G Meneghesso

M Meneghini
email: matteo.meneghini@dei.unipd.it

E Zanoni

Recent results on the degradation of white LEDs for lighting

Over the last years, GaN-based LEDs have shown to be excellent candidates for the realization of highefficiency light sources. White LEDs based on phosphor conversion can reach record efficiencies in excess of 150 lm/W, as demonstrated by several manufacturers and research groups. However, the reliability of white LEDs is still limited by a number of issuesthat must be addressed before these devices can find wide application in the market. This paper gives an overview on the most important physical mechanisms that limit the reliability of GaN-based LEDs for application in solid-state lighting. Starting from general considerations on the reliability of state-of-the-art white LEDs, the following degradation mechanisms are described in detail: (i) the degradation of the active layer of LEDs, due to increased non-radiative recombination and to reverse-bias stress; (ii) the degradation of the package/phosphor system, with subsequent worsening in the chromatic properties of the LEDs; (iii) the failure of GaN-based LEDs submitted to Electrostatic Discharge events. The data presented in this paper are critically compared to those reported in the literature.

Introduction

More that 20 % of the electricity generated in the United States is used for lighting [START_REF] Azevedo | The Transition to Solid-State Lighting[END_REF]; furthermore, worldwide lighting is responsible for the emission of more than 1900 million of tons of CO 2 per year. The use and development of highly efficient light sources would decrease of more than 50 % the worldwide lighting consumption [START_REF] Tsao | Solid State Lighting[END_REF], with subsequent economic and environmental benefits.

Over the last decade, GaN-based LEDs have emerged as good candidates for the realization of high-efficiency light sources for general lighting. Thanks to the continuous optimization of the growth and processing procedures, blue and white LEDs with outstanding performance have been recently demonstrated: blue LEDs have a record wall-plug efficiency in excess of 60 % [START_REF] Laubsch | High-Power and High-Efficiency InGaN-Based Light Emitters[END_REF], while white LEDs can reach luminous efficacies in excess of 150 lm/W [START_REF] Dupuis | History, Development, and Applications of High-Brightness Visible Light-Emitting Diodes[END_REF]. These advancements came from the improvement of the following parameters: (i) internal quantum efficiency (IQE); (ii) extraction efficiency; (iii) technology used for the realization of phosphors; (iv)packaging and assembling procedures. However, efficiency is not the sole parameter that is taken into account by consumers: LEDs are semiconductorbased devices, and for this reason they are expected to have an intrinsically high reliability, compared to conventional light sources (incandescent and fluorescent lamps). Incandescent lamps have a typical lifetime of 1000 hours, and during aging can show a 10-15 % lumen depreciation, due to the condensation of the tungsten contained in the filament on the inner part of the glass bulb. Fluorescent lamps can reach a 10000-hours lifetime, with a limited (10-20 %) lumen decrease, which is due to the degradation of the phosphors used for white light generation, and to the increase in absorption within the lamp. On the other hand, LEDs can have a significantly longer theoretical lifetime (in excess of 50000 h, [START_REF] Zehnder | Industrial production of GaNand InGaN-light emitting diodes on SiC-substrates[END_REF]), making them good candidates for the realization of longlasting light sources. While the degradation mechanisms of conventional light sources are well known, the origin of the degradation of LEDs is still subject of intense study.

Over the last few years, several authors have investigated the origin of the degradation of LEDs submitted to accelerated ageing tests. In particular, it was shown [START_REF] Yanagisawa | Estimation of the degradation of InGaN/A1GaN blue Light-Emitting Diodes[END_REF][START_REF] Manyakhin | Aging Mechanisms of InGaN/AlGaN/GaN Light-Emitting Diodes Operating at High Currents[END_REF][START_REF] Fang | Changes in Electrical Characteristics Associated with Degradation of InGaN Blue Light-Emitting Diodes[END_REF][START_REF] Polyakov | Enhanced tunneling in GaN/InGaN multiquantum-well heterojunction diodes after short-term injection annealing[END_REF][START_REF] Cao | Defect generation in InGaN/GaN light-emitting diodes under forward and reverse electrical stresses[END_REF][START_REF] Uddin | Study of degradation mechanism of blue light emitting diodes[END_REF][START_REF] Rossi | Influence of short-term low current dc aging on the electrical and optical properties of InGaN blue light-emitting diodes[END_REF]] that stress at constant current level can determine a significant decrease in the internal efficiency of the devices: degradation was attributed to the increase in the non-radiative recombination rate in the active layer of the LEDs, due to the generation/propagation of defects [START_REF] Polyakov | Enhanced tunneling in GaN/InGaN multiquantum-well heterojunction diodes after short-term injection annealing[END_REF][START_REF] Cao | Defect generation in InGaN/GaN light-emitting diodes under forward and reverse electrical stresses[END_REF][START_REF] Uddin | Study of degradation mechanism of blue light emitting diodes[END_REF][START_REF] Rossi | Influence of short-term low current dc aging on the electrical and optical properties of InGaN blue light-emitting diodes[END_REF], or to the diffusion of dopants or impurities in the quantum well (QW) region [START_REF] Rigutti | Redistribution of multi-quantum well states induced by current stress in InGaN/GaN lightemitting diodes[END_REF][START_REF] Lee | Effects of Mg dopant on the degradation of InGaN multiple quantum wells in AlInGaN-based light emitting devices[END_REF]. It was also shown that operation at high temperature levels can induce a significant degradation of the optical characteristics of GaN-based LEDs: high-temperature degradation was attributed (i) to the worsening of the electrical properties of the ohmic contact and semiconductor material at the p-side of the diodes [START_REF] Meneghini | Reversible degradation of ohmic contacts on p-GaN for application in high brightness LEDs[END_REF][START_REF] Meneghini | Reversible degradation of ohmic contacts on p-GaN for application in high brightness LEDs[END_REF][START_REF] Meneghini | A model for the thermal degradation of metal/(p-GaN) interface in GaN-based LEDs[END_REF], due to the interaction between hydrogen and the magnesium dopant, and (ii) to the thermally-activated darkening of the package and phosphors system, with subsequent worsening of the chromatic properties of white LEDs [START_REF] Meneghini | Stability and performance evaluation of high-brightness light-emitting diodes under DC and pulsed bias conditions[END_REF][START_REF] Trevisanello | Accelerated Life Test of High Brightness Light Emitting Diodes[END_REF][START_REF] Ishizaki | Lifetime estimation of high power LEDs[END_REF][START_REF] Meneghini | High temperature electro-optical degradation of InGaN/GaN HBLEDs[END_REF][START_REF] Hu | Electrical, optical and thermal degradation of high power GaN/InGaN light-emitting diodes[END_REF][START_REF] Trevisanello | Thermally activated degradation and package instabilities of low flux LEDs[END_REF]. Recent studies [START_REF] Cao | Defect generation in InGaN/GaN light-emitting diodes under forward and reverse electrical stresses[END_REF][START_REF] Meneghini | Degradation of High-Brightness Green LEDs Submitted to Reverse Electrical Stress[END_REF] highlighted that also exposure to reverse-bias can determine the degradation of GaN-based LEDs: when submitted to reverse-bias stress, devices can show a significant increase in reverse current (corresponding to a decrease in breakdown voltage), which was ascribed to the generation of point defects in proximity of pre-existing defective leakage paths. Finally, some authors [START_REF] Meneghesso | Electrostatic Discharge and Electrical Overstress on GaN/InGaN Light Emitting Diodes[END_REF][START_REF] Horng | GaN-Based Power LEDs With CMOS ESD Protection Circuits[END_REF][START_REF] Jeon | The effect of the internal capacitance of InGaN-light emitting diode on the electrostatic discharge properties[END_REF] indicated that also Electrostatic Discharge (ESD) events can represent an issue for GaN-based LEDs: when submitted to ESD events, LEDs can show catastrophic failure, with subsequent shortening of the junction. Failure usually takes place in proximity of a weak region [START_REF] Meneghini | A review on the physical mechanisms that limit the reliability of GaN-based LEDs[END_REF], corresponding to the presence of lattice or morphological defects.

