# Long-Term Lifetime Prediction of Power MOSFET Devices Based on LSTM and GRU Algorithms

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## Abstract

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## 1. Introduction

_{dson}), threshold voltage (V

_{th}), and junction temperature (T

_{j}), while collector–emitter voltage (V

_{CE}) and collector–emitter current (I

_{CE}) [8,9,10,11] are used for IGBTs.

## 2. Description of the Proposed Theory and Methodology

#### 2.1. An Overview of RNN, LSTM, and GRU

#### 2.1.1. Standard Recurrent Neural Networks (RNN) Architecture

_{dson}) for power MOSFETs is shown in Figure 2.

#### 2.1.2. Long Short-Term Memory (LSTM) Algorithm Architecture

#### 2.1.3. Gated Recurrent Unit (GRU)

#### 2.2. Training Algorithm for LSTM and Variants

#### 2.3. Model Regularization to Overcome Overfitting

#### 2.4. Prediction of Long-Term Lifetime

_{th}) and drain current (I

_{d}) are also considered failure precursors when the threshold values reach 20% [7] and five times (5×) [5] of their initial values, respectively [29]. Thus, for power MOSFETs, the RUL can be estimated when a certain failure precursor crosses the failure threshold.

_{EOL}is about a 17% increment from the pristine state R

_{dson}value, considering on-state resistance as the main failure precursor (degradation parameter); ${T}_{pred}$ is the time when the prediction started considering a certain portion (30%, 50%, or 70% of training data) from degradation trend data.

## 3. Experimental Setup and Data Collection

#### 3.1. Description of Experimental Test Samples

#### 3.2. Experiment Design, Setup, and Data Collection

_{j}) swing scenarios. Each degradation testing scenario consisted of four test samples, where each group was set for a T

_{j}swing of 45 °C, 100 °C, and 110 °C, in which the T

_{jmin}and T

_{jmax}range from 40 °C to 85 °C, 25 °C to 125 °C, and 25 °C to 135 °C, respectively. The design of the experiment for the different T

_{j}swing scenarios is based on the various working environments of power MOSFETs, which can be related to real-world conditions. The test samples in all groups were aged under a normal ambient temperature of 23 ± 2 °C for a total of 77,600 cycles. The various static and dynamic electrical characteristics, which are considered as failure precursors, were collected every 400 cycles, where a single cycle covers a time of 45 secs ON (heating) and 90 secs OFF (cooling) with a power tester (MicReD PowerTester 1500 A). In general, the experiment had two phases: accelerated aging and failure precursor parameters testing, which continued until sufficient degradation data were obtained. An overview of the overall experimental design for an accelerated degradation test, the experimental setup, and the data collection procedure is shown in Figure 6.

#### 3.3. Failure Precursors Data Collection

_{dson}), threshold voltage (V

_{th}), body diode forward voltage (V

_{sd}), breakdown voltage (V

_{br}), drain current (I

_{dss}), drain-source on-state voltage (V

_{dson}), input, output, and reverse transfer capacitances (C

_{iss}, C

_{oss}, and C

_{rss}), using a power device analyzer (Keysight B1505 A). A change in a failure precursor parameter can be attributed to various failure mechanisms that lead to a certain failure mode when they cross a specified failure threshold that varies based on a specific application. More details on the failure precursors of power MOSFETs will be reported in a separate study. The failure precursor chosen for this study is the on-state resistance, and the results for test samples 1, 2, 5, 6, 9, and 10 are shown in Figure 7.

_{dson}) demonstrates the presence of die degradation and bond-wire lift-off, which could be caused by a high electric field and thermal runaway [1]. Some failure modes can be caused by a shift in one or multiple failure precursors, which makes the degradation modeling of power devices challenging. The failure precursors will show either an increasing, decreasing, or constant trend depending on the power-MOSFET response to dynamic thermal and electrical stresses.

