# Lifetime Modelling Issues of Power Light Emitting Diodes

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Total Luminous Flux Maintenance Projections

#### 2.1. IES LM-80

#### 2.2. IES TM-21-11

#### 2.3. The Degradation Model Used by TM-21-11

#### 2.4. Further Possible Degradation Trends

_{70}lifetime from the 10,000-h results is halved or doubles compared to the estimation from the 6000-hour results.

## 3. The Pn-Junction Temperature During the LM-80 Test

#### 3.1. Analytical Calculation of the Pn-Junction Temperature

#### 3.2. Determination of the Pn-Junction Temperature by Measurement

#### 3.3. The Transient Testing Based Calculation of the Arrhenius-Equation

- (1).
- Determine the pn-junction temperature during the LM-80 process, at the test current and case temperature.
- (2).
- Determine the pre-exponential factor $A$ and the activation energy ${E}_{a}$ of the Arrhenius-equation from the continuously increasing junction temperature values of each measurement time and the corresponding measured radiant flux values.
- (3).
- Determine the luminous flux maintenance curve belonging to a fixed junction-temperature value, applying an arbitrary time profile of the junction temperature.
- (4).
- Determine the ${S}_{{\mathsf{\Phi}}_{e}}$ temperature sensitivity of the radiant flux and calculate the light output parameters at any arbitrary junction temperature and at any time of the aging process.

#### 3.3.1. Determine the Pn-Junction Temperature

#### 3.3.2. Determine the Pre-Exponential Factor and the Activation Energy

#### 3.3.3. Determine the Luminous Flux Maintenance Curve at a Fixed ${\mathrm{T}}_{\mathrm{J}}$

#### 3.3.4. Calculating the Light Output Parameters at any ${\mathrm{T}}_{\mathrm{J}}$

#### 3.4. Case Study

- (1).
- (2).
- ${S}_{{\mathsf{\Phi}}_{e}}$ was calculated.
- (3).
- ${\mathsf{\Phi}}_{e}$ (${T}_{J}$ = 85 °C) was calculated for all the control measurements (Equation (31); the red dots in Figure 6).
- (4).
- (5).
- $A$ and ${E}_{a}$ were determined; the measured ${T}_{J}$ values at ${T}_{A}$ = 55 °C and the maintenance curve determined in step 4 were used. Applying the same method described in Section 3.3.2 the formulas for the logarithmic model are:$$A=-{D}_{{t}_{1}}\xb7{t}_{1}\xb7exp\left[\frac{{E}_{a}}{{k}_{B}\xb7{T}_{J}\left({t}_{1}\right)}\right]$$$${E}_{a}=\frac{{k}_{B}\xb7{T}_{J}\left({t}_{1}\right)\xb7{T}_{J}\left({t}_{2}\right)}{{T}_{J}\left({t}_{2}\right)-{T}_{J}\left({t}_{1}\right)}\xb7ln\left(\frac{{D}_{{t}_{2}}\xb7{t}_{2}}{{D}_{{t}_{1}}\xb7{t}_{1}}\right)$$

- (1).
- To check the accuracy of the achieved model we calculated the maintenance curve belonging to T
_{J}= 85 °C (dashed dark red line in Figure 6). The simulation run with a time increments of 1 h. - (2).
- We also calculated the maintenance curves belonging to ${T}_{A}$ = 25 °C and to ${T}_{A}$ = 55 °C (dashed dark blue and green lines in Figure 6).

^{2}values of the simulation are 0.992 and 0.988 for the 25 °C and 55 °C measurements while that of the logarithmic approximation are 0.993 and 0.983. These values show that the accuracy of the new aging model and the classical curve fitting method is practically the same.

