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We have performed three-dimensional characterization of the TPA effective laser spot size in silicon using an integrated knife-edge sensor. The TPA-induced response of a CMOS integrated circuit is analyzed based on these results and compared to simulation; we have found that the charge injection capacity in IC’s active layer could be influenced by irradiance energy and focus depth.
©2011 Optical Society of America
1. Introduction
Two-photon Absorption (TPA) processes are commonly used in laser scanning microscopy to stimulate selectively a particular imaging process or to improve lateral and axial resolution [1]. Indeed, due to the quadratic dependence of TPA with the optical intensity, lateral resolution is reduced and axial resolution can be limited to a few times the wavelength using high numerical aperture (NA) microscope objectives. These features are interesting in the context of microelectronics for testing integrated circuits (IC) by imaging the circuit response to localized TPA-induced electron-hole pairs generation. The TPA approach using sub-bandgap wavelengths has been shown to improve the lateral resolution of classical defect localization techniques like OBIC (Optical Beam Induced Current) [2,3]. Axial resolution can be used for evaluating the depth extension of charge collection mechanisms involved in radiation-induced single-event effects (SEE) [4]. In both applications, it is critical to have an accurate geometrical description of the TPA-induced carrier generation rate in silicon in order to analyze the circuit response. In this work, we first review the basic equations of the optical nonlinear response of silicon and then present the three-dimensional experimental characterization of the TPA interaction volume of a femtosecond near infrared beam in silicon under high NA using a specifically designed knife-edge optical sensor. These measurements are then used to analyze the results of TPA-induced timing fault injection in a shift-register IC.
2. Nonlinear response of silicon
When an electric field Eω is applied to a material, the polarization can be expressed according to Eq. (1):
where ε0 is the permittivity of free space and χ(i) is the ith order order susceptibility.The first term is related to linear optical properties, whereas higher orders describe nonlinear effects. In the case of silicon, the χ(2) term is equal to zero because this medium is a centro-symmetric crystal structure. The real part of χ(3) describes the optical Kerr effect and the imaginary part is responsible for TPA.
The Kerr effect induces a nonlinear modification of the material refractive index with the intensity light beam as ΔnKerr = n2I where n2 is the nonlinear index and I the light intensity. This refraction index change induces phenomena such as self-phase modulation, cross-phase modulation, Kerr self-focusing and four-wave mixing. In the case of integrated circuit testing with beam energy below few nJ, the main effect that must be considered is Kerr lensing.
TPA will induce a depletion of our optical beam and the generation of free-carriers. The total losses are expressed in Eq. (2):
The first term of Eq. (2) describes linear absorption, the second term describes TPA and the third term is the Free-Carrier Absorption (FCA) due to the free-carriers density N. Linear absorption coefficient α was considered negligible, TPA coefficient β and FCA cross-section σFC used in simulation are given in the next paragraph.
Number of free-carriers N in silicon is shown in Eq. (3). The time-varying optical intensity will create free-carriers N which will then decrease according to the recombination rate τ.
The recombination rate is on the order of several 10ns which is long compared to our laser pulse duration of 150fs.
Free-carriers will cause plasma effect. The negative refractive index modification can be expressed at 1.3µm according to [5] as Eq. (4):
where ΔNe and ΔNh are electrons and holes density respectively.We have simulated the beam propagation in silicon based on the analytic equations given above. The laser beam at 1.3µm with a pulse duration of 150fs is focused with a 100X (NA = 0.8) objective inside the silicon. Values used for simulation are 2.7e-18 m2/W [6] for n2, 0.41 cm/GW [7] for the TPA coefficient β and 1.02e-17 cm2 [8] for the FCA cross-section σFC. The position of the waist is chosen to be 50µm inside silicon. The refractive index change at the waist for two different energies is shown in Fig. 1 :Figure 1 shows that with entrance energy of 100pJ the pulse is more affected by the Kerr effect but for energies from 750pJ the plasma effect is the main effect that influences propagation of our beam.
Fig. 1 Refraction index modification at 100pJ (left) and 750pJ (right) induced by Kerr and plasma effects (ΔnTotal = ΔnKerr + ΔnFC).
3. TPA effective laser spot size
When using sub-bandgap wavelength (>1.1µm in silicon) for photoelectric testing of ICs, significant carriers generation only takes place within the high-intensity focal volume of the focused beam. First order analytical models can be used to estimate the lateral and axial extensions of this volume that we call the TPA effective laser spot. However, the level of confidence of these models can be altered by non-paraxial propagation effects (typically NA≥0.7) and an experimental calibration is preferred for daily monitoring of drifts in the optical setup (mainly laser output beam quality, pulse chirp, and microscope injection).
We have performed 3D characterization of the TPA laser spot using an integrated optical sensor for spot size measurement based on the knife-edge technique [9] and designed in a standard CMOS technology. A metal interconnection layer with a 20µm aperture plays the role of the knife edge over a silicon Nwell-Psub junction. A 1.3µm wavelength laser beam, with pulse duration of 150fs, is focused using a 100X (NA = 0.8) microscope objective lens to induce TPA in the sensor (Fig. 2(a) ). Classical knife-edge spot size measurement was performed by scanning the device through the static beam along X axis with steps of 0.1µm for different Z positions, while monitoring the electrical charge collected through the junction diode.
