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C: Surfaces, Interfaces, Porous Materials, and Catalysis
Informatics-Aided Raman Microscopy for Nanometric 3D Stress Characterization Hongxin Wang, Han Zhang, Bo Da, Motoki Shiga, Hideaki Kitazawa, and Daisuke Fujita J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b12415 • Publication Date (Web): 14 Mar 2018 Downloaded from http://pubs.acs.org on March 14, 2018
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The Journal of Physical Chemistry
Informatics-Aided Raman Microscopy for Nanometric 3D Stress Characterization Hongxin Wanga*, Han Zhanga, Bo Daa, Motoki Shigab, c, Hideaki Kitazawaa, Daisuke Fujitaa* Abstract: The advanced confocal Raman microscopy provides a unique non-destructive, sub-micron feature resolving and utility-convenient methodology for material stress analysis. Conventionally, only materials transparent to the excitation laser are allowed for depth-resolved 3D characterization. For opaque materials, the collected Raman-scattering signal is inevitably an ensemble of contributions from multiple specimen layers. In this work, an informatics approach was adopted while considering both laser attenuation and confocal exclusivity to decompose true local stress components in three dimensions with sub-micron resolution. Such analytical power was demonstrated on a laser-opaque silicon wafer, where depth-dependent study of stress dynamics was made possible. The technique extends to narrow band semiconductorbased microelectronic, solar cell and battery materials, where stress plays a key role in device performance and durability.
Introduction Confocal Raman microscopy (CRM) is a combination of two ingenious inventions of the past century: Raman spectroscopy and confocal microscopy. The concept utilizes a pin-hole aperture confocal with the specimen plane of interest to allow Raman scattering collection only from the excitation laser focal spot, thereby realizing physical chemistry analysis in a three1 dimensional space. Rigorously, only materials transparent to excitation laser follows this ideal picture of laser-specimen interaction. For an opaque material, signal attenuation may be caused by photon absorption besides the confocal exclusivity intended by the pin-hole aperture. This effect leads to inseparable signals generated at close specimen depths. The signal collected when the laser was focused at a single position would then contain spectral information from multiple 2 positions along the specimen depth direction. This effect compromises spatial selectivity and becomes especially noticeable in stress characterization, where Raman frequency shift caused by local stress in neighbouring specimen regions usually differs by as little as a fraction of wavenumber. It is for this reason that depth-resolved 3D characterization of material stress by CRM is now limited only 3 to specimen that is transparent to excitation laser in use. To find a solution to this problem is urgent. As a typical example, Si is industrially important as the base material for microelectronics, MEMS/NEMS devices, solar cells and secondary batteries. Residue stresses in Si, intentionally created or unavoidably produced during device fabrication, 4-7 play essential roles in device performance in applications. Si has long been used as a textbook example for 2D Raman stress analysis because of its well-understood Raman responsive vibration modes. However, till now, 3D stress analysis for Si using CRM stays unavailable because excitation laser wavelength opaque to Si has to be used in order to ensure 8 adequate Raman scattering intensity.
In recent years, informatics-aided Raman spectroscopy, which applied sophisticated mathematical methods on large number of acquired data, have made significant successes in revealing critical biochemical information for living systems under diverse physiological and pathological conditions.9 Though this type of informatics approach was developed mainly for organic/biological specimens, the 3D stress distribution in an inorganic material coincides with the targeted problem: a multivariate system with critical signals bearing only minor spectral changes. In this work, by calculating both laser attenuation from adsorption and confocal aperture exclusivity to reduce complexity, we applied an informatics-aided CRM approach to decompose true local stress values from the superposition of total Raman signals in three dimensions. The method assumes the mixture effect among laser signals from different 3D layers, which can be given by theoretical calculation, and then decomposes observed mixture signals into original ones to detect peak positions of Raman signals, to avoid specifically pseudo-peak generated from different layers. Its effectiveness was demonstrated by both synthetic dataset and real datasets in a silicon wafer pre-stressed by indentation. The local stress resolved from specimen planes separated with submicrometer distance was found to develop at different velocity in response to thermal annealing. Oxygen concentration gradient was accounted for such depth-dependent stress dynamic variation through impeding dislocation slip. Such mechanism was also confirmed quantitatively by 3D elemental analysis using Time-of-flight-secondary-ion-mass-spectroscopy (TOFSIMS). The developed informatics-aided 3D CRM is believed to have provided a unique capability to characterize stresses of a specimen, both transparent and opaque to excitation laser, with portable equipment set-ups, atmospheric sample observation condition, and non-invasiveness in specimen original forms.10.
