Relationships between junction temperature, electroluminescence spectrum and ageing of light-emitting diodes

The lamp types studied with their key parameters are presented in table 1. At the beginning of the work, several new specimens of each five lamp type were chosen for different types of tests to study their ageing mechanisms. Some lamps were studied as they are, some were disassembled to extract the individual LEDs used as building blocks of the lamps, and some underwent ageing tests of different types. From the lamps selected, the Osram PAR16, Classic A40 and Classic A60 utilized blue InGaN LEDs with luminophore coating. Osram Classic A80 contained red AlGaInP LEDs in addition to InGaN LEDs with luminophore coating. Philips Master LED consisted of LED printed circuit boards (PCBs) and a bulb with remote luminophore plates. The disassembled LED PCBs consisted of uncoated blue InGaN LEDs.

The LED PCBs of all lamps disassembled were further equipped with conducting wires and studied in oil baths to derive the relationships between the forward voltage, junction temperature and operating current [13, 14]. The LEDs were driven by current pulses with a pulse length of 1.9 ms repeated every 10 s. The self-heating effect due to the pulses [15, 16] was not corrected from the forward voltage measurements, but afterwards the effect was studied with the result that the junction temperatures may be underestimated by 1 K to 3 K with low current levels of a few 100 mA. The self-heating becomes more pronounced at higher current levels. The LED spectra were measured at known temperatures by applying knowledge of the forward voltage over the LED. The final dataset contains the electroluminescence spectra of three LED specimens of each LED type (one red, one blue and four white types) at various known temperatures and electrical current levels.

Figure 1(a) presents the spectra of all lamp types tested. Although all the lamps are mainly based on blue LEDs with luminophore coating, the spectra deviate significantly from each other. The cool white spectrum of Osram PAR16 is obtained with yellow luminophore and Osram Classic A80 consists of similar yellow luminophore and red AlGaInP LEDs [18, 19]. The rest of the bulb types produce warm white light by mixing green, yellow and red luminophores in different ratios.

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We have six years of ageing data available for a set of LED lamps [5]. Four lamps of each type were aged under laboratory conditions and monitored periodically for luminous flux, luminous efficacy, relative spectral radiant flux and correlated colour temperature (CCT). Such long-term monitoring requires a reliable realization of the absolute scale of luminous flux, and thus all the luminous flux measurements made in monitoring the lamps were carried out using an integrating sphere facility with an expanded uncertainty of 0.9% [5, 20]. All spectral data measured for the ageing test were corrected for the spectral responsivity of the integrating sphere photometer, as well as for the spectral self-absorption of the lamps. Figure 1(b) shows the average relative luminous flux as a function of time for the different types of lamps.

The spectral models introduced later in this work need one spectrum at a known temperature to obtain material parameters for the DOS before the model can be used to derive junction temperature from measured spectra.

The forward voltage method, developed by Xi and Schubert [13] and JEDEC [14, 21], is one of the most accurate methods of calibrating individual LEDs for their junction temperature against the forward voltage of the LED. The forward voltage method is based on the old industry standard MIL-STD-750D [22], more specifically method 3101.3 that was adapted from the publication by Siegal [23]. The LEDs are submerged in a temperature-controlled oil bath and each LED is driven by short current pulses with simultaneous forward voltage measurement. As each LED component has its individual forward voltage properties, such calibration needs to be carried out separately for each LED. After the calibration, the LED spectrum at a known temperature can be measured by driving the LED with direct current corresponding to the amplitude of the current pulses during calibration and by varying the heatsink temperature until the forward voltage reaches the desired value.

The method by Zong and Ohno [24] applies the forward voltage method [13]. Instead of an oil bath, the LED is mounted on a heatsink, which can be set at temperatures between 10 °C and 100 °C. When no current is flowing through the LED, its junction and the heatsink are at the same temperature. The LED is driven by an electrical pulse and the forward voltage is measured simultaneously over the LED junction. Then, the LED is operated with a direct current that matches the amplitude of the pulse used in the calibration. The heatsink is cooled or heated until the forward voltage reaches the calibrated voltage. The junction temperature is now known and the spectrum can be measured. Later, self-heating of a few kelvins was observed even with short current pulses, and thus extrapolation of the rising temperature to the start of the pulse [15] was added to the method and documented to CIE 225:2017 [16].

