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如图1所示,文中详细介绍了半导体激光器寿命预测的总体方案,它分为两个部分,第一是模型建立部分,第二是寿命预测部分。其中模型建立部分主要内容为建立基于光输出功率的退化轨迹模型和基于双应力步进加速试验的加速模型。在确立理论模型后,接下来根据最小二乘估计与参数估计确定模型参数并求解MTTF。
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为了对半导体激光器光输出功率退化轨迹进行拟合,文中首先需要建立性能退化模型,求解每只器件在各个加速应力条件下的性能退化特征参数,进而根据失效阈值估计该条件下的寿命。
假设单一试验器件在应力条件
$[S_i^{\left( 1 \right)},S_j^{\left( 2 \right)}]$ 下的退化率保持恒定不变,那么每个器件的功率退化数据可根据YamaKoshi方程[16]用如下模型描述:$$\begin{split} & P\left(t\mid {S}_{i}^{\left(1\right)},{S}_{j}^{\left(2\right)}\right)={P}^{0}{}_{i,j}\mathrm{exp}\left(-{\beta }_{i,j}{t}\right)\text{,}\\ & t > 0,i \leqslant j,i,j=0,1,\cdots ,l \end{split} $$ (1) 该式称为性能退化模型。式中
$S_i^{\left( 1 \right)},S_j^{\left( 2 \right)}$ 分别代表试验设置的第$i$ 个温度应力条件和第$j$ 个电流应力条件,它们的交叉步进关系如图2所示。其中$i,j$ 分别表示两种应力水平等级,$i,j = 0,1, \cdots ,l,i \leqslant j$ 。${P^0}_{i,j}$ ,$\;{\beta _{i,j}}$ 代表在应力条件$[S_i^{\left( 1 \right)},S_j^{\left( 2 \right)}]$ 下,样品的初始光功率值和退化率。公式(1)描述了光输出功率在$[S_i^{\left( 1 \right)},S_j^{\left( 2 \right)}]$ 的应力条件下随时间的变化曲线,可以表示成一个指数函数的形式。$\;{\beta _{i,j}}$ 可以利用最小二乘法结合实际退化轨迹求得。激光器失效阈值设定为光输出功率下降到为初始值的80%[5,10,14-16],那么从公式(1)推导得到在第$i$ 个温度应力条件和第$j$ 个电流应力条件下达到失效阈值的退化时间(寿命)与退化率成反比:$$ - {\rm ln}0.8\frac{1}{{{\varepsilon _{i,j}}}} = {\beta _{i,j}} $$ (2) 图 2 交叉步进加速退化试验的应力条件变化示意图
Figure 2. Schematic diagram of the change in stress conditions for the cross-step accelerated degradation test
用
$P\left( t \right)$ 来表示器件在整个试验流程中随应力交叉步进变化的退化曲线。每只器件的退化轨迹曲线都可以表示为分段函数:$$ P(t) = \left\{ \begin{gathered} P(t|S_i^{\left( 1 \right)},S_j^{\left( 2 \right)}), \\ 0 \leqslant t \leqslant {t_{0,1}},\left( {i,j} \right) = \left( {0,1} \right); \\ P(t + {w_{i - 1,j}} - {t_{i - 1,j}}|S_i^{\left( 1 \right)},S_j^{\left( 2 \right)}), \\ {t_{i - 1,j}} \leqslant t \leqslant {t_{i,j}},\left( {i,j} \right) = \left( {1,1} \right),\left( {2,2} \right), \cdots ; \\ P(t + {w_{i,j - 1}} - {t_{i.j - 1}}|S_i^{\left( 1 \right)},S_j^{\left( 2 \right)}), \\ {t_{i,j - 1}} \leqslant t \leqslant {t_{i,j}},\left( {i,j} \right) = \left( {1,2} \right),\left( {2,3} \right), \cdots . \\ \end{gathered} \right. $$ (3) 式中:
${w_{i,j}}$ 为折算时间,它代表在$ {t}_{i,j} $ 前其他应力水平条件下所有的退化过程折算为下一个应力水平条件下所需的退化时间。从某一加速应力条件折算到另一条件的时间与其退化率之比相关。在应力条件$[S_i^{\left( 1 \right)},S_j^{\left( 2 \right)}]$ 下${w_{i,j}}$ 折算时间可以具体地表示为:$$ {w}_{i,j}=\left\{\begin{gathered}\left(\frac{{\beta }_{i,j}}{{\beta }_{i+1,j}}\right){t}_{i,j},\\ \left(i,j\right)=\left(0,1\right);\\ \left(\frac{{\beta }_{i,j}}{{\beta }_{i,j+1}}\right)\left({w}_{i-1,j}-{t}_{i-1,j}+{t}_{i,j}\right),\\ \left(i,j\right)=\left(1,1\right),\left(2,2\right),\cdots ;\\ \left(\frac{{\beta }_{i,j}}{{\beta }_{i+1,j}}\right)\left({w}_{i,j-1}-{t}_{i,j-1}+{t}_{i,j}\right),\\ \left(i,j\right)=\left(1,2\right),\left(2,3\right),\cdots .\end{gathered} \right.$$ (4) 这样表示的目的是将某一时刻之前的退化过程全部折算到下一个应力水平条件下,在同一应力水平退化曲线上进行计算[23]。图3表示双应力步进加速退化试验的曲线