## 4. LM-80 Based Lifetime Modelling of Power LEDs

#### 4.1. Continuous In-Situ Lifetime Modelling of LEDs

#### 4.2. Lifetime Modelling of Iso-Flux Operation; a Case Study

## 5. Lifetime Modelling Based on Multi-Domain Modelling of the LEDs

#### 5.1. Evaluation of Precious Life Testing Results

#### 5.2. Launch of a Targeted LM-80 Based Test Sequence

#### 5.3. Results of the LM-80 Based Test

#### 5.4. The Elapsed Lifetime Dependent Multi-Domain LED Model

#### 5.5. The Enhanced Time Functions

#### 5.6. Extrapolation Capabilities of the Model

#### 5.7. The Required Measurement and Testing Time

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- IESNA. IES Approved Method: Measuring Lumen Maintenance of LED Light Sources; IES LM-80-08; Illuminating Engineering Society of North America: New York, NY, USA, 2008; p. 7. [Google Scholar]
- Poppe, A.; Gábor, M.; Csuti, P.; Szabó, F.; Schanda, J. Ageing of LEDs: A Comprehensive Study Based on the LM80 Standard and Thermal Transient Measurements. In Proceedings of the 27th Session of the CIE, Sun City, South Africa, 9–16 July 2011; pp. 467–477. [Google Scholar]
- Hegedüs, J.; Hantos, G.; Poppe, A. Lifetime Iso-flux Control of LED based Light Sources. In Proceedings of the 23rd International Workshop on Thermal Investigation of ICs and Systems (THERMINIC’17), Amsterdam, The Netherlands, 27–29 September 2017. [Google Scholar] [CrossRef]
- Hegedüs, J.; Hantos, G.; Poppe, A. Reliability Issues of Mid-Power LEDs. In Proceedings of the 25th International Workshop on Thermal Investigation of ICs and Systems (THERMINIC’19), Lecco, Italy, 25–27 September 2019. [Google Scholar] [CrossRef]
- Delphi4LED Project Website. Available online: https://delphi4led.org (accessed on 14 April 2020).
- Martin, G.; Marty, C.; Bornoff, R.; Poppe, A.; Onushkin, G.; Rencz, M.; Yu, J. Luminaire Digital Design Flow with Multi-Domain Digital Twins of LEDs. Energies
**2019**, 12, 2389. [Google Scholar] [CrossRef] [Green Version] - Poppe, A.; Farkas, G.; Gaál, L.; Hantos, G.; Hegedüs, J.; Rencz, M. Multi-domain modelling of LEDs for supporting virtual prototyping of luminaires. Energies
**2019**, 12, 1909. [Google Scholar] [CrossRef] [Green Version] - Hantos, G.; Hegedüs, J.; Bein, M.C.; Gaál, L.; Farkas, G.; Sárkány, Z.; Ress, S.; Poppe, A.; Rencz, M. Measurement issues in LED characterization for Delphi4LED style combined electrical-optical-thermal LED modeling. In Proceedings of the 19th IEEE Electronics Packaging Technology Conference (EPTC’17), Singapore, 6–9 December 2017. [Google Scholar] [CrossRef]
- Alexeev, A.; Bornoff, R.; Lungten, S.; Martin, G.; Onushkin, G.; Poppe, A.; Rencz, M.; Yu, J. Requirements specification for multi-domain LED compact model development in Delphi4LED. In Proceedings of the 2017 18th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems (EuroSimE), Dresden, Germany, 3–5 April 2017; pp. 1–8. [Google Scholar] [CrossRef]
- Poppe, A.; Di Bucchianico, A.; Vaumorin, E.; Juntunen, E.; Bosschaartl, K.; Yu, J.; Thomé, J.; Joly, J.; Szabo, F.; Merelle, T.; et al. Inter Laboratory Comparison of LED Measurements Aimed as Input for Multi-Domain Compact Model Development within a European-wide R&D Project. In Proceedings of the Conference on “Smarter Lighting for Better Life” at the CIE Midterm Meeting, Jeju, Korea, 23–25 October 2017; pp. 569–579. [Google Scholar] [CrossRef]
- Bornoff, R.; Mérelle, T.; Sari, J.; Di Bucchianico, A.; Farkas, G. Quantified Insights into LED Variability. In Proceedings of the 24th International Workshop on Thermal Investigation of ICs and Systems (THERMINIC’18), Stockholm, Sweden, 26–28 September 2018. [Google Scholar] [CrossRef]
