# Color Shift Failure Prediction for Phosphor-Converted White LEDs by Modeling Features of Spectral Power Distribution with a Nonlinear Filter Approach

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## Abstract

**:**

## 1. Introduction

## 2. LED Test Sample and Accelerated Degradation Test

_{c}= 200 mA) provided by a DC power supply (Model: Agilent E3611A). The thermal chamber provided a constant aging temperature (T

_{a}= 90 °C) for this test. After finishing a 23-h cycle aging, the test sample was removed from the thermal chamber to be cooled to the ambient temperature for SPD data measurement by a Gigahertz-Optik BTS256-LED tester (Türkenfeld, Germany) When the measurement was finished, the test sample was then returned to the thermal chamber to undergo the next round of aging until its color shift failure happened.

_{f}= 529 h.

## 3. Theory and Methodology

#### 3.1. Luminous Mechanisms of pc-WLEDs

#### 3.2. SPD Feature Extraction with Statistical Method

_{0}is the baseline offset, A is the total area under the curve from baseline, λ is the center of the peak, Δλ is the full width of the peak at half height, and w equals two standard deviations, that is approximately 0.849 the width of the peak at half height. B and Y represent LED chip and phosphor, respectively.

^{2}values of two models, which are closer to 1, indicate that both statistical functions have well goodness-of-fitting results for the SPD of this type of pc-WLED package. According to the quantum point of view, the recombination in p-n junction is governed by the electron transition probability to a fundamental state that depends on the coordinated configuration for the electronic/vibrational levels in the blue LED chip. The recombination probability function usually follows a discrete Poisson distribution and it can be assumed as a continuous Gaussian function to describe the SPD of blue LED chip [25]. Otherwise, as compared to the fitting results in the phosphor part, the Lorentzian model is more suitable. Thus, in this paper, both two statistical models were used to extract the features of SPDs collected from the aged test sample.

#### 3.3. Color Shift Failure Prediction with Nonlinear Modeling

_{k}~ p(x

_{k}|z

_{1:k}), with sequential Monte Carlo (SMC) simulation [28]. The state-space model of this study can be expressed as follows [29]:

_{k}is the degradation (or shift) state, α

_{k}is the model parameter, z

_{k}is the measurement data, υ

_{k}is the measurement noise, and ʘ

_{k}(x

_{k}, α

_{k}, δ

_{k}) is the vector of parameters in PF.

**Step 1: Parameter initialization**

**Step 2: Parameter sampling and prediction**

_{k}|z

_{1:k−1}), can be calculated based on the state model with the Chapman-Kolmogorov equation.

**Step 3: Dynamic updating**

_{k}|z

_{1:k}), can be updated by using the Bayesian algorithm and the Markov assumption. The likelihood function of the ith particle at cycle k, p(z

_{k}|θ

_{ik}), can be expressed as a Gaussian distribution:

**Step 4: Particle weighting and resampling**

**Step 5: Prediction of extracted features**

_{k}~ p(x

_{k}|z

_{1:k}) and the future states of the extracted features are predicted by extrapolating the estimated kth step state based on the state model.

## 4. Results and Discussion

#### 4.1. Failure Mechanism Analysis

_{B}and A

_{Y}, which are dependent on the luminous energy emitted by the LED chip and phosphors, respectively.

_{B}/A

_{Y}, increases exponentially, which can support the conclusion that the phosphor degradation may be the dominant failure mechanism of the test sample under the designed accelerated degradation test.

_{c}= 200 mA and T

_{a}= 90 °C, its thermal distribution was simulated with the finite element analysis (FEA) method in the ANSYS FLUENT software and the material parameters used in FEA modeling are listed in Table 2. As shown in Figure 9, the highest temperature of the phosphor layer is more than 100 °C even without considering the self-heating effect from phosphors. According to the other studies on the thermal quenching effects of phosphors [32,33], the accelerated oxidization of europium ion caused by both the high-temperature heat treatment and blue light irradiation may result in the irreversible decrease in emission intensity of phosphors. That could be the main cause of the faster degradation of phosphors than that of other materials in the selected pc-WLED aged under this condition.

#### 4.2. Color Shift Failure Prediction

_{B}, 1/w

_{B}, and λ

_{Y}, kept almost constant during the designed degradation test until 345 h. Thus, it is assumed that these three features are not degraded in this case, however, the remaining four features, including y

_{0}, A

_{B}, 1/w

_{Y}, and A

_{Y}, are supposed to exponentially degrade. Therefore, the state model described in Equation (8) can be rewritten as given in Equation (12), in which the shift trajectories of four normalized features are exponential modeled.

