Lifetime Test of Pulsewidth Modulated LEDs Supplemented With Thermal Investigations

The ability to dim LEDs is a big advantage compared to previous light sources, but it can also lead to new aging mechanisms. Due to the different coefficients of thermal expansion of the individual structural layers, the temperature cycle can negatively affect the main thermal path. In this article, we investigate how different dimming frequencies influence the aging of LEDs and to what extent they impair the thermal conductivity of structural layers belonging to different thermal time constants. In this article, the methodology of the joint examination of the integral structure function and the time constant spectrum is described, i.e., the determination of the time constants and the frequency values that expose the individual structural layers to the most mechanical stress. The theoretical results are demonstrated using an LM-80-based LED lifetime test supplemented with thermal transient testing, which is also presented in this article.


Lifetime Test of Pulsewidth Modulated LEDs
Supplemented With Thermal Investigations János Hegedüs , Gusztáv Hantos, Máté Lukács, Bence Bodnár, Gyula Lipák, and András Poppe Abstract-The ability to dim LEDs is a big advantage compared to previous light sources, but it can also lead to new aging mechanisms.Due to the different coefficients of thermal expansion of the individual structural layers, the temperature cycle can negatively affect the main thermal path.In this article, we investigate how different dimming frequencies influence the aging of LEDs and to what extent they impair the thermal conductivity of structural layers belonging to different thermal time constants.In this article, the methodology of the joint examination of the integral structure function and the time constant spectrum is described, i.e., the determination of the time constants and the frequency values that expose the individual structural layers to the most mechanical stress.The theoretical results are demonstrated using an LM-80-based LED lifetime test supplemented with thermal transient testing, which is also presented in this article.