- Mérelle, T.; Bornoff, R.; Onushkin, G.; Gaál, L.; Farkas, G.; Poppe, A.; Hantos, G.; Sari, J.; Di Bucchianico, A. Modeling and quantifying LED variability. In Proceedings of the 2018 LED Professional Symposium (LpS 2018), Bregenz, Austria, 25–27 September 2018; Luger Research e.U.—Institute for Innovation & Technology: Dornbirn, Austria, 2018; pp. 194–207, ISBN 978-3-9503209-9-2. [Google Scholar]
- Merelle, T.; Sari, J.; Di Bucchianico, A.; Onushkin, G.; Bornoff, R.; Farkas, G.; Gaal, L.; Hantos, G.; Hegedus, J.; Poppe, A. Does a single LED bin really represent a single LED type? In Proceedings of the 29th Session of the CIE, Washington, WA, USA, 14–22 June 2019; pp. 1204–1214. [Google Scholar] [CrossRef]
- Hegedüs, J.; Hantos, G.; Nemeth, M.; Pohl, L.; Kohári, Z.; Poppe, A. Multi-domain characterization of CoB LEDs. In Proceedings of the 29th Session of the CIE, Washington, WA, USA, 14–22 June 2019; pp. 387–397. [Google Scholar] [CrossRef]
- Zhang, S.U.; Lee, B.W. Fatigue life evaluation of wire bonds in LED packages using numerical analysis. Microelectron. Reliab.
**2014**, 54, 2853–2859. [Google Scholar] [CrossRef] - Hu, J.; Yang, L.; Shin, M.W. Mechanism and thermal effect of delamination in light-emitting diode packages. Microelectron. J.
**2007**, 38, 157–163. [Google Scholar] [CrossRef] [Green Version] - Schubert, E.F. Light Emitting Diodes, 2nd ed.; Cambridge University Press: Cambridge, UK, 2006. [Google Scholar]
- Kim, H.; Yang, H.; Huh, C.; Kim, S.W.; Park, S.J.; Hwang, H. Electromigration-induced failure of GaN multi-quantum well light emitting diode. Electron. Lett.
**2000**, 36, 908–910. [Google Scholar] [CrossRef] - de Orio, R.L.; Ceric, H.; Selberherr, S. Physically based models of electromigration: From Black’s equation to modern TCAD models. Microelectron. Reliab.
**2010**, 50, 775–789. [Google Scholar] [CrossRef] - Pradhan, S.; Di Stasio, F.; Bi, Y.; Gupta, S.; Christodoulou, S.; Stavrinadis, A.; Konstantatos, G. High-efficiency colloidal quantum dot infrared light-emitting diodes via engineering at the supra-nanocrystalline level. Nat. Nanotechnol.
**2019**, 14, 72–79. [Google Scholar] [CrossRef] - Vasilopoulou, M.; Kim, H.P.; Kim, B.S.; Papadakis, M.; Gavim, A.E.X.; Macedo, A.G.; Da Silva, W.J.; Schneider, F.K.; Teridi, M.A.M.; Coutsolelos, A.G.; et al. Efficient colloidal quantum dot light-emitting diodes operating in the second near-infrared biological window. Nat. Photonics
**2020**, 14, 50–56. [Google Scholar] [CrossRef] - Won, Y.-H.; Cho, O.; Kim, T.; Chung, D.-Y.; Kim, T.; Chung, H.; Jang, H.; Lee, J.; Kim, D.; Jang, E. Highly efficient and stable InP/ZnSe/ZnS quantum dot light-emitting diodes. Nature
**2019**, 575, 634–638. [Google Scholar] [CrossRef] - Gao, L.; Na Quan, L.; De Arquer, F.P.G.; Zhao, Y.; Munir, R.; Proppe, A.H.; Quintero-Bermudez, R.; Zou, C.; Yang, Z.; Saidaminov, M.I.; et al. Efficient near-infrared light-emitting diodes based on quantum dots in layered perovskite. Nat. Photonics
**2020**, 14, 227–233. [Google Scholar] [CrossRef] - NANOTHERM Poject Website. Available online: http://project-nanotherm.com/ (accessed on 21 June 2020).
- Lago, M.D.; Meneghini, M.; Trivellin, N.; Mura, G.; Vanzi, M.; Meneghesso, G.; Zanoni, E. “Hot-plugging” of LED modules: Electrical characterization and device degradation. Microelectron. Reliab.