In this paper, we give an overview on the most important physical mechanisms that affect the reliability of stateof-the-art white LEDs. Starting from recent results obtained on commercially available power LEDs, we describe in detail the degradation processes that affect (i) the electrical and optical properties of InGaN-based LEDs, and (ii) the optical efficiency of the package/phosphors system. Finally, we describe the failure of LEDs submitted to ESD events.

Physics of LED failure

Structure of commercially available LEDs

High-power LEDs are complex systems, constituted by several elements: the core of a white LED structure is a blue GaN-based LED chip, with an emission wavelength of 450-460 nm. This chip typically has an area of 1 mm 2 , and is mounted on a thermally-conductive frame in a power LED package, in order to achieve a good heat dissipation. The power LED chip is usually covered with a lens, which has the twofold aim of improving the efficiency of the light extraction process, and of modifying the shape of the emitted light beam. Blue light is converted into white light by means of a phosphorous layer, which can be deposited directly on the chip (Chip Level Conversion, CLC), or incorporated in the encapsulating lens. As an example, in Figure 1 we report a Scanning Electron Microscopy (SEM) image of a commercially available power LED chip: the image was taken after the removal of the encapsulating lens, and is referred to an LED with vertical current conduction path.

Commercially available power LED chips usually have a nominal operating current in the range 350-1000 mA (corresponding to current densities in the range 35-100 A/cm 2 for 1 mm 2 chips), and an operating voltage in the range 3.2-3.4 V. These devices are therefore rated for an electrical power consumption between 1 and 3.5 W.

In their final application, the thermal resistance of power LEDs is in the range between 10 K/W and 20 K/W, depending on the optimization of the heat extracting path. Therefore, under normal operating conditions devices can show a certain self-heating, with a temperature increase (with respect to ambient temperature) ranging between 20 °C and 80 °C. As it will be clear in the following, the current and temperature levels reached by LEDs during ageing time can strongly influence the degradation kinetics of LEDs: for this reason an accurate definition of the operating conditions, and a careful optimization of the heat dissipation process are mandatory steps for the achievement of a long LED lifetime.

As stated above, LEDs are complex systems, composed by several elements: during device lifetime, each of these components can degrade, leading to a depreciation of emission intensity and chromatic properties. The blue LED chip, if submitted to constant current stress, can show a significant optical power decrease, due to the increase in non-radiative recombination rate [START_REF] Fang | Changes in Electrical Characteristics Associated with Degradation of InGaN Blue Light-Emitting Diodes[END_REF][START_REF] Polyakov | Enhanced tunneling in GaN/InGaN multiquantum-well heterojunction diodes after short-term injection annealing[END_REF][START_REF] Cao | Defect generation in InGaN/GaN light-emitting diodes under forward and reverse electrical stresses[END_REF][START_REF] Pursiainen | Identification of aging mechanisms in the optical and electrical characteristics of light-emitting diodes[END_REF][START_REF] Grillot | Sixty Thousand Hour Light Output Reliability of AlGaInP Light Emitting Diodes[END_REF]. Furthermore, operation at high current/temperature levels can lead to significant modifications in the chromatic properties of LEDs, due to the darkening of the phosphorous material and to the worsening of the reflective properties of the package [START_REF] Meneghini | Stability and performance evaluation of high-brightness light-emitting diodes under DC and pulsed bias conditions[END_REF][START_REF] Ishizaki | Lifetime estimation of high power LEDs[END_REF][START_REF] Hu | Electrical, optical and thermal degradation of high power GaN/InGaN light-emitting diodes[END_REF]. Finally, the lens -usually adopted to improve the efficiency of the light extraction process -can also show a significant darkening as a consequence of device ageing, both due to the high temperatures reached during LED operation, and to the short wavelengths emitted by the device itself [START_REF] Barton | Single-quantum well InGaN green light emitting diode degradation under high electrical stress[END_REF].

Lifetime tests are usually carried out by submitting LEDs to accelerated ageing, under relatively high current and/or temperature levels. Under these conditions, it is quite difficult to understand whether degradation processes are mainly due to the flow of a relatively high current density through the junction, or to the high temperatures reached by the devices during operation. Furthermore, when the many components of and LED structure degrade simultaneously, it is quite difficult to understand whether degradation is mainly due to the ageing of the blue LED chip, or to processes related to the package/phosphors/lens system. In order to achieve a good understanding of the physical processes that limit the reliability of advanced LED structures, it is therefore necessary to develop specific testing procedures, capable of separately analyzing the degradation of the individual components of an LED during ageing time. In the following we will describe some general results on the reliability of state-of-the-art white LEDs, and more specific data concerning the degradation of the blue LED chip (weaknesses of InGaN-LED technology) and of the package/phosphors system.

Reliability testing of high-power white LEDs

Ageing tests of high power LEDs are usually carried out under slightly accelerated conditions. A reasonable acceleration can be obtained by ageing the LEDs at the maximum current indicated in the datasheet, with an ambient temperature between room temperature and 85 °C [40][START_REF]Approved Method: Measuring Lumen Maintenance of LED Light Sources[END_REF][42]. For the stress tests, devices are mounted on proper heat sinks, by means of thermally-conductive adhesive, in order to keep the junction-to-ambient thermal resistance sufficiently low. The thermal resistance of the LEDs can be evaluated by means of the indirect forward-voltage method, proposed by the group of E. F. Schubert and described in detail in [START_REF] Xi | Junction temperature measurement in GaN ultraviolet light-emitting diodes using diode forward voltage method[END_REF]. The ageing current should be applied continuously, except for the time spent for the measuring procedures. Devices are considered to be failed when they show a 10-30 % decrease in the luminous flux, or a certain operating voltage shift (typically 200 mV) (see for instance [42]).In Figure 2 we report typical optical power degradation curves measured on three families of state-of-the-art white LEDs, aged at 100 A/cm 2 , 80 °C during a benchmarking test carried out in our laboratories. Analyzed LEDs come from three leading manufacturers, and were acquired in October 2009: as can be noticed, one of the three families of analyzed LEDs showed a significant optical power degradation during the mid-term stress test, demonstrating an high sensitivity to the applied stress conditions.

From the results of this -or similar -ageing tests, it is possible to compare different device technologies in terms of reliability. On the other hand, by simply measuring the optical power degradation (or the operating voltage shift) during the stress tests, no significant information on the physical mechanism responsible for degradation can be achieved. In order to analyze the origin of lumen depreciation, specific stress tests must be carried out, on suitable test and device structures. In the following we report the results of a number of stress tests that we have carried out with the aim of analyzing specific degradation mechanisms affecting the efficiency and the optical properties of the InGaN-based LED chip, of the package, and of the phosphors of advanced LED structures.

Degradation of the InGaN-based LED chip

The degradation of the InGaN-based LED chip can be studied by submitting bare LED samples to specific stress tests. The results described within this section were obtained on LED samples mounted on metallic TO18 package: no phosphors/plastic package/lens was used for these devices. Therefore, the degradation modes described in the following can be ascribed to the ageing of the InGaN LED chip.

In order to describe the degradation of InGaN-based LED chips, we submitted several commercially-available and R&D samples to stress under constant current level. For the stress tests, devices were mounted on Peltiercontrolled fixtures, allowing for an accurate control of case temperature. Stress current levels ranged in the interval 20-180 A/cm 2 , while case temperature levels ranged between 15 °C and 85 °C. During the execution of the stress tests, a complete optical and electrical characterization of the devices was carried out, in order to achieve a description of the degradation process.

