May_EDFA_Digital

edfas.org 33 ELECTRONIC DEVICE FAILURE ANALYSIS | VOLUME 22 NO. 2 Another major advantage of the arbitrary waveform excitation is theabsenceof the “off”periodof the sequence as compared to the square wave excitation illustrated in the top image of Figure 4. For square-wave excitation, the sample is powered only for half of the measurement period and remains unpowered for the other half. The active measurement time is extended by a factor of two without increasing the overall acquisition time required for the LIT analysis when applying arbitrarily shaped excitation signals, leading to either a reduced acquisition time or an increased SNR. The latter results in a higher precision of the estimated phase transfer function. In all three cases considered (classical LIT, TRTR-analysis with square wave excitation and TRTR-analysis with arbitrary waveform excitation), the phase estimate is a measure of the delay of the thermal response of a defect relative to the electrical excitation signal. The phase values as a func- tion of frequency represent the phase transfer function that characterizes the frequency-dependent propagation time; it is the key parameter for a 3D defect-localization that can largely benefit from a fast and robust estimation based on arbitrary waveform excitation in combination with TRTR analysis. Figure 7 contains the phase transfer functions esti- mated by four different methods, including classical LIT and three different TRTR analyses employing a standard square-wave excitation, a squarewave signal generatedas an arbitrary waveform, and amulti-sine signal containing Fig. 6 Arbitrarywaveformexcitation in LIT. Top: Trace of an arbitrarily shaped waveform for sample excitation. The signal has been designed according to the spectral power distribution. Bottom: Power spectrum of the signal in top graph. Fig. 7 Comparison of the phase values estimated us- ing classical LIT (purple), TRTR analysis using con- ventional square wave excitation (blue), TRTR analysis using a square wave signal that was arbi- trarily designed (red), and TRTR analysis using a cus- tom designed multi-sine signal with energy at 7 Hz, 24 Hz, 40 Hz, 58 Hz, and 81 Hz (green). Fig. 8 (a) Schematic of a two-die stacked device with thermal defects A and B at different die levels, (b) amplitude images of a defect at the upper die at the indicated frequencies extracted from the data of a 1 Hz LIT-TRTR measurement, and (c) related phase shift to frequency characteristics of the two defects at the upper and the lower die, extracted from the TRTR data. (a) (b) (c)