_{DS}). The increasing trend of on-state resistance for aged power MOSFETs has also been reported in [8,30]. There is an obvious unit-to-unit variability among samples under the same scenario, which may arise from manufacturing imperfections. On the other hand, the degree of degradation shows that samples with higher temperature swings (110 °C and 100 °C) have shown a higher degree of on-state resistance variation compared with samples with a lower T

_{j}(45 °C). From the comprehensive accelerated test, the on-state resistance data are found to be representative of the degradation pattern in power MOSFETs when exposed to long-term power cycling tests or applications. Based on this long-term time series precursor data, the LSTM and GRU neural network can be used to predict the future lifetime of power MOSFETs.

#### 3.4. Data Preprocessing and Evaluation Metrics

## 4. Results and Discussion

#### 4.1. Data Preprocessing, Parameter Setting, and Model Formation for the Models

#### 4.2. Implementation of RNN/ LSTM/GRU Models and Prediction Results

#### 4.3. Discussion Based on Lifetime Prediction Metrics and Model Robustness

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 7.**Variation in the actual on-state resistance (R

_{ds(on)}) value with respect to the power cycling time. The values passed through normalizations for analysis during the prediction process.

**Figure 11.**Rdson prediction result for MOSFET 1 with (

**a**) RNN, (

**b**) LSTM, and (

**c**) GRU; (

**d**) comparison of the three models; (

**e**) prediction error using RNN/LSTM/GRU.

**Figure 12.**Comparison of Prediction Results (

**a**) at 40,000 cycles and (

**b**) at 24,000, 40,000, and 54,000 cycles. Starting Points for MOSFET 1.

**Figure 13.**Rdson prediction result for MOSFET 5 using (

**a**) RNN, (

**b**) LSTM, and (

**c**) GRU; (

**d**) comparison of the three models; (

**e**) prediction error (AE) using RNN, LSTM, and GRU.

**Figure 14.**Rdson prediction result for MOSFET 9 using (

**a**) RNN, (

**b**) LSTM, and (

**c**) GRU; (

**d**) comparison of the three models with the prediction error.

**Figure 17.**Long-term lifetime prediction for MOSFET 9 at 24,000 cycles of starting points with three models and prediction error plots.

**Figure 18.**Long-term lifetime prediction for MOSFET 5 at 54,000 cycles of the starting point. (

**a**) Prediction plots of the three models; (

**b**) distribution of prediction error.

Parameters | Description of Parameters and Values |
---|---|

V_{ds} @ T_{jmax} | 650 V |

Pulsed drain current I_{D,pulse} | 272 A |

Continuous drain current (ID) | 77.5 A @ T_{C} = 25 °C49 A @ T _{C} = 100 °C |

E_{oss} @ 400 V | 22 μJ |

Power Dissipation, P_{tot} | 481 W @ T_{C} = 25 °C |

Body diode d_{i}/d_{t} | 300 A/μs |

Terms | Parameters | Test Conditions |
---|---|---|

Testing duration | Number of cycles/hours | 77,600 cycles |

Testing cycle | ON/OFF time | 135 s (45 s on and 90 s off) |

Interval of precursor data collection | On-state resistance (R_{ds(on)}) | every 400 cycles |

Threshold Voltage (V_{gs(th)}) | ||

Body Diode Voltage (V_{sd}) | ||

Drain Current (I_{dss}) | ||

Capacitance (C_{iss}, C_{oss}, C_{rss}) | ||

Testing conditions (input electrical and thermal parameters) | Scenario 1: T_{j} = 40 °C to 85 °CScenario 2: T _{j} = 25 °C to 125 °CScenario 3: T _{j} = 25 °C to 125 °C | Current: ≤49 A rated current Voltage: 8 V for 4 MOSFETs for each scenario 14.2 V supplied for the PCB |

Temperature | Ambient | ${T}_{c}$ = 22 ± 3 °C |

Model | Number of Units | Optimizer | Training Loss Function | Dropout | Activation |
---|---|---|---|---|---|