**2013**, 53, 1524–1528. [Google Scholar] [CrossRef] - Meneghini, M.; Podda, S.; Morelli, A.; Pintus, R.; Trevisanello, L.; Meneghesso, G.; Vanzi, M.; Zanoni, E. High brightness GaN LEDs degradation during dc and pulsed stress. Microelectron. Reliab.
**2006**, 46, 1720–1724. [Google Scholar] [CrossRef] - van Driel, W.D.; Fan, X.J. (Eds.) Solid State Lighting Reliability; Springer: New York, NY, USA, 2013; ISBN 978-1-4614-3066-7. [Google Scholar] [CrossRef]
- van Driel, W.D.; Fan, X.; Zhang, G.Q. Solid State Lighting Reliability Part 2 (Solid State Lighting Technology and Application Series); Springer International Publishing: Cham, Switzerland, 2018; ISBN 978-3-319-58174-3. [Google Scholar] [CrossRef]
- Chang, M.H.; Das, D.; Varde, P.V.; and Pecht, M. Light emitting diodes reliability review. Microelectron. Reliab.
**2012**, 52, 762–782. [Google Scholar] [CrossRef] - Koh, S.; van Driel, W.D.; Zhang, G.Q. Thermal and moisture degradation in SSL system. In Proceedings of the 2012 13th International Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems, EuroSimE 2012, Cascais, Portugal, 16–18 April 2012. [Google Scholar] [CrossRef]
- Singh, P.; Tan, C.M. Degradation Physics of High Power LEDs in Outdoor Environment and the Role of Phosphor in the degradation process. Sci. Rep.
**2016**, 6, 24052. [Google Scholar] [CrossRef] [Green Version] - Trevisanello, L.; Meneghini, M.; Mura, G.; Vanzi, M.; Pavesi, M.; Meneghesso, G.; Zanoni, E. Accelerated life test of high brightness light emitting diodes. IEEE Trans. Device Mater. Reliab.
**2008**, 8, 304–311. [Google Scholar] [CrossRef] - Csuti, P.; Kránicz, B.; Krüger, U.; Schanda, J.; Schmidt, F. Photometric and Colorimetric Stability of LEDs. In Proceedings of the CIE Expert Symposium on Advances in Photometry and Colorimetry, Turin, Italy, 7–8 July 2008. [Google Scholar]
- Paisnik, K.; Rang, G.; Rang, T. Life-time characterization of LEDs. Est. J. Eng.
**2011**, 17, 241–251. [Google Scholar] [CrossRef] [Green Version] - Ikonen, E.; Vaskuri, A.; Baumgartner, H.; Pulli, T.; Poikonen, T.; Kantamaa, O.; Kärhä, P. Online measurement of LED junction temperature for lifetime prediction. In Proceedings of the Conference at the CIE Midterm Meeting, Jeju, Korea, 23–25 October 2017; pp. 36–37. [Google Scholar]
- Vaskuri, A.; Kärhä, P.; Baumgartner, H.; Kantamaa, O.; Pulli, T.; Poikonen, T.; Ikonen, E. Relationships between junction temperature, electroluminescence spectrum and ageing of lightemitting diodes. Metrologia
**2018**, 55, S86–S95. [Google Scholar] [CrossRef] - Vaskuri, A. Spectral Modelling of Light-Emitting Diodes and Atmospheric Ozone Absorption. Ph.D. Thesis, Aalto University, Espoo, Finland, 2018. ISBN 978-952-60-8442-4. Available online: https://aaltodoc.aalto.fi/handle/123456789/34252 (accessed on 19 June 2020).
- Vaitonis, Z.; Miasojedovas, A.; Novičkovas, A.; Sakalauskas, S.; Zukauskas, A. Effect of long-term aging on series resistance and junction conductivity of high-power resistance and junction conductivity of high-power. Lith. J. Phys.
**2009**, 49, 69. [Google Scholar] [CrossRef] - Alexeev, A.; Linnartz, J.-P.; Onushkin, G.; Arulandu, K.; Martin, G. Dynamic response-based LEDs health and temperature monitoring. Measurement
**2020**, 156, 107599. [Google Scholar] [CrossRef] - Alexeev, A. Characterization of Light Emitting Diodes with Transient Measurements and Simulations. Ph.D. Thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 2020. ISBN 978-90-386-5035-7. Available online: https://research.tue.nl/en/publications/characterization-of-light-emitting-diodes-with-transient-measurem (accessed on 19 June 2020).
- JEDEC. JESD22-A101C Standard, Steady State Temperature Humidity Bias Life Test; JEDEC: Arlington, VA, USA, 2009. [Google Scholar]
- JEDEC. JESD22-A104D Standard, Temperature Cycling; JEDEC: Arlington, VA, USA, 2009. [Google Scholar]
