVB, focal length 13 mm and numerical aperture (NA) of 0.32, with antireflection (AR) coating for the 240-360 nm wavelength range, and a 50:50 beam-splitter (Thorlabs BSW19, AR coated for 250-450 nm) to distribute the light to the focusing lenses of a viewing camera.
The viewing camera consists of an infrared (IR) camera (Infrasight IS640) incorporated with an uncooled amorphous silicon microbolometer with an array size of 640 Â 480 pixels and a spectral response ranging from 7 to 14 lm.

III. RESULTS AND DISCUSSION
The diode forward voltage method is based on the Shockley diode equation 15 where J F is the applied current density, J S is the saturation current density, n is the ideality factor, V F is the forward voltage, k is the Boltzmann constant, and T is the temperature.In order to obtain the relation between the voltage and the temperature (and considering V F ) kT/e), we need to rewrite Eq. ( 1) as 15 And the change of junction voltage as a function of temperature can be expressed as 15 It is noted that the temperature dependence of junction voltage is due to the temperature dependence of intrinsic carrier concentration, effective densities of states in the conduction and valence bands, and material bandgap energy and that the contribution of the latter is approximately 24% for GaN. 23xperimentally, with increasing temperature, the junction voltage decreases when working at constant current.Such linear dependence of V F and T can be fitted as where K T is the temperature coefficient and T O is the temperature of the heat sink.Figure 1(a) shows the I-V curve of the AlGaN NW LED on the metal and silicon substrate under DC operation.The turn-on voltages of the devices are $8 and 10 V, respectively, while the turn-on resistances are $14 and 80 X.During the calibration measurement of the AlGaN NWs on metal, the current was increased from 1 to 7 mA and the measured V F versus T plot is shown in Fig. 1(b).The temperature coefficient, i.e., dV F /dT, of À6.3 mV/ C is slightly lower than previously experimentally measured UV AlGaN and GaN planar LEDs of À5.8 mV/ C 14 and -2.3 mV/ C, 15 and lower than theoretical values (À1.76 mV/ C). 23 In fact, the latter defines the lower limit of the magnitude of dV F /dT.Moreover, it does not take into account the contribution from the resistive-higher-doping-activation neutral regions at high temperatures, where the resistivity decreases together with the voltage.Figure 1(c) shows the V F versus T plot for the AlGaN NWs on the silicon substrate with a temperature coefficient of -5.2 mV/ C. From Eq. ( 4), the junction temperature can be obtained as 24 where T A is the ambient temperature and V FT and V FO are the equilibrium and instant voltage. 24An example of the V FT at 50 mA (DC operation) at room temperature for the device on silicon is shown in Fig. 1(d).The V FT is the constant forward voltage at thermal equilibrium, i.e., measured after 30 min at constant current.At thermal equilibrium, the voltage reaches a plateau.At 50 mA, the instant (initial) voltage is 18.90 V, while after equilibrium it is 18.48 V.The high voltage measured is a consequence of the high device resistance that is possibly due to the spontaneous SiN x layer at the GaN/Si interface.The resultant DV is equal to 42 mV that is substantially higher than GaN-based planar devices.It is also noted that, as the current increases, the DV further increases.
In order to compare the results obtained using the forward voltage method, we measured the T j using the EL emission peak-shift method.The band-gap-dependent temperature coefficient K k needs to be extracted and the T j can be calculated as follows: 25 where T O is the ambient temperature and Dk is the peak emission wavelength difference measured in DC and pulsed current.Figure 2(a) shows the emission peak shift as a function of temperature for the AlGaN NW LED on the metal substrate.Different devices were tested and an average K k of 0.027 nm/ C was calculated for a pulsed injection current of 90 mA.It is noted that K k did not change much with injection current, confirming that the duty cycle used is small enough to prevent the device from heating. in the DC mode is due to the device heating and internal bandgap reduction.The EL peak shift is more susceptible to effects of alloy-broadening and kT broadening, and it has been reported that the accuracy of the peak wavelength is $10% of the EL full-width at half-maximum (FWHM).The T j comparison of the two samples, calculated using the forward voltage method, as a function of injection current, is shown in Fig. 3(a).Lower values are obtained for the NWs on the metal substrate.As the current increases from 5 to 80 mA, the T j increases from 36 to 71 C. On the other hand, the T j for the NWs on silicon shows higher values.At 50 mA the T j is $105 C, higher than that of the sample on metal, 61 C.Moreover, the increment of T j of the sample grown directly on silicon is steeper than that of the sample grown on metal, especially at elevated injection currents.This, however, cannot be explained by the thermal conductivity of the substrate as Ti (13-22 WÁm À1 ÁK À1 ) 26 has a thermal conductivity lower than silicon (50-149 WÁm À1 ÁK À1 ). 27nstead, this is due to the better electrical-to-optical energy conversion.We recently demonstrated the growth of AlGaN NW LEDs on Ti/TaN/Si to circumvent the SiN x formation and substrate delamination. 20We reported a higher injection current density due to the reduction of Si interdiffusion in the metal layer.This reduces the potential barrier at the semiconductor/substrate interface, increasing the injection efficiency and reducing Joule heating.However, it is noted that the LEDs grown on the Si substrate have a larger active region compared to the one grown on metal and this may also contribute to an increase in T j .In Fig. 6(b), by comparing the corresponding increase in temperature at different heat source densities (Q) for the LED on silicon with 10 and 15 quantum disk-stacks, it is found that temperature increases with active region thickness as there is a larger heating volume.Furthermore, by comparing the LEDs on silicon and metal with the same 10 quantum disk-stacks, the temperature also increases by a similar amount for that grown on silicon.and AlGaN NWs T j vs injection current using both the diode forward voltage and EL emission peak-shift method.The NW devices show lower T j compared to the planar devices grown on sapphire.This can be explained by the heat dissipation through the metal substrate.In fact, it has been reported that the substrate plays a crucial role in the LED T j .Blue InGaN LEDs on sapphire and silicon substrates have shown Tj of $80 C and $65 C, respectively, when operated at 50 mA. 28Similarly, at 100 mA, T j values of InGaN LEDs on both sapphire and GaN substrates were reported to be $204 C and $83 C, respectively, 5 confirming the higher heat conductance in GaN and silicon compared to sapphire.Table I lists a summary of the III-nitride planar LED T j in the chronological order.Specifically, in the UV region, GaN LEDs emitting at 375 nm have shown a T j of $75 C at 50 mA, 15 whereas T j of the AlGaN LED emitting at 295 nm has been reported to be $90 C for the same injection current. 