Fig. 2 (a) Front side knife-edge characterization of the TPA-effective laser spot size schematic and scan principles; (b) collected charge vs. scan position for different pulse energies; (c) TPA-effective laser spot profiles derived from (b).
In a first-order approximation, this method provides a signal proportional to the square of the integral of the beam intensity transmitted into the silicon as a function of the position of the edge of the metal layer with respect to the beam. Key to this approximation is the short distance (approximately one wavelength) between the knife-edge (Al layer) and the sensor (Si region) so diffraction on the knife edge causes much smaller variation of the beam intensity profile on the sensor than with classical macroscopic knife-edge instruments. We also assume that the charge collection efficiency remains constant whatever the amount of transmitted beam, which seems reasonable given the area of the diode and the small amount of collected charge (<1pC).
Figure 2(b) presents typical results of collected charge vs X and Z position of the knife-edge sensor for different laser pulse energies. Considering a Gaussian beam, the root square of this signal is supposed to have an erf-like variation along the X axis. Thus, by plotting the square of the derivative along the X axis of the root square of the signal, we obtain a view of the TPA effective laser spot size (Fig. 2(c)). We can clearly see that two-photon charge injection only occurred within the focal volume, and that the volume leading to a given amount of charge expands as energy increases. Energy variation appears to have more influence on the axial extension than on the lateral one. At 2nJ, the measured FWHM extension is 1.6µm on X axis and 8µm on Z axis, and the peak collected charge of 0,16pC gives a TPA conversion efficiency ratio of 500 collected electrons/pJ.
In Fig. 2(c), the left part of each plot is quite noisy because it corresponds to positions where the beam is mostly blocked by the knife, thus a low signal to noise ratio typical from knife-edge signal derivation. The right part shows a dissymmetry with respect to the Z plane of maximum signal.
Figure 2(c) clearly shows that the axial extension of the TPA-effective laser spot increases with pulse energy. This can be observed also on the profiles along the Z axis plotted in Fig. 3(a) . This expected behavior implies that the axial resolution of the TPA approach depends on the pulse energy. This is an important point to consider when TPA is used to measure the depth extension of charge collection volumes, for example for SEE rate prediction [10].
Fig. 3 (left) TPA-effective spot profile along Z for different energies; (right) TPA-effective spot profile along X at minimum width and peak spot.
Due to the distance between the metal layer and the junction (Fig. 2(a)), the lateral extension measured in the Z plane of the peak is slightly larger than the minimum spot size which is obtained in a Z plane distant of 2.3µm from the peak plane (Fig. 3-right). This offset is in very good agreement with the combined thickness of Al and SiO2 layers shown in Fig. 2(a). This result demonstrates that, with careful analysis of the data, the TPA approach allows extracting thicknesses much smaller than the effective axial extension. This high axial sensibility of TPA method offers a great potential for 3D imaging and characterization of ICs.
Considering that the distance between the metal layer and the junction is only 1.65µm (Fig. 2(a)), which is close to the laser’s wavelength in the oxide, we make the simplifying assumption that diffraction between the knife and the junction has negligible impact on the results.
4. Application to the analysis of the TPA sensitivity profile of a CMOS IC
We have tested a commercial CMOS 8-bit shift register using TPA photoelectric stimulation. Due to the high density of metal interconnections on the front side of the device under test (DUT), this test was performed through the backside of the substrate. The DUT backside was thinned down to 200µm and polished to mirror quality. The test consisted in mapping the output test vector as a function of the laser position. A typical result is presented in Fig. 4 (left), on which red areas highlight three regions sensitive to TPA-induced charge injection, superimposed with a standard confocal cw 1.3µm laser scanning microscope (LSM) image. The red areas correspond to a variation in the electrical output pulse duration from the nominal value (14ns) to a value exceeding 24ns, which can be considered as a fault in the DUT operation.Figure 4 (middle) presents TPA results obtained by moving the device by 2µm along the axial direction with respect to the image of Fig. 4 (left), which is equivalent to a displacement of the TPA effective laser spot of approximately 7µm in silicon substrate. This small change on the Z axis leads to the disappearance of only the sensitive area at the bottom of the image, whereas the two areas at the top remain present. However, when we increase 10% of the laser pulse energy, as shown in Fig. 4 (right), the bottom sensitive area is back. This result reveals that the TPA approach is extremely sensitive to the focus position and irradiance energy. This feature should be taken into account since sample’s thickness variations or surface obstacles (ex: dust or roughness) could easily lead to focus position or irradiance energy change, thus causing the loss of sensitive areas in the mapping. A better way to avoid this kind of mistake is performing TPA scans at different Z positions around the optimal focus to make sure that all sensitive areas are identified.