- IESNA. IES TM-21-11: Projecting Long Term Lumen Maintenance of LED Light Sources; Illuminating Engineering Society of North America: New York, NY, USA, 2013. [Google Scholar]
- IESNA. IES Approved Method: Measuring Luminous Flux and Color Maintenance of LED Packages, Arrays and Modules; IES LM-80-15; Illuminating Engineering Society of North America: New York, NY, USA, 2015; p. 8. [Google Scholar]
- Richman, E. The Elusive Life of LEDs: How TM21 Contributes to the Solution; Pacific Northwest National Lab: Richland, WA, USA, 2011. [Google Scholar]
- Chemistry LibreTexts: First-Order Reactions. Available online: https://chem.libretexts.org/Core/Physical_and_Theoretical_Chemistry/Kinetics/Reaction_Rates/First-Order_Reactions (accessed on 14 April 2020).
- van Driel, W.D.; Schuld, M.; Jacobs, B.; Commissaris, F.; Van Der Eyden, J.; Hamon, B. Lumen maintenance predictions for LED packages. Microelectron. Reliab.
**2016**, 62, 39–44. [Google Scholar] [CrossRef] - Chemistry LibreTexts: More Complex Reactions. Available online: https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Map%3A_Physical_Chemistry_for_the_Biosciences_(Chang)/09%3A_Chemical_Kinetics/9.04%3A_More_Complex_Reactions (accessed on 14 April 2020).
- Miller, C. IES TM-21-11 Overview, History and Q&A Session. EPA ENERGY STAR Lamp Round Table. National Institute of Standards & Technology, Sensor Science Division, San Diego, CA, USA, 24 October 2011. Available online: https://www.energystar.gov/sites/default/files/specs/TM-21%20Discussion_0.pdf (accessed on 14 April 2020).
- Hantos, G.; Hegedüs, J.; Rencz, M.; Poppe, A. Aging Tendencies of Power MOSFETs—A Reliability Testing Method Combined with Thermal Performance Monitoring. In Proceedings of the 22nd International Workshop on Thermal Investigation of ICs and Systems (THERMINIC’16), Budapest, Hungary, 21–23 September 2016; pp. 220–223. [Google Scholar] [CrossRef]
- Hantos, G.; Hegedüs, J.; Rencz, M. An efficient reliability testing method combined with thermal performance monitoring. Microelectron. Reliab.
**2017**, 78, 126–130. [Google Scholar] [CrossRef] - JEDEC. JESD51-50 Standard. Overview of Methodologies for the Thermal Measurement of Single- and Multi-Chip, Single- and Multi-PNJunction Light-Emitting Diodes (LEDs); JEDEC: Arlington, VA, USA, 2012. [Google Scholar]
- JEDEC. JESD51-51 Standard. Implementation of the Electrical Test Method for the Measurement of Real Thermal Resistance and Impedance of Light-Emitting Diodes with Exposed Cooling; JEDEC: Arlington, VA, USA, 2012. [Google Scholar]
- JEDEC. JESD51-52 Standard. Guidelines for Combining CIE 127-2007 Total Flux Measurements with Thermal Measurements of LEDs with Exposed Cooling Surface; JEDEC: Arlington, VA, USA, 2012. [Google Scholar]
- JEDEC. JESD51-53 Standard. Terms, Definitions and Units Glossary for LED Thermal Testing; JEDEC: Arlington, VA, USA, 2012. [Google Scholar]
- CIE 127:2007 Technical Report, “Measurement of LEDs”; CIE: Vienna, Austria, 2007; ISBN 978-3-901-906-58-9.
- CIE 225: 2017 Technical Report, “Optical Measurement of High-Power LEDs”; CIE: Vienna, Austria, 2017; ISBN 978-3-902842-12-1. [CrossRef]
- Poppe, A.; Farkas, G.; Székely, V.; Horváth, G.; Rencz, M. Multi-domain simulation and measurement of power LED-s and power LED assemblies. In Proceedings of the 22nd IEEE Semiconductor Thermal Measurement and Management Symposium (SEMI-THERM’06), Dallas, TX, USA, 14–16 March 2006; pp. 191–198. [Google Scholar] [CrossRef]
- Poppe, A.; Gábor, M.; Temesvölgyi, T. Temperature dependent thermal resistance in power LED assemblies and a way to cope with it. In Proceedings of the 26th IEEE Semiconductor Thermal Measurement and Management Symposium (SEMI-THERM’10), Santa Clara, CA, USA, 21–25 February 2010; pp. 283–288. [Google Scholar] [CrossRef]