I. BACKGROUND
T HE electrical and optical parameters of LEDs are con- stantly shifting and changing over their operation time; these effects stem naturally from their operation and physical structure.In the early lifetime period, in many cases, even a slight increase may be observed in the radiated power and luminous flux values, that is, the so-called burn-in phase.However, the subsequent life stages are usually connected with the typically strictly deteriorating tendency of the optical parameters, the rise of the forward voltage, and, as a result of these, with increasing self-heating effect.
The two-volume publication by van Driel et al. [1], [2] provides the detailed information on the reliability of The authors are with the Department of Electron Devices, Faculty of Electrical Engineering and Informatics, Budapest University of Technology and Economics, 1111 Budapest, Hungary (e-mail: hegedus.janos@vik.bme.hu).
Color versions of one or more figures in this article are available at https://doi.org/10.1109/TCPMT.2023.3278101.
Digital Object Identifier 10.1109/TCPMT.2023.3278101 semiconductor-based light sources, starting from the component level and ending with a discussion of the possible failures of the system-level products.Chang et al. [3] prepared a comprehensive study on aging of an encapsulated LED.The full-page long [ [3], Table II] summarizes the individual failure types of LEDs and their long-and short-term effects.Typical failure mechanisms of power LEDs include, among others, breaks during heating and cooling periods during the manufacturing processes [4], diffusion of dopants injected to reduce the series resistance into the quantum wells [5], or short circuits caused by electromigration of contact metallization [6], [7].Due to the different thermal expansion factors, many failure modes can occur, such as breakage of wires and ball bonds caused by active thermal cycling [8], [9] or delamination of contact surfaces [10].In addition, different plastic parts of the case absorb moisture depending on the external humidity and temperature [11], [12], [13].A change in moisture content also results in a change in volume.Different materials absorb different amounts of moisture, so they change their size to different extents.The changing temperature and humidity, therefore, create thermo-hygro-mechanical stresses in the case, which continuously fatigues the boundary layers as the number of cycles increases and in the long term can cause cracks and separation of the layers [14].The reader interested in the topic will of course find many more excellent readings, and works [15], [16], [17], [18], [19], [20], [21], and [22] are just a few examples of these.
A detailed discussion of the different LED aging mechanisms is beyond the scope of this article, but the above references surely provide copious background material and a wide range of literature review to the reader.
One of the main reasons for the fast spread of LEDs in lighting applications was their rapid increase in efficiency and efficacy, but several other factors also played an important role.Dimming possibilities and high-end reliability of these devices had a great contribution on the recent decades' market success of LED-based light sources.However, any new feature raises new questions as well: what is the relationship between high reliability and device dimmability?It may seem to be obvious that these two parameters have opposite effects, but this cannot be stated obviously.
LED dimming based on pulsewidth modulation (PWM) is indeed an industry-wide used method to set the desired illumination value and to control the overall operating point of the light source.It must not be forgotten, however, that during such operation, the LEDs typically operate in less favorable conditions than if they were driven with a constant current of a value that provides the same brightness sensation to the human eye as in the case of PWM control.
To derive the previous assumption, let us first assumegreatly simplifying the problem-that the area under the time function of the forward current connected to the device is proportional to the sense of brightness created.Thus, in the example, a 1-A forward current drive with a 50% duty cycle would give the same feeling as a 0.5-A direct current drive.However, in the case of real LEDs, it should be known that the value of efficiency and efficacy usually decreases as the forward current increases.Accordingly, the 1-A PWM drive with 50% duty cycle will not be equivalent to a 500-mA direct forward current, but to a smaller one-or at least apparently.
It is also necessary to consider the fact that in addition to the higher forward current, the forward voltage of the device is also higher, so the electrical power consumed is also higher, which could even compensate for the efficiency that deteriorates with the increase in current value and even result in a higher radiated power value.However, it should be noted that the radiated power of today's modern power LEDs typically shows a quadratic dependence on the forward current, even with the same chip temperatures.
Moreover, higher forward currents also have a higher dissipated power, meaning that the chip temperature will certainly be higher at such an operating point, so its radiated power cannot be linearly proportional either.Thus, the radiated power of the LED driven with a current of 1 A and a 50% fill factor square signal will be comparable to that of an LED driven with a 400-450-mA forward current.At the same time, the temperature of the PWM-controlled LED chip will be even higher, which further downgrades the efficiency of radiative recombinations, inflicting an additional self-heating effect.
The consequence of the above assumptions on PWM driving is active thermal cycling, during which the LED case is subjected to mechanical stresses due to different coefficients of thermal expansion.A further question, however, is whether the effect of different PWM frequencies degrades the mechanical structure of the LED case to different degrees or not?The research work presented in this article attempts to find answers to these questions by combining classical LED aging procedures with the so-called thermal transient test method.
The greatest novelty of the methodology described here is the joint examination of the integral structure function and the time constant spectrum, i.e., the determination of the time constants and at the same time frequency values that expose the individual structural layers to the most mechanical stress.The theoretical results are tested using a real lifetime test.

II. METHODOLOGY AND TEST SAMPLES A. Methodology
The combined electrical, thermal, and optical characterization of LEDs is described in detail in the JEDEC JESD51-5x family of standards [23], [24], [25], [26].The results of these measurements include but are not limited to the forward voltage, radiant flux, luminous flux, dissipated power of the tested LED, as the function of forward current and junction temperature, and the various forms of the structure function that can be acquired with thermal transient testing [27].By sweeping the forward current and the ambient temperature in the normal operation range of the device, the full characteristics of the LED can be captured.Combining these measurement techniques with various LED aging procedures, such as with the well-known LM-80 aging test [28], [29], [30], [31], enables to monitor certain parameters of LEDs in the function of the elapsed operating time.
By varying each aging parameter (e.g., forward current, ambient temperature [32], humidity [33] or moisture [34], and PWM frequency) during the tests, it is possible to investigate the device aging tendencies depending on each operating condition and, ultimately, how the total radiant flux of the LED degrades.