RNN | (128, 64) | Adam | Mean Squared Error | 20% (0.2) | relu |

LSTM | (128, 64) | Adam | Mean Squared Error | 20% (0.2) | relu |

GRU | (128, 64) | Adam | Mean Squared Error | 20% (0.2) | relu |

Model | Starting Points | MAPE | MSE | RMSE |
---|---|---|---|---|

RNN | 24,000 | 0.0197 | 0.245 | 0.495 |

40,000 | 0.0172 | 0.699 | 0.832 | |

57,600 | 0.0165 | 0.746 | 0.864 | |

LSTMs | 24,000 | 0.0079 | 0.203 | 0.451 |

40,000 | 0.009 | 0.366 | 0.459 | |

57,600 | 0.0103 | 0.264 | 0.514 | |

GRU | 24,000 | 0.0092 | 0.236 | 0.485 |

40,000 | 0.0078 | 0.318 | 0.422 | |

57,600 | 0.0103 | 0.268 | 0.518 |

Test Samples | Indices | RNN | LSTM | GRU |
---|---|---|---|---|

MOSFET #1 | MAPE | 0.0197 | 0.0079 | 0.0092 |

MSE | 0.2452 | 0.2031 | 0.2356 | |

RMSE | 0.4952 | 0.451 | 0.4854 | |

MOSFET #5 | MAPE | 0.0090 | 0.0066 | 0.0073 |

MSE | 0.1948 | 0.1271 | 0.1309 | |

RMSE | 0.4413 | 0.3565 | 0.3618 | |

MOSFET #9 | MAPE | 0.0075 | 0.0083 | 0.0074 |

MSE | 0.1462 | 0.1681 | 0.1363 | |

RMSE | 0.3824 | 0.4099 | 0.3692 |

Test Sample | Indices | RNN | LSTM | GRU |
---|---|---|---|---|

MOSFET #1 | MAPE | 0.0172 | 0.009 | 0.0078 |

MSE | 0.6992 | 0.3664 | 0.3178 | |

RMSE | 0.832 | 0.459 | 0.422 | |

MOSFET #5 | MAPE | 0.0090 | 0.0066 | 0.0060 |

MSE | 0.2250 | 0.1174 | 0.1017 | |

RMSE | 0.4743 | 0.3426 | 0.3189 | |

MOSFET #9 | MAPE | 0.0105 | 0.0091 | 0.0078 |

MSE | 0.2831 | 0.2048 | 0.1569 | |

RMSE | 0.5321 | 0.4525 | 0.3961 |

Test Sample | Indices | RNN | LSTM | GRU |
---|---|---|---|---|

MOSFET #1 | MAPE | 0.0165 | 0.0103 | 0.0103 |

MSE | 0.7458 | 0.2641 | 0.2678 | |

RMSE | 0.8636 | 0.5139 | 0.5175 | |

MOSFET #5 | MAPE | 0.0103 | 0.0074 | 0.0065 |

MSE | 0.1811 | 0.1697 | 0.245 | |

RMSE | 0.4256 | 0.4119 | 0.3528 | |

MOSFET #9 | MAPE | 0.0107 | 0.0089 | 0.0065 |

MSE | 0.2706 | 0.1952 | 0.1035 | |

RMSE | 0.5202 | 0.443 | 0.3217 |

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## Share and Cite

**MDPI and ACS Style**

Ibrahim, M.S.; Abbas, W.; Waseem, M.; Lu, C.; Lee, H.H.; Fan, J.; Loo, K.-H.
Long-Term Lifetime Prediction of Power MOSFET Devices Based on LSTM and GRU Algorithms. *Mathematics* **2023**, *11*, 3283.
https://doi.org/10.3390/math11153283

**AMA Style**

Ibrahim MS, Abbas W, Waseem M, Lu C, Lee HH, Fan J, Loo K-H.
Long-Term Lifetime Prediction of Power MOSFET Devices Based on LSTM and GRU Algorithms. *Mathematics*. 2023; 11(15):3283.
https://doi.org/10.3390/math11153283

**Chicago/Turabian Style**

Ibrahim, Mesfin Seid, Waseem Abbas, Muhammad Waseem, Chang Lu, Hiu Hung Lee, Jiajie Fan, and Ka-Hong Loo.
2023. "Long-Term Lifetime Prediction of Power MOSFET Devices Based on LSTM and GRU Algorithms" *Mathematics* 11, no. 15: 3283.
https://doi.org/10.3390/math11153283