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<p>Stress relaxation in tin films can result in microstructural changes visible on the surface, referred to as “surface defects,” and can include whisker and hillock formation, cracking, nucleation of new grains, and grain growth. Sn whiskers are of particular concern for microelectronics reliability in which Sn whiskers growing from component surface and cause catastrophic short-circuiting. While prior research has identified the conditions and mechanisms for surface defect evolution during aging and thermal cycling, the response of tin films due to mechanical stress, especially high frequency vibration, is not fully understood. In practical terms, high frequency vibration is an important source of mechanical stress generation in microelectronics for automotive and aerospace applications. This research, based on high frequency vibration of cantilevers, adds to the existing mechanisms for stress relaxation process in metal thin films, not just for tin films, as well as proposed new mechanisms for such processes.</p> <p>In the first study, the piezoelectric drive of small atomic force microscopy (AFM) cantilevers vibrated at resonance are used for high frequency cyclic bending experiments. Intermetallic (IMC) formation as well as initial film morphology and thickness (corresponding to surface grain size) all influence the response of tin films for cyclic bending. A laser doppler vibrometer (LDV) system was used to identify the real-time strain along the cantilever during cycling, suggesting that the small strains are responsible for the limited nucleation and growth for defects though the defect density increases with the number of cycles and strain distribution along the cantilever.</p> <p>In the second study, the effect of larger strains on defect evolution was determined using vibration of larger cantilevers at resonance as a function of number of cycles, frequency, temperature, and whether the vibration was continuous or interrupted for SEM characterization of defect type and density. In addition to typical micro-sized whiskers and hillocks, intragranular breakup (IGB) with intrusions and extrusions and nanowhiskers (NWs) with diameters < 1 𝜇m were observed. Both increasing number of cycles and strain amplitude/rate promote defect formation for a fixed frequency, with the defect density being strongly frequency dependent.Vibration at low temperature and interrupting measurements for SEM characterization affected the relative densities. The density of larger surface defects is strongly influenced by interruptions while NW density is almost unaffected. </p><p>Both low resonant frequency and low T (223 K) promote IGB formation during cyclic bending due to large maximum strain amplitude and slower diffusion/creep at low T, respectively. Though the overall defect density for low T is smaller than that at room temperature (RT), the response of films is similar to that at RT, indicating the same mechanisms. The defect density decrease at low T is mainly determined by NW formation, and there is a transition from micro-sized surface defects to IGBs for cyclic bending at low T.</p><p>This research demonstrated that cyclic bending of cantilevers can be used to quantify the stress relaxation of tin films in an important stress regime for microelectronics and to develop defect mitigation strategies to improve the reliability of interconnects in electronic applications.</p>

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Pure Sn and Sn-alloys are widely used in electrical and microelectronic devices as protective layer to prevent oxidation of Cu conductors and also as a component of Pb-free, Sn-based solders. Sn coatings, typically 0.5-10 μm thick, deposited on substrates, e.g., Cu, brass, etc., are prone to spontaneous growth (i.e., without any external stimuli) of Sn whiskers under ambient conditions. The growth of whiskers from Sn plating has caused numerous failures in micro-electronic devices, mainly due to short-circuiting, leading to failure of components or devices. Whisker growth is, thus especially very critical in aviation, space and defines applications, where the electronic components are designed for longer life span. Furthermore, due to miniaturization of electronic devices, the spacing between adjacent conductors or interconnects can be as small as a few hundred nanometres to a few micrometres, making them more prone to whisker induced short-circuiting. Minor alloying of Sn with Pub was the principle way for mitigating the whisker growth in Sn plated components; however, due to the recent worldwide acceptance of European Union’s Restriction of Hazardous Substances (RoHS) act, enforcing Pub-free manufacturing, whisker growth has re-emerged as a reliability issue in Pub-free solders and the Sn plating finishes. Even after decades of research, a universal whisker growth mechanism and hence effective mitigation technique is still not available in the public domain. This is mainly due to the fact that large number of factors that affect the whisker growth directly or indirectly, making it difficult to devise an experimental procedure, which allows studying effect of one factor at a time while keeping other factors constant. Although many mechanistic models for Sn whispering have been proposed in the past, the experimental evidences to support them are lacking. For example, recrystallization