In Figure 3 we report the optical power vs current density (L-J) characteristics measured on one InGaN-based LED chip submitted to stress under constant current conditions. As can be noticed, stress can induce a decrease in the optical power emitted by the samples. This effect is more prominent at low measuring current levels, as also described by the optical power vs stress time curves reported in Figure 4. This result suggests that stress induced an increase in the non-radiative recombination rate: at low measuring current levels, the non-radiative recombination centers present in the active layer can efficiently trap the carriers flowing through the junction, thus reducing the amount of electrons that undergo radiative recombination. An increase in non-radiative recombination rate therefore results in a decrease in the optical power emitted by the LEDs at low measuring current levels. On the other hand, at high measuring current levels, the injection of a large amount of electrons can lead to the saturation of the non-radiative centers: therefore, the L-J characteristics of LEDs are not significantly modified at high measuring current levels [START_REF] Pursiainen | Identification of aging mechanisms in the optical and electrical characteristics of light-emitting diodes[END_REF][START_REF] Grillot | Sixty Thousand Hour Light Output Reliability of AlGaInP Light Emitting Diodes[END_REF]. This kind of degradation process is only slightly thermally activated, at least within the nominal operating range of commercially available samples (maximum temperature is 105-125 °C). Stress tests carried out at different case temperature levels (and with the same stress current level) indicated only a weak dependence of the degradation kinetics on stress temperature (see Figure 5 for an example). This result suggests that currentrather than temperature -is the main driving force for the degradation of bare LED chips submitted to constant current stress. This hypothesis is supported by recent reports describing the degradation of InGaN-based laser diodes, both in the lasing and sub-threshold operating region [START_REF] Meneghini | Analysis of the role of current, temperature, and optical power in the degradation of InGaNbased laser diodes[END_REF][START_REF] Meneghini | Degradation of InGaN-Based Laser Diodes Related to Nonradiative Recombination[END_REF]. A linear dependence of the degradation rate on the stress current level was found for these devices, which are -in their inner structure -very similar to LED chips [START_REF] Meneghini | Analysis of the role of current, temperature, and optical power in the degradation of InGaNbased laser diodes[END_REF]: on the other hand, degradation was found to have a weak dependence on temperature, with activation energies in the range 0.25-0.30 eV [START_REF] Meneghini | Analysis of the role of current, temperature, and optical power in the degradation of InGaNbased laser diodes[END_REF].

A similar degradation process is usually explained by supposing that the injection of charged carriers through the junction leads to the generation/propagation of defects (such as vacancies or impurities), due to the interaction between highly energetic electrons and the lattice [START_REF] Manyakhin | Aging Mechanisms of InGaN/AlGaN/GaN Light-Emitting Diodes Operating at High Currents[END_REF][START_REF] Polyakov | Enhanced tunneling in GaN/InGaN multiquantum-well heterojunction diodes after short-term injection annealing[END_REF][START_REF] Rossi | Influence of short-term low current dc aging on the electrical and optical properties of InGaN blue light-emitting diodes[END_REF]. This may determine an increase in the non-radiative recombination rate in the active layer of the devices, a the decrease in the efficiency of the light generation process.

Furthermore, recent reports [START_REF] Rossi | Influence of short-term low current dc aging on the electrical and optical properties of InGaN blue light-emitting diodes[END_REF][START_REF] Rigutti | Redistribution of multi-quantum well states induced by current stress in InGaN/GaN lightemitting diodes[END_REF] demonstrated that during constant current stress the distribution of charge in the active region can significantly change: this result was obtained by means of Capacitance-Voltage (C-V) profiling. C-V measurements represent a powerful tool for the analysis of the distribution of charged carriers in the active layer of LEDs: starting from C-V characterization, it is possible to extrapolate the Apparent Charge Distribution (ACD) of free carriers within the junction [START_REF] Rossi | Influence of short-term low current dc aging on the electrical and optical properties of InGaN blue light-emitting diodes[END_REF], and to detect possible changes arising as a consequence of stress. In Figure 6 we report the C-V characteristics measured before and during constant current stress on one InGaN-based LED. As can be noticed, stress induced a significant increase in junction capacitance, in the voltage region between -4 and 0 V. For the analyzed devices, when the voltage is varied in this range, the border of the space charge region is located within the quantum-well region, as described in detail in [START_REF] Meneghini | A review on the physical mechanisms that limit the reliability of GaN-based LEDs[END_REF]. Therefore, an increase in junction capacitance measured in this voltage region corresponds to significant variations in the charge density in the active layer of the LEDs. By integrating the differential capacitance increase reported in Figure 6, it is possible to quantitatively evaluate the amount of charge increase induced by the constant current stress experiment [START_REF] Rigutti | Redistribution of multi-quantum well states induced by current stress in InGaN/GaN lightemitting diodes[END_REF]. The most important result of this analysis is shown in Figure 7. This figure reports on the horizontal axis the variation in the optical power induced by constant current stress, and on the vertical axis, the variation in the charge concentration detected as a consequence of stress. Results indicate that there is a nearly linear correlation between the amount of optical power decrease and the variation of charge concentration in the quantum-well region. Results can be interpreted by considering that stress induces the propagation of charged defects towards the active layer of the LEDs. The rate of non-radiative recombination is directly correlated to the density of defects located within the active region. Therefore, an increase in charged defect density can lead to a decrease in the optical efficiency of the devices and to an increase in the apparent charge concentration in the quantum-well region (detected by means of C-V characterization). Recent studies indicated that these modifications in the charge distribution can be correlated to the presence of deep levels with activation energies in the range 160-430 meV [START_REF] Rossi | Influence of short-term low current dc aging on the electrical and optical properties of InGaN blue light-emitting diodes[END_REF][START_REF] Meneghesso | Degradation Mechanisms of GaN-Based LEDs After Accelerated DC Current Aging[END_REF]. However, the origin of the deep levels responsible for the degradation of LEDs was not univocally identified, and several efforts are currently in progress in this direction. Furthermore, investigations carried out by means of Secondary Ion Mass Spectroscopy (SIMS) suggested that also the penetration of dopant towards the active layer of the devices, activated by the stress test, can play a role in determining LED degradation [START_REF] Lee | Effects of Mg dopant on the degradation of InGaN multiple quantum wells in AlInGaN-based light emitting devices[END_REF]. In particular, it was suggested that the diffusion of acceptor dopant (Magnesium) through dislocations in the quantum well region, might determine a significant increase in non-radiative components, and the subsequent degradation of the efficiency of the devices.