- Hantos, G.; Hegedüs, J. K-factor calibration issues of high power LEDs. In Proceedings of the 23rd International Workshop on Thermal Investigations of ICs and Systems (THERMINIC’17), Amsterdam, The Netherlands, 27–29 September 2017. [Google Scholar] [CrossRef]
- Hantos, G.; Hegedüs, J.; Poppe, A. Different questions of today’s LED thermal testing procedures. In Proceedings of the 34th IEEE Thermal Measurement, Modeling & Management Symposium (SEMI-THERM’18), San Jose, CA, USA, 19–23 March 2018; pp. 63–70. [Google Scholar] [CrossRef]
- JEDEC. JESD51-1 Standard. Integrated Circuits Thermal Measurement Method—Electrical Test Method (Single Semiconductor Device); JEDEC: Arlington, VA, USA, 1995. [Google Scholar]
- JEDEC. JESD51-14 Standard. Tranisent Dual Interface Test Method for the Measurement of the Thermal Resistance Junction-To-Case of Semiconductor Devices with Heat Flow through a Single Path; JEDEC: Arlington, VA, USA, 2010. [Google Scholar]
- Székely, V.; Bien, T.V. Fine structure of heat flow path in semiconductor devices: A measurement and identification method. Solid State Electron.
**1988**, 31, 1363–1368. [Google Scholar] [CrossRef] - Vaitonis, Z.; Pranciškus, V.; Zukauskas, A. Measurement of the junction temperature in high-power light-emitting diodes from the high-energy wing of the electroluminescence band. J. Appl. Phys.
**2008**, 103, 093110. [Google Scholar] [CrossRef] - Smirnov, V.I.; Sergeev, V.A.; Gavrikov, A.A.; Shorin, A.M. Modulation method for measuring thermal impedance components of semiconductor devices. Microelectron. Reliab.
**2018**, 80, 205–212. [Google Scholar] [CrossRef] - Poppe, A. Simulation of LED Based Luminaires by Using Multi-Domain Compact Models of LEDs and Compact Thermal Models of their Thermal Environment. Microelectron. Reliab.
**2017**, 72, 65–74. [Google Scholar] [CrossRef] - Hegedüs, J.; Hantos, G.; Poppe, A. Light output stabilisation of LED based streetlighting luminaires by adaptive current control. Microelectron. Reliab.
**2017**, 79, 448–456. [Google Scholar] [CrossRef] - Hegedüs, J.; Horváth, P.; Hantos, G.; Szabó, T.; Szalai, A.; Poppe, A. A New Dimming Control Scheme of LED Based Streetlighting Luminaires Using an Embedded LED Model Implemented on an IoT Platform to Achieve Constant Luminous Flux at Different Ambient Temperatures. In Proceedings of the Lux Europa 2017, Lubljana, Slovenia, 18–20 September 2017; pp. 87–92. Available online: https://pdfs.semanticscholar.org/f4a2/2878f59aa0a87a886402f638d3fb516dc710.pdf (accessed on 14 April 2020).
- Hegedüs, J.; Horváth, P.; Szabó, T.; Szalai, A.; Poppe, A. A New Dimming Control Scheme of LED Streetlighting Luminaires Based on Multi-Domain Simulation models of LEDs in order to Achieve Constant Luminous Flux at Different Ambient Temperatures. In Proceedings of the Conference on “Smarter Lighting for Better Life” at the CIE Midterm Meeting, Jeju, Korea, 23–25 October 2017; pp. 267–276. [Google Scholar] [CrossRef]
- Mentor Graphics T3Ster Product Website. Available online: https://www.mentor.com/products/mechanical/micred/t3ster/ (accessed on 14 April 2020).
- Mentor Graphics TeraLED Product Website. Available online: https://www.mentor.com/products/mechanical/micred/teraled/ (accessed on 14 April 2020).
- Hegedüs, J.; Hantos, G.; Poppe, A. A step forward in lifetime multi-domain modelling of power LEDs. In Proceedings of the 29th Session of the CIE, Washington, WA, USA, 14–22 June 2019; pp. 1154–1161. [Google Scholar] [CrossRef]

