A method for junction temperature and luminous flux prediction of a white LED array

Abstract

The application belongs to the technical field of optical measurement, and particularly relates to a junction temperature and luminous flux prediction method of a white light LED array. The application combines a junction temperature prediction model and a luminous flux prediction model by analyzing a heat coupling heat transfer process of the LED array to construct an optical-thermal-electric prediction model. The model considers the heat coupling effect inside the LED array, and respectively performs junction temperature prediction through a TCM matrix model and a numerical algorithm model. The luminous flux model of a single LED is extended to the LED array. By inputting a driving current, a heat power and a temperature, the optical and thermal parameters of the LED array under different lighting modes are predicted. The application expands the current variation range and improves the prediction precision under the junction temperature condition.

Description

Technical Field

[0001] This invention belongs to the field of optical measurement technology, specifically relating to a method for predicting the junction temperature and luminous flux of a white LED array. Background Technology

[0002] In terms of junction temperature prediction, most junction temperature predictions are based on single-chip LEDs. Luo[1] predicted the junction temperature of a single Luxeon-packaged LED chip based on an analytical model. Some scholars predict the junction temperature based on the spectrum. Tamura et al.[2] pointed out in 2000 that the decay rate of blue light chips and phosphors is different with increasing temperature. Based on Tamura's work, Gu[6] proposed to use the blue-to-white ratio to characterize GaN-based white LEDs. The ratio of the total radiant energy (W) of the white LED to the radiant energy (B) of the blue light emission spectrum is used as the predicted value of the junction temperature. Chen[3] used the center wavelength method to characterize the junction temperature of AlGaInP-based LEDs. Lin et al.[4] proposed to use the centroid wavelength or half-wavelength (FWHM) combined with the driving current to characterize the junction temperature of the LED.

[0003] When multiple LED chips are combined into an LED array, the light emitted by each chip is absorbed, scattered and reflected by the surrounding materials, generating heat and affecting the performance and lifespan of the device. In LED array devices, the light emitted by the LED chip is absorbed by the surrounding materials, including the LED chip itself, the packaging material and the substrate. These materials undergo a thermalization process after absorbing the light, generating heat, which affects the temperature distribution and stability of the LED chip [5]. The LED chip itself also generates heat, which is transferred to the surrounding materials through thermal conduction, convection and radiation. Lu solved the problem of temperature measurement method for high-power multi-chip LED modules (MCM) [6] and proposed a fast and simplified measurement method to predict the junction temperature of the multi-chip module in a high-power LED system using a thermal coupling matrix. The proposed method uses the equivalent circuit (EEC) method to establish a thermal coupling matrix model to predict the junction temperature. Chen [7] also used the equivalent circuit method to simulate the lateral thermal coupling effect in the LED array and used the thermal coupling matrix to predict the junction temperature distribution of the LED array. Pohl et al. [8,9] proposed a numerical algorithm called "photothermal flux tracking" to solve the three-dimensional heat conduction problem, which includes simulating the thermal effects (heat transfer and generation) in the substrate and phosphor, as well as tracking the propagation and absorption of light. The method was finally validated using LED package samples with known phosphor ratios and parameters (conversion efficiency at different temperatures). Tang

[10] conducted a numerical investigation of the thermal performance of multi-chip (MC) LED modules using general analytical solutions.

[0004] In predicting the optical performance of white LEDs, Hui et al.

[11] linked the emission, electrical, and thermal aspects of LED systems. This theoretical model can be used to predict the optimal operating point for an LED system to achieve maximum luminous flux under specific thermal conditions. Based on this theoretical model, it is also possible to explain why the maximum luminous flux of an LED system may not occur under rated power conditions, and experimental verification has been conducted to support this theory. Based on this theory, they

[12] provided a theoretical tutorial on LED systems based on the extended PET theory. This tutorial provides materials for electronic engineers with a background in switching power supply design to optimize LED system design, such as k h k c Bin-Juine Huang et al.

[13] proposed a thermo-electric-optical model for multi-chip multi-color lighting fixtures for lighting control. Jeong Park et al.

[14] studied the influence of current diffusion layer and junction temperature on LED characteristics by combining the electrical and optical characteristics of GaN / InGaN multi-quantum-well sapphire LEDs, and can specifically conclude the influence of series resistance heating and junction temperature rise on LED efficiency.

[0005] Existing LED models clearly demonstrate their working mechanisms and the entire process of electroluminescence and heat dissipation. However, the heat transfer process in an LED array is more complex than when a single LED chip operates independently. The thermal coupling process is particularly intricate. Especially in high-power LED array systems, due to thermal coupling effects, the temperature distribution of the LED array is more influenced by adjacent chips, thus the photothermal equations for a single LED chip cannot be directly applied. Current research largely focuses on single-packaged white LEDs or the thermal coupling effect of LEDs, rarely combining both approaches to consider the thermal coupling effect between LED arrays while predicting their optical performance. Furthermore, current research primarily focuses on thermal coupling under ambient temperature conditions, largely neglecting the influence of case temperature (ambient temperature) at a fixed temperature.