$P\left( t \right)$ 与以各个应力条件恒定的加速退化试验曲线$P\left( {t\mid S_i^{\left( 1 \right)},S_j^{\left( 2 \right)}} \right)$ 的换算关系。红色曲线为实际步进应力加速试验得到的性能退化轨迹。它们分别对应着起始就以各自应力条件,进行加速试验得到的性能退化轨迹的蓝色曲线部分。 -
加速模型建立的目的是根据每只器件在各个加速应力条件下的预测寿命外推得到其在额定工作条件下的寿命。
Eyring等人根据量子力学原理进行推导,提出若同时考虑热应力T,电应力I,则关于两个应力可将寿命特征表示为一个函数,据此笔者建立因变量为器件寿命的加速模型,又称广义艾琳模型:
$$ \varepsilon = \frac{A}{T}{\rm exp}\left\{ {\frac{B}{{KT}}} \right\}{\rm exp}\left\{ {I\left( {C + \frac{D}{{KT}}} \right)} \right\} $$ (5) 式中:A, B, C, D均为待求参数项;K为玻耳兹曼常数;最后一项为电应力与热应力的交互作用项[24]。
根据加速模型外推得到每只器件的预测寿命,拟合这批器件整体的寿命分布,从而计算MTTF。电子元器件的寿命分布服从威布尔分布[25],计作
$\varepsilon \sim{{W}}\left( {{{m}},{{\eta}}} \right)$ ,它的分布函数和概率密度函数分别为:$$ F\left( t \right) = 1 - \exp \left[ { - {{(t/\eta )}^m}} \right] $$ (6) $$ f\left( t \right) = \left( {\frac{{m{t^{m - 1}}}}{{{\eta ^m}}}} \right)\exp \left[ { - {{(t/\eta )}^m}} \right] $$ (7) 式中:
${{m}}$ 为形状参数;${{\eta }}$ 为尺度参数。威布尔分布的分布函数可以用来描述一批器件在一段工作时间后的失效百分比。由于实际试验中只能取有限个器件,器件数量为离散变量,那么失效率$ {F}_{i} $ 的无偏估计为:$$ {F_{{n_i}}} = \frac{{{n_i}}}{{n + 1}} $$ (8) 式中:
${n_i}$ 为$ t $ 时间以前(包括$ t $ 时间)所有已经失效的器件数量;$ n $ 为器件总数。 -
文中选取12只830 nm F-mount的单管器件作为研究对象。器件实拍图如图4所示。器件在温度22 ℃下工作,额定工作电流为0.9 A,额定输出功率为1 W。
文中自主搭建了大功率半导体激光器单管老化测试平台,如图5所示。平台包括12组器件夹具、Ophir NovaⅡ光功率计、可编程直流电源、可编程步进电机驱动的丝杆滑台、恒温循环冷水机、计算机。该平台集成了控制、监测、试验功能于一体,试验器件功率由PC控制步进电机带动的功率计监测并保存在计算机中[26]。应力设定为温度与电流,并根据单管LIV曲线,温度取22 ℃,42 ℃和62 ℃,电流取1.4 A与1.8 A,两应力条件交叉步进,共组成四种不同的应力条件:A[22 ℃,1.4 A],B[42 ℃,1.4 A],C[42 ℃,1.8 A],D[62 ℃,1.8 A]。在试验中记录全部的光输出功率数据及其对应的应力条件,见表1,器件编号从1#~12#,光输出功率每间隔100 h记录一次,单位W。
图 5 830 nm F-mount单管器件加速试验平台示意图
Figure 5. Schematic diagram of 830 nm F-mount single-emitter devices accelerated test platform
表 1 830 nm F-mount单管器件在不同的应力条件下的加速退化试验数据(光输出功率/W)
Table 1. Accelerated degradation test data of 830 nm F-mount single-emitter devices under different stress conditions (optical output power/W)
Stress condition Time/h 1# 2# 3# 4# 5# 6# 7# 8# 9# 10# 11# 12# A[22 ℃,1.4 A] 100 1.43 1.38 1.39 1.41 1.41 1.40 1.36 1.42 1.44 1.36 1.45 1.39 200 1.42 1.38 1.40 1.40 1.40 1.38 1.37 1.43 1.42 1.36 1.44 1.37 300 1.39 1.37 1.37 1.39 1.38 1.35 1.41 1.39 1.39 1.34 1.43 1.34 400 1.40 1.33 1.35 1.40 1.40 1.34 1.34 1.40 1.37 1.35 1.40 1.34 B[42 ℃,1.4 A] 500 1.36 1.33 1.33 1.37 1.38 1.30 1.29 1.36 1.31 1.31 1.36 1.29 600 1.32 1.30 1.29 1.34 1.32 1.27 1.32 1.33 1.28 1.28 1.36 1.31 700 1.28 1.30 1.31 1.34 1.34 1.27 1.29 1.31 1.30 1.27 1.35 1.25 800 1.30 1.29 