**Figure 1.**The change in aging trends: extrapolation of the 6k and 10k hours may differ dramatically (based on [49]) (

**a**) L

_{70}(6k) = 60,000 h vs. L

_{70}(10k) = 30,000 h; (

**b**) L

_{70}(6k) = 30,000 h vs. L

_{70}(10k) > 60,000 h.

**Figure 2.**Theoretical pn-junction temperature increase during an LM-80 test in case of (

**a**) a high-power and (

**b**) a mid-power LED, as the function of the forward current, the thermal resistance, the zero-hour radiant efficiency and the reached luminous flux decay (assuming a constant thermal resistance and a Figure 3. V forward voltage). Note that the curves on (

**a**) and (

**b**) are identical implying that the junction temperature increase may affect high- and mid-power LEDs equally, depending on the thermal resistance.

**Figure 3.**Effects of the increase in the forward voltage and in the thermal resistance on the pn-junction temperature increase during an LM-80 test. The initial parameters are: 1 A forward current, 40% radiant efficiency, 15 K/W thermal resistance, 3 V forward voltage. The figures show the junction temperature increase during the test as the function of the end of test thermal resistance and forward voltage. The end of test relative light outputs are (

**a**) 95% and (

**b**) 80%. The black crosses indicate values corresponding to that of in Figure 2a.

**Figure 4.**Shift of the forward voltage—forward current characteristics during the first 9000 h of a Luxeon Z LED sample (aged at 85 °C case temperature and 1 A forward current).

**Figure 5.**Pn-junction temperatures of the tested mid-power LED (#S11) over the testing time, measured at 300 mA forward current, (

**a**) at 25 °C and (

**b**) at 55 °C ambient temperatures.

**Figure 6.**Measurement and simulation results of the aged mid-power blue LED; the logarithmic regression fitting parameters to the 85 °C values are indicated just as an example.

**Figure 7.**(

**a**) Averaged LM-80 measurement results of 9 pieces of Luxeon Z samples and extrapolation until 50k hours (${T}_{J}$ = 120 °C, ${I}_{F}$ = 1 A); (

**b**) Exponential curve fit to the LM-80 measurement set along with the eight assumed aging trends.

**Figure 9.**The forward currents applied during the simulation (the absolute maximum DC forward current of the Luxeon Z LEDs is 1 A).

**Figure 13.**The sample mid-power LEDs mounted on FR4 strips; the printed circuit boards were provided with increased thermal interfaces for better cooling capabilities.

**Figure 15.**The attained total radiant flux maintenance results of the mid-power blue LEDs, sorted by case temperature and forward current.

**Figure 17.**(

**a**) Comparison of the simulated and measured total radiant flux maintenance curves of #S07; (

**b**) The simulation results of #S07 with higher time resolution—the discontinuity can be clearly seen.

**Figure 18.**Simulated and measured total radiant flux maintenance of #S07 (

**a**) and sample #S11 (

**c**); Measured and simulated time function of the forward voltage of sample #S07 (

**b**) and sample #S11 (

**d**).

**Table 1.**Aging models of different decay rates with the closed form solution, i.e., the integral form (after [49]).

# | Decay Rate | Integral Form | |
---|---|---|---|

1 | $\frac{d{I}_{V}}{dt}={k}_{1}$ | ${I}_{V}={I}_{V}^{0}+{k}_{1}\xb7\left(t-{t}^{0}\right)$ | |

2 | $\frac{d{I}_{V}}{dt}={k}_{2}\xb7{I}_{V}$ | ${I}_{V}={I}_{V}^{0}\xb7exp\left[{k}_{2}\xb7\left(t-{t}^{0}\right)\right]$ | |

3 | $\frac{d{I}_{V}}{dt}={k}_{1}+{k}_{2}\xb7{I}_{V}$ | ${I}_{V}=\left({I}_{V}^{0}+\frac{{k}_{1}}{{k}_{2}}\right)\xb7exp\left[{k}_{2}\xb7\left(t-{t}^{0}\right)\right]-\frac{{k}_{1}}{{k}_{2}}$ | Model 1 + Model 2 |

4 | $\frac{d{I}_{V}}{dt}=\frac{{k}_{3}}{t}$ | ${I}_{V}={I}_{V}^{0}+{k}_{3}\xb7ln\left(\frac{t}{{t}^{0}}\right)$ | |