[0006] Terminology Explanation:

[0007] (1) Junction temperature: The actual operating temperature of semiconductors in electronic devices, which is usually higher than the package temperature during operation;

[0008] (2) Luminous flux: refers to the radiant power that the human eye can perceive. It is equal to the product of the radiant energy of a certain band per unit time and the relative visibility of that band. Summary of the Invention

[0009] The purpose of this invention is to provide a method for predicting the junction temperature and luminous flux of a white LED array with high prediction accuracy.

[0010] To analyze the optical performance of LED arrays under different driving currents and temperatures, this invention proposes a light-thermal-electric prediction model that combines a junction temperature prediction model and a luminous flux prediction model by analyzing the thermal coupling heat transfer process of the LED array. The model considers the thermal coupling effect within the LED array and uses both a TCM matrix model and a numerical algorithm model to predict the junction temperature. Furthermore, the luminous flux model for a single LED is extended to the entire LED array. By inputting the driving current, thermal power, and temperature, this invention predicts the optical and thermal parameters of the LED array under different lighting conditions.

[0011] The method for predicting the junction temperature and luminous flux of a white LED array provided by this invention includes the following specific steps:

[0012] (a) Constructing an LED luminous flux prediction model for predicting LED luminous flux.

[0013] The luminous flux of an LED is affected by current and temperature. As the current and heat power increase, the luminous flux increases, and the heat generated by the chip also increases, which will lead to a decrease in the luminous efficiency of the LED device, thereby reducing the luminous efficacy of the chip. In order to predict the luminous flux of a single LED and an LED array under different operating conditions, a luminous flux response surface model is proposed

[15] . This model is named Model I, as shown in formula (1):

[0014]

[0015] Wherein, HC (heating coefficient) represents the degree to which luminous efficacy changes with junction temperature, and D represents the degree to which luminous efficacy changes with current. Indicates the rated drive current, rated operating temperature, and luminous flux at the rated drive current and operating temperature; I f ,T j These are parameters for drive current and operating temperature.

[0016] With the maturity of LED technology, more and more white LEDs are being used in various fields, and Model I can well describe the light emission of phosphor-converted white LEDs. However, for some extreme cases and special scenarios, Model I cannot accurately capture the LED light emission. When pursuing high luminous efficacy, minimal input current, high power, and high luminous flux, Model I is not well applicable. Based on this, Model II is proposed, which can accurately predict LED luminous flux over a large current variation range.

[0017]

[0018] α1 and α2 are obtained from the following formula:

[0019] α1=1+α2 , (3)

[0020]

[0021]

[0022]

[0023] Where HC0 is the rated HC factor, m is the current coefficient of the HC factor, and n is the temperature power coefficient of the luminous flux.

[0024]

[0025] Compared to Model I, Improved Model II introduces... and HC(I) f The function improves the range of current variation; at the same time, it introduces... Increase prediction accuracy under junction temperature conditions, Φ v For the rated luminous flux, C e is the coefficient of change of luminous flux with current.

[0026] (ii) Constructing an LED array junction temperature prediction model for LED array junction temperature prediction.

[0027] (a) TCM model

[0028] When an LED is placed on a temperature-controlled platform and lit, the thermal conductivity above the chip is very low, and very little heat dissipates from above; the heat dissipation path is from the LED chip downwards. According to thermal resistance theory, its equivalent thermal resistance model is as follows: Figure 6 As shown in (a), the junction temperature of a single LED under different driving currents can be obtained through thermal resistance, as shown in equation (8):

[0029] T j =T c +ΔT=T c +P i ×R=T c +P i ×(R1+R2+R3), (8)

[0030] Among them, T c It refers to the temperature of the temperature control platform. (P) i For thermal power, R is equivalent to LED. i The thermal resistances are given by R1, R2, and R3, which represent the thermal transfer resistance between the LED chip and the PCB board, the thermal transfer resistance between the PCB board and the temperature control platform, and the thermal convection resistance between the heat sink and the environment, respectively.

[0031] According to the LED array Figure 6 As shown in (b), n identical LED chips are mounted on the same PCB, P1, P2, P3…P jR represents the heat power generated by each LED. ij Let P be the equivalent thermal resistance between the i-th LED and the j-th LED. For the i-th LED, P i The temperature rise caused by this process can be expressed as ΔT. ii =R ii ×P i If the j-th LED will reduce the total heat power P j η ij If the heat is transferred to the i-th LED via a lateral heat path, then the temperature rise of the i-th LED can be expressed as its own temperature rise plus the lateral temperature rise, i.e.:

[0032]

[0033] Introducing parameter μ ij =η ij ×R ij , and η ii =1. This parameter is the thermal coupling coefficient, reflecting the degree of thermal coupling. When the structure and materials of the LED array are determined, the coefficient μ is a constant, and the temperature rise can be represented by a matrix as follows:

[0034] Abbreviated as:

[0035]

[0036] The junction temperature of the matrix can then be expressed as formula (11):

[0037]

[0038] (b) Numerical Algorithm Model

[0039] Since thermal coupling directly affects the chip junction temperature when multiple LEDs are illuminated, it is necessary to model the thermal coupling phenomenon separately. The steady-state Laplace equation for heat transfer is expressed as follows:

