Journal Club for September 2018: Nanomechanics of Covalent Crystals and Elastic Strain Engineering

Nanomechanics of Covalent Crystals and Elastic Strain Engineering

Yang Lu

Department of Mechanical Engineering, City University of Hong Kong

Solids are normally divided into three main categories: crystalline, noncrystalline (amorphous), and quasicrystalline [1]. Crystalline solids possess highly ordered atomic arrangement and can be further classified into four principal types based on their atomic bonds: metallic crystals, ionic crystals, covalent crystals, and molecular crystals. Among them, networked covalent crystals, such as silicon (Si), germanium (Ge), and diamond, are known for their high hardness [2] and functional properties as semiconductor (diamond can be regarded as wide-bandgap semiconductor), but their elasticity and plasticity at nanoscale was less studied when compared to metallic materials. The fracture of covalent solids involves cleavage and breaking of a large number of covalent bonds, leading to typical brittle behavior [3]. In the past decades, with the rapid developments in micro/nano-fabrication and characterization techniques, interesting phenomena have been unveiled on micro/nanostructures which turned out to be significantly deviated from their bulk counterparts [4, 5]. For nanosized covalent crystals, enhanced strength and ability to bear mechanical deformation originating from the so-called “size effect” have been recently reported. So in this journal club, we will focus on the nanomechanics of three typical networked covalent solids: Si, Ge and diamond, and discuss their unusual properties (especially elasticity) exhibited at small scales. In addition to mechanical property, strain-induced functional property changes as well as the potential “elastic straining engineering” applications will be also briefly introduced for these promising nanodevice building blocks.

Silicon is no doubt one of the most important semiconductor materials in electronic industry. For bulk silicon, it’s normally considered to be hard and brittle, and its tensile strength was generally measured around ~130 MPa [1, 3]. After being shaped into Si dies and wafers, the fracture strength of Si could be up to ~300 MPa [6, 7]. The strength of Si will increase with the decrease of their sizes into micrometers scale, and the maximum fracture strength can reach ~830 MPa [8, 9]. For fine Si whisker with diameter a few micrometers, the maximum fracture strength quickly increased to ~3.8 GPa [10, 11]. All these results suggest the size dependency of the mechanical strength, as observed in metals. However, beside strength, the deformability of Si could also be increased with the decrease of their sizes [12, 13]. Research found that microfabricated silicon beams at microscale exhibit enhanced deformability [14-16] although the local max strains are not very high (~1-2%). In recent years, Si nanowires with higher quality have been chemically fabricated [17], and attracted more studies on their mechanical properties because of the exceptional physical properties and potential application. Previous researches using localized deformation such as indentation and bending showed that, the fracture stress of Si nanowires will increase to ~12 GPa, with the decrease of the nanowires’ diameters down to tens of nanometers. In such cases, with the slightly varied Young’s modulus ~100-180 GPa at small scales, the corresponding local deformability was measured from ~1.5% to ~6% [18-21]. In a few extreme cases, the reported maximum local strain can reach above 10% based on calculating the local radius of curvature [20]. Later, tensile testing of individual Si nanowires was achieved by newly developed nanomechanical techniques. The measured tensile strength of Si nanowires was around ~3-5.5 GPa with measured strain was still relatively small [22, 23]. For nanowires with diameters below 100 nm, research shows that they can withstand larger tensile strength to ~12.2 GPa with enhanced fracture strain to ~7% [24]. Noting that most of the previous works focused on measuring the fracture strength, while the elastic property of Si nanowires was less characterized. Theoretical calculations suggest that, in principle over 17% elastic/lattice strain (up to ~19 to 23%, depending on crystallographic directions) can be achieved in a perfect Si crystal [25-27]. Therefore, how closely one can experimentally approach the ideal elastic limit in Si nanowires is of great interest. In 2016, we showed that vapor-liquid-solid–grown (VLS) single-crystalline Si nanowires with diameters of ~100 nm can be repeatedly stretched to over 10% elastic strain at room temperature [28], approaching the theoretical elastic limit of silicon. A few samples even reached ~16% tensile strain, with estimated fracture stress up to ~20 GPa. Loading-unloading experiments further confirmed that the samples can consistently achieve over 10% elastic strain with full recovery upon cyclic straining with varied strain rates. The failure still occurred in a brittle manner, with no visible sign of plasticity, and the fracture process involved a multi-step process due to the extremely high elastic strain energy [29, 30].  The elastic strains here exceed one-half of the bulk theoretical limit of Si (~17% for <110> uniaxial tension), which go far beyond the definition (1/10) of “ultra-strength” [31, 32], thus, we refer to this behavior as “deep ultra-strength” [28]. In addition to the enhanced elasticity, another interesting nanomechanical phenomena, so called “anelasticity” behavior [33] was also reported for Si nanowires.

Germanium is also an important semiconductor material. At bulk state, its tensile strength was measured as ~135-150 MPa with Young’s modulus of ~130 GPa [34]. Theoretical calculations predicted the ideal shear and tensile strength of germanium (Ge) can be ~4.5 GPa and ~14 GPa, respectively [25]. Previously the mechanical studies on small scale Ge were mainly carried out by AFM bending test, similar with that applied on Si. Ge nanowires with diameters between 20 nm and 80 nm were initially investigated through a clamped beam experimental set-up, where the ultimate failure strength of Ge nanowires reached ~15 GPa [35]. After introducing a tungsten probe inside SEM, the deformation behaviors of Ge nanowires with diameters between 23 and 97 nm were further investigated [36]. The flexural deformation behavior of Ge nanowires exhibited a diameter-dependent trend with the maximum bending strain up to 17% prior to fracture. Ge nanowires with the smallest diameter can be severely bent with the maximum local bending strength of 18 GPa, which is in accordance with the ideal strength of a perfect Ge crystal [36]. Similar with Si nanowires, Young’s modulus appears less dependent to the diameter from the AFM three-points bending tests, with the measured value ~92 GPa for <111>-oriented Ge nanowires [37]. With the recent development of nanomechanical testing strategy, biaxial tensile tests were conducted on Ge with a measured tensile strain up to 0.6% [38]. While in our recent study on micro-fabricated Ge nanostructures, we also observed significantly enhanced elasticity and strength.

Diamond is a solid form of carbon with a diamond cubic crystal structure [1]. It is famous for being the hardest material