We have studied the possibility of deriving an LED spectrum at room temperature, without the need for any synchronous measurements that could potentially be applied to LED lamps with a dimming option. An LED is driven by a pulse-width-modulated electrical current and the modulation ratio is changed. The electrical power causing excess heat that raises the junction temperature, reduces as the modulation ratio drops. For linear systems, the junction temperature waveform for any modulation ratio can be obtained from measurement of the step response [25]. The spectrum at ambient temperature can be constructed by extrapolating the relative changes in the spectral irradiance at each wavelength to the duty cycle of 0% according to figure 2. Duty cycles above 10% were used in order to reduce the effect of thermal transients close to the rising edge of the current pulse. One way to estimate whether these distortions are dominant is to check which normalized spectra intersect at the temperature-invariant energy value introduced in [26]. Broadened spectra affected by transients do not pass through the intersection point of other spectra and are excluded from the analysis.

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In our earlier studies [33], we modelled the spectra of the red AlGaInP quantum-well LEDs at various junction temperatures. These LEDs are similar to those in Osram Classic A80 lamps. In [33], the spectrum of an LED at a temperature of 303 K was divided by the corresponding Maxwell–Boltzmann distribution, and the obtained DOS was modelled as two exponentially broadened step functions:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \rho (\hbar \omega) =\, & \frac{A_{1}}{1 + \exp \! \left(- \frac{\hbar \omega - E_{\rm{g}} (T_{\rm j}) }{\xi_{1} + \Delta \xi_{1}}\right)} \nonumber \\ & + \frac{A_{2}}{1 + \exp \! \left(- \frac{\hbar \omega - \left(E_{\rm{g}} (T_{\rm j}) + \Delta E \right)}{\xi_{2} + \Delta \xi_{2}}\right)} , \label{eq:DOSred} \nonumber \end{align} \tag{ 7 }$$

where A₁ and A₂ are the step heights, $\xi_{1} + \Delta \xi_{1}$ and $\xi_{2} + \Delta \xi_{2}$ are the broadening parameters, and $\Delta E$ is the split-off energy of the sub-bands. For AlGaInP LEDs, the splitting of the valence band arises from the spin–orbit interactions [31]. According to our experiments, parameters $A_{1}/A_{2} = 2.13$, $\xi_{1} = 8.86$ meV, $\xi_{2} = 22.68$ meV and $\Delta E = 112.7$ meV are common for a specific LED type at varied junction temperatures and operating currents. Thus, they only need to be obtained once for each LED type. The absolute step heights and parameters E_g, $\Delta \xi_{1}$ and $\Delta \xi_{2}$ depend on T_j and operating current and thus need to be fitted for each normalized spectrum measured. Alternatively, as the bandgap energy $E_{\rm g} (T_{\rm j})$ is a function of T_j, it can be modelled using the Varshni formula with the mixing ratios x and y of a quaternary (Al_yGa_1−y)_xIn_1−xP alloy [31] as free parameters. Both ways produce the same results.

Experiments by Katahara and Hillhouse [34] and Wu et al [35] have shown that an exponentially broadened step function also describes the effective DOS of gallium arsenide (GaAs) LEDs and indium nitride (InN) thin films.

Junction temperatures obtained by modeling were compared with calibrated T_j obtained by the forward voltage method over the temperature range 303 K–398 K at current levels of 200 mA, 300 mA and 370 mA. The standard deviation between the modelled and measured junction temperatures was about 2.4 K (0.7%) and the maximum difference was 8.5 K [33]. When our method was compared with the slope method [9] and the peak shift method [10], it gave the most accurate junction temperatures while being able to model both sides of the spectra.

The temperature dependence of the electroluminescence spectrum emitted by a blue InGaN LED obtained from a Philips Master LED lamp is shown in figure 3. The spectra were measured using the setup and methods described in more detail in [33]. The modelled spectra (black solid lines) were fitted to measured spectra (coloured dotted lines) by the relative least-squares fitting method [36, 37]. Figure 4 presents the effective DOS obtained by fitting the spectral model to the measured spectrum with the Maxwell–Boltzmann distribution at the known temperature. Similar effective DOS shapes have been measured by, e.g. Nakamura [38], O'Donnell et al [39], Wang et al [27] and Lock et al [40]. As can be seen, the DOS does not follow an exponentially broadened step function as was the case for AlGaInP and GaAs LEDs. Instead, we have developed another DOS model,

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \rho (\hbar \omega) = \frac{A_{1}}{1 + \exp \! \left(- \frac{\hbar \omega - E_{\rm{g}} (T_{\rm j}) }{\sigma_{1} + \Delta \sigma}\right) + \exp \! \left(- \frac{\hbar \omega - \left(E_{\rm{g}} (T_{\rm j}) + \Delta E \right)}{\sigma_{2} + \Delta \sigma}\right)} , \label{eq:blueDOS} \nonumber \end{align} \tag{ 8 }$$

where A₁ is the step height; $\Delta E$ breaks the symmetry of the sigmoid function with the broadening parameters $\sigma_{1} + \Delta \sigma$ and $\sigma_{2} + \Delta \sigma$. Parameters that need to be calibrated using the reference spectrum at the known temperature are $\Delta E$, $\sigma_{1}$ and $\sigma_{2}$. The step height A₁, bandgap energy $E_{\rm{g}} (T_{\rm j})$ and the additional broadening parameter $\Delta \sigma$ change with changing T_j. The effective mixing ratio x in $E_{\rm{g}} (T_{\rm j})$ of equation (6) was also set as a temperature-independent free fitting parameter so that the spectral model with the DOS parameters calibrated could be used to model the spectrum of other LED specimens of the same type. The spectral range of  ±0.22 eV around the energy corresponding to the spectral irradiance peak was modelled.