B. Test Samples and Conditions
The new LED lifetime test supplemented with thermal investigations at our department was launched on blue and phosphor-converted white LEDs from an unrecognized vendor (see Fig. 1).The exact type of the test samples is unknown.They were offered mounted on starboards by the distributor.Their maximum forward current is 700 mA, and their maximum allowed chip temperature is 125 • C. Combined electrical, thermal, and optical characterization of the samples compliant with the JEDEC JESD51-5x family of standards was carried out in prior and during the life test.In between the measurements, the samples were aged at 85 • C ambient temperature with 700-mA forward current, while the samples were driven at 50% duty cycle on five different frequencies (10, 100 Hz, 1, 5, and 10 kHz) besides dc (also at 700 mA, thus presupposing much faster aging).Unpowered samples were also placed in the chamber and tested to gain additional aging data.
Basically, two test samples of both white and blue LEDs were assigned to each test condition.Further additional spare samples were initially measured, from which, for example, samples that failed during the test were replaced and switched-off samples were also placed in the test chamber.Including more samples in the test would not have been realistic due to the extremely long total characterization time.
Results of the 0-h characterization during the measurement results discussion will be examined separately from the aging-related test data as the preaging values may serve as the reference conditions.As for intermittent data, it is expedient to examine in which direction and to what extent the initial values changed as a function of the aging conditions.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

A. Forward Voltage
For the blue samples, the forward voltage values were measured to be around 3.3 V (min: 3.24 V . . .max: 3.35 V for a total of 16 samples).
For the white LEDs, the forward voltage values had a relatively large deviation (min: 3.37 V . . .max: 3.96 V for a total of 14 samples).

B. Blue Peak Wavelengths
In the case of the blue LEDs, a very small deviation was observed (between 453.64 and 454.96 nm).
In the case of the white LEDs, a larger but still not significant deviation was observed (between 449.78 and 461.72 nm).A possible reason for the larger scatter could be the manufacturing uncertainty in the light converting proximate conformal phosphor layer.

C. Temperature Dependence of the Total Radiant Flux
For the blue LEDs, the slope of the radiant flux-chip temperature function of two samples differed more, but the difference between that of the samples was approximately 8%.
For the white LEDs, the deviation was larger, and the maximum difference in the slope was around 30%.

D. Temperature Dependence of the Total Luminous Flux
In the case of the blue LEDs, the deviation of the results is mainly determined by the measurement uncertainty.The results of the two integrating spheres used during the test show different trends.The assumption is that the matching of the eye sensitivity function of the detectors' filters is different at the edges of the V (λ) function, and therefore, the temperature-dependent change of the total luminous flux value and the peak wavelength shift results in different trends in the measurement results.
In the case of the white LEDs, there is also a maximum difference of around 30% between the chip temperature dependences on the total luminous fluxes of the individual samples.

E. Conclusion About the Selected LED Samples: Hypothetical Binning of the Samples
The following conclusions can be drawn about the hypothetical binning of the samples: 1) Blue LED Samples: Based on the forward voltage and peak wavelength values, the LED chips of the samples could be originated from the same wafer and even from adjacent positions, but it is also possible that they came from a binning sorted by the forward voltage.2) White LED Samples: Based on the blue-peak wavelength values, they could be originated from the same LED die group as the blue samples (even from adjacent chips on the same wafer), but there is a significant difference between the forward voltages and the optical parameters, which makes this assumption very unlikely.Perhaps, the manufactured wavelength converting phosphor layer has such an effect on the quality of the electrical contacts, but it is more likely that the white LEDs were sorted by some photometric or colorimetric parameters during the final binning procedure.Regarding the binning criteria or method, no data were available from the LED vendor.