InGaN-based LED chips can degrade also when exposed to reverse-bias, as suggested by some recent reports [START_REF] Cao | Defect generation in InGaN/GaN light-emitting diodes under forward and reverse electrical stresses[END_REF][START_REF] Meneghini | Degradation of High-Brightness Green LEDs Submitted to Reverse Electrical Stress[END_REF]. In order to investigate the degradation mechanisms activated by reverse-bias, we have submitted a number of InGaN-based LEDs to stress under constant current and constant voltage level. We have used stress voltage levels in the range -20 V / -45 V, and stress current density levels in the range between -0.3 A/cm 2 and -2.4 A/cm 2 . Results indicated that LEDs can show a remarkable increase in reverse current, when they are submitted to negative-bias stress. As an example, in Figure 8 we report the I-V curves measured in the reversebias region on one LED submitted to stress under constant negative current. The measured increase in reverse current corresponds to a significant decrease in the breakdown voltage. On the other hand, reverse-bias stress does not significantly affect the forward-bias electrical characteristics (and the forward-bias operating voltage) of InGaN-based LEDs (see the I-V curves in Figure 9). Experimental data indicated that the optical performance of LEDs is only slightly affected by the reverse-bias stress: even samples aged under significantly high reversecurrent densities (up to -2.4 A/cm 2 ), showed a limited decrease in optical power (see Figure 10). The significant degradation of the reverse-bias electrical characteristics of LEDs was explained according to the following interpretation [START_REF] Cao | Defect generation in InGaN/GaN light-emitting diodes under forward and reverse electrical stresses[END_REF][START_REF] Meneghini | Degradation of High-Brightness Green LEDs Submitted to Reverse Electrical Stress[END_REF]: when LEDs are submitted to reverse-bias stress, current flows by tunneling through localized leakage paths, related to the presence of structural defects [START_REF] Meneghini | Degradation of High-Brightness Green LEDs Submitted to Reverse Electrical Stress[END_REF]. Injected carriers are significantly accelerated by the high electric field present under reverse-bias conditions, and can achieve enough energy to interact with the lattice and induce the generation of point defects. Defect generation takes place close to the pre-existing leakage paths responsible for reverse-current conduction. This mechanism induces a significant increase in the reverse-leakage current of LEDs submitted to negative-bias stress. On the other hand, no significant modification is detected in the forward-bias electrical and optical characteristics of LEDs as a consequence of reverse-bias stress. This can be explained by considering that (i) degradation interests nanometer-size regions, which are considerably small with respect to the whole device area; (ii) under forwardbias conditions, the impedance of the junction is low compared to that of generated defective leakage paths. For this reason, the forward-bias behavior of LEDs is dominated by the conduction and recombination mechanism of the LED junction, rather than by the presence of defective tunneling paths.

Degradation of the package and of the phosphors

One of the core elements of a white LED structure is the phosphorous layer used for the conversion of blue light into white light. Furthermore, the external efficiency of white LEDs is maximized if LEDs are placed in reflective packages, with optimized optical properties. Recent reports [START_REF] Meneghini | Stability and performance evaluation of high-brightness light-emitting diodes under DC and pulsed bias conditions[END_REF][START_REF] Ishizaki | Lifetime estimation of high power LEDs[END_REF][START_REF] Hu | Electrical, optical and thermal degradation of high power GaN/InGaN light-emitting diodes[END_REF][START_REF] Trevisanello | Thermally activated degradation and package instabilities of low flux LEDs[END_REF] indicate that the package/phosphors system can significantly degrade during LED lifetime. This can result in a significant decrease in LED efficiency, and in possible modifications of the chromatic properties of the devices.

Degradation of the phosphors and of the package is mostly correlated to thermal effects, and is particularly present when heat dissipation is not properly optimized. Phosphors and package usually degrade when they are exposed to temperatures in the range between 100 °C and 200 °C [START_REF] Meneghini | Stability and performance evaluation of high-brightness light-emitting diodes under DC and pulsed bias conditions[END_REF][START_REF] Trevisanello | Accelerated Life Test of High Brightness Light Emitting Diodes[END_REF][START_REF] Ishizaki | Lifetime estimation of high power LEDs[END_REF][START_REF] Meneghini | High temperature electro-optical degradation of InGaN/GaN HBLEDs[END_REF][START_REF] Hu | Electrical, optical and thermal degradation of high power GaN/InGaN light-emitting diodes[END_REF][START_REF] Trevisanello | Thermally activated degradation and package instabilities of low flux LEDs[END_REF]. On the other hand, within this temperature range the efficiency of the blue LED chip is stable over storage time [START_REF] Meneghini | Reversible degradation of GaN LEDs related to passivation[END_REF]. Therefore, the most convenient way to study the degradation of the package/phosphors system is to carry out "purely thermal" stress tests, by submitting the LEDs to high temperatures without any applied bias. In this way, degradation can be only ascribed to the worsening of the optical properties of the package and of the phosphors.

The Spectral Power Distribution (SPD) of a white LED is constituted by the superposition of a blue emission band, centered around 460 nm, and a broad yellow-green peak, related to the luminescence of the phosphorous material (see the black line in Figure 11, as an example). In general, high temperature storage can determine significant modifications in the spectral output of a white LED. As an example, in Figure 8 we report the SPD of a state-of-the-art white LED, submitted to stress at 140 °C, no bias. Stress was found to induce both a decrease in the external efficiency of the white LED, and modification in the shape of the electroluminescence spectrum.

The intensity of the blue and yellow luminescence peak showed a different percentage variation during stress time: in Figure 12 (a) we report -for the same device -the decrease in the intensity of blue and yellow luminescence induced by high temperature treatment. Data are referred to the same sample as in Figure 11. As can be easily understood, besides the overall optical power decrease, stress induced a significant decrease in the intensity of the phosphor-related luminescence with respect to the main blue emission peak (Figure 12 (b)). This corresponds to a shift of the chromatic coordinates of the analyzed LEDs towards bluish light [START_REF] Meneghini | Extensive analysis of the degradation of phosphor-converted LEDs[END_REF].

In most of the cases, the degradation of the spectral output of white LEDs can be ascribed to (i) the browning of the material used for the incorporation of the phosphors, (ii) or to the darkening of the package, with subsequent worsening of its reflective properties. Of course, these degradation modes can take place also when devices are submitted to stress at moderate current levels (i.e. within the nominal operating range), with junction temperatures greater than 100-120 °C. In Figure 13 and 14 we report two examples, obtained on commerciallyavailable devices aged under similar conditions. As a consequence of stress, the device in Figure 13 showed a significant darkening of the package material, without any visible degradation of the phosphorous layer. As described in [START_REF] Meneghini | High temperature electro-optical degradation of InGaN/GaN HBLEDs[END_REF], a similar degradation process can result in a reduced optical output, since after stress the reflective properties of the package are significantly altered. On the other hand, the LED in Figure 14 showedas a consequence of stress -a significant browning of the phosphorous layer in proximity of the center of the emitting area. This process, related to the high temperatures reached by the junction during operation, can result in a significant quenching of device luminescence, and in the modification of the spectral properties of the LED (see Figure 11 and12). Degradation processes related to the phosphors/package system are significantly thermally activated, as reported by a number of authors [START_REF] Ishizaki | Lifetime estimation of high power LEDs[END_REF][START_REF] Meneghini | High temperature electro-optical degradation of InGaN/GaN HBLEDs[END_REF][START_REF] Meneghini | Extensive analysis of the degradation of phosphor-converted LEDs[END_REF]: typical activation energy values range in the interval 0.47-1.5 eV, depending on the analyzed device technology. Stress tests carried out on moderately-biased devices indicated that the Time-To-Failure (TTF) of white LEDs is significantly dependent on the operating junction temperature, with no significant dependence on the stress current level (at least within the nominal operating range). As an example, in Figure 15 we report the Arrhenius plot for the TTF 50% (time necessary for a 50 % decrease in luminous flux) for a number of white LEDs submitted to stress at different current and junction temperature levels. From the slope of this diagram, the activation energy of the degradation process can be extrapolated (equal to 470 meV for this specific device technology).

ESD Failure of LEDs

Recent reports [START_REF] Meneghesso | Electrostatic Discharge and Electrical Overstress on GaN/InGaN Light Emitting Diodes[END_REF][START_REF] Horng | GaN-Based Power LEDs With CMOS ESD Protection Circuits[END_REF][START_REF] Jeon | The effect of the internal capacitance of InGaN-light emitting diode on the electrostatic discharge properties[END_REF] indicate that advanced LED structures -especially those with high indium contentcan be particularly susceptible to ESD events. The ESD stability of LEDs is usually evaluated by means of the Human Body Model (HBM): the human body is modeled as a 100 pF capacitor, that is discharged on the device through a 1.5 kΩ resistance and a switch. The ESD robustness is defined as the maximum voltage a device can withstand before ESD failure. While HBM can be an excellent predictor of the ESD robustness of an electronic device, by means of this method no information on the physical mechanism responsible for failure and on the electrical behavior of LEDs at high current/voltage levels can be extrapolated [START_REF] Ashton | Transmission Line Pulse measurements: a tool for developing ESD robust integrated circuits[END_REF]. For this reason, over the last decades, another method has been widely adopted for a better investigation of the characteristics of electronic devices submitted to ESD events: the Transmission Line Pulse (TLP) method [START_REF] Amerasekera | ESD in Silicon Integrated Circuits[END_REF]. The TLP method is based on discharging a (pre-charged) transmission line on the LED under test. By the TLP method it is possible to generate ESD-like pulses with increasing voltage amplitude. The length of the pulses (100 ns for the results described in the following) depends on the length of the transmission line used for the tests. The TLP method has the unique advantage of permitting the accurate control and measurement of the characteristics of the devices at extremely high current levels. For this reason, TLP method is adopted in many research laboratories, to study the effect of ESD on the electrical characteristics of electronic devices. In the following we will mainly refer to results on the ESD robustness of LEDs obtained by means of the TLP method.