[0040]

[0041] The coordinate axes are centered at the top surface corner of the substrate, with the positive Z-axis pointing in the direction of heat conduction. Figure 10 As shown. The substrate size is L. x *L Y The LED has dimensions a*b. The coordinates of the center point of the LED are (X, B, C). c ,Y c );

[0042] Assume the substrate is insulated on all sides. The bottom surface maintains a temperature constant T0. The top surface has heat input only in the area covered by the chip; other locations are set as adiabatic boundaries. Under these boundary conditions, the temperature distribution at each location when a single chip is heated can be expressed as:

[0043]

[0044]

[0045]

[0046]

[0047]

[0048] A o =T0, (18)

[0049]

[0050] Among them, θ(x,y,z)=T(x,y,z)-T f ,λ=mπ / L x ,δ=nπ / L y , A i =φ(ξ)B i Let i = 1, 2, 3, where ξ = λ, δ, or β. The substrate thickness is t, the thermal conductivity of the material is k, the heat power generated by the LED is Q, and θ represents the temperature rise. f This represents the ambient temperature. Due to the linear superposition property of heat conduction, the temperature distribution of multiple heat sources applied to the substrate can be expressed as:

[0051]

[0052] As ambient temperature increases, the temperature distribution of multiple heat sources on the substrate can be represented as follows:

[0053]

[0054] Where T air The ambient temperature.

[0055] (III) Calculation of LED Array Luminous Flux Prediction

[0056] LED array luminous flux prediction model, such as Figure 11 As shown, firstly, the junction temperature of the LED array under different lighting methods, driving currents, and temperatures is predicted using a junction temperature model to obtain the junction temperature of each LED in the LED array. Then, based on the obtained junction temperature of each LED and the luminous flux model of a single LED, the luminous flux of each LED is obtained. Finally, the luminous flux of all individual LEDs in the LED array is summed to obtain the luminous flux of the LED array. The junction temperature model is either a TCM model or a numerical algorithm model; the single LED luminous flux model is either Model I or Model II. Attached Figure Description

[0057] Figure 1 For LUXEON Neo CW 0.5mm² LED: (a) LED structure diagram; (b) packaged single LED module; (c) chip physical image.

[0058] Figure 2 This is an LED array module. (a) is a physical image, and (b) is a 3D model.

[0059] Figure 3 There are six ways to light up an LED array.

[0060] Figure 4 This is a junction temperature testing system.

[0061] Figure 5 This is a system for testing the photoelectric parameters of a single LED.

[0062] Figure 6 This is a heat transfer model for LEDs. (a) shows a single LED, and (b) shows an LED array.

[0063] Figure 7 Simulation of a 3x3 LED array.

[0064] Figure 8 (a)ΔT2,ΔT3,ΔT4,ΔT5,ΔT6,ΔT7,ΔT8,ΔT9 VS Pth of 1st LED; Figure 8 (b) is ΔT1 VS Pth of 1st LED.

[0065] Figure 9 This is a flowchart illustrating the thermal coupling between any chips in a 3×3 chip model.

[0066] Figure 10 An isotropic plate with a single heat source.

[0067] Figure 11 This is a flowchart for predicting the luminous flux of an LED array.

[0068] Figure 12 The junction temperature of the LED array is predicted under a case temperature of 60℃ and a driving current of 0.2A. (a) shows the finite element simulation results, and (b) shows a comparison of the results.

[0069] Figure 13 This paper presents the prediction of the junction temperature of an LED array under the illumination mode. (a) shows the finite element simulation results, and (b) shows a comparison of the results.

[0070] Figure 14 The temperature distribution is shown in the LED array area. (a) is on the top surface of the PCB; (b) is on the bottom surface of the PCB.

[0071] Figure 15 Comparison of junction temperatures of numerical models under different Fourier iteration numbers and different timing lengths.

[0072] Figure 16 The results are the fitting results for a single LED model I. (a)#LED1; (b)#LED2; (c)#LED3.

[0073] Figure 17 The fitting results for single LED Model II are as follows: (a)#LED1; (b)#LED2; (c)#LED3.

[0074] Figure 18 This is a comparison of the sample luminous flux with experimental results. Detailed Implementation

[0075] The present invention will be further described below with reference to the embodiments and accompanying drawings.

[0076] I. Samples and Experiments

[0077] The sample used in this invention is a LUXEON Neo CW 0.5mm² LED chip manufactured by Lumilieds, such as... Figure 1 As shown:

[0078] like Figure 1 As shown in (a), the main structure of an LED chip includes phosphor on the top of the chip, polarity markings to distinguish the anode and cathode when soldering current is applied, a side coating protecting the package structure, an embedded transient voltage suppressor, an optical character recognition code to distinguish the chip type, and electrical pads for the anode and cathode. The LED chip area is 0.5 mm². 2 The light-emitting area is 0.76mm x 0.76mm, and the package size is 1.13mm x 1.13mm. The rated voltage and rated current of the LUXEON Neo CW 0.5mm² LED are 3.13V and 350mA, respectively. To obtain the luminous flux and junction temperature parameters of a single LED, the chip was packaged, and a LUXEON Neo CW 0.5mm² LED single-chip module was fabricated, as shown below. Figure 1 As shown in (b), the PCB is an aluminum-based copper-clad board with a size of 10mm x 10mm, an aluminum substrate thickness of 1.6mm, a copper wire thickness of 35um, and a wire diameter and spacing of 0.3mm.