1.30 1.33 1.30 1.26 1.25 1.30 1.29 1.23 1.31 1.26 C[42 ℃,1.8 A] 900 1.62 1.63 1.62 1.70 1.69 1.64 1.69 1.72 1.70 1.60 1.69 1.69 1000 1.57 1.60 1.59 1.65 1.65 1.60 1.67 1.65 1.68 1.57 1.67 1.69 1100 1.55 1.58 1.50 1.64 1.60 1.57 1.62 1.61 1.61 1.53 1.60 1.63 1200 1.50 1.51 1.52 1.58 1.58 1.50 1.56 1.62 1.57 1.54 1.60 1.56 D[62 ℃,1.8 A] 1300 1.39 1.44 1.43 1.50 1.45 1.39 1.52 1.50 1.47 1.40 1.49 1.42 1400 1.35 1.37 1.38 1.44 1.41 1.33 1.45 1.44 1.40 1.35 1.45 1.41 1500 1.27 1.34 1.33 1.41 1.34 1.31 1.43 1.41 1.35 1.32 1.36 1.35 1600 1.26 1.28 1.27 1.36 1.26 1.25 1.38 1.39 1.29 1.30 1.30 1.30 -
如图6所示,经过1600 h试验后,得到了12只不同器件的实际性能退化数据
$R\left( t \right)$ ,$R\left( t \right)$ 与理论性能退化曲线$P\left( t \right)$ 存在一定误差。为了使理论与实际曲线的程度拟合最大,需要使误差最小化。利用非线性最小二乘拟合,可以得到理论性能退化曲线$P\left( t \right)$ ,即求得实际退化数据$R\left( t \right)$ 与理论退化曲线$P\left( t \right)$ 之差的平方和最小时${\;\beta _{i,j}}$ 的取值。图 6 830 nm F-mount单管器件的性能退化数据
Figure 6. Performance degradation data of 830 nm F-mount single-emitter devices
由此可以得到
$ \;{\beta }_{i,j} $ 的点估计值,如表2所示。$\; {\beta }_{i,j} $ 随着应力条件的增大而增大,其物理意义是应力条件越高,退化的速度越快。根据公式(1),文中进行双应力交叉步进条件下的加速退化试验共计1600 h,从光输出功率退化量可以反推出[22 ℃ ,1.4 A]条件下需要的退化时间。可以计算得出,四种条件下总计1600 h的加速试验相当于约3783 h在[22 ℃ ,1.4 A]的条件下的恒定应力加速试验。若按照传统的恒定电流加速寿命试验并外推器件的寿命预测方法,则至少需要在试验中设置除[22 ℃,1.4 A]条件以外的两组以上其他条件下的加速试验,相当于节约了大于57.7%的试验时间。表 2 每个激光器在各个应力条件下的退化率
Table 2. Degradation rate of each laser diode at each stress condition
Laser
diode IDβ22 ℃,1.4 A β42 ℃,1.4 A β42 ℃,1.8 A β62 ℃,1.8 A 1 $ 9.152\times {10}^{-5} $ $ 1.358\times {10}^{-4} $ $ 2.711\times {10}^{-4} $ $ 3.674\times {10}^{-4} $ 2 $ 9.245\times {10}^{-5} $ $ 1.367\times {10}^{-4} $ $ 2.613\times {10}^{-4} $ $ 3.624\times {10}^{-4} $ 3 $ 8.167\times {10}^{-5} $ $ 1.251\times {10}^{-4} $ $ 2.420\times {10}^{-4} $ $ 3.635\times {10}^{-4} $ 4 $ 8.321\times {10}^{-5} $ $ 1.242\times {10}^{-4} $ $ 2.338\times {10}^{-4} $ $ 3.137\times {10}^{-4} $ 5 $ 8.905\times {10}^{-5} $ $ 1.337\times {10}^{-4} $ $ 2.566\times {10}^{-4} $ $ 3.893\times {10}^{-4} $ 6 $ 9.458\times {10}^{-5} $ $ 1.415\times {10}^{-4} $ $ 2.805\times {10}^{-4} $ $ 3.684\times {10}^{-4} $ 7 $ 7.345\times {10}^{-5} $ $ 1.097\times {10}^{-4} $ $ 2.089\times {10}^{-4} $ $ 3.259\times {10}^{-4} $ 8 $ 7.563\times {10}^{-5} $ $ 1.124\times {10}^{-4} $ $ 2.073\times {10}^{-4} $ $ 3.126\times {10}^{-4} $ 9 $ 9.011\times {10}^{-5} $ $ 1.344\times {10}^{-4} $ $ 2.569\times {10}^{-4} $ $ 3.698\times {10}^{-4} $ 10 $ 8.583\times {10}^{-5} $ $ 1.261\times {10}^{-4} $ $ 2.372\times {10}^{-4} $ $ 3.521\times {10}^{-4} $ 11 $ 9.774\times {10}^{-5} $ $ 1.440\times {10}^{-4} $ $ 2.719\times {10}^{-4} $ $ 3.973\times {10}^{-4} $ 12 $ 9.804\times {10}^{-5} $ $ 1.464\times {10}^{-4} $ $ 2.878\times {10}^{-4} $ $ 3.868\times {10}^{-4} $ 为了验证加速模型公式(7)中电流与温度是否存在交互作用,需要检验由样本得到的交互作用项参数