In Figure 16 we report the pulsed Current-Voltage (I-V) characteristics measured under forward and reverse bias on two InGaN-based LEDs. Measurements were taken by means of a Transmission Line Pulse system, i.e. by applying a series of (100 ns) voltage pulses with increasing amplitude to the devices. In the forward-bias region (Figure 16 (a)), the I-V curve has a linear behavior: at high current levels, the electrical behavior of LEDs is dominated by the series resistance of the junction and of the measuring system (approx. 6 Ω in this case), while the voltage drop on the junction is negligible. Under forward-bias ESD events, devices can withstand a TLP current in excess of 10 A without reaching the failure. On the other hand, under reverse-bias, the pulsed I-V curve of the LED (Figure 16 (b)) has a nearly exponential shape, with a turn-on voltage around -70 V and a significant series resistance component. LEDs can show a low failure threshold, when submitted to reverse-bias ESD. In the I-V curve in Figure 16 (b), ESD failure can be recognized as a sudden decrease in the impedance of the device, with subsequent snap-back of the electrical characteristics. Device failure under reverse-bias ESD events is usually explained by considering that reverse-current conduction occurs via small-size leakage paths, related to the presence of structural defects, such as dislocations/V-defects or Indium related-defects [START_REF] Meneghini | A review on the physical mechanisms that limit the reliability of GaN-based LEDs[END_REF]. The position of these paths can be identified by emission microscopy, as suggested by recent research reports [START_REF] Meneghini | Leakage current and reverse-bias luminescence in InGaN-based lightemitting diodes[END_REF].

The injection of reverse current through defective states gives rise to a weak luminescence signal (Figure 17).

Reverse-bias luminescence is localized in specific positions, corresponding (i) to the presence of preferential paths responsible for leakage (and ESD) current conduction (related to the presence of structural defects) or (ii) to the presence of morphological defects (pits) that are known to promote light extraction. Under reversebias ESD events, an high current density flows through nanometer-size defective paths: this results in a subsequently high power dissipation, that can lead to the localized failure of the junction [START_REF] Meneghini | A review on the physical mechanisms that limit the reliability of GaN-based LEDs[END_REF]. After ESD failure, devices behave as short circuits, and failure cannot be recovered. The position of the failed region can be identified by means of Scanning Electron Microscopy (SEM, Figure 18), or by optical microscopy: in many cases the failure point is located in correspondence of pre-existing structural defects [START_REF] Meneghini | A review on the physical mechanisms that limit the reliability of GaN-based LEDs[END_REF]. Several methods have been proposed with the aim of improving the ESD robustness of InGaN-based LEDs, including (i) the use of a silicon-based protection circuit in parallel to the LED [START_REF] Horng | GaN-Based Power LEDs With CMOS ESD Protection Circuits[END_REF], (ii) the use of optimized growth procedures, capable of reducing the defectiveness of the active layer and the Dislocation Density [52,[START_REF] Meneghini | Soft and Hard Failures of InGaN-Based LEDs Submitted to Electrostatic Discharge Testing[END_REF] and (iii) a careful optimization of junction capacitance, that can result in an improved ESD performance [START_REF] Jeon | The effect of the internal capacitance of InGaN-light emitting diode on the electrostatic discharge properties[END_REF].

Discussion and conclusions

With this paper we have presented an analysis of the physical processes that limit the reliability of GaN-based LEDs. State-of-the-art LEDs are complex devices, constituted by several components. All of these components can degrade during stress time: as a consequence of ageing, LEDs can show a reduction of the total luminous flux and a worsening of the chromatic properties. Degradation may be ascribed to several driving forces, as briefly summarized in the following:

1. Current flow through the active layer of the LEDs may induce the generation/propagation of defects, with subsequent increase in the non-radiative recombination rate. It was recently shown that LED degradation can be correlated to significant modification of the apparent charge distribution in the quantum-well region [START_REF] Rossi | Influence of short-term low current dc aging on the electrical and optical properties of InGaN blue light-emitting diodes[END_REF][START_REF] Rigutti | Redistribution of multi-quantum well states induced by current stress in InGaN/GaN lightemitting diodes[END_REF], that may be due to the increase in the concentration of deep levels [START_REF] Rossi | Influence of short-term low current dc aging on the electrical and optical properties of InGaN blue light-emitting diodes[END_REF],

or to the diffusion of dopant or impurities towards the active layer of the LEDs [START_REF] Lee | Effects of Mg dopant on the degradation of InGaN multiple quantum wells in AlInGaN-based light emitting devices[END_REF] 2. Temperature can play a significant role in limiting the reliability of white LEDs. When LEDs are exposed to high temperature levels (or operated with non-optimized thermal dissipation) the optical properties of the package and of the material used for the encapsulation of the phosphors can severely degrade [START_REF] Trevisanello | Accelerated Life Test of High Brightness Light Emitting Diodes[END_REF][START_REF] Ishizaki | Lifetime estimation of high power LEDs[END_REF][START_REF] Hu | Electrical, optical and thermal degradation of high power GaN/InGaN light-emitting diodes[END_REF]. This can result in a significant reduction of the luminous flux emitted by the devices, and in modifications of the spectral characteristics of the LEDs. Degradation of the package and phosphors system is generally thermally activated, with activation energies in the range 0.45-1.5 eV depending on the analyzed device technology 3. Reverse-bias ESD current can represent a critical driving force for catastrophic LED failure [START_REF] Meneghesso | Electrostatic Discharge and Electrical Overstress on GaN/InGaN Light Emitting Diodes[END_REF][START_REF] Horng | GaN-Based Power LEDs With CMOS ESD Protection Circuits[END_REF][START_REF] Jeon | The effect of the internal capacitance of InGaN-light emitting diode on the electrostatic discharge properties[END_REF].

When LEDs are submitted to reverse-bias ESD events, a significantly high reverse current flows through localized leakage paths, related to the presence of structural defects. This may result in an extremely high and localized power dissipation, which determines the catastrophic shortening of the junction. An improvement of the quality of the active layer (reduction of the concentration of defects), and/or the use of suitable ESD-protection structures can result in a significant improvement of the robustness of LEDs towards ESD events.

The results described within this paper and in the quoted references indicate that, despite the excellent potential of LEDs, a number of factors can limit the reliability of these devices. Some of the degradation mechanisms described above, including the generation of defects in the active layer and the ESD failures, are strongly related to the quality of the heterostructure. A significant increase in the reliability of the devices may be obtained only through an improvement of the growth and processing procedures.