[0079] The configuration of the LED array module experimental sample and the 3D LED module is as follows: Figure 2As shown, an LED array is formed by connecting 84 LEDs in series. The module consists of LEDs and a PCB substrate, and the LEDs in the module are completely identical to those in a single module sample. Each LED is spaced 1.6mm horizontally and 2.42mm vertically. The PCB substrate measures 8cm × 13cm, and the aluminum substrate is 2mm thick. In the experiment, different lighting modes were achieved by short-circuiting the LEDs with wires. The lighting modes involved in the array experiment are as follows... Figure 3 As shown, there are six possible scenarios: (a) all four lights are on, (b) all four lights are on with a gap between them, (c) two lights are on diagonally opposite each other, (d) two lights are on side by side, (e) all six lights are on, and (f) all nine lights are on. These six scenarios are named: Sample1, Sample2, Sample3, Sample4, Sample5, and Sample6 for easy differentiation later.

[0080] To obtain Figure 1 LUXEON Neo CW 0.5mm² LED single-chip module and Figure 2 The junction temperature, luminous flux, and other parameters of the LED array under different lighting methods were investigated, and a relationship model between luminous flux and junction temperature was established. The following test scheme was designed, and Table 1 lists the test schemes for the samples under different currents and different casing temperatures.

[0081] Table 1. Test Scheme for Single LED and LED Module

[0082]

[0083] To ensure experimental accuracy, reduce experimental errors, and eliminate the influence of factors such as airflow, personnel interference, and ambient temperature, all experiments were conducted in a windproof chamber with the ambient temperature controlled at 27℃. Junction temperature was measured using a LEETS LEDT-300B junction temperature measuring instrument (K-coefficient error within ±0.5, junction temperature error within ±1℃). The junction temperature testing equipment consisted of: a data acquisition computer, a LEETS junction temperature measuring instrument, a heating oven (ESPEC, ST-110), a DC power supply (KEYSIGHTN 5751), and a temperature-controlled heating platform. Figure 4 As shown. The junction temperature is measured using the forward voltage method, which mainly includes two parts: calibration and measurement. The calibration part mainly obtains the coefficient relationship of K, and is mainly carried out in an oven. The testing part uses a temperature control platform to control the sample's shell temperature. To ensure good thermal conductivity between the sample and the heating platform, thermal grease needs to be applied to the LED sample substrate. At the same time, the LED sample is fixed on the temperature control platform with a clamp to ensure good thermal contact between the bottom of the LED sample substrate and the temperature control platform.

[0084] Individual LEDs and LED array modules use integrating spheres with radii of 0.5m and 2m respectively to collect photoelectric parameters, using the same acquisition method. For example... Figure 5 As shown, the photoelectric parameter testing device consists of an integrating sphere (EVERFINE HASS2000), a DC power supply (KEYSIGHT N5751), a temperature control platform (EVERFINE LED-220T), and a computer for data collection. The test sample is fixed to the temperature control platform with silicone grease, and data is collected after ten minutes when thermal equilibrium is reached.

[0085] II. Model Construction

[0086] (1) Single LED luminous flux response model:

[0087] The luminous flux of an LED is affected by current and temperature. As the current and heat power increase, the luminous flux increases, and the heat generated by the chip also increases, which will lead to a decrease in the luminous efficiency of the LED device, thereby reducing the luminous efficacy of the chip. In order to predict the luminous flux of a single LED and an LED array under different operating conditions, a luminous flux response surface model is proposed

[15] . This model is named Model I, as shown in formula (1):

[0088]

[0089] Wherein, HC represents the degree to which luminous efficacy changes with junction temperature, and D represents the degree to which luminous efficacy changes with current. It indicates the rated drive current, rated operating temperature, and luminous flux at the rated drive current and operating temperature.

[0090] With the maturity of LED technology, more and more white LEDs are being used in various fields, and Model I can well describe the light emission of phosphor-converted white LEDs. However, for some extreme cases and special scenarios, Model I cannot accurately capture the LED light emission. When pursuing high luminous efficacy, minimal input current, high power, and high luminous flux, Model I is not well applicable. Based on this, Model II is proposed, which can accurately predict LED luminous flux over a large current variation range.

[0091]

[0092] α1 and α2 are obtained from the following formula:

[0093] α1 = 1 + α2, (3)

[0094]

[0095]

[0096]

[0097] Where HC0 is the rated HC factor, m is the current coefficient of the HC factor, and n is the temperature power coefficient of the luminous flux.

[0098]

[0099] Compared to Model I, Improved Model II introduces... and HC(I) f The function improves the range of current variation; at the same time, it introduces... Increase the accuracy of predictions under junction temperature conditions.