14igure 4 shows the T j of the reported group-III nitride LEDs in the literature using the forward voltage and peak-shift methods.Despite the lack of reports for a proper comparison on UV AlGaN light emitters, the NW devices on the metal substrate show the lowest T j values at similar injection current.All the curves in Fig. 3(b) are linear with current and K represents the speed with which the temperature increases.As it can be noticed, T j in planar structures increases faster compared to the NW structure, with a K value of 1.04 in the forward voltage method and 0.62 for the EL peak-shift method, compared to K values of 0.33 and 0.24 for the AlGaN NWs.This can be explained by the lower lateral and vertical (through the substrate) heat dissipation for the planar devices.Moreover, the EL peak-shift method shows lower T j in both samples.For similar reasons, the T j of the AlGaN NW sample on silicon using the EL peak-shift method could not be measured.The EL emission was too weak and together with the high inhomogeneity of the emission, it impeded the clear peak distinction in DC and pulsed current, especially at low injection.Moreover, especially for nanowire-based devices, where the inhomogeneity is more prominent, the peak-shift method is expected to impose an even larger error.In this regard, Xi et al. reported a variation of the junction temperature of 624 C that, if taken into account, agrees well with the results obtained by the forward voltage method. 14he overall devices temperatures were then measured using an IR camera.Figure 5(a) shows the current-dependent IR images of the 0.5 Â 0.5 mm 2 devices on the metal and silicon substrate.At 10 mA, the Joule heating is negligible for both devices.However, the device on silicon heats up faster compared to the one on the metal substrate.If we compare the devices at 50 mA, we notice that the one on metal shows lower temperature on the device area and on the surrounding area.This means that the absence of SiN x contributes to a better heat spreading across the substrate.The current vs. temperature plot is depicted in Fig. 5(b).We show that the two samples reach the same temperature of 45 C at 60 mA (sample on silicon) and 110 mA (sample on the metal).These temperatures are lower compared to the ones obtained using the forward voltage method, meaning that the T j can reach values much higher than the overall device temperature.In fact, the IR camera measures the overall heating escaping the device under test.We also show the temperature curves for 1 Â 1 and 2 Â 2 mm 2 devices on the metal.At low injection currents, the different size does not play a prominent role in the Joule heating across the device.However, for high current (80 mA), the temperature starts deviating due to the reduced current density with the increased device area.
To study the heat transfer across the device, we simulated the AlGaN NW LED on metal and silicon substrates using the finite element method (FEM) (COMSOL Multiphysics software).The heat source is generated in the active region and is dissipated by conduction through the substrate and by convection and radiation through the contact pads.The bottom of the NW LED is in contact with a heat sink kept at RT.The heat transfer was modeled by using the following 3D steady-state heat equations where Q is the heat source density, k is the thermal conductivity, h is the convection heat transfer, T amb and T are the ambient temperature and the NW temperature, e is the surface emissivity, and r is the Stefan-Boltzmann constant.Figure 6(a) shows the device schematic at a heat source density of 10 14 W/m 3 for the sample grown on the metal substrate.As the heat convection and radiation in NWs are negligible, the higher temperature is reached at the contact pads and heat dissipates faster through the substrate.characteristics.Figure 6(c) shows the log-log L-I curves for the AlGaN NWs on the metal and silicon substrate at room temperature.The heat source density can be calculated as 24 where U QDisks is the volume of the quantum disks.Figure 6(d) represents the calculated heat source density with increasing current for the samples on the metal and silicon substrate.As expected, the Q values increased with injection current.At low injection, the heat source densities have similar values, while above $20 mA the trends start deviating with the device on silicon showing slightly smaller values.This can be explained by the higher operating current of the sample on the metal substrate compared to the one on silicon that highly affects the heat source density calculation.Moreover, from Fig. 6(b), the two samples follow the same trend until Q ¼ $10 14 W/m 3 , where the device on silicon starts deviating and the temperature increases.However, in the experimental results [Fig.6(d)] the device on silicon does not reach a heat source density of 10 14 W/m 3 as it cannot withstand such injection current.Hence, although we cannot experimentally verify it, simulation results indicate that after 10 14 W/m 3 the Q value of the sample on the silicon substrate overcomes the one of metal.It is noted that the larger the thickness of the active region, the larger the temperature output at a given heat source density.From the experimental results, below $10 14 W/m 3 the heat source density for the sample on silicon is slightly lower compared to the one on metal, despite the larger number of quantum disks.Also, the junction temperature calculated using the forward voltage method shows higher values for the former, indicating that the thickness of the active region is not the only parameter affecting the temperature rise.
At 50 mA, the Q values were measured as 2.51 Â 10 13 W/m 3 and 1.8 Â 10 13 W/m 3 , respectively, that are similar to that of the reported InGaN/GaN planar LEDs ($4.6 Â 10 13 W/m 3 at 60 mA). 24These values, however, slightly differ from the simulated results obtained in Fig. 6(b), where for a heat source density of 2.51 Â 10 13 W/m 3 the temperature is $26 C that is lower than the expected 61 and 105 C.This can be explained by the high thermal contact resistance caused by the rough surface between the device substrate and the heat sink that leads to air pockets and causes a temperature drop across the interfaces.