5 | $\frac{d{I}_{V}}{dt}={k}_{1}+\frac{{k}_{3}}{t}$ | ${I}_{V}={I}_{V}^{0}+{k}_{1}\xb7\left(t-{t}^{0}\right)+{k}_{3}\xb7ln\left(\frac{t}{{t}^{0}}\right)$ | Model 1 + Model 4 |

6 | $\frac{d{I}_{V}}{dt}={k}_{4}\xb7{I}_{V}^{2}$ | ${I}_{V}=\frac{{I}_{V}^{0}}{1+{I}_{V}^{0}\xb7{k}_{4}\xb7\left(t-{t}^{0}\right)}$ | |

7 | $\frac{d{I}_{V}}{dt}={k}_{5}\xb7\frac{{I}_{V}}{t}$ | ${I}_{V}={I}_{V}^{0}\xb7{\left(t/{t}^{0}\right)}^{{k}_{5}}$ | |

8 | $\frac{d{I}_{V}}{dt}={k}_{2}\xb7{I}_{V}+{k}_{5}\xb7\frac{{I}_{V}}{t}$ | ${I}_{V}={I}_{V}^{0}\xb7exp\left[{k}_{2}\xb7\left(t-{t}^{0}\right)\right]\xb7{\left(t/{t}^{0}\right)}^{{k}_{5}}$ | Model 2 + Model 7 |

9 | ${I}_{V}={I}_{V}^{0}\xb7exp{\left[-\frac{\left(t-{t}^{0}\right)}{{k}_{6}}\right]}^{{k}_{7}}$ |

**Table 2.**Elapsed time till 50k hours of operation of a streetlighting luminaire in years, in Hungary.

Dark-Hours in-Between | 50k Dark-Hours (Years) | Dark-Hours during a Year (Hours) | |
---|---|---|---|

Sunset to Sunrise | 12 years | 4291 h | |

Civil | Twilights | 13 years | 3875 h |

Nautical | 15 years | 3373 h | |

Astronomical | 18 years | 2802 h |

**Table 3.**Comparison of operation with constant forward current (700 mA) and with constant light output (425 mW), simulated with the help of our LED aging theory.

Examined Parameter | ${\mathit{I}}_{\mathit{F}}=\mathit{c}\mathit{o}\mathit{n}\mathit{s}\mathit{t}.$ | ${\mathsf{\Phi}}_{\mathit{e}}=\mathit{c}\mathit{o}\mathit{n}\mathit{s}\mathit{t}.$ | Advantages of the Proposed CLO |
---|---|---|---|

Time to L(90) (hours) | 64.4k h | 83k h | +29% |

Working years till L(90) | 16.7 years | 21.4 years | +4.7 years |

Electricity consumed till 64.4k hours | 130.8 kWh | 112.8 kWh | −13.7% |

Used energy in the 1st operational year | 7.9 kWh | 6.5 kWh | −17.7% |

Sample | ${\mathit{V}}_{\mathit{F}}$ Mismatch (mV) | ${\mathit{V}}_{\mathit{F}}$ Mismatch Compared to the Zero-Hour Results (%) | ${\mathsf{\Phi}}_{\mathit{e}}$ Mismatch (mW) | ${\mathsf{\Phi}}_{\mathit{e}}$ Mismatch Compared to the Zero-Hour Results (%) |
---|---|---|---|---|

#S07 | 10.2 mV | 0.3% | −21.7 mW | 5.4% |

#S11 | 0.1 mV | 0.003% | 3.2 mW | 0.8% |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Hegedüs, J.; Hantos, G.; Poppe, A.
Lifetime Modelling Issues of Power Light Emitting Diodes. *Energies* **2020**, *13*, 3370.
https://doi.org/10.3390/en13133370

**AMA Style**

Hegedüs J, Hantos G, Poppe A.
Lifetime Modelling Issues of Power Light Emitting Diodes. *Energies*. 2020; 13(13):3370.
https://doi.org/10.3390/en13133370

**Chicago/Turabian Style**

Hegedüs, János, Gusztáv Hantos, and András Poppe.
2020. "Lifetime Modelling Issues of Power Light Emitting Diodes" *Energies* 13, no. 13: 3370.
https://doi.org/10.3390/en13133370