[0100] (2) LED array junction temperature model

[0101] (a) TCM model

[0102] When an LED is placed on a temperature-controlled platform and lit, the thermal conductivity above the chip is very low, and very little heat dissipates from above; the heat dissipation path is from the LED chip downwards. According to thermal resistance theory, its equivalent thermal resistance model is as follows: Figure 6 As shown in (a), the junction temperature of a single LED under different driving currents can be obtained through thermal resistance, as shown in equation (8):

[0103] T j =T c +ΔT=T c +P i ×R=T c +P i ×(R1+R2+R3), (8)

[0104] Among them, T c It refers to the temperature of the temperature control platform. (P) i For thermal power, R is equivalent to LED. i The thermal resistances are given by R1, R2, and R3, which represent the thermal transfer resistance between the LED chip and the PCB board, the thermal transfer resistance between the PCB board and the temperature control platform, and the thermal convection resistance between the heat sink and the environment, respectively.

[0105] According to the LED array Figure 6 As shown in (b), n identical LED chips are mounted on the same PCB, P1, P2, P3…P j R represents the heat power generated by each LED. ij Let P be the equivalent thermal resistance between the i-th LED and the j-th LED. For the i-th LED, P i The temperature rise caused by this process can be expressed as ΔT. ii =R ii ×P i If the j-th LED will reduce the total heat power Pj η ij If the heat is transferred to the i-th LED via a lateral heat path, then the temperature rise of the i-th LED can be expressed as its own temperature rise plus the lateral temperature rise, i.e.:

[0106]

[0107] Introducing parameter μ ij =η ij ×R ij , and η ii =1. This parameter is the thermal coupling coefficient, reflecting the degree of thermal coupling. When the structure and materials of the LED array are determined, the coefficient μ is a constant, and the temperature rise can be represented by a matrix as follows:

[0108] The gap is:

[0109]

[0110] The junction temperature of the matrix can then be expressed as formula (11):

[0111]

[0112] This model is based on finite element thermal simulation performed in Autodesk CFD 2023 to estimate the temperature of the sample and verify the TCM. To verify the thermal coupling between any two chips in the LED array and derive the TCM rules, [the model is then used to]... Figure 7 The 3x3 chip model shown is used for simulation. The three chips are arranged in a row, for a total of three rows, and are labeled as LED1#, 2#, 3#, 4#, 5#, 6#, 7#, 8#, and 9# from left to right and top to bottom, respectively. The key parameters used for simulation (including thermal resistance and key materials) are listed in the tables, as shown in Tables 2 and 3.

[0113] Table 2. Thermal resistance used in the simulation

[0114]

[0115] Table 3. Key material parameters in the simulation

[0116]

[0117] LED1# can heat up, which can be expressed as ΔT1=μ 11 P1+μ 12 P2+μ 13 P3+μ 14 P4+μ 15 P 5+ μ 16 P6+μ 17 P7+μ 18 P8+μ19 P9. Keeping the power of other LEDs constant, change the thermal power of P2, measure ΔT1, and fit the curve to obtain μ. 12 (like Figure 8 (As shown). Similarly, the coefficients of the remaining matrix can also be obtained. To verify the TCM matrix, the flowchart (as shown) is provided. Figure 9 The process of thermal coupling between any two chips is illustrated in the figure. Finally, the ninth-order TCM of sample 6 can be expressed as:

[0118]

[0119] (b) Numerical Algorithm Model

[0120] Since thermal coupling directly affects the chip junction temperature when multiple LEDs are illuminated, it is necessary to model the thermal coupling phenomenon separately. The steady-state Laplace equation for heat transfer is expressed as follows:

[0121]

[0122] The coordinate axes are centered at the top surface corner of the substrate, with the positive Z-axis pointing in the direction of heat conduction. Figure 10 As shown. The substrate size is L. x *L Y The LED has dimensions a*b. The coordinates of the center point of the LED are (X, B, C). c ,Y c ).

[0123] Assume the substrate is insulated on all sides. The bottom surface maintains a constant temperature T0. The top surface has heat input only in the area covered by the chip; other locations are set as adiabatic boundaries. Under these boundary conditions, the temperature distribution at each location when a single chip is heated can be expressed as:

[0124]

[0125]

[0126]

[0127]

[0128]

[0129] A o =T0, (18)

[0130]

[0131] Among them, θ(x,y,z)=T(x,y,z)-T f ,λ=mπ / Lx ,δ=nπ / L y , A i =φ(ξ)B i The substrate thickness is t. The thermal conductivity of the material is k. The heat power generated by the LED is Q. θ represents the temperature rise. T f This represents the ambient temperature. Due to the linear superposition property of heat conduction, the temperature distribution of multiple heat sources applied to the substrate can be expressed as:

[0132]

[0133] As ambient temperature increases, the temperature distribution of multiple heat sources on the substrate can be represented as follows:

[0134]

[0135] (3) LED array luminous flux model

[0136] LED array luminous flux prediction model, such as Figure 11 As shown:

[0137] First, the junction temperature of the LED array under different lighting methods, drive currents, and temperatures is predicted using a junction temperature model to obtain the junction temperature of each LED. Then, based on the obtained junction temperatures of each LED, the luminous flux of each LED is calculated and summed according to the single LED luminous flux model to obtain the luminous flux of the LED array.