IV. P-N JUNCTION TEMPERATURES
The time function of the p-n junction temperature of LEDs driven by a pulsewidth modulated signal is far from obvious.Its measurement is only possible with the help of rather complicated indirect steps, while its simulation requires multidomain modeling.The peculiarity of both methods is that they require full characterization of the LED in advance, in a wide chip temperature range.
The thermal transient test methods of semiconductor devices can essentially be traced back to the measurement of the forward voltage.If the temperature dependence of the forward voltage on a given current value is known, then the chip temperature can also be determined based on the current-voltage value.
At low forward current values, measuring the temperature dependence of the forward voltage is simple, since in this case, the device's own heating is negligible; placed in an environment with a controlled temperature, the so-called K -factor calibration procedure can be performed.
However, in the case of large forward currents, when the dissipated power already causes a significant temperature rise between the environment and the chip, the abovementioned calibration procedure is only possible in indirect steps.One possible method is provided by the JEDEC JESD51-5x family of standards.The optical and electrical parameters of the LED are measured in a thermally stable state, and then, the thermal transient is completed during a switch-off transient.The chip temperature for the operating condition is determined during the subsequent evaluation.
Another possible solution is the so-called CIE method, during which the base temperature of the switched-off LED is initially set to the desired value.In a thermally steady state, the temperature of the chip is the same as that of the cold plate.After that, the value of the operating forward current is switched to the LED, while the continuously decreasing voltage is measured during the heating transient.Finally, by extrapolating the time function back to the moment of switching, the forward voltage value corresponding to the specified temperature can be determined.By performing the method at different temperatures, the entire temperature dependence can be mapped.
Whichever characterization method is used, approximately the same instrument is required and the corner points of the measurement will be the same; the switching speed, the accuracy and sampling of the measured voltage, and the accuracy of the back extrapolation are decisive.
In the case of pulsewidth modulated LEDs, the time function of the chip temperature can therefore be measured if the temperature dependence of the forward voltage on the operating forward current is known and, in the OFF state, a current of such a small value is passed through the device under which the self-heating is negligible, but by measuring the voltage, one can still gain information about the current temperature of the chip.The measurement and the SPICE simulation results of the compact thermal model of a blue LED sample can be seen in Fig. 2. The high-current temperature sensitivity function was measured using the JEDEC method.The measured values of the switch-on parts are slightly lower than the simulated values.This can be caused by the fact that the temperature dependence of the LED efficiency was not considered during the simplified simulations, and thus, when the switch-on transients are running, the LED efficiency is higher and a lower dissipation power is produced; therefore, the degree of heating is also lower.For the simulation, the amplitude of the PWM signal simulating the dissipated power is the value of the optically corrected power step and a network of a Cauer RC ladder of ten elements was used.
It is worth noting in the figure that by increasing the frequency, the switched-on sections become shorter, thereby shortening the heating and cooling sections, i.e., the average temperature of the device remains the same, but its fluctuation around is smaller.

V. DETERMINING THE STRUCTURAL LAYER BOUNDARIES
The frequency values used during aging were chosen in accordance with the time constants of each structural layer boundary.The structural layer boundaries and their associated time constants were determined using the structure functions obtained as a result of the thermal transient analysis.
Interpretation of structure functions is far from being as trivial as it may seem at first and it is made extremely challenging by two fundamental principles.
On the one hand, the ratio of thermal capacity/thermal resistance per unit thickness depends on the material of each structural layer, which obviously varies from layer to layer in the structure.On the other hand, moving away from the heat source, the cross section of the mechanical structure typically increases more and more.The value of the heat capacity is proportional to the size of the surface, i.e., approximately to the square of the distance from the heat source.Meanwhile, the thermal resistance is inversely proportional to the size of the surface, i.e., moving away from the heat source, the value of the thermal resistance per unit thickness decreases in a quadratic manner depending on the distance.
All this has two important consequences.On the one hand, with the help of thermal transient testing, it is only possible to determine the thermal resistance/heat capacity ratio interpreted per unit thickness, which, however, depends on the material component and the geometry.In the simplified case, with constant material and cross section, this is a straight line with a constant slope.It may break at the material boundaries, but it may even be constant, if, for example, the increasing cross section is compensated by the decreasing specific thermal conductivity or by the decreasing specific heat capacity or perhaps by both effects at the same time.On the other hand, due to the large heat capacity differences, the heat capacity values as a function of the thermal resistance (i.e., the integral structure function) can only be visualized when plotted on a logarithmic scale, on which the straight lines become exponential curves of a saturating nature and the breaking points occurring at the previously mentioned layer boundaries can be examined by further detailed analysis of the derivatives only.Accordingly, the boundary of the layers with a proportionally higher heat capacity than the previous ones is marked by an inflection point.Recognizing layers with proportionally decreasing heat capacity is much more difficult than this because the saturation curve runs into an even more saturating character.It is important to note that it is also true for these findings that both the material parameters and the geometry can change at the layer boundaries, and their combined effect is not known as a basic assumption.
After the above, three methods can be used to separate the structural layer boundaries.In the simplest case, on the integral structure functions displayed on the linear-logarithmic scale, we distinguish between horizontal-and vertical-like segments (see Fig. 3).This solution is the most common method for interpreting structure functions, although it can only provide an approximate estimate, which is actually flawed in principle.A solution that is a little closer to reality is to examine the first and second derivatives of the structure function (see Fig. 4) to search for inflection points, but with this method, only one type of layer boundaries can be recognized, and in such cases, the method may lead to artificial results.Moreover, the function analysis, in this case, is greatly complicated by the fact that the individual layer boundaries are far from sharply separated on the structure functions, as we would expect in theory.The third method is the modeling and simulation of the structure, but to do this, it is necessary to know the exact geometry and material parameters.In principle, this method can provide quite accurate results, but it is an essential condition that the model itself is sufficiently accurate, which can only be proven with the help of measurements.Overall, the combined application of the three described methods can provide satisfactory results.