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Ideally, the DOS of a quantum-well LED should form a step function. There are multiple mechanisms that may distort the InGaN DOS from this ideal form. The spectral peak emission of blue InGaN LEDs can be varied from 3.4 eV to 2.0 eV by increasing the indium content during the manufacturing process, until the collapse of the crystal structure [41]. The dislocations of the InGaN lattice arising from the lattice mismatch of the layers may reach  ∼10⁹ cm⁻² [42], and thus the DOS is broadened due to the variations in the local indium content and the spatial thickness in the quantum-well layer [29, 43], whereas the AlGaInP and GaAs LEDs can be grown with high crystal quality with dislocations less than  ∼10³ cm⁻² [42]. The deep localized states of the local indium-rich environment form excitons near the bound states [43, 44]. Such excitons are hydrogen-like systems and they have localized energies. At low temperatures with low carrier densities, they can be seen as additional peaks at the edges of each energy state contributing to the DOS [44]. Actually, the spin–orbit and crystal-field splitting of the valence band states can be determined from the exciton peaks present in reflectance and photoluminescence data measured at extremely low temperatures, e.g. 2 K [45].

What we see in the measured InGaN DOS in figure 4 is the rising edge of the lowest energy state [46], distorted by potential fluctuations of the lowest radiative states. A metallic p-contact acting as a mirror is sometimes used to enhance the light emission from the LED chip, which causes interference. Figure 3 shows the interference [47, 48] at 3.05 eV for the emission spectrum of Luxeon flip-chip blue LEDs [49] of Philips Master LED lamps.

The model in equations (4) and (8) was tested on three blue InGaN LEDs from Philips Master LED lamps operated at six values of T_j between 303 K and 398 K and four current levels I. The DOS parameters were calibrated against the normalized spectrum of LED #1 measured at $T_{\rm j} = 348$ K and I  =  205 mA. These model parameters were then used to derive junction temperatures of other spectra at various T_j and I, and also of spectra of the two other LED specimens of the same type. The junction temperatures derived are compared with the known reference temperatures presented in table 3. As can be seen, the model varies slightly. Differences change as a function of T_j and I, but mostly for different LED specimens. The standard deviation between the three samples over all the temperatures and current levels of table 3 is 11.2 K. The varying temperature introduces a standard deviation of 1.8 K and the varying current a standard deviation of 2.1 K. The results indicate that the model parameters vary among specimens and to a smaller extent as a function of T_j and I. The sample-to-sample variation can be explained to a large extent by variations in the material substrate and their effects on the DOS. The mixing ratios x converge to sample-specific values of $x = 0.1651 \pm 0.0016$ for LED #1, $x = 0.1556 \pm 0.0015$ for LED #2 and $x = 0.1611 \pm 0.0007$ for LED #3. If each LED specimen is calibrated separately using one spectrum at a known temperature, the overall standard deviation between the modelled and measured junction temperatures decreases from 11.2 K to 3.5 K.

Table 3. Differences $\Delta T_{\rm j}$ between the modelled and the reference junction temperatures of InGaN blue LEDs extracted from the Philips Master LED lamp. Calibration of the DOS parameters was carried out by fitting the spectral model in equation (4) with the DOS model of equation (8) to an experimental spectrum of LED #1 measured at the known junction temperature of 348 K and a current of 205 mA. Other spectra (also for LEDs #2 and #3) were modelled using these calibrated parameters so that the junction temperature was one of the fitting parameters.