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Results and discussion The experimental principle is illustrated in Figure 1a. As excitation laser enters Si wafer surface, its attenuation follows a coefficient Ci, which is dependent on d, depth of the analyzed plane from wafer surface and k, absorption 11 coefficient of Si at 532nm wavelength: = e (1) Several parts in a million of the incident photons were Raman scattered by optical phonons in the specimen. These photons exit specimen surface following attenuation coefficient Co, which equals to Ci, due to the close frequency values. A collection coefficient Cc is further applied to the collected 12 signal as the exclusivity effect by the confocal aperture: = (2) ( /)
Where D is the distance between the analyzed plane and the focal plane of laser spot; l is projection depth of the confocal aperture, which could be calculated as: = cot () (3)
Where s is the physical size of confocal aperture; M is the magnification of the objective lens; and α is the incident angle of the objective. The collected signal strength of the local Raman scattering from the analyzed plane would then be with a combined detection coefficient Cl=CiCoCc relative to the initial excitation laser intensity. The total Raman signal collected by the CCD detector would then be a superposition of local Raman scatterings from all the contributing planes modulated by their corresponding coefficients, Cl. In this experiment, stress field in the Si wafer is created intentionally by indentation. Figure 2a is a map of Raman shift frequencies about the indentation pit. Figure 2a is also inserted with an atomic force microscope image of the same area. The central indentation pit is with a square-shaped opening, which diagonals are parallel to [110] direction of Si -1 crystal. Unstressed Si Raman shift is centered at 520cm . While the blue shift of this frequency indicates compressive 13 stress, red shift indicates tensile stress. Four Raman spectra were collected from locations on Si wafer marked from 1 to 4 and those are shown in figure 2b. Full-width-at-half-maximum -1 (FWHM) of the peaks are around 4 cm , mainly depending on 14, 15 the level of defects of the wafer material. The Raman peak -1 positions near 520cm , the local frequency fl, is shifted from that of the unstressed state with amount proportional to the local stress tensor component interacting with the incident photon. The highest gradient of frequency shifts corresponding to the highest gradient of stress field occurs -1 near the indentation pit, with value about 1cm /um. The interested analysis depth of Si with 532nm wavelength laser is around 3um, which is mainly limited by the signal-to-noise ratio obtainable at the detector governed by photon absorption. It suggests that the interested f1 shifts difference is -1 no larger than 3cm , which is well within the peak broadening width. Therefore, the superposition of local scattered signals would appear as a single peak as the spectra shown in figure2b and could not be decomposed by finding its local maxima. This effect is also illustrated in the right panel of figure 1a. The
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relative heights of the local scattering peaks are determined by each Cl values. As mentioned above, an observed Raman spectrum at a spatial position in a layer consists of a mixture of pure spectra of different layers at same spatial position because Raman spectra of different layers are inferenced by each other. When the hidden pure spectrum at spatial position (x, y) in the j-th plane is modeled by a Gauss function: ,, ;
,, !
= ℎ,, ∙
$%&'(,),*
exp -−
%'(,),*
%
− /,, ! 0
(4) -1 where t is the index of Raman shift/cm , ℎ,, is the intensity parameter of the peak in the i-th plane, /,, is the peak % position parameter, 1,, is the peak width parameter and the set of parameters at position (x, y) % then an observed Raman ,, = ℎ,, , /,, , 1,, ! , spectrum at spatial position (x,y) in the j-th plane is modeled by 23,, ; , ! = ∑5 6 ,3 ∙ ,, ; ,, !, 7 = 1,2, … , ;, = 1,2, … , ? @1 −
√B
C
implemented by TOFSIMS. Argon ion sputtering was used to expose material at the desired depth for compositional
(6)
5
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Figure 4. (a) 2D TOFSIMS map of 16O- for the indented area on a Si wafer after annealing at 300oC for 240min, showing uniform 16O- distribution except in the indentation pit; (b) 3D map of 16O- showing decreasing concentration with respect to specimen depth; (c) Total detected ion counts summated for each analyzed plane with respect to specimen depths for 16O- ion and 30Si- ion. Residue stress plotted against normalized oxygen ion concentration. analysis. Focused Ga primary ion was used to scan the entire 16 region near an indentation pit. The generated secondary O ions were detected through a mass analyzer to identify its existence at the scanned spot in three dimensions. A total depth of 3um was analyzed with 150nm step size. The 16 16 accumulated distribution of O ions is shown in figure 4a. O ions are evenly distributed over area around the indentation pit. It suggests that these oxygen interstitial atoms were introduced through into-body diffusion from surface oxide 16 during Si wafer fabrication. [23] 3D view of the O ions is 16 displayed in figure 4b, which shows O ion concentration decreasing from the surface layer. To quantify such ion 16 gradient, all counts of O ions from the same layer were then summated and the value was plotted against its layer depth, as 30 shown in figure 4c. Same profile was also created for Si ions. 30 Though concentration of Si in a Si wafer should stay constant in a depth profile, 19% reduction in ion number was found in 16 this case. On the contrary, the collected number of O ions shows 58% reduction though the total counts are in similar 30 30 range to that of Si . Therefore, the decrease of Si should reflect a depth-dependent relative sensitivity of the
instrument. One could then deduce oxygen concentration 24 decrease of 39% with increasing depth from Si wafer surface. Normalized oxygen ion concentration after deduction of instrument background is also plotted in figure 4c as a solid line. It is well-known that oxygen interstitial atoms/clusters 25-27 could impede dislocation movement. Hu has suggested the relationship between critical stress and oxygen concentration m follows τc=c , where m was proposed to be 1/2