A. Forward Voltage
The blue LED samples did not show significant changes even after 4750 h of aging.The measured voltage values were different only in the case of two samples (+10 and −10 mV); otherwise, it was stable during the aging time.
The white LED samples showed a more significant change.Initially, after 950 h of aging, the change was 30 mV in the smallest and 380 mV in the largest case.As the test continued, the forward voltage continuously increased, and in some cases, the thermal transient tester equipment could no longer measure it, which means that the forward voltage of those LEDs increased above 5 V during aging.

B. Total Radiant Flux Maintenance
At 950 h of the test time, the blue LEDs had only 79.8%-87.9% of their initial radiant flux.Regarding the PWM frequency dependence, the aging was apparently stronger as the frequency increased.Contrary to the initial expectations, samples aged the least under 700-mA dc drive.
However, after 1900 h of aging, the case had drastically changed: a clear frequency dependence cannot be identified from the measurement readings, while both LED samples suffered catastrophic failure aged under direct current drive.
Further observations on the blue samples are the following.
1) The lens of the samples aged under direct current drive typically swelled after 1900 h, except for one sample, which, however, was already defective at the next measurement point at 2850 h, but at 1900 h, it still radiated 74.3% of the original value, which is slightly below the aging of the PWM driven samples.
2) Light output of sample B_10 (driven at 100 Hz) degraded from 73% to 41% at 4750 h, and its lens has also started to turn into brown, which is a presign of lens swelling.
In the case of the white samples (see Fig. 5), after 950 test h, the light output was measured to be in between 70.1% and 77.7% of the original value.According to the PWM frequency, no correlation could be noticed.Contrary to expectations, the aging of the dc-driven samples was average.
The additional experiences about the white samples are given as follows.
1) At 4750 h, the radiant flux was only between 25% and 40% of the starting value, while that of the samples driven at 10 kHz decreased less, at 2850 h, the measured values were about 10%-15% above the average.