[0138] III. Results and Discussion

[0139] (1) Junction temperature model

[0140] (a) TCM model

[0141] The 9th-order TCM matrix of sample 6 was obtained through simulation at a shell temperature of 60℃. Simulation was then performed with a driving current of 0.2A, and the simulation results were compared with those calculated using the TCM model. The simulation results and TCM model prediction results are shown below. Figure 12 As shown:

[0142] Under the same conditions, sample 1 ( Figure 3 (a) Finite element simulation of all four LEDs lit to verify whether the TCM model is still applicable when some LEDs in the array are lit. The input thermal power of the remaining five unlit LEDs is 0W, and the input power of LEDs 1#, 2#, 4#, and 5# is 0.46W, as shown in Formula 12:

[0143]

[0144] The calculated array junction temperature and finite element simulation results for sample 1 are as follows: Figure 13 As shown:

[0145] from Figure 12 and Figure 13 As can be seen, the error between the finite element simulation results and the TCM results is within 0.0015%, indicating that the TCM model can be applied to predict junction temperature under different case temperatures, drive currents, and LED array lighting methods without requiring finite element simulation. From the TCM model, we can conclude that: 1) μ is only related to distance; the larger the distance, the smaller the coefficient; 2) the TCM matrix is ​​a symmetric matrix, μ... ij =μ ji 3) When some LEDs in the array are lit or in different lighting modes, the junction temperature can also be predicted using this TCM.

[0146] (b) Numerical Algorithm Model

[0147] The connection between LED chips is between air and the PCB substrate. Air has very weak convective heat transfer capabilities, so it is reasonable to analyze thermal coupling only on the PCB where heat conduction is vertical. Under the same chip parameters and input power, the temperature rise caused by the thermal resistance above the substrate is also the same for each chip. To verify the accuracy of the numerical modeling, [the following was used]. Figure 12 Simulation settings. Figure 14 The temperature distribution on the top surface of sample 6 is shown. As numerical thermal modeling progressed, the junction temperatures of each chip on the bottom surface of the PCB were summarized and analyzed in Table 4.

[0148] Table 4 Comparison of junction temperature modeling in numerical models (Sample 6)

[0149]

[0150]

[0151] When all nine LEDs are lit simultaneously, multiple temperature peaks are clearly visible. Due to the larger chip spacing on the X-axis compared to the Y-axis, the thermal coupling effect is weaker, resulting in a wider low-temperature region between adjacent chips. The temperature predicted by the numerical simulation is typically 3°C lower than that of the TCM. This difference stems from the absence of contact thermal resistance in the numerical model. The stepped temperature rise caused by the contact thermal resistance between the LEDs and solder, and between the PCB and the temperature control platform, can be directly superimposed at the end of the calculation. The accuracy of the calculation significantly impacts the results. The junction temperature of a single chip with an input power of 0.5W and the computation time for 10, 30, 50, and 80 Fourier iterations were compared, with step sizes of 100e-5, 50e-5, and 20e-5, respectively.

[0152] A comparison of junction temperatures of numerical models under different Fourier iteration numbers and different timing lengths is shown in [reference needed]. Figure 15 .from Figure 15It can be seen that the number of Fourier iterations determines the flatness of the waveform. The calculation step size determines the accuracy of the evaluation. The step size has no effect on the temperature calculation, but the number of iterations does affect the temperature. The junction temperature increases with the number of iterations. The TCM model is suitable for predicting the junction temperature of fixed samples under different shell temperatures and currents. The TCM matrix solution process is relatively time-consuming, but it can be used for rapid prediction without needing to re-simulate under different conditions. Numerical calculation methods can also characterize the junction temperature prediction results. The calculation speed is faster than the TCM matrix solution process for different samples; however, it is slower than the same sample under various modes with a known TCM matrix.

[0153] (2) Luminous flux model

[0154] (a) Luminous flux response surface model of a single LED

[0155] After completing the optical-electrical-thermal data acquisition, the luminous flux and junction temperature under different currents and case temperatures were obtained. The data from the three single LED chip samples were fitted using Model I and Model II, and the fitting results are shown below. Figure 16 , Figure 17 The parameters of the two extracted models are listed in Tables 5 and 6, respectively:

[0156] Table 5. Fitting results of Model I

[0157] #LED1 0.86312 0.77636 0.99684 #LED2 0.82419 0.81788 0.99388 #LED3 0.84843 0.81076 0.99263

[0158] Table 6. Fitting results of Model II

[0159] #LED1 0.86361 -0.02096 0.97948 1.59403 0.901584 0.99906 #LED2 0.80845 -0.0286 0.95215 1.60895 0.901584 0.99919 #LED3 0.82552 -0.04099 0.91987 1.25231 0.901584 0.99935

[0160] Simulation results show that both Model I and Model II achieve good fitting results. However, the improved luminous flux response surface model adds three parameters: n, m, and C. e Model II R 2 Slightly higher than Model I, both Model I and Model II can be used for luminous flux prediction. However, it is worth noting that Model II is more accurate for extreme conditions than Model I, and the improved luminous flux response surface model is more suitable for capturing and describing the luminous flux of LED products under different operating conditions. When D is closer to 1, it indicates that the luminous flux changes linearly with the current. In Models I and II, #LED2 has the smallest D, indicating that the luminous efficacy of #LED2 decreases more severely with increasing current.