$ d $ 的显著性。只要取两组模型参数(管1和管2共八个退化率数据)进行假设检验,根据统计决策的结果认为存在或不存在交互作用。根据加速退化模型公式(9)作线性方程组进行最小二乘估计得到12组模型参数估计值$ \hat{a},\hat{b},\hat{c},\hat{d} $ ,那么线性方程组可表示为:$$ Ax = b $$ (9) 式中:
$ A $ 为由加速模型组成的系数矩阵;$ b $ 为加速寿命的对数组成的列矩阵,则$x={[\hat{a},\hat{b},\hat{c},\hat{d}]}^{\rm T}$ 的最小二乘估计具体的矩阵计算形式如下:$$ x = {\left( {{A^{\rm T}}A} \right)^{ - 1}}{A^{\rm T}}b $$ (10) 依照上述参数估计方法,得到
$ \hat{a},\hat{b},\hat{c},\hat{d} $ ,如表3所示。表 3 取管1和管2两组(共八个退化率数据)求得的加速退化模型参数
Table 3. Parameters of the accelerated degradation model obtained by taking two sets of single-emitter 1 and single-emitter 2 (a total of 8 degradation rate data)
$ a $ $ b $ $ c $ $ d $ 4.40 1 830 −1.66 −3.36 其中广义艾琳模型默认电流、温度应力是交互作用的,即两个变量非独立。需要对交互作用项的存在进行假设检验以确保模型没有多余的变量存在,防止模型出现过拟合。
假设
$$ {H_0}:d = 0 $$ (11) 那么统计量
${{t}}$ 的表达式为:$$ t = \hat d/{s_{\hat d}}\sim t\left( {2l - q - 1} \right) $$ (12) 式中:
$ q $ 为自变量个数,在这里取3;$ 2 l $ 代表不同应力水平下的方程个数,取8;$ {s}_{\widehat{d}} $ 为回归系数$ \widehat{d} $ 的抽样分布的标准差。给定显著性水平0.1,查
$t$ 分布表得到$t{\left( {2 l - q - 1} \right)_{0.05}} = 2.131\;8$ 。由$\left| {{t}} \right| = 0.238\;7 < 2.131\;8$ ,所以接受假设${H_0}$ 。因此,模型假设无交互作用项成立。于是加速模型公式(5)改写为:$$ {\rm ln}\varepsilon = a + \frac{b}{T} + cI $$ (13) 将表2中的
$\; {\beta _{i,j}} $ 代入公式(8)可以求得${\varepsilon _{i,j}}$ 。根据加速退化模型作线性方程组最小二乘估计得到12组模型参数的估计值$\hat a,\hat b,\hat c$ ,如表4所示。表 4 每个激光器对应的加速退化模型参数以及外推的寿命
Table 4. Accelerated degradation model parameters corresponding to each laser diode and extrapolated lifetime
Laser diode ID a b c ε22 ℃,0.9 A/h 1 4.01 1 833 −1.73 5805 2 3.90 1 816 −1.62 5420 3 3.51 1 981 −1.65 6249 4 3.80 1 862 −1.58 5942 5 3.73 1 880 −1.63 5630 6 3.81 1 873 −1.71 5542 7 3.95 1 865 −1.61 6789 8 3.89 1 841 −1.53 6334 9 3.79 1 856 −1.62 5561 10 4.02 1 786 −1.58 5722 11 3.85 1 799 −1.59 5001 12 3.81 1 853 −1.69 5273 确定加速模型后,将光输出功率下降为初始光功率的80%定为失效标准,将它和标准工作应力条件[22 ℃,0.9 A]代入公式(2)可以得到12只器件的预测寿命
$\varepsilon $ ,如上表所示。由$\varepsilon \sim {{W}}\left( {{{m}},{\textit{η }}} \right)$ ,将威布尔分布函数等式移项后两边同时求对数,利用直线最小二乘估计法求得形状参数${{m}}$ 和尺度参数${\textit{η }}$ 。由公式(6)得到:$$ \begin{array}{*{20}{c}} {{\rm lnln}{{\left[ {1 - F\left( t \right)} \right]}^{ - 1}} = - m{\rm ln}\eta + m{\rm ln}t} \end{array} $$ (14) 这样就将威布尔分布函数改写成了关于(
${\rm ln}t$ ,${\rm lnln}{\left[ {1 - F\left( t \right)} \right]^{ - 1}}$ )的一次函数。根据上式进行直线最小二乘法拟合,如图7(a)所示,求得斜率即形状参数m=11.68,再利用截距求得尺度参数η=5994 h。基于威布尔分布的失效分布函数标准形式如图7(b)所示。根据威布尔分布函数的性质,失效率为50%时所对应的时间$t$ 即为MTTF,计算结果为5811 h。图 7 失效数据点与威布尔分布函数拟合曲线,拟合度达到了92.24%。(a)坐标变换后的威布尔图估计结果;(b)失效分布函数拟合结果
