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edfas.org ELECTRONIC DEVICE FAILURE ANALYSIS | VOLUME 22 NO. 2 30 camera. Despite thedegradation in lateral resolutionowed to lateral spreading of the thermal wave, lock-in thermog- raphy does allow for thedetectionof deeply burieddefects evenwithin complex 3D architectures without the need of direct optical access. The depth information of the thermal source can be obtained by a quantitative analysis of the time delay between the electrical stimulation and the reception of the corresponding thermal response that is measured at the device's surface. [4-5] This delay is normalized to the analysis frequency and expressed in terms of a phase shift. The classical lock-in approach repeats the data acquisi- tion at multiple frequencies to obtain a phase shift versus frequency characteristics. In recent developments, the time-resolved temperature response (TRTR) is analyzed to simultaneously extract amplitude and phase values at multiple-harmonics [6] of the fundamental frequency. In addition, specific excitation signals were also employed to further improve the phase shift analysis in terms of spectral range and measurement time. [7-8] Opposite to the phase shift analysis, other approaches perform LIT measurements under the variation of the focusing and analyze the observed hot-spot diameters for deriving the axial defect location. [9] This article describes phase-shift analysis for analyzing stackeddiepackages as anapproach to 3D defect localization based on lock-in thermography. PHASE-SHIFT ANALYSIS FOR LOCALIZING HOT SPOTS IN STACKED DIES In lock-in thermography, the device under test is excited by periodically applying electrical power. The repetition frequency of the stimulation is the lock-in frequency of the measurement, necessary to perform lock-in amplification. Stimulation of a resistive defect that is located within a stack of multiple dies using the lock-in scheme leads to a periodically occurring local heating. The resulting thermal signal can then be analyzed to laterally isolate the defect and to estimate its axial position for guiding subsequent physical failure analysismethodswith the goal of uncovering the defects root cause. The periodic excitation of a resistive defect results in a periodically occurring thermal signal that propagates from the defect site through the die stack and the mold compound toward the component's surface. The repeti- tion rate of the measurement together with the electrical parameters (current and voltage) define the total dis- sipated power per cycle. These parameters have to be selected sample-specific since there is a trade-offbetween detection sensitivity and thermal spreading. The modulated thermal signal that is captured by the camera exhibits a specific delaywith respect to the stimu- lation signal. This delay represents the time the thermal signal required for propagating from the defect site to the surface of the sample where it radiated off towards the camera. Thepropagation time is not only influencedby the depth of the thermal sourcewithin the sample but also by the thermal propagationproperties of the individualmate- rials; [5] for example, the thermal conductivity of silicon is substantially higher than that of mold compound. The overall delay between electrical stimulation and reception of the thermal signal can, therefore, be considered as an accumulation of the propagation times within the indi- vidual regions of the sample. Conversely, this approach allows the estimation of the depth of a thermal source according to the delay between stimulation and recep- tion of the thermal signal. A highly precise determination of temporal delays can be obtained by measuring phase shifts at distinct frequencies which is inherent within the lock-in amplification method. This phase shift is then converted into the distance value the thermal signal propagated from its source to the sample surface. The expected phase of a thermal signal propagating through a known structure can be calculated from the analytical solution of the heat propagation equation (Eq 1). [5] Each layer of the stack between the heat source and the surface of the sample contributes to a certain phase shift as the thermal wave requires a certain amount of time to propagate through. Figure 3 contains a sche- matic of a stacked die samplewith a resistive defect in the stack. The dissipated thermal energy propagates through the stack until it reaches the surface where it radiates off. The graph at the bottomof Fig. 3 contains the phase-shift versus frequency curves calculated for the thermal sources at the various die levels of the stack. The overall phase-shift can be obtained by: (Eq 1) where m is the number of all physical layers the thermal signal needs to propagate through, z the thickness of the individual layer, λ the corresponding thermal conductiv- ity, c p the specific heat capacity, ρ the mass density, and f the analysis frequency. Consequently, the result is a cumulated value of the phase shifts of the individual dies within the stack, as described in Fig. 3, that can be related to the experimentally obtained phase shift to derive the defect's depth.