[0161] (b) Validation of LED array luminous flux model

[0162] From section 4.1, the junction temperature of sample array 1 under a driving current of 0.2A and a case temperature of 60℃ can be obtained. Substituting the junction temperature and driving current into the luminous flux response surface model, the luminous flux of each LED under Model I and Model II conditions is obtained respectively. The luminous flux of the array is obtained by superimposing these values. Table 7 shows a comparison between the prediction results obtained through the luminous flux response surface model and the experimental results.

[0163] Table 7. Results of the luminous flux model (for sample 1 under driving current of 0.2A and shell temperature of 60℃)

[0164]

[0165] Meanwhile, the results for samples 2, 3, 4, 5, and 6 at 60℃ were compared with the experimental results, as follows: Figure 18 As shown:

[0166] For LED arrays, the error of Model II can be controlled within 3%, while the error of Model I exceeds 20%. Model II's luminous flux is more accurate than Model I's, verifying the conclusion in 4.2.1 that Model II is more suitable for extreme conditions. The predicted luminous flux is higher than the experimentally measured luminous flux, which may be related to the fact that the minimal light loss of the LED is due to photon collisions in space, resulting in energy reduction and a slight decrease in luminous flux. The model error increases with the number of samples, possibly due to differences between samples. The three single LED samples also show a certain difference in luminous flux between samples under the same conditions. At a shell temperature of 60℃ and a current of 0.2A, the luminous flux of a single LED is 56.83 ml. The average luminous flux of each LED in samples 1, 2, 3, 4, 5, and 6 is lower than that of a single LED, indicating a coupling effect in the LED array. Sample 6 shows the most significant decrease in luminous flux, indicating the most severe coupling phenomenon. As the spacing between LEDs decreases, the thermal coupling effect intensifies and the LED temperature rises; as the number of LEDs in the LED array module increases, the thermal coupling effect intensifies and the LED temperature rises significantly.

[0167] IV. Summary

[0168] This invention first collects the junction temperature and luminous flux of a single LED operating under different driving currents and case temperatures, establishing a luminous flux response surface model for a single chip. Then, thermal coupling analysis and junction temperature prediction are performed on the array of LEDs using a TCM model and a numerical algorithm model. Comparing the junction temperatures obtained from the TCM model and the numerical algorithm model, the differences are small, but the numerical algorithm model significantly accelerates the computation speed and efficiency. Substituting the junction temperature, driving current, and case temperature of each LED obtained through the junction temperature prediction model into the luminous flux response surface model and comparing it with the experimentally measured luminous flux, the error of Model II is within 5%. The results show that: 1) The luminous flux response surface model can predict the luminous flux of a single LED well. For LED arrays, the junction temperature increases due to thermal coupling. In this case, Model II is more accurate than Model I, indicating that Model II can also be used under extreme conditions; 2) The proposed junction temperature prediction model, which indirectly reflects the experiment, including the TCM model and the numerical algorithm model, is feasible for describing the thermal coupling effect of LED arrays and has high junction temperature prediction accuracy. It can also be used when some LEDs in the array are lit; 3) The optical-electrical-thermal model realizes the combination of optical, electrical and thermal, and can be used to predict the optical and thermal parameters of LED arrays with an accuracy of 95%. Using this model to quickly predict the junction temperature and luminous flux of large LED systems with array structures is very effective.

[0169] To achieve optimal optical performance of LED arrays under varying drive currents and temperatures, this invention proposes a photo-thermal-electrical model that combines a junction temperature prediction model with a luminous flux prediction model. Junction temperature prediction is performed using both a TCM matrix model and a numerical algorithm model, taking into account the thermal coupling effect within the LED array. The developed luminous flux model models individual LEDs and then the entire LED array. By combining the luminous flux model with the junction temperature prediction model, and inputting drive current, thermal power, and temperature, the optical and thermal parameters of the LED array under different lighting conditions are predicted. This photo-electrical-thermal model achieves a combination of photo-electrical and thermal parameters and can be used to predict the optical and thermal parameters of LED arrays with an accuracy of 95%. Using this model is highly effective for rapidly predicting the junction temperature and luminous flux of large-scale LED systems with array structures.

[0170] Compared to Lu[6], which not only provides the junction temperature and considers the coupling phenomenon between LED arrays, but also adds optical parameters to link the light, heat and electricity. Given the current, thermal power and case temperature, the luminous flux distribution can be obtained. Compared to Tang

[10] , the numerical algorithm in this article improves the model and considers the influence of case temperature. The light-electricity-heat model realizes the combination of light, electricity and heat, and can be used to predict the optical and thermal parameters of LED arrays with an accuracy of 95%. Using this model to quickly predict the junction temperature and luminous flux of large LED systems with array structures is very effective.