On the other hand, the thermally-activated degradation mechanisms can be avoided (or at least slowed down) through a careful optimization of the thermal management process. Since the activation energies for the degradation processes related to the package and the phosphors can be quite high, a reduction of the operating temperature can make a significant difference in terms of device reliability. In conclusion, if on one hand the manufacturer is responsible for the degradation processes related to the quality of the LED chip, on the other hand the designer of the final LED application/luminaire can play a significant role towards the improvement of the reliability LED-based lamps, through a careful optimization of the operating conditions and of the thermal dissipation process. Output Power (%)

Figure captions

Stress Time (h)

Figure 1 :

 1 Figure 1: SEM image of a power LED chip, mounted in its package. The image was taken after the removal of the plastic lens, and is referred to a 1 mm 2 LED chip

Figure 2 :Figure 3 :

 23 Figure 2: optical power degradation curves measured on three different families of commercially-available white LEDs. Devices were stressed at a constant current level of 100 A/cm 2 , with an ambient temperature of

Figure 4 :

 4 Figure 4: optical power degradation measured during stress at constant current level on one of the bare InGaN-

Figure 5 :

 5 Figure 5: optical power degradation measured during stress at different case temperature levels

Figure 6 :

 6 Figure 6: capacitance-voltage characteristics measured during stress at constant current level on one of the InGaN-based LEDs analyzed within this work (f=1 MHz)

Figure 7 :

 7 Figure 7: variation of charge concentration in the quantum well region, plotted as a function of the optical

Figure 8 :Figure 9 :Figure 10 :Figure 11 :

 891011 Figure 8: current density vs voltage characteristics measured (in the reverse-bias region) on an InGaN-based LED submitted to negative-bias stress (stress conditions are -0.3 A/cm2, room temperature) Figure 9: current density vs voltage characteristics measured (in the forward-bias region) on an InGaN-based LED submitted to negative-bias stress (stress conditions are -0.3 A/cm2, room temperature)

Figure 12 :

 12 Figure12:(a) variation of the integral of the blue and yellow luminescence for a white LED submitted to stress at 140 °C, no bias. (b) Variation of the ration between the intensity of the yellow and blue peak measured on a white LED submitted to stress at 140 °C, no bias. Data are referred to the same LED as in Figure11

Figure 13 :Figure 14 :Figure 15 :Figure 16 :Figure 17 :Figure 18 :Figure 1 :

 1314151617181 Figure 13: micrograph of a white LEDs. Left: before stress. Right: after stress at 100 A/cm 2 , 100 °C Figure 14: micrograph of two white LEDs. Top: untreated sample. Bottom: after stress at 100 A/cm 2 , 120 °C Figure 15: Arrhenius plot for the Time-To-Failure of white LEDs submitted to high temperature/moderate current stress. As can be noticed, Time-To-Failure has only a slight dependence on stress current level. On the

Figure 2 : 2 Figure 3 : 2 Figure 4 : 2 Figure 5 :

 2232425 Figure 2: optical power degradation curves measured on three different families of commercially-available white LEDs. Devices were stressed at a constant current level of 100 A/cm 2 , with an ambient temperature of 80 °C. Each data point is the average obtained by measuring 4 identical samples (measuring current level is 70 A/cm 2 )

Figure 6 :

 6 Figure 6: capacitance-voltage characteristics measured during stress at constant current level on one of the InGaN-based LEDs analyzed within this work (f=1 MHz)

Figure 7 :

 7 Figure 7: variation of charge concentration in the quantum well region, plotted as a function of the optical power decrease measured on one InGaN-based LED submitted to constant current stress

Figure 8 :Figure 9 : 2 Figure 10 :Figure 11 : 2 0Figure 12 :

 8921011212 Figure 8: current density vs voltage characteristics measured (in the reverse-bias region) on an InGaN-based LED submitted to negative-bias stress (stress conditions are -0.3 A/cm 2 , room temperature)

Figure 14 :

 14 Figure 14: micrograph of two white LEDs. Top: untreated sample. Bottom: after stress at 100 A/cm 2 , 120 °C

Acknowledgments

This work was partially supported by the CARIPARO Fundation, and by the ALADIN project (Italian Ministry of Industry). The authors kindly acknowledge Dr. Berthold Hahn and Dr. Rainer Butendheich (OSRAM OptoSemiconductors Regensburg, Germany), Dr. Nicola Trivellin and Dr. Augusto Tazzoli (University of Padova, Italy), Prof. Massimo Vanzi and Dr. Giovanna Mura (University of Cagliari, Italy) for their fruitful contributions to the research activity.

Measurements were carried out by the TLP method (100 ns voltage pulses)

Failed region


Kyle G Webber

Emil Aulbach

Jürgen Rödel

High temperature blocking force measurements of soft lead zirconate titanate

Piezoelectric actuators outperform other technological solutions in the area of high speed, high force, and high accuracy displacement, but are only able to generate strains of about 0.2%. The load capability is generally quantified in terms of a blocking force, which is the force sustained under electric field at zero displacement. Stress-strain curves in a temperature regime from room temperature until 150°C on electrically loaded soft lead zirconate titanate (PZT) are generated to determine the blocking stress. The ensuing non-linear behavior is discussed in terms of ferroelectric and ferroelastic switching and contrasted to idealized linear constitutive behavior as often assumed by manufacturers. The blocking stress is shown to increase with temperature due to an additional stiffening effect as a function of electric field.

The actual mechanical work done is found to be larger than in the idealized case where linear constitutive behavior is assumed.

Introduction

Strong electromechanical coupling in ferroelectric materials, i.e., lead zirconate titanate (PZT), makes them ideal candidates for actuator applications, such as diesel fuel injection systems [1,2]. Typical piezoelectric actuators consist of a cofired multilayer design, where the internal electrodes terminate abruptly within the bulk of the actuator and are used to electrically activate thin, stacked layers of piezoelectric ceramic material [3]. Variation in the thickness of the layers can reduce the required actuation voltage while maintaining the necessary maximum electric field, which is typically on the order of 2 to 3 kV mm -1 for doped PZT [4].

Multilayer actuators, currently being implemented into diesel injection systems, have a number of advantages over existing electromagnetic solenoid systems, such as short actuation time and greater fuel mass injection precision, resulting in increased fuel efficiency, lower engine noise, and decreased CO 2 emissions [1,5]. However, in addition to elevated ambient temperatures found in a diesel engine, piezoactuators can also experience "self-heating" due to the loss factor of donor-doped PZT (soft PZT) [6,7]. Acceptor-doped PZT (hard PZT) displays lower losses as well as lower piezoelectric coefficients, reducing both the self-heat generation and the overall strain that can be obtained from a piezoactuator. Previous studies have shown temperature increases for multilayer stack actuators of PZT on the order of 60 to Confidential: not for distribution. Submitted to IOP Publishing for peer review 22 July 2010 100 °C, depending on actuator size, actuation frequency, actuation time, and duty cycle [6][7][8][9][10], which can impact actuator characteristics.

Actuator applications have a number of stringent requirements, including actuation response time, stroke amplitude, and blocking force. The free displacement (Df) and the blocking force (F b ) are common values supplied by the manufacturer for specific piezoactuator models. Because displacement and force are measured, not strain and stress, comparison between different commercially available actuators with different materials, geometries, and insulating materials (e.g., end cap material and insulating lacquer) can be difficult. Blocking stress and free strain, however, are material, not application, specific parameters that can be directly compared. Figure 1 shows the typical schematic representation of the force-displacement relationship presented by manufacturers. Most often the free displacement is measured during the application of a specific driving voltage on a poled sample, followed by the application of a monotonically increasing mechanical load until the actuator height is reduced back to the original value of the poled, zero electric field state. The load required to reduce the electric field-induced displacement to zero is termed the blocking force. A line is drawn between these two points, which represents the assumed operational range of this particular actuator. With increasing applied voltage there is an increase in both the free strain and the blocking force.