C. Temperature of the p-n Junction During Aging
The LM-80 approved test method and the corresponding TM-21 evaluation procedure [35] deal exclusively with the test chamber temperatures, even though the LED chip-related aging phenomena are obviously not determined by the temperature of the test chamber but by that of the LED chip.This fact is also true in the case of those LED case parts that are in close thermal contact with the die itself, such as the lens and the proximity phosphor arrangements.The situation is further complicated by the fact that, as the LEDs age, their efficiency typically and continuously decreases, while the consumed electrical power continuously increases (due to the increase in the forward voltage with constant forward current drive).It is true that in the very early aging period (i.e., the burn-in period), a short-term possible improvement may occur, but this part of the LED lifetime can still be accompanied by increasing junction temperature if the forward voltage and the power consumption also rise.
Accordingly, junction temperature increases continuously during aging even if the thermal resistance remains unchanged, and therefore, this increase becomes even more significant in the case of any possible degradation of the main heat conduction path.The details of this proposal have already been discussed in detail in a previous article [36].In this article, the characteristics of the LED samples under investigation are only considered.
The p-n junction temperature of the blue LEDs was initially about 20 • C lower than in the case of the white samples.This difference was mainly caused by the large difference between the efficiency of the blue and white LEDs.The loss caused by the light converting phosphor is significant, and even in an ideal case, it could not be zero.The theoretical minimum of the loss during the wavelength conversion is determined by the so-called Stokes shift.
On average, the operating chip temperature rise (i.e., the ambient-to-junction temperature rise) of the dc-driven LED samples is about double that of the PWM-driven ones (for the chosen 50% duty cycle).Nevertheless, in the case of the LEDs driven with direct current, the samples did not age more strongly.At this point, it should be noted that the generally accepted view is that frequent switching does not damage LEDs, and light output control schemes using PWM are particularly common in daily applications.However, despite previous suggestions, it can be said that the white samples powered by dc did not fail, but the lens of the blue LEDs swells.To explain this phenomenon, it is worth examining the lens materials used for the two LED types.

D. Lens Material of the Tested LEDs
The main goal of the test was to reveal any active thermal cycling effect on the main heat flow path.The base concept behind the performed test was that the different PWM frequencies degrade different structural layers of the LED package.In order to explore this, it was critical to continuously examine the thermal resistance heat capacity map of the enclosures during the test.However, the test results were not as expected.As shown in Fig. 6, the lenses of some LED samples turned severely browned during aging.The lens of the blue LED samples is made of a double-layer polycarbonate-like material.Presumably, this arrangement was aimed at improving the external quantum efficiency of the packaged LED.As a result of aging, first, the upper polycarbonate layer turned brown and then (probably driven by a thermal run-away) swelled up.The metal-colored reflective layer found underneath the LED chip was completely matted within 1000-2000 h in every case.
As a result, the radiant flux and thermal transient measurements became absolutely inaccurate because some of the light emitted by the chip was reabsorbed by the lens, but only a certain portion of this absorbed power reheated the LED chip, while the rest of it left the case by secondary (parallel) thermal conduction paths.
The lens of the white LEDs is a polydimethylsiloxane-like material.A small amount of browning was visible on the thin phosphor carrying layer due to aging.The reflective surface behind is assumed to have browned as well, but the material of the lens itself did not suffer any visually noticeable changes during the test.Apart from that, the phosphor layer browned a bit and became slightly transparent.
The unpowered samples aged also.After 3800 h, radiant flux is 76.4% in the case of the white sample placed unpowered in the test chamber and 89% for the blue one.In the case of the blue sample, a small browning can be seen on the edge of the reflective surface.

VII. AGING-RELATED CHANGES IN THE MAIN HEAT-FLOW PATH
When determining the dissipated power, the value of the radiant flux must be considered during the evaluation of the thermal transient test results of light-emitting diodes.Without it, the calculated thermal resistance value is false and smaller than the real value.Consequently, it is obvious that the lens browning in the case of the blue LED samples falsifies the results of the thermal transient testing.In an extreme case (such as in the case of a completely opaque lens), we experience approximately the same as if we did not perform the optical correction required by the standard at all during the thermal evaluation.
Several ideas for further investigation of the phenomenon and for solving the measurement issue have been examined so far, both theoretically and practically.Our concept is based on Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.the so-called thermal dual interface method (TDIM) [37] and also takes advantage of the different efficiency values of the LEDs at different operating points.