[0171] References:

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[0174] [3]K. Chen and N. Narendran, "Estimating the average junction temperature of AlGaInP LED arrays by spectral analysis," Microelectronics Reliability, vol. 53, no. 5, pp. 701-705, 2013.

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Claims

1. A method for predicting the junction temperature and luminous flux of a white LED array, characterized in that, By analyzing the thermal coupling heat transfer process of LED arrays, a light-heat-electricity prediction model is constructed by combining the junction temperature prediction model and the luminous flux prediction model. The model considers the thermal coupling effect within the LED array, and the junction temperature is predicted using both the TCM matrix model and the numerical algorithm model. Specifically, the luminous flux model of a single LED is extended to the entire LED array. By inputting the driving current, thermal power, and temperature, the optical and thermal parameters of the LED array under different lighting conditions are predicted. The specific steps are as follows: (i) Construct an LED luminous flux prediction model for predicting LED luminous flux. A luminous flux response surface model, named Model I, is shown in formula (1): ， （1） in, The HC coefficient of thermal conductivity represents the degree to which luminous efficacy changes with junction temperature, while D represents the degree to which luminous efficacy changes with current. , , These represent the rated drive current, rated operating temperature, and luminous flux at the rated drive current and operating temperature, respectively. These are parameters for drive current and operating temperature. To adapt to the pursuit of high luminous efficacy with low input current, as well as high power and high luminous flux, Model II is further proposed. This model can accurately predict LED luminous flux over a large range of current variations. ， （2） and It can be obtained from the following formula: ， （3） ， （4） ， （5） ， （6） in, For rated factor, The current coefficient of the HC factor. The temperature power coefficient of luminous flux; ， (7) Compared to Model I, Improved Model II introduces... and Functions are introduced to improve the range of current variations; at the same time, the following are also introduced: This increases the accuracy of predictions under junction temperature conditions; Rated luminous flux, The coefficient of change of luminous flux with current; (ii) Construct an LED array junction temperature prediction model for predicting LED array junction temperature. (a) TCM model According to the thermal resistance theory, the junction temperature of a single LED under different driving currents can be obtained through thermal resistance, as shown in equation (8): ， （8） in, It refers to the temperature of the temperature control platform; For thermal power, Equivalent substitution The thermal resistance, of which These represent the thermal resistance for heat transfer between the LED chip and the PCB board, the thermal resistance for heat transfer between the PCB board and the temperature control platform, and the thermal resistance for heat convection between the heat sink and the environment, respectively. In an LED array, n identical LED chips are mounted on the same PCB. , , … These represent the heat power generated by each LED. Let be the equivalent thermal resistance between the i-th LED and the j-th LED. For the i-th LED, The increase in its own temperature is represented as If the j-th LED will reduce the total heat power of If the heat is transferred to the i-th LED via a lateral heat path, then the temperature rise of the i-th LED is expressed as its own temperature rise plus the lateral temperature rise, i.e.: ， （9） Introducing parameters ,and This parameter is the thermal coupling coefficient, reflecting the degree of thermal coupling. When the structure and materials of the LED array are determined, the coefficient... As a constant, the temperature rise can be represented by a matrix as follows: Abbreviated as: The junction temperature of the matrix is ​​then expressed as formula (11): ， （11） (b) Numerical algorithm model Since thermal coupling directly affects the chip junction temperature when multiple LEDs are illuminated, the thermal coupling phenomenon needs to be modeled separately; the steady-state Laplace equation for heat transfer is expressed as follows: The coordinate axes are centered at the top surface corner of the substrate, with the positive Z-axis pointing in the direction of heat conduction. The substrate dimensions are given as follows: The LED dimensions are a*b; the coordinates of the LED's center point are ( ); Assuming the substrate is insulated on all sides; the bottom surface maintains a temperature constant T0; the top surface only has heat input in the area covered by the chip, with other locations set as adiabatic boundaries; under these boundary conditions, the temperature distribution at each location when a single chip is heated is expressed as: in, , , , , , or The substrate thickness is t; the thermal conductivity of the material is k; the heat power generated by the LED is... ; This indicates a rise in temperature; This represents the ambient temperature; due to the linear superposition characteristic of heat conduction, the temperature distribution of multiple heat sources applied to the substrate is represented as: As ambient temperature increases, the temperature distribution of multiple heat sources on the substrate can be represented as follows: in, The ambient temperature; (III) Calculation of LED array luminous flux prediction First, the junction temperature of the LED array under different lighting methods, driving currents, and temperatures is predicted using a junction temperature model to obtain the junction temperature of each LED in the LED array. Then, based on the obtained junction temperature of each LED, the luminous flux of each LED is obtained according to the single LED luminous flux model. The luminous flux of all single LEDs in the LED array is then superimposed to obtain the luminous flux of the LED array. The junction temperature model is either a TCM model or a numerical algorithm model. The single LED luminous flux model is either Model I or Model II.

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