IV. CONCLUSION
Junction temperature measurements are presented on the UV AlGaN NW LEDs on metal and silicon substrates.Reduced T j measured using the forward voltage method was obtained for the device grown on a metal thin film with values ranging from 36-71 C (5 to 80 mA) compared to 56-110 C (5 to 65 mA) for the sample on the silicon substrate.The EL peak-shift method showed lower the T j due to the larger error of the energy peak and FWHM of the EL spectra.A comparison with the previously reported AlGaNbased planar LED on sapphire showed that the AlGaN NW LED presents lower T j that we assumed due to the better lateral and vertical heat dissipation as well as thermal conductivity of the metal substrate compared to sapphire.Measurements using the IR camera are also presented, confirming the reduced Joule heating and better heat dissipation for the LEDs grown on the metal substrate.Finite element method simulations were performed to study the heat transfer across the device and to understand the device temperature at specific active region heat source densities.This work aims to shed light on the uncharted heating problems in AlGaN NW light emitters on the Si substrate and presents a solution for eventual high power and reliable emitting devices on thin metal films.
FIG. 1. Forward voltage method calibration.(a) I-V curve for the AlGaN NW LEDs on metal and silicon substrate under DC.(b) Forward voltage vs heat sink temperature for the AlGaN NWs LED on metal.(c) Forward voltage vs heat sink temperature for the AlGaN NWs LED on silicon, and (d) forward voltage variation as a function of time at 50 mA for the sample on silicon.