of whisker grain was proposed by various researchers; however, a direct observation confirming whisker grain is indeed a recrystallized grain has never been reported. Nevertheless, it is well understood that whisker growth is a form of stress relaxation process and diffusion plays important role in the formation of whiskers. Since Sn is extremely anisotropic with tetragonal crystal structure, the stress state of Sn coatings, as well as the diffusion needed for mass transport of atoms, varies drastically depending upon the direction of interest. Therefore, it is important to study the role of crystallographic texture (both macroscopic and microscopic) on whisker propensity by systematically varying the crystallographic texture of Sn coating while keeping thickness, grain size, substrate material, and post-deposition storage conditions the same. Better understanding of role of macro- and micro- texture is very crucial before any whispering mechanism can be proposed. Furthermore, recent studies indicate that role of stresses in Sn coatings driving whisker growth is not fully understood. It is generally accepted that compressive stress in Sn coating is the main factor that drives the whisker growth. However, whiskers were also observed when Sn coating was under tensile stress, making the role of stress controversial. Again, the stresses in Sn have multiple origins and need a systematic approach to understand their origin, quantify them and then relate it to whisker growth. Such systematic approach was never adopted in previous works. Hence, the current thesis aims to address the role of macro- and micro- crystallographic texture, stress regeneration mechanism, nature (i.e., magnitude and sign) of stress and stress gradient in the Sn coatings via systematic variation of texture, post-deposition storage conditions and substrate composition, including deposition of an interlayer in between Sn coating and the brass or Cu substrate. Whisker growth was studied from electro-deposited Sn coatings. The deposition parameters were optimized for producing different thickness and grain orientations. X-Ray diffraction (XRD) techniques were used to extract macro-texture of the coatings. The macro-texture measurement using XRD and micro-texture measurement using electron backscatter diffraction (EBSD) showed the same dominant and the second dominant orientations. It was observed that current density and deposition temperature, which are the two main electro-deposition parameters, significantly influence the crystallographic orientation of the grains. Thus, the global or macro-texture can be manipulated by changing the deposition parameters systematically. It was observed that whisker propensity increases drastically by growth of low index planes, such as (100) and (110), during deposition. Hence, proper selection of deposition parameters that lead to growth of high index planes can be used to suppress the whisker growth. Furthermore, micro-texture surrounding whisker grain was studied using EBSD technique by observing the same set of grains surrounding a whisker grain before and after whispering. Orientation imaging microscopy (OIM) maps of several whisker regions clearly indicate that whiskers preferentially grow from low index planes, such as (100), etc. Furthermore, using orientation dependent stiffness mapping (in-plane and out-of-plane), it was noticed that whiskers preferentially grew from regions of soft oriented grains (low modulus) surrounded by hard orientations. In addition, grain boundary disorientation analysis revealed presence of high fraction of high angle grain boundaries (HAGBs) in the vicinity of whisker grain. It was observed that overall fraction of HAGBs in the whispering region was 0.7 while the fraction of HAGBs surrounding and leading to whisker grain was 0.85. In addition, it was observed that whisker grew from pre-existing grain and not from the recrystallized grain. Also, grain boundary sliding was not observed as a pre-requisite for whisker growth in Sn coatings on brass substrate. The local stress field around the whisker grain also plays a crucial role in whisker growth. Therefore, local stress field around whisker site was simulated using crystal plasticity simulation by incorporating grid resolved spatial description of orientation in terms of Euler’s angles. The crystal plasticity model included slip systems of Sn and other material parameters, such as anisotropic elastic stiffness constants, critical resolved shear stresses for different slip systems, etc. Thus, the slip in individual grain was accounted following homogenization to maintain compatibility at grain boundaries. The simulated stress field shows that both in-plane and out-of-plane stresses were highly inhomogeneous without any unique condition around whisker grain. It has been observed that high compressive hydrostatic stresses develop in the vicinity of the whisker grain, while whisker grain is slightly tensile. Therefore, the gradient of hydrostatic stress around the whisker suggests whisker growth is mainly controlled by vacancy transport phenomenon. The stress in Sn coatings may originate from many factors, such as residual stress inherent to electro-deposition, diffusion of substrate atoms (Cu, Zn, etc.) into the coating, formation of interfacial intermetallic compound (IMC) layer, segregation of impurities at Sn grain boundaries, formation of surface oxide layer, and