edfas.org ELECTRONIC DEVICE FAILURE ANALYSIS | VOLUME 27 NO. 4 6 beam power at sample surface. Reflected beam power Pr is then given by: Pr = R(T)Pin (Eq 5) where R(T) is temperature-dependent reflectance at given wavelength. When the temperature varies by ∆T(t) over time, t, the material’s reflectance changes, resulting in a corresponding change in the reflected beam power, denoted as ∆Pr. For example, when the sample is electrically modulated at angular frequency, ω, the temperature change is expressed as ∆T(jwt + j), where t and j are time and an imaginary unit, respectively. j represents timing difference relative to the timing of exercising the device. Then Eq 5 is rewritten as: (Eq 6) Lock-in detection of ∆Pr(t) with a reference signal from the sample exercising apparatus provides an amplitude of and phase j. These are collected by a computer and mapped two-dimensionally by raster scanning the probing beam. The resulting images are called TD Imaging amplitude and phase image. Alternatively, the operation of amplitude × cos cos phase generates an in-phase image. The sensitivity of TD Imaging is calculated by dividing the reflected beam power changes ∆Pr by the reflected beam power Pr. (Eq 7) The thermo-reflectance coefficient (TR Coeff) depends on the material and wavelength. In semiconductor devices, Al or Cu are commonly used for interconnects, and TR Coeffs are expected to be larger in the visible wavelength than in the infrared. Table 2 shows measured TR Coeff values of Al and Cu at two wavelengths in the lab with HIL values of 1300 nm and 670 nm. The temperature modulation, expressed as increases when electrically modulated at a lower angular frequency ω. As a result, TD imaging systems are optimally compatible with low-frequency modulation. However, the frequency is limited because there is noise when the probing beam is vibrating slightly. Figure 2 is the amplitude image of TD Imaging using the optics chart Fig. 1 Working principle and experimental system setup of TD Imaging. A circuit biased with a periodic current with an interconnect anomaly is buried under the metal surface. The periodic current induces significant Joule heating at the confinement anomaly, while other sections of the interconnect remain unaffected. This localized heating modulates the optical reflectance in the vicinity of the anomaly. One of 1300 nm and 670 nm HILs is focused on sample surface, and the reflected beam is guided to APD. The photocurrent of APD is lock-in detection with reference signal provided by pulse generator. Amplitude and phase measured by lock-in amplifier are recorded in a computer as pixel intensity. Table 2 Comparison of TR Coeff values of Al and Cu at two wavelengths in this system Wavelength of Light Source |TR Coeff, ppm/K| Cu Al 670 nm 20 50 1300 nm 10 20
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