FIG. 2 .
FIG. 2. EL peak-shift method calibration for the AlGaN NWs LED on metal substrate.(a) Peak wavelength shift as a function of heat sink temperature (b) Normalized EL intensity in DC and pulse modes at 90 mA.

Figure 3 (
Figure 3(b) reports a comparison between AlGaN planar14 and AlGaN NWs T j vs injection current using both the diode forward voltage and EL emission peak-shift method.The NW devices show lower T j compared to the planar devices grown on sapphire.This can be explained by the heat dissipation through the metal substrate.In fact, it has been reported that the substrate plays a crucial role in the LED T j .Blue InGaN LEDs on sapphire and silicon substrates have shown Tj of $80 C and $65 C, respectively, when operated at 50 mA.28Similarly, at 100 mA, T j values of InGaN LEDs on both sapphire and GaN substrates were reported to be $204 C and $83 C, respectively, 5 confirming the higher heat conductance in GaN and silicon compared to sapphire.Table I lists a summary of the III-nitride planar LED T j in the chronological order.Specifically, in the UV region, GaN LEDs emitting at 375 nm have shown a T j of $75 C at 50 mA,15 whereas T j of the AlGaN LED emitting at 295 nm has been reported to be $90 C for the same injection current.14Figure4shows the T j of the reported group-III nitride LEDs in the literature using the forward voltage and peak-shift methods.Despite the lack of reports for a proper comparison on UV AlGaN light emitters, the NW devices on the metal substrate show the lowest T j values at similar injection current.All the curves in Fig.3(b) are linear with current and K represents the speed with which the temperature increases.As it can be noticed, T j in planar structures increases faster compared to the NW structure, with a K value of 1.04 in the forward voltage method and 0.62 for the EL peak-shift

Figure 6 (
FIG.4.T j vs. wavelength/current plot for the reported group-III nitride LEDs, using the forward voltage and peak-shift method.The substrate is sapphire where not specified.

FIG. 6 .
FIG. 6.(a) Temperature distribution in the NWs LED on metal substrate with a source heat density of 10 14 W/m 3 .(b) Simulated semilog plot of temperature vs. heat source density (Q) for the devices grown on metal and silicon substrates with 10 and 15 quantum disks-stack (QDs).The inset shows the contour cross section image of the device on metal.(c) Log-log L-I plot of AlGaN NW LEDs for samples on metal and silicon in DC operation.(d) Heat source density vs. current, calculated from (c) and Fig. 1(a).

TABLE I .
Summary of the reported planar group-III nitride LED junction temperatures.