A. Blue LED Samples-Application of a Known Thermal Staircase-Like Structure
The first solution attempt was a kind of a theoretical combination of the TDIM method with the so-called squeeze theorem (also known as the sandwich theorem) from mathematics.Fig. 7 shows the experimental setups created for the targeted tests.
The basic idea is to place layers with different thermal properties in a sandwich-like manner in the main heat conduction path.To achieve this, two types of materials were used: layers with high specific heat capacity and good thermal conductivity (such as brass and copper), and materials with low specific heat capacity and relatively poor heat conductivity (such as iron, soldering tin or FR4 plates).As a result of the sandwich arrangement, in the form of the integral structure function, the layers with high specific heat capacity and good thermal conductivity appear as abrupt, high-slope sections, while the layers with low specific heat capacity and poor thermal conductivity appear as flat, small-slope sections.In other words, the "thermal imprint" of the copper layers vertically delimits the horizontal imprint of the included soldering tin or FR4 layers, thereby creating distinct steps in the integral structure functions.If these steps can be clearly identified in the integral structure function, then any deviation from the previously known step structures indicates a measurement artifact.Fig. 7(a) shows the very first implementation of the above concept in the form of a copper-soldering tin-copper "sandwich" structure.The further development of the basic concept is shown in Fig. 7(b), where the seven layers aimed to The latter purpose is also served by isolating the surrounding air, which can be seen in Fig. 7(c).The assembly shown in Fig. 7(d) was realized by considering the fact that the integral structure function is typically drawn on a linear-logarithmic scale, i.e., successive layers appear to be steps of similar size if their heat capacity is of increasing order of magnitude.

B. Blue LED Samples-Consideration of Different Efficiencies on a Known Reference Thermal Structure
The second solution attempt is based on the different efficiency values of the LEDs at different operating points.The temperature dependence of the efficiency of LEDs is typically a strict monotonic decreasing function.The efficiency value as a function of the forward current is not so obvious; starting from small current values, the efficiency first rises suddenly; then after a peak, it decreases continuously as the current further increases.From a practical point of view, the current values above the peak are interesting since the value of the signal-to-noise ratio below the peak is typically particularly poor.In accordance with all of this, the best efficiency of an LED is achieved at the lowest possible temperature and at low current values, while the worst efficiency is achieved at the highest possible temperature and at the highest allowed forward current value.The lower limit of the achievable temperature is typically determined by the dew point of the measurement environment, while the upper limit is typically determined by the highest LED chip temperature allowed by the manufacturer.
Measurements with different efficiencies can be useful since, in this case, the reduction in light transmission of the lens affects the value of the thermal resistance determined during the optical correction to a degree proportional to the variable efficiency.In the case of a layer with a known reference thermal resistance, the current value of the transparency should therefore be deduced.
During the experiments, the aging-induced decrease in the lens transparency was imitated using a black permanent marker.The experiment was carried out in four steps, by painting 90 • circular sectors in a chessboard-like manner, in order to achieve the best symmetry.Fig. 8 shows one of the samples after painting the second segment.As the result of these investigations, it was revealed that in the case of the first proposed method, contrary to the previous LTspice simulations, results in the integral structure functions were completely blurred, while the other method could be used only for qualitative detection of the investigated phenomenon, but it did not serve to provide quantitative results.

C. Phosphor-Converted White LED Samples
In the case of the white samples, Fig. 3 shows the time evolution of the so-called integral structure function.The assumed structural layers forming the main heat conduction path are marked in the figure.The reading of the change in the structure function is most accurate where the heat capacity increases drastically.In addition to the die, there are two such layers in this structure: one is the heatsink slug and the other is ambient, appearing as an asymptote at the end of the structure function.
The time evolution of the thermal resistance values read at the heat capacity of 0.01 Ws/K is shown in Fig. 9.At the beginning of the heatsink slug, the total thermal capacity and thermal resistance values are in the range of 0.001 Ws/K and 7-8 K/W, so the thermal time constant of the die attach layer is approximately in the range of 10 ms.This layer is therefore mostly affected by changes slower than 10 ms, and the results shown in the figure also suggest that at frequencies on and above the order of 1 kHz, the change in the thermal resistance of this layer is apparently smaller than at lower frequencies.
The thermal time constant that can be determined for the end of the heatsink slug is already above 1 s, while the thermal resistance value above it is greatly influenced by the clamping force applied during reassembling before and after the control measurements.