		LED #1				LED #2				LED #3
I/mA	100	150	205	250	100	150	205	250	100	150	205	250
Tj/K		$\Delta T_{\rm j}$/K				$\Delta T_{\rm j}$/K				$\Delta T_{\rm j}$/K
303	−0.7	2.3	3.4	4.1	9.9	15.2	18.4	19.1	−15.4	−12.0	−10.3	−13.8
313	−0.5	1.4	2.0	3.8	7.8	12.6	16.9	18.7	−17.3	−13.7	−11.2	−10.5
323	−2.2	0.5	1.7	3.5	7.8	12.2	14.2	16.8	−15.1	−12.5	−11.9	−11.4
348	−2.0	0.1	−0.3	0.6	8.8	11.0	13.4	15.2	−14.1	−11.6	−10.5	−11.7
373	−1.7	−0.4	−0.4	0.0	11.0	13.8	14.1	15.1	−15.2	−13.2	−12.7	−11.7
398	−4.3	−3.3	−3.9	−2.8	9.1	11.3	13.1	13.0	−16.8	−15.9	−15.7	−14.1
$\Delta \bar{T}_{\rm j}$/K	−1.9	0.1	0.4	1.5	9.1	12.7	15.0	16.3	−15.7	−13.1	−12.0	−12.2

White LED spectra are spectrally more complex than blue LED spectra due to the photoluminescence of the luminophore coating. Modelling the photoluminescence would require knowing the absorption, excitation and emission spectra of each luminophore type used in the final mixture, and the thickness of the luminophore layer [50]. As the lamps studied in this work are of commercial type, we do not have access to such data, and thus we have to use more practical methods to account for the photoluminescence. The broadening parameters $\sigma_{1} + \Delta \sigma$ and $\sigma_{2} + \Delta \sigma$ of the effective DOS model in equation (8) can account for distortion by the photoluminescence. In addition, since the electroluminescence spectra of red LEDs can be modelled using equation (7), we separated their spectra from the white spectra of Osram Classic A80 according to figure 5.

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The spectral model developed for blue InGaN LEDs, validated using the blue LEDs extracted from Philips Master LED lamps, was tested on three white InGaN LEDs from Osram PAR16, Osram Classic A60 and Osram Classic A80 lamps. Osram Classic A40 was left out of the analysis because the blue peak and photoluminescence overlapped considerably. The LEDs were operated at their nominal currents as stated in table 1, at values of T_j between 303 K and 423 K. Three specimens of each LED type were considered. The effective DOS for each LED type was determined by determining DOS separately for the three LED specimens and averaging the model parameters. Spectra at other temperatures were then analyzed to derive optical junction temperatures that were compared with the known reference temperatures. The results are presented in table 4. Results are given as the averages of the LED specimens with standard deviations. On average, the standard deviation among the three white LED types is 8 K. Table 5 presents the average model parameters obtained for the different LED types.

Table 4. Average differences $\Delta T_{\rm j}$ between the modelled and the reference junction temperatures of three InGaN LED specimens of each lamp type with their standard deviations. The spectra were measured with direct currents of 205 mA for Master LED, 790 mA for PAR16, 380 mA for CL A60, and 370 mA for CL A80. The spectral ranges fitted are between $E_{\rm peak} \pm 0.22$ eV for Master LED, and between $E_{\rm peak} - 0.15$ eV and $E_{\rm peak} + 0.28$ eV for PAR16, CL A60 and CL A80. We could not measure all spectra of LED specimens of Master LED, CL A60 and CL A80 due to limitations in cooling and heating their junction.

Lamp type	Master LED	PAR16	CL A60	CL A80
Tj/K	$\Delta T_{\rm j}$/K	$\Delta T_{\rm j}$/K	$\Delta T_{\rm j}$/K	$\Delta T_{\rm j}$/K
303	$3.6 \pm 14.4$	$-9.8 \pm 7.5$	$-5.0 \pm 9.9$	—
313	$2.3 \pm 14.0$	$-2.4 \pm 7.1$	$-3.3 \pm 7.4$	—
323	$1.1 \pm 13.0$	$-0.8 \pm 6.6$	$0.1 \pm 7.4$	—
348	$0.7 \pm 12.0$	$-0.8 \pm 10.1$	$-0.7 \pm 7.1$	$-0.4 \pm 5.1$
373	$0.2 \pm 13.5$	$\ \ 3.2 \pm 11.5$	$6.1 \pm 6.9$	$4.2 \pm 4.5$
398	$-2.2 \pm 14.3$	$\ \ 4.4 \pm 14.5$	$7.5 \pm 7.3$	$6.7 \pm 3.2$
423	—	$\ 12.8 \pm 19.7$	—	$10.2 \pm 2.8$
$\Delta \bar{T}_{\rm j}$/K	$1.0 \pm 11.5$	$0.9 \pm 11.9$	$0.8 \pm 8.0$	$5.2 \pm 5.3$

Table 5. Average model parameters describing the effective DOS for each LED type, derived from the relative electroluminescent spectra measured at 348 K.

Parameters	Master LED	PAR16	CL A60	CL A80
$\sigma_{1}$/meV	18.63	19.20	21.07	20.43
$\sigma_{2}$/meV	69.13	50.63	53.17	55.67
$\Delta E$/meV	117.5	105.5	142.1	129.9