During the electrical activation of a piezoactuator work is done on a spring load, represented in the inset (Fig. 1) as a linear spring element with a spring constant k, which is equal to the area below the load-displacement curve. For a linear spring load this is one half of the product of the force applied and the distance through which it acts. When the spring constant is zero there is no force required to compress the spring. In this situation the displacement of the actuator is equivalent to the free displacement at activation voltage V, ( )

V D f
, and no work is done. When the spring constant is infinite there is no displacement of the actuator. In this case the force on the actuator is equivalent to the blocking force at activation voltage V, ( )

V F b
, and there is again no work done. However, for realistic loads that lie between these two limits the maximum achievable work occurs at one half of the blocking force and free displacement for the activation voltage used, often termed an impedance matched spring load [11]. The maximum work done for other nonlinear loads, however, does not necessarily occur exactly at one half of the blocking force and free displacement. The linear force-displacement model is obviously highly idealistic; ignoring much of the nonlinear behavior inherent in ferroelectric materials with a large change in Young's modulus during application of compressive stresses [12][13][14].

Ferroelectric/ferroelastic lead zirconate titanate (PZT) with various dopants has been utilized for actuator applications due to exceptional material behavior over a range of temperatures [15]. However, macroscopic constitutive behavior of PZT in response to electric field [15,16] and stress [13,14,17] has been shown to depend strongly on temperature. A temperature increase results in a decrease in the coercive electric field [16] as well as an observed increase in the maximum strain obtained during unipolar cycling [15], both principally due to an increase in domain wall mobility. However, in addition to their ability to ferroelectrically switch in response an external electric field, ferroelastic domain switching due to mechanical loads is also possible. In application, actuators usually operate under a compressive prestress to reduce the tensile stresses at electrode edges. This compressive stress enhances back-switching during electrical loading with the effect that multilayer actuators exhibit a maximum in achievable strain at approximately -30 MPa at room temperature [18,19]. However, at elevated temperatures a modest compressive preload (~5 MPa) can be large enough to cause a loss of the remanent state [13], necessitating an additional poling cycle.

This study presents high temperature ferroelectric and ferroelastic data used to determine the free strain and blocking stress of a commonly utilized material in piezoactuators.

To date there have been few studies of high temperature ferroelasticity [13,14,17], despite the increasing importance of ferroelectrics in certain automotive applications. To this end, this study focuses on experimentally measuring the high temperature blocking stress of bulk polycrystalline donor-doped PZT commonly found in commercially available multilayer actuators. Specimens are applied with large field electrical and mechanical loads while the longitudinal strain is measured at various temperatures. Results are contrasted with common industry measurement procedures.

Experimental Methods

Experimental measurements were conducted on a commercial-grade soft PZT, Pb 0.99 (Zr 0.45 Ti 0.47 (Ni 0.33 Sb 0.67 ) 0.08 )O 3 (PIC 151, PI Ceramics, Lederhose, Germany) with a composition in the vicinity of the morphotropic phase boundary. This material was chosen due to the excellent electromechanical properties, i.e., d 33 500 pC/N, and its wide use in commercially produced actuators. Previous XRD measurements have shown a loss in spontaneous strain between 300 and 320 °C, corresponding with the Curie temperature [16].

Cylindrical samples with a diameter of approximately 5.9 mm and a height of 6 mm were core drilled from a PZT plate for mechanical testing. Samples electrically tested were ground to a height of 3 mm. Prior to electromechanical testing each sample was annealed at 600 °C for 1 hr, with a cooling rate of 50 °C hr -1 . Annealing was performed to ensure a fully depoled sample and to help eliminate possible residual stress induced during specimen preparation.

Samples were sputtered with an Ag electrode on both circular faces perpendicular to the 6 mm axis.

During this investigation a custom built differential dilatometer setup was used to measure the longitudinal strain of each sample in response to applied electric field and compressive stress (Fig. 2). The experimental arrangement, previously described in detail [13], was fitted with a silicone oil bath enabling the measurement of the stress-strain behavior in response to an applied electric field. The sample was positioned between a tungsten carbide platform and conical loading die, shown in Fig. 2 directly above and below the specimen.

Strain was measured as the relative displacement by an LVDT located well outside of the heating chamber. Alumina rods contacted the bottom of the platform and the bottom of the conical loading die, essentially measuring the combined strain of the sample and the platform.

Additional experiments were conducted at each temperature under consideration to determine the strain of the platform without a sample. This was used to correct the strain measurements of the PZT samples.

To determine blocking force it was required to apply electrical and mechanical loads simultaneously. A schematic of the strain as a function of the electric field during the testing procedure is shown in Fig. from an initial stress of -3.7 MPa to a maximum stress of approximately -112 MPa.

Electromechanical testing was done at 25, 50, 100, and 150 °C. Each temperature and electric field loading combination was repeated to ensure measurement repeatability.

It was found that at elevated temperatures without the application of an electric field there was significant creep of PZT accelerated by the mechanical preload, resulting in the time-dependent loss of the remanent state of the poled sample. At lower temperatures (25 and 50 °C) this was not a problem. To alleviate this issue, additional samples were electrically tested in a silicone oil bath to determine the stress-free unipolar electric field-strain behavior as a function of temperature. These measurements were used to calibrate the initial free strain measurements of the mechanical loading experiments. At 25 and 50 °C the additional free strain measurements corresponded well with the free strain determined in the load frame. This will be discussed in further detail in the following sections. Specimens were poled with an electric field of 3 kV mm -1 for ten minutes prior to unipolar electric field cycling, which consisted of five triangular loading cycles with a maximum electric field of 3 kV mm -1 and a frequency of 0.05 Hz. During testing the strain was measured in response to electric field at 25, 50, 100, and 150 °C. A minimum of five samples were tested at each temperature to ensure measurement consistency.

Results

Due to the above mentioned creep at elevated temperatures additional quasi-static unipolar electric field-strain measurements were performed. Figure 4 displays representative unipolar hysteresis curves at 25 and 150 °C. From these measurements the free strain was determined at various levels of electric field represented in Fig. 4 as the points on the loading curve. It can be observed that there was an increase in measured free strain at each electric field level (0.5, 1, 1.5, 2, 2.5, and 3 kV mm -1 ) with an increase in temperature from 25 to 150 °C.

At each of the electric field levels and temperatures under consideration the free strain was determined from the unipolar strain-electric field hysteresis measurements (Fig. 5a). For each electric field level there is an apparent maximum in the achievable strain at 100 °C. This trend can be more clearly observed when the free strain is normalized by the maximum strain at the corresponding electric field value (ε max ), where it can be seen that the maximum strain occurs at 100 °C for 1, 2, and 3 kV mm -1 (Fig. 5b). Although not shown, this trend was also observed for the other electric fields as well. Below 100 °C there is an obvious increase in ratio of free strain to maximum strain with increased electric field loading. At 150 °C, however, there is a decrease in measured free strain with respect to the maximum strain for each electric field loading level.

The ferroelastic constitutive behavior in response to a constant electric field was characterized as a function of temperature. Figure 6 displays representative stress-strain measurements for various electric field levels at 25 °C. It can be clearly observed that with increasing electric field there is a corresponding increase in both the free strain (strain at zero stress) and the blocking stress (stress at zero strain). In addition, the measured stress-strain behavior is nonlinear and depends on the applied electric field and temperature. Due to the limitations of the measurement setup the free strain does not begin from zero stress. This represents a known error. The tangent modulus was measured at the initial stress (-3.7 MPa) and used to approximate the material behavior at low loads. The point where the dotted line crossed the x-axis was assumed to be the free strain.

