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edfas.org 31 ELECTRONIC DEVICE FAILURE ANALYSIS | VOLUME 22 NO. 2 FromEq 1 it can be seen that themeasured phase-shift is also a function of the applied lock-in frequency. Besides the relationship between the phase and the frequency, additional frequency-dependent phenomena such as attenuation may occur. Thus, an analysis of the defect depth is based on measuring the complete phase-shift- versus-frequency characteristics rather than performing a single frequency analysis. [4-5] The modeling approach, however, lacks accuracy since exact values of the thermal properties of the used adhesive and mold compound materials which are necessary for an accurate modeling are not readily available in many practical cases. As a consequence, the required referencedata-sets for estimat- ing the relationship between phase shift and excitation frequency of a specific stacked die architecture needs to be acquired experimentally prior to the 3D-analysis. Alternatively, internal I/O diodes with known axial loca- tion can be employed as thermal sources to achieve cali- bration. [5] Another option is the stepwise delayering of a stacked die device to expose the individual die-levels for applying stimulation by external thermal sources e.g. con- ductive probing or laser excitation through the backside. ENHANCED PHASE SHIFT ANALYSIS BY SPECTRAL DECOMPOSITION OF THE TIME RESOLVED THERMAL RESPONSE As described above, LIT employs the lock-in amplifi- cation approach that benefits from the combination of periodic averaging over the entire measurement of the repeated sample excitation and the correlation to the exci- tation function, resulting in signals with sufficiently high signal-to-noise ratio (SNR). In classical measurements, the time sequence is correlated to a sine and a cosine signal of the lock-in frequency which are synchronized to the excitation signal. These correlation functions are then integrated over the lock-in period resulting in an in-phase and an out-of-phase value for each pixel of the recorded frame as illustrated in Fig. 2. This approach results in excellent SNR values of even extremely weak thermal signals. However, when following this scheme, the entire temporal and thus spectral information that is contained in the signal is neglected. In common LIT measurements, the sample is peri- Fig. 3 Schematic of a stacked die device (top). The phase shift to frequency characteristic (bottom) is calculated and measured enabling a fingerprinting of the defect site related to the die level. [4-5] Fig. 4 Excitation signal in classical LIT. Top: Signal in timedomain. Bottom: Signal in spectral domain. The spectral rep- resentation shows that the signal contains energy at the fundamental frequency and even multiples of it.