_{G}and B

_{L}is the pre-parameters of state models from the Gaussian and Lorentzian model-fittings respectively. The initial distributions of the parameters defined in the vector of ʘ

_{k}(x

_{k}, α

_{k}, δ

_{k}) are assumed as uniform distributions, which can be represented in Equation (13). As there is an over-fitting for A

_{B}with the Lorentzian model, it is assumed as the same uniform distribution from Gaussian model.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**(

**a**) The 3D model of selected light-emitting diodes (LED) package; (

**b**) its packaging materials and construction shown in the scanning electron microscope image of cross-section.

**Figure 2.**(

**a**) Spectral power distribution (SPD) data collected under the accelerated degradation test; (

**b**) color shift failure time T

_{f}= 529 h defined as when du′v′ = 0.007.

**Figure 3.**SPD and luminous mechanism of the selected phosphor-converted white LED (pc-WLED) package.

**Figure 4.**Feature extraction from the initial SPD of pc-WLED package with both Gaussian and Lorentzian models (the red (

**a**) and blue (

**b**) dash lines with shadow areas represent the Gaussian and Lorentzian models respectively).

**Figure 6.**Failure mechanism classification in a pc-WLED package (the blue and red curves represent the initial and aged SPDs, respectively).

**Figure 9.**(

**a**) The 3D model of test sample soldered on a substrate used for FEA simulation; (

**b**) its simulated Kelvin temperature distribution.

**Figure 10.**Shift trajectories of normalized features extracted from SPDs by (

**a**) Gaussian model and (

**b**) Lorentzian model until 345 h.

**Figure 11.**PF prediction results of four normalized features extracted from the Gaussian model until 529 h (

**a**) Normalized y

_{0}; (

**b**) Normalized A

_{B}; (

**c**) Normalized 1/w

_{Y}; (

**d**) Normalized A

_{Y}.

**Figure 12.**PF prediction results of four normalized features extracted from the Lorentzian model until 529 h (

**a**) Normalized y

_{0}; (

**b**) Normalized A

_{B}; (

**c**) Normalized 1/w

_{Y}; (

**d**) Normalized A

_{Y}.

**Figure 13.**Prediction errors of (

**a**) u′; (

**b**) v′, (

**c**) correlated color temperature (CCT) and (

**d**) color rendering index (CRI) based on the Gaussian and Lorentzian models.

Models | y_{0} | λ_{B} | w_{B} | A_{B} | λ_{Y} | w_{Y} | A_{Y} | R^{2} |
---|---|---|---|---|---|---|---|---|

Gaussian model | 2.26 × 10^{−5} | 459.684 | 25.144 | 0.0249 | 573.775 | 82.259 | 0.0849 | 0.99175 |

Lorentzian model | –8.97 × 10^{−5} | 458.656 | 23.221 | 0.03089 | 574.349 | 96.326 | 0.1467 | 0.98638 |

Material Parameters | Air | LED Chip | Silicone | Lead and Thermal Pad | Substrate |
---|---|---|---|---|---|

Density (kg/m^{3}) | 1.225 | 6150 | 1200 | 8920 | 2700 |

Thermal conductivity (W/m·K) | 0.0257 | 130 | 5 | 398 | 100 |

Specific heat (J/kg·K) | - | 490 | 1700 | 390 | 880 |

Models | y_{0} | A_{B} | 1/w_{Y} | A_{Y} | |
---|---|---|---|---|---|

Gaussian Model | B_{G} | 0.96267 | 1.00464 | 0.99632 | 0.97489 |

α_{G} | 4.09 × 10^{−4} | 7.23 × 10^{−5} | 3.62 × 10^{−5} | 3.33 × 10^{−4} | |

Lorentzian Model | B_{L} | 0.98579 | 0.07459 | 0.99607 | 0.97595 |

α_{L} | 2.4 × 10^{−4} | 0.84435 | 4.0 × 10^{−5} | 3.21 × 10^{−4} |

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**MDPI and ACS Style**

Fan, J.; Mohamed, M.G.; Qian, C.; Fan, X.; Zhang, G.; Pecht, M. Color Shift Failure Prediction for Phosphor-Converted White LEDs by Modeling Features of Spectral Power Distribution with a Nonlinear Filter Approach. *Materials* **2017**, *10*, 819.
https://doi.org/10.3390/ma10070819

**AMA Style**

Fan J, Mohamed MG, Qian C, Fan X, Zhang G, Pecht M. Color Shift Failure Prediction for Phosphor-Converted White LEDs by Modeling Features of Spectral Power Distribution with a Nonlinear Filter Approach. *Materials*. 2017; 10(7):819.
https://doi.org/10.3390/ma10070819

**Chicago/Turabian Style**

Fan, Jiajie, Moumouni Guero Mohamed, Cheng Qian, Xuejun Fan, Guoqi Zhang, and Michael Pecht. 2017. "Color Shift Failure Prediction for Phosphor-Converted White LEDs by Modeling Features of Spectral Power Distribution with a Nonlinear Filter Approach" *Materials* 10, no. 7: 819.
https://doi.org/10.3390/ma10070819