Discussion

The electrical activation of ferroelectric materials has both an intrinsic and extrinsic component. During the initial application of an electric field on an unpoled specimen there is large scale domain switching (extrinsic) at the coercive field resulting in nonlinear strainelectric field behavior observed during the poling process, shown schematically in Fig. 3 (dashed line a-b), in addition to intrinsic contributions. However, during the determination of the blocking stress the remanent strain is taken as the reference strain. This neglects the large strain gains from initial, large-scale domain reorientation during the determination of the stress required to bring the strain back to zero (Fig. 3). This is because piezoactuators, where blocking stress is an important characteristic, are actuated in the poled state by a unipolar electric field. It can be observed from Fig. 5 that there is an increase in the free strain up to 100 °C, followed by a decrease at 150 °C. Previous experimental measurements have shown an increase in poling strain with temperature for various compositions of LaSr-doped PZT around the morphotropic phase boundary (MPB) [15]. This increase in poling strain, however, is not linear and was shown to saturate, dependent on PZ/PT ratio and dopant content. This is due, in part, to the shape of the MPB [START_REF] Jaffe | Piezoelectric Ceramics[END_REF], which curves towards the rhombohedral phase. As the temperature is increased there can be a shift in phase towards tetragonal, out of the MPB region corresponding to a decrease in electromechanical properties.

Utilizing the electrical and mechanical measurements presented, the blocking stress was determined as a function of constant electric field and temperature (Fig. 7). The results from each measurement are presented on the same plot to demonstrate repeatability. It can be clearly observed that at each temperature there was an approximately linear relationship between applied electric field and blocking stress measured as -22.7, -24.2, -27.2, and -28.6 N m -1 V -1 for 25, 50, 100, and 150 °C, respectively. Similar linear blocking force behavior was previously predicted, although not experimentally observed, for bending actuators at room temperature [START_REF] Wang | [END_REF]. There have been numerous additional investigations into the observed blocking force-electric field relationship observed in bending actuators [22][23][24][25]. In addition, there is an apparent increase in blocking stress with temperature at each electric field level. This is due to the increase in free strain obtained with temperature as well as changes in the ferroelectric and ferroelastic behavior. At temperatures up to 100 °C there was an increase in free strain, corresponding with the increase in blocking stress. However, at 150 °C there was an observed increase in blocking stress as well as a decrease in free strain. This indicates that the applied electric field at 150°C increased the coercive stress required to ferroelastically switch domains, thereby increasing the stiffness of the sample throughout the tested stress range [18,[26][27][28]. It is important to note here, however, that the initial Young's moduli at 100 and 150 °C were measured as 36.2 and 36.4 GPa, respectively. The increase in blocking stress at 150 °C was due to the increased effect of the electric field with temperature. With the increase in temperature additional mechanical energy was required to ferroelastically reorient the electrically activated domains, leading to a stiffer system. This also indicates that thermal, in addition to electrical [18], fluctuations will lead to changing actuator stiffness.

The constitutive behavior of the ferroelectric materials used in piezoactuators is nonlinear (Fig. 6). There are two potential significant impacts of nonlinear ferroelasticity on the operation of actuators utilizing ferroelectric materials: (1) the mechanical work done on the load (linear spring) and ( 2) the spring constant required to impedance match the actuator are different than in the idealized model (Fig. 8). The ratio of ideal to actual mechanical work done on a linear spring is a function of both applied electric field and temperature (Fig. 9a).

At low electric field values, or elevated temperatures, the actual work done approaches that of the idealized model (Fig. 9a). In both cases, low electric field and high temperature, this is due to an approximately linear stress-strain behavior in the considered stress region. At low electric field levels (0.5 kV mm -1 ) the free strain is relatively small, meaning that only the initial portion of the ferroelastic constitutive behavior is important for determination of the blocking stress. At mechanical loads below the coercive stress, approximately -5 to -20 MPa for PZT at room temperature, dependant on dopant content [29][30][31], approximately linear stress-strain behavior is found. However, at 25 and 50 °C there is a significant observed decrease in the ratio of ideal to actual work at 1 kV mm -1 , which is not seen at 100 and 150 °C.

This is due to a decrease in coercive field at elevated temperatures [16], which results in an additional electrical stabilization of ferroelectric domains. Previous studies have shown that the coercive stress is more stable with increasing temperature [14], decreasing approximately 20 % from 25 to 200 °C, than the electric poling field [16], which decreases by approximately 51 % from 25 to 200 °C. This indicates that with increasing temperature the influence of the constant electric field increases, while the effect of the stress remains relatively constant. This necessitates increased mechanical loads to ferroelastically switch an electrically activated domain at higher temperatures, thereby increasing the linearity (stiffness) of the PZT specimens throughout the stress range tested. At each temperature there was a decrease in the ideal to actual mechanical work ratio, although, as seen in Fig. 9a, this ratio is generally larger at higher temperatures. This is due to the increase in stiffness with increasing electric field, with this effect being more dominant at elevated temperatures.

Interestingly, however, despite the increase in the potential maximum work at elevated thermal and electrical loads it was found that the linear spring constant required for impedance matching was approximately equivalent for the ideal and actual material behavior, as shown in Fig. 9b. The approximate maximum variation between the ideal and actual cases was approximately 4%. This effect was not dependent on electric field or temperature, indicating that in terms of determining the ideal impedance matched load the idealized material model is sufficient.

Conclusion

The longitudinal strain of a soft PZT commonly used in piezoactuators was measured in response to unipolar electric field and compressive mechanical stress at various temperatures.

The electromechanical measurements were performed to determine the blocking stress as a function of electric field and temperature. The significant results are as follows:

(i) Increasing electric field and temperature both increased the measured blocking force, due to the increase in material stiffness and the increased stabilization of the poled domain state by the applied electric field at elevated temperatures;

(ii) There was a linear relationship at each temperature tested between the applied electric field and the blocking force;

(iii) The mechanical work done as computed from the actual nonlinear constitutive behavior exceeded the work computed from the ideal linear spring model used commonly by manufacturers by up to 10 %, depending on temperature and applied electric field;

(iv) The linear spring constant required to impedance match the PZT material was reasonably determined from the simple linear force-displacement relationship commonly used by manufacturers.

Displacement

Force V 0 V 1 > V 0 ( ) 0 V D f ( ) 0 V F b ( ) 1 V F b W max (V 1 ) W max (V 0 ) ( ) 2 0 V D f ( ) 2 0 V F b ( ) 2 1 V D f ( ) 2 1 V F b ( ) 1 V D f D k k Figure 2.
Experimental arrangement for measuring longitudinal strain in response to electric field and stress at elevated temperatures. As an indication of scale the specimen height parallel to the applied load is 6 mm.

3 .

 3 Each specimen was initially unpoled (Point a). During testing the PZT samples were poled at the temperature of interest with an electric field of 3 kV mm -1 for ten minutes (Point b). The nonlinear poling curve is shown in Fig. 3 as the dashed line between Points a and b. Following the poling stage the electric field was removed and the measured displacement was set to zero (Point c). The horizontal dotted line at Point cindicates the reference strain used to determine the blocking force. A constant dc electric field (0.5, 1, 1.5, 2, 2.5, and 3 kV mm -1 ) was again applied to the already poled sample (Point d), followed by the application of a uniaxial mechanical load (Point e). The strain difference between the poled, electrically unloaded state and the poled, electrically loaded state approximately equated to the free strain of the material, f ε . The mechanical load was applied monotonically to the poled, electrically activated specimen with a loading rate of 1.8 MPa s-1

Figure 1 .

 1 Figure 1. Typical force-displacement curve provided by most piezoactuator manufacturers. Please note that the force is in the compressive direction, whereas it is shown in the figure in the opposite sense.

Figure 3 .Figure 4 .Figure 5 .Figure 6 .Figure 7 .Figure 8 .Figure 9 .

 3456789 Figure 3. Unipolar electric field-strain hysteresis loop for an initially unpoled sample (Point a). The remanent strain (Point c) was used as the reference in order to determine the free strain of bulk PZT (Point d) as a function of electric field and temperature. The mechanical load required to eliminate the free strain was the blocking stress (Point e). Inset figure displays the three states (c, d, and e).important for determination of blocking stress.