VIII. CONCLUSION
Among the findings of the study is the dependence of the forward voltages as the function of test time, which is different for the white and blue LED samples; the forward voltage of the blue LEDs showed only a slight change, while the forward voltage of the white LEDs showed a significant increase.The radiated power of the white LEDs also decreased to a greater extent than was observed for the blue samples, and however, a sudden failure of the blue samples occurred on several occasions due to lens browning and swelling.The blue peaks of the spectral power distribution did not change significantly.
We showed that thermal transient testing could be rendered completely unusable by aging of the LED optics.In the case of blue LED samples, thermal characterization by thermal transient measurement is subject to an error due to the aging of the lens.
By examining the structure function of aged white LEDs, we demonstrated that the aging of the die attach layer can be seen through the increase in the thermal resistance of this layer.Using the introduced the time constant spectrum analysis, we showed the methodology to identify aging frequencies to target selected layers in the mechanical structures.As a result for the white LED samples used, the degradation of the die attach layer was significantly below the frequency of 1 kHz.This supports our theoretical findings of the time constant spectrum analysis that frequencies up to 313 Hz affect the die attach layer, and in our case, the highest frequency below 1 kHz was 100 Hz.This methodology could be used to trigger and investigate aging at any layer in a mechanical structure during active cycling.
In Section I, we deduced that a PWM drive with a duty factor of 50% theoretically causes a worse efficiency and, therefore, an expected faster aging than a dc drive with a current value of 50% compared to the current value of the PWM drive.This statement is also supported by our results, according to which, at frequency values that expose the mechanical structure to active thermal cycling, PWM mode causes faster degradation than dc mode, even with the same current value.The comparison of PWM and dc drive modes, which provide the same luminous flux output, will be carried out in another study.
Further conclusions of the study can be related to sampling; on the one hand, in the case of too many samples, the number of measurements that can be performed decreases significantly, while by reducing the number of samples, the statistical power of the measurement results degrades.On the other hand, testing high-quality LED types may not bring the expected changes even in the long run, but testing poor-quality LED types can sometimes raise more questions than they actually answer.

Manuscript received 1
March 2023; revised 27 April 2023; accepted 12 May 2023.Date of publication 19 May 2023; date of current version 20 September 2023.This work was supported in part by the European Union's Horizon 2020 Research and Innovation Program through the H2020 ECSEL Project AI-TWILIGHT under Agreement 101007319; in part by the AI-TWILIGHT Project; in part by the AI-TWILIGHT Project by the Hungarian Government through the National Research, Development and Innovation Fund under Grant 2019-2.1.3-NEMZ_ECSEL-2021-00008;and in part by the Hungarian National Research, Development and Innovation Fund through the OTKA Project under Grant K_128315.Recommended for publication by Associate Editor L. Codecasa upon evaluation of reviewers' comments.(Corresponding author: János Hegedüs.)

Fig. 1 .
Fig. 1.LED samples of the selected blue (to the left) and phosphor-converted white (to the right) LED types.

Fig. 2 .
Fig. 2. Measured and simulated p-n junction temperature of a blue LED during the turn-on transient by a PWM modulated signal, at the ambient temperature of 85 • C. Measurement and SPICE simulation results of the compact thermal model of a Cauer RC ladder network of ten elements.

Fig. 3 .
Fig. 3. Time-dependent integral structure function of a phosphor-converted white LED sample, aged at 1 kHz.The assumed structural layers are marked in the figure.

Fig. 4 .
Fig. 4. First and second derivatives of the logarithmic integral structure function.The location of the assumed layer boundaries is quite uncertain, marked by wider bands.

Fig. 5 .
Fig. 5. Radiant flux of the phosphor-converted white LEDs relative to the 0-h results.

Fig. 7 .
Fig. 7. Experimental structures: (a) rudimentary three-layer (copper-soldering tin-copper) structure, (b) improved fine-structure seven-layer (brass, tin, and copper) structure, (c) installation of the improved structure with ambient thermal insulation, and (d) three-layer structure of highly increased heat resistance and capacity.

Fig. 8 .
Fig. 8.One of the test sample LEDs after painting black the second segment of its lens.

Fig. 9 .
Fig. 9. Relative change of the thermal resistance values read at the heat capacity of 0.01 Ws/K as the function of the elapsed operating time.