coefficient of thermal expansion (CTE) mismatch between in Sn and substrate as well as between differently orientated grains of Sn. Therefore, it is important to understand the dominant stress regeneration mechanism responsible for whisker growth. To identify dominant mechanism, which can continuously regenerate the compressive stress in Sn, samples deposited under fixed electro-deposition conditions were exposed to different post-deposition storage conditions, such as isothermal aging at room temperature, 50 °C, 150 °C, and thermal cycling from -25 to 85 °C with and without hold time at the highest temperature. It has been observed that Cu6Sn5 IMC growth due to the inter-diffusion of Cu and Sn atoms is the dominant mechanism responsible for whisker growth. Both growth kinetics and morphology of IMC have a significant impact on whisker growth. The role of CTE mismatch in regenerating compressive stresses in Sn coatings on brass substrate for whisker growth is highly limited. The substrate composition as well as the under layer metallization affects the inter-diffusion between Sn and the substrate atoms and therefore IMC growth, which is mainly responsible for whisker growth in Sn coatings on brass or Cu substrates. The effects of substrate composition on whisker growth was studied by using pure Cu, brass (65 wt. % Cu 35 wt. % Zn) and Ni (bulk and electro-deposited under layer) as substrate. Whisker growth was more rapid if brass substrate was used instead of pure Cu. Whiskers were not observed when Sn was deposited on either bulk Ni or when Ni under layer was electro-deposited on brass or Cu substrates prior to Sn deposition. Ni under layer effectively stops the diffusion of Cu into Sn, thus avoiding the growth of Cu6Sn5 (which places Sn coatings under compressive stress). Thus, it is clear that continuous formation of Cu6Sn5 at the interface provides the long-term driving force for whisker growth. Since the whisker growth is a stress driven phenomenon, it is important to understand the stress evolution in Sn coatings. Stress state of the Sn coatings was studied using custom-built laser curvature set-up with multi-beam optical stress sensor (MOSS). This allowed monitoring of curvature change of the coating-substrate system in real time and the bulk average stress was calculated using Stoney’s equation. For multi-layer system such as Sn deposited on pre-deposited Ni under layer on brass substrate modified Stoney’s equation was used. In case of Sn deposited on brass without any under layer, it is known that the Cu6Sn5 IMC do not form a continuous layer at the interface between Sn and substrate under aging at ambient conditions, therefore, the curvature change due to IMC can be neglected. In addition, glancing angle X-ray diffraction was employed to analyse stress in the top surface region of the coating. The variation of glancing angle allowed probing strain at different penetration depths. Both the bulk stress and the stress in only near surface region evolve with time. The residual bulk stresses in Sn coatings are tensile immediately after deposition. The residual stresses relax very quickly upon room temperature aging and become compressive. The bulk of Sn coatings on brass substrate progressively become more compressive upon continued aging. However, stresses in Sn coatings deposited on brass substrate with Ni under layer saturate quickly at low compressive stress. Surprisingly, stress in the top-most region of Sn coating measured using XRD evolve differently. The surface of Sn coating deposited on brass substrate is compressive initially and progressively become more tensile (less compressive), while the initial compressive stress in the sample with Ni under layer saturated at a higher compressive stress than the bulk stress value recorded from curvature measurement. Therefore, the surface of the Sn coatings with Ni under layer is always more compressive than the bulk stress in the Sn coating. Therefore, a negative stress gradient for the diffusion of Sn atoms towards surface is never established and whiskers do not grow in these Sn coatings. Interestingly, through thickness voids are observed in the Sn coatings on Ni. Contrarily, in Sn coatings without Ni under layer after 170 h of aging, the surface stress becomes more tensile than the bulk of the Sn coating, favouring continuous migration of atoms from the highly compressed region near Cu6Sn5 IMC layer to the stress-free whisker root. Aforementioned observation indicates the crucial role of negative stress gradient in the mass transport of atoms required for whispering. The importance of stress and stress gradient was further studied by analysing the effect of externally imposing stress and stress gradient on whisker growth. The stresses were applied using a three-point bend setup. It has been observed that externally applied stress accelerates the whisker growth. This is mainly because applied stress alters the diffusion kinetics and growth of Cu6Sn5 IMC at the interface. However, the coating under tensile stress shows more whisker growth as compared to the coating under high compressive stress. This is attributed to the fact the coating under tensile stress is under higher negative stress gradient. Therefore, it is proposed that out-of-plane stress gradient is more important rather than the sign and the magnitude of stress in determining the propensity of whisker growth in Sn coatings.