Fig. 4 TPA TRLS (Time Resolved Laser Scanning [13]) mappings for TPA sensitivity test: (left) optimal position and laser energy; (middle) result obtained when only moving the device 2µm away from the optimal focus position; (right) result with 10% energy increase from the 2µm shifted position.
The same scan was repeated for different Z positions of the DUT along the beam axis in order to determine the lower and upper limits of the sensitive volume. This operation was then repeated for increasing pulse energies. Results are summarized by Fig. 5 . As observed previously, the axial extension of the sensitive volume increases with energy. To correlate this result with previous TPA-effective spot size measurement, we have to take into account the difference between front side and backside approaches. Considering the refractive index ratio between SiO2 and Si (respectively around 1.5 and 3.5 at 1.3µm), the backside TPA-effective laser spot is estimated, in a first order approximation, to be around 19µm at 2nJ. Figure 2(c) shows a Z extension of 23µm at this energy, so we can estimate the collection depth of this DUT to be around 4µm, which was found to be consistent with the thickness of the epitaxial layer of this device’s technology.
We also compared experimental measurements with simulations performed according to section 2.
The Z-axis on Fig. 4 corresponds to the displacement of the objective. The red curve represents the Z positions giving the maximum signal for each energy. Its shape seems to indicate that the peak of the TPA-induced generation rate moves along the Z axis depending on the pulse energy. This shift of the effective focus could be explained as we mentioned in section 2, by the opposite contributions of Kerr effect and plasma effect [11,12]. With a free-carriers density threshold of 0.7x1024 m−3, simulation results are in good agreement with measurements. Simulations are able to show the sensitive depth and displacement of the waist position due to plasma effect. However, simulation results do not show the same inflection as can be seen on the measured data for the maximum signal for energies below 750pJ. This seems to indicate that simulation under-estimates the contribution of Kerr effect, leading to a quasi-monotonic evolution of the maximum signal curve.
5. Conclusion
We have investigated the optical nonlinear response of silicon, and then presented the 3D characterization of the TPA-effective laser spot size in silicon using a specific integrated knife-edge sensor. The results provide essential inputs for quantifying lateral and axial resolutions of TPA for laser testing of ICs, and will contribute to the current industrial developments of this technique. Laser energy must be precisely controlled near threshold in order to limit undesirable nonlinear properties and extension of the sensitive volume that will significantly decrease the resolution of this technique.
References and links
1. W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248(4951), 73–76 (1990). [CrossRef] [PubMed]
2. C. Xu and W. Denk, “Two photon optical beam induced current imaging through the backside of integrated circuits,” Appl. Phys. Lett. 71(18), 2578–2580 (1997). [CrossRef]
3. K. A. Serrels and D. T. Reid, “Two-photon X-Variation mapping based on a diode-pumped femtosecond laser,” in 36th International Symposium for Testing and Failure Analysis (2010), pp. 14–19.
4. D. McMorrow, W. Lotshaw, J. Melinger, and J. Pellish, “Single-event effects in microelectronics induced by through-wafer sub-bandgap two-photon absorption,” in Non Linear Optics Conference (2009).
5. R. Soref and B. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987). [CrossRef]
6. R. W. Boyd, Nonlinear Optics (Academic Press, 2008).
7. W. T. Lotshaw, D. McMorrow, and J. S. Melinger, “Measurement of nonlinear absorption and refraction in doped Si below the band edge,” in Nonlinear Optics: Materials, Fundamentals and Applications (Optical Society of America, 2007), paper WE10.
8. R. Claps, V. Raghunathan, D. Dimitropoulos, and B. Jalali, “Influence of nonlinear absorption on Raman amplification in silicon waveguides,” Opt. Express 12(12), 2774–2780 (2004). [CrossRef] [PubMed]
9. A. H. Firester, M. E. Heller, and P. Sheng, “Knife-edge scanning measurements of subwavelength focused light beams,” Appl. Opt. 16(7), 1971–1974 (1977). [CrossRef] [PubMed]
10. E. Faraud, V. Pouget, K. Shao, C. Larue, F. Darracq, D. Lewis, A. Samaras, F. Bezerra, E. Lorfevre, and R. Ecoffet, “Investigation on the SEL sensitive depth of an SRAM using linear and two-photon absorption laser testing,” accepted for presentation at IEEE Nuclear and Space Radiation Effects Conference (NSREC), Las Vegas, July 25–29, 2011.
11. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990). [CrossRef]
12. T. Boggess, K. Bohnert, K. Mansour, S. Moss, I. Boyd, and A. Smirl, “Simultaneous measurement of the two-photon coefficient and free-carrier cross section above the bandgap of crystalline silicon,” IEEE J. Quantum Electron. 22(2), 360–368 (1986). [CrossRef]
13. A. Douin, V. Pouget, D. Lewis, P. Fouillat, and P. Perdu, “Picosecond timing analysis in integrated circuits with pulsed laser stimulation,” in Proceedings of the 45th Annual IEEE International Reliability Physics Symposium (IEEE, 2007), pp. 520–525.