Figure 7. Failure data points were fitted with the curve of Weibull distribution function and the fit was 92.24%. (a) Estimation results of the Weibull plot after coordinate transformation; (b) Fitting results of the failure distribution function
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如表5所示,不考虑交互作用项,文中使用12个单管器件在A[22 ℃,1.4 A],B[42 ℃,1.4 A],C[42 ℃,1.8 A]三种应力条件下的性能退化数据拟合模型后,计算D[62 ℃,1.8 A]条件下的退化率βtest,并与真实退化率β62 ℃,1.8 A进行对比。误差均在10%以下,说明了文中建立模型的准确性。
表 5 模型计算得到的理论退化率βtest与实际退化率β62 ℃,1.8 A的对比
Table 5. Comparison of the theoretical degradation rate βtest calculated by the model with the actual degradation rate β62 ℃,1.8 A
Laser diode ID β62 ℃,1.8 A βtest Error 1 $ 3.674\times 1{0}^{-4} $ $ 3.837\times 1{0}^{-4} $ $ 4.44\text{%} $ 2 $ 3.624\times 1{0}^{-4} $ $ 3.686\times 1{0}^{-4} $ $ 1.02\text{%} $ 3 $ 3.635\times 1{0}^{-4} $ $ 3.522\times 1{0}^{-4} $ $ 3.11\text{%} $ 4 $ 3.137\times 1{0}^{-4} $ $ 3.328\times 1{0}^{-4} $ $ 6.09\text{%} $ 5 $ 3.893\times 1{0}^{-4} $ $ 3.657\times 1{0}^{-4} $ $ 6.09\text{%} $ 6 $ 3.684\times 1{0}^{-4} $ $ 4.001\times 1{0}^{-4} $ $ 8.60\text{%} $ 7 $ 3.259\times 1{0}^{-4} $ $ 2.975\times 1{0}^{-4} $ $ 8.71\text{%} $ 8 $ 3.126\times 1{0}^{-4} $ $ 2.939\times 1{0}^{-4} $ $ 5.98\text{%} $ 9 $ 3.698\times 1{0}^{-4} $ $ 3.651\times 1{0}^{-4} $ $ 1.27\text{%} $ 10 $ 3.521\times 1{0}^{-4} $ $ 3.327\times 1{0}^{-4} $ $ 5.51\text{%} $ 11 $ 3.973\times 1{0}^{-4} $ $ 3.824\times 1{0}^{-4} $ $ 3.75\text{%} $ 12 $ 3.868\times 1{0}^{-4} $ $ 4.097\times 1{0}^{-4} $ $ 5.92\text{%} $
Lifetime prediction method for high-power laser diodes under double-stress cross-step accelerated degradation test
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摘要: 高可靠性已成为大功率半导体激光器实用化的重要指标之一,而寿命预测是大功率半导体激光器可靠性评估的首要环节。文中提出了一种双应力交叉步进加速退化的试验方法,对830 nm F-mount封装的大功率半导体激光器进行了四种不同的双应力条件A[22 ℃, 1.4 A],B[42 ℃,1.4 A],C[42 ℃,1.8 A],D[62 ℃,1.8 A]下的电流-温度交叉步进加速退化试验研究,对光输出功率退化轨迹进行拟合,按照80%功率退化作为失效判据,结合修正后的艾琳模型和威布尔分布外推得到器件在正常工作条件下的平均失效时间(MTTF)为5 811 h。文中给出了完整的加速退化模型建立过程与详细的外推寿命计算方法,并对模型进行了准确性检验,误差不超过10%。该方法相比单应力恒定加速试验方法,可以大幅度节约试验时间和试验成本,这对于大功率半导体激光器的自主研制具有重要的指导意义。Abstract:
Objective High reliability becomes very important for the application of high-power laser diodes, and lifetime prediction is the primary aspect of reliability assessment of high-power laser diodes. Accelerated degradation test is a test method to accelerate the degradation process in the laboratory in accordance with the degradation model, which can obtain statistically significant lifetime prediction in a short time. With the advancement of device technology and its reliability, single-stress accelerated degradation test faces problems such as long test time, high cost, and excessive stress application in the degradation mechanism. Therefore, it is necessary to propose an accelerated degradation test for lifetime prediction of highly reliable and long-lived devices. For this purpose, a double-stress cross-step accelerated degradation technological method is designed in this paper. Methods A double-stress cross-step accelerated degradation test is proposed. Aging test platform for high-power laser diodes was built (Fig.5). The device (Fig.4) was subjected to 1600 h accelerated degradation test, and the accelerated degradation data of optical output power under different stress conditions were collected (Tab.1). Performance degradation model was established to analyze the data with the accelerated model to obtain the lifetime prediction values, and the accuracy of the model was tested for significance (Tab.5). Results and Discussions The overall scheme of high-power laser diodes lifetime prediction (Fig.1) has three main steps of bringing degradation data into the model, fitting the lifetime probability density distribution function, and checking accuracy. The double-stress cross-step accelerated degradation test sets the temperature and current as the stress conditions, and the two stress conditions are cross-stepped to form a total of four different stress conditions (Fig.2) as A [22 ℃, 1.4 A], B [42 ℃, 1.4 A], C [42 ℃, 1.8 A], and D [62 ℃, 1.8 A], respec-tively. The performance degradation model is built according to the YamaKoshi equation and the laser optical output power failure threshold is set. The acceleration model is established according to the generalized Irene model, and the degradation track of the optical output power during the accelerated degradation test is expressed as a segmentation function. After the estimation of the model conversion parameters, the lifetime prediction results were obtained and the parameter errors were compared (Tab.5), and they were all below 10%, which verified the accuracy of the model. Conclusions The accelerated degradation test of 12 830 nm F-mount single-emitter device was conducted for 1600 h using four different current-temperature double-stress conditions in cross-step by self-designed experimental platform. The MTTF of the device is 5 811 h. The accelerated test method used in this paper saves at least 57.7% of the test time compared with the conventional single-stress constant accelerated lifetime test method, and has the advantages of less sample size and more flexibility in stress conditions. The method has been experimentally validated to provide statistically significant results for device lifetime prediction with experimental cost savings for different high-power laser diodes. -
Key words:
- high-power laser diodes /
- accelerated degradation test /
- double-stress /
- lifetime
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图 7 失效数据点与威布尔分布函数拟合曲线,拟合度达到了92.24%。(a)坐标变换后的威布尔图估计结果;(b)失效分布函数拟合结果
Figure 7. Failure data points were fitted with the curve of Weibull distribution function and the fit was 92.24%. (a) Estimation results of the Weibull plot after coordinate transformation; (b) Fitting results of the failure distribution function
表 1 830 nm F-mount单管器件在不同的应力条件下的加速退化试验数据(光输出功率/W)
Table 1. Accelerated degradation test data of 830 nm F-mount single-emitter devices under different stress conditions (optical output power/W)
Stress condition Time/h 1# 2# 3# 4# 5# 6# 7# 8# 9# 10# 11# 12# A[22 ℃,1.4 A] 100 1.43 1.38 1.39 1.41 1.41 1.40 1.36 1.42 1.44 1.36 1.45 1.39 200 1.42 1.38 1.40 1.40 1.40 1.38 1.37 1.43 1.42 1.36 1.44 1.37 300 1.39 1.37 1.37 1.39 1.38 1.35 1.41 1.39 1.39 1.34 1.43 1.34 400 1.40 1.33 1.35 1.40 1.40 1.34 1.34 1.40 1.37 1.35 1.40 1.34 B[42 ℃,1.4 A] 500 1.36 1.33 1.33 1.37 1.38 1.30 1.29 1.36 1.31 1.31 1.36 1.29 600 1.32 1.30 1.29 1.34 1.32 1.27 1.32 1.33 1.28 1.28 1.36 1.31 700 1.28 1.30 1.31 1.34 1.34 1.27 1.29 1.31 1.30 1.27 1.35 1.25 800 1.30 1.29 1.30 1.33 1.30 1.26 1.25 1.30 1.29 1.23 1.31 1.26 C[42 ℃,1.8 A] 900 1.62 1.63 1.62 1.70 1.69 1.64 1.69 1.72 1.70 1.60 1.69 1.69 1000 1.57 1.60 1.59 1.65 1.65 1.60 1.67 1.65 1.68 1.57 1.67 1.69 1100 1.55 1.58 1.50 1.64 1.60 1.57 1.62 1.61 1.61 1.53 1.60 1.63 1200 1.50 1.51 1.52 1.58 1.58 1.50 1.56 1.62 1.57 1.54 1.60 1.56 D[62 ℃,1.8 A] 1300 1.39 1.44 1.43 1.50 1.45 1.39 1.52 1.50 1.47 1.40 1.49 1.42 1400 1.35 1.37 1.38 1.44 1.41 1.33 1.45 1.44 1.40 1.35 1.45 1.41 1500 1.27 1.34 1.33 1.41 1.34 1.31 1.43 1.41 1.35 1.32 1.36 1.35 1600 1.26 1.28 1.27 1.36 1.26 1.25 1.38 1.39 1.29 1.30 1.30 1.30 表 2 每个激光器在各个应力条件下的退化率
Table 2. Degradation rate of each laser diode at each stress condition
Laser
diode IDβ22 ℃,1.4 A β42 ℃,1.4 A β42 ℃,1.8 A β62 ℃,1.8 A 1 $ 9.152\times {10}^{-5} $ $ 1.358\times {10}^{-4} $ $ 2.711\times {10}^{-4} $ $ 3.674\times {10}^{-4} $ 2 $ 9.245\times {10}^{-5} $ $ 1.367\times {10}^{-4} $ $ 2.613\times {10}^{-4} $ $ 3.624\times {10}^{-4} $ 3 $ 8.167\times {10}^{-5} $ $ 1.251\times {10}^{-4} $ $ 2.420\times {10}^{-4} $ $ 3.635\times {10}^{-4} $ 4 $ 8.321\times {10}^{-5} $ $ 1.242\times {10}^{-4} $ $ 2.338\times {10}^{-4} $ $ 3.137\times {10}^{-4} $ 5 $ 8.905\times {10}^{-5} $ $ 1.337\times {10}^{-4} $ $ 2.566\times {10}^{-4} $ $ 3.893\times {10}^{-4} $ 6 $ 9.458\times {10}^{-5} $ $ 1.415\times {10}^{-4} $ $ 2.805\times {10}^{-4} $ $ 3.684\times {10}^{-4} $ 7 $ 7.345\times {10}^{-5} $ $ 1.097\times {10}^{-4} $ $ 2.089\times {10}^{-4} $ $ 3.259\times {10}^{-4} $ 8 $ 7.563\times {10}^{-5} $ $ 1.124\times {10}^{-4} $ $ 2.073\times {10}^{-4} $ $ 3.126\times {10}^{-4} $ 9 $ 9.011\times {10}^{-5} $ $ 1.344\times {10}^{-4} $ $ 2.569\times {10}^{-4} $ $ 3.698\times {10}^{-4} $ 10 $ 8.583\times {10}^{-5} $ $ 1.261\times {10}^{-4} $ $ 2.372\times {10}^{-4} $ $ 3.521\times {10}^{-4} $ 11 $ 9.774\times {10}^{-5} $ $ 1.440\times {10}^{-4} $ $ 2.719\times {10}^{-4} $ $ 3.973\times {10}^{-4} $ 12 $ 9.804\times {10}^{-5} $ $ 1.464\times {10}^{-4} $ $ 2.878\times {10}^{-4} $ $ 3.868\times {10}^{-4} $ 表 3 取管1和管2两组(共八个退化率数据)求得的加速退化模型参数
Table 3. Parameters of the accelerated degradation model obtained by taking two sets of single-emitter 1 and single-emitter 2 (a total of 8 degradation rate data)
$ a $ $ b $ $ c $ $ d $ 4.40 1 830 −1.66 −3.36 表 4 每个激光器对应的加速退化模型参数以及外推的寿命
Table 4. Accelerated degradation model parameters corresponding to each laser diode and extrapolated lifetime
Laser diode ID a b c ε22 ℃,0.9 A/h 1 4.01 1 833 −1.73 5805 2 3.90 1 816 −1.62 5420 3 3.51 1 981 −1.65 6249 4 3.80 1 862 −1.58 5942 5 3.73 1 880 −1.63 5630 6 3.81 1 873 −1.71 5542 7 3.95 1 865 −1.61 6789 8 3.89 1 841 −1.53 6334 9 3.79 1 856 −1.62 5561 10 4.02 1 786 −1.58 5722 11 3.85 1 799 −1.59 5001 12 3.81 1 853 −1.69 5273 表 5 模型计算得到的理论退化率βtest与实际退化率β62 ℃,1.8 A的对比
Table 5. Comparison of the theoretical degradation rate βtest calculated by the model with the actual degradation rate β62 ℃,1.8 A
Laser diode ID β62 ℃,1.8 A βtest Error 1 $ 3.674\times 1{0}^{-4} $ $ 3.837\times 1{0}^{-4} $ $ 4.44\text{%} $ 2 $ 3.624\times 1{0}^{-4} $ $ 3.686\times 1{0}^{-4} $ $ 1.02\text{%} $ 3 $ 3.635\times 1{0}^{-4} $ $ 3.522\times 1{0}^{-4} $ $ 3.11\text{%} $ 4 $ 3.137\times 1{0}^{-4} $ $ 3.328\times 1{0}^{-4} $ $ 6.09\text{%} $ 5 $ 3.893\times 1{0}^{-4} $ $ 3.657\times 1{0}^{-4} $ $ 6.09\text{%} $ 6 $ 3.684\times 1{0}^{-4} $ $ 4.001\times 1{0}^{-4} $ $ 8.60\text{%} $ 7 $ 3.259\times 1{0}^{-4} $ $ 2.975\times 1{0}^{-4} $ $ 8.71\text{%} $ 8 $ 3.126\times 1{0}^{-4} $ $ 2.939\times 1{0}^{-4} $ $ 5.98\text{%} $ 9 $ 3.698\times 1{0}^{-4} $ $ 3.651\times 1{0}^{-4} $ $ 1.27\text{%} $ 10 $ 3.521\times 1{0}^{-4} $ $ 3.327\times 1{0}^{-4} $ $ 5.51\text{%} $ 11 $ 3.973\times 1{0}^{-4} $ $ 3.824\times 1{0}^{-4} $ $ 3.75\text{%} $ 12 $ 3.868\times 1{0}^{-4} $ $ 4.097\times 1{0}^{-4} $ $ 5.92\text{%} $ -
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