Lorsque les rongeurs explorent leur environnement, ils contactent activement les objets environnants avec leurs vibrisses qui sont ainsi défléchies selon des séquences spatiotemporelles complexes. Le système vibrissal est néanmoins capable d'extraire des informations pertinentes de ces stimulations pour générer un comportement tactile-dépendant. Une question se pose alors: Comment l’information multivibrissale globale est-elle encodée? La représentation corticale des vibrisses au sein du cortex somatosensoriel primaire (S1) du rongeur est dotée de structures anatomiquement remarquables, nommées "tonneaux", au niveau de la couche IV, qui sont organisées de la même manière que les vibrisses sur le museau de l’animal. A chaque "tonneau" correspond une colonne corticale, unité de traitement de l’information, qui reçoit en priorité les informations provenant la vibrisse principale (VP) correspondante. Des enregistrements extracellulaires réalisés dans notre équipe chez le rat ont révélé que les réponses des neurones du cortex S1 et du thalamus sont non seulement sensibles à la direction de déflection locale de leur VP, mais aussi à la direction d'un mouvement global de l’ensemble de leurs vibrisses. Afin de mieux comprendre la manière dont le réseau cortical traite ces scènes tactiles globales, nous avons construit un poste expérimental permettant d’enregistrer en temps réel l’activité du cortex S1 chez la souris par imagerie sensible au potentiel, tout en appliquant des stimuli tactiles complexes à l'aide d'une matrice de 24-stimulateurs vibrissaux. Nous avons de plus développé une méthode permettant d’aligner les données fonctionnelles ainsi obtenues par rapport la carte cytoarchitecturale du réseau cortical sous-jacent. Nous avons ainsi étudié premièrement la distribution spatiale de la sélectivité à la direction de déflection locale d’une vibrisse au niveau d’une colonne corticale. Les réponses aux différentes directions étaient localisées de manière légèrement distincte, autour du centre de la colonne, mais selon une organisation différente de celle précédemment décrite chez le rat. Nous avons montré par la suite que la sélectivité à la direction globale est spatialement organisée dans le cortex "en tonneaux" à l’échelle supra-colonnaire. Les colonnes correspondant aux vibrisses rostrales étant plus sélectives à la direction globale que les colonnes associées aux vibrisses caudales. En outre, les colonnes correspondant aux vibrisses dorsales répondent préférentiellement aux directions globales ventrales, tandis que les colonnes associées aux vibrisses ventrales répondent préférentiellement aux directions globales caudales. Enfin, les réponses induites par des directions globales caudo-ventrales étaient en moyenne les plus fortes pour toutes les colonnes. Nous avons montré que la répartition spatiale de la sélectivité à la direction globale peut être expliquée ni par la saillance prédominante de la position de départ de la séquence de stimulation multivibrissale (effet de bord), ni par la sommation linéaire des réponses aux déflections de quelques vibrisses. Les réponses aux stimulations globales de l'ensemble des vibrisses sont en effet fortement sous-linéaires, indépendamment de la direction de la stimulation. Brièvement, nous montrons ici que sortir de la vision classique du système vibrissal permet une meilleure compréhension de la façon dont les différentes caractéristiques des stimuli complexes sont traitées et de la manière dont les propriétés émergentes du cortex, comme la sélectivité à la direction globale, sont construites. / While rodents explore their environment they actively contact surrounding objects with their array of whiskers, resulting in a complex pattern of multiwhisker deflections. Despite this complexity, the whisker system is able to extract relevant information from the spatiotemporal sequence of deflections to generate touch-dependent behavior. The question that arises is: How is global multiwhisker information encoded? Whiskers are mapped onto layer 4 of the primary somatosensory cortex (S1) as discrete units named “barrels”. Each barrel-related vertical column processes information coming primarily from its corresponding principal whisker (PW). Previous experiments in our lab done with extracellular recordings have revealed that neurons in the rat S1 and thalamus not only show a preferred direction for the local deflection of the PW but also for the direction of a global motion across the whisker pad. To further understand how the cortical network processes global tactile scenes, we built a set-up that enables to perform voltage sensitive dye imaging of the mouse barrel cortex while applying precise tactile stimuli using a 24-multi-whisker stimulator. We further developed a technical method to map the recorded functional data onto the cortical structure. We first studied whether local direction selectivity is spatially distributed within the barrel-related column. Responses to different directions were slightly segregated on space close to the barrel center, but the distribution differed from the one previously described in rat S1, namely a pinwheel-like structure. We then showed that global direction selectivity is spatially organized in the barrel cortex. Columns related to rostral whiskers were more selective to the global direction than columns related to caudal whiskers. Moreover, the columns related to dorsal whiskers preferred ventral global directions, while the columns related to ventral whiskers preferred caudal global directions. Overall the responses to the caudo-ventral global directions were the strongest in average for all the columns. We showed that the spatial distribution of the global direction selectivity can be explained neither by the high salience of the starting position of the deflections on the whiskerpad (a border effect), nor by the linear summation of the responses to deflections of several whiskers. Responses to the global motion of the whisker array are indeed highly sublinear independently of the direction of stimulation. In conclusion, we show here that stepping aside from the classical view of the whisker-to-barrel cortex system allows a better understanding of how different features of complex stimuli are processed and how the emergent properties of the cortex, like the global direction selectivity, are built-up.

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