Experimental Setup
We test nine high-performance, Fabry-Perot QCLs using an accelerated burn-in process where the lasers are operated in continuous wave (CW) mode at an elevated heat sink temperature. The QCLs are from different portions of a single epitaxial wafer grown by metal organic chemical vapor deposition and therefore share the same multiple quantum well heterostructure design. The lasers are processed as buried heterostructures using InP regrowth and mounted epitaxial-side down on CuW C-mounts for efficient heat extraction. The QCLs are all 5 mm long, but their ridge width varies. Two identical testing stages are used for the accelerated burn-in testing. Each stage uses a temperature-controlled thermoelectric cooler mounted on a water-cooled base. The stages are both equipped with two thermopiles; thus, four QCLs (two per stage) can undergo the accelerated burn-in process simultaneously as depicted in Fig. 1.
During the accelerated burn-in process, the QCLs are operated in CW mode at 80% of their peak CW optical power at a heat sink temperature of 313 K. Measurements of the CW current, voltage, and optical power are recorded every minute. Here, these frequent measurements are only used to determine when a device fails, which is indicated by measuring no output optical power from the biased device. Continuous wave light-current-voltage (LIV) measurements are performed approximately every 2.5 hours where the current, voltage, and output optical power are measured as the CW current is swept in 10 mA steps from zero to the operating point (80% of the peak output power). The planned burn-in time for seven of the QCLs is 150 hours, but there are differences in the overall test length due to starting and stopping the burn-in process manually. Two of the devices fail before the end of the planned burn-in procedure. Two additional QCLs undergo longer accelerated burn-in testing that is planned for 250 hours. During the burn-in process for these devices, the interval between CW LIV measurements is increased and ranges from 10 to 48 hours between measurements.
Figure 2 shows every measured LIV for all nine QCLs obtained during the accelerated burn-in processes. The devices labeled GN (N = 1…5) indicate QCLs that are operational at the end of the burn-in testing. The devices labeled BN (N = 1…4) indicate QCLs that failed during the burn-in testing. In Fig. 2, we omit measurements after device failure for devices B1 to B4. This data is also excluded when training and testing the SVM. Importantly, for the measurements shown in Fig. 2, there is no easily apparent distinction between the LIVs of devices that remain operational and devices that fail. However, we will show that incorporating the LIV measurements into SVMs can predict premature failure of the QCLs with very high accuracy.
We incorporate the LIV measurements into a SVM by extracting features from the measurements that express the significant characteristics of the data. The parameters are extracted automatically using custom software that generates a feature matrix for each LIV. Examples of extracted features include the wall-plug efficiency (WPE) at peak optical power; laser threshold current density; applied voltage at lasing threshold; maximum output optical power; slope of optical power versus current density at several operating points; and differential resistance (slope of voltage versus current density) at several operating points. In total, we extract 28 features describing each LIV measurement. All of the features are listed in Table 1. Here, V is the voltage; P is the measured optical power, Pmax is the peak optical power measured from one facet, J is the current density, and R is the differential resistance.
Table 1: Features used in the SVM model.
Training and Testing
To predict premature device failure, we use the 28 features in a SVM with a radial basis function (RBF-SVM) kernel as the overall accuracy and number of false negatives was superior compared to the linear SVM. The training and testing of the model consist of two stages. In the initial stage, the model is trained and tested with data from the first set of devices with planned burn-in times of 150 hours (Gi; i = 1…5, Bj; j = 1,2). During training and testing, the LIVs of a single device are categorized according to the operational status of the device at the end of the burn-in period. For a device that fails during testing, all the LIVs are categorized as belonging to a failed device. Likewise, for a device that is operational at the end of testing, all the LIVs for that device are assumed to come from an operational device. For the set of QCLs part of the 150-hour burn-in process, there are 444 individual LIV measurements in total. 95 of the LIVs are from devices that fail during testing. The remaining 349 LIV measurements are from devices that are operational at the end of testing.
The RBF-SVM has two hyperparameters that are adjusted during training to achieve high classification accuracy. To tune these hyperparameters, we employ a grid-search algorithm, where we vary the parameters between 10− 3 to 103 with an adaptive step size, yielding a parameter matrix of 72 rows by 72 columns. For each pair of hyperparameters, we calculate the accuracy of the SVM. To avoid overfitting to a particular set of training data, we repeat this process for 10 different sets of training data. Each of the 10 training data sets consists of LIVs from four operational devices and one failed device. A score is assigned to each pair of hyperparameters, by averaging the classification accuracy scores of the 10 cases. In the end, the SVM with the hyperparameter pair yielding the highest score is selected for use in the model. We emphasize that even though we use different combinations of devices in the training and test sets, we never mix the two sets in any experiment. In other words, the SVM is never trained on the devices in the test set. When using the RBF-SVM to classify the LIVs for the two devices that underwent the longer burn in process, we train the SVM using (Gi; i = 1…5, Bj; j = 1,2). The RBF-SVM uses the same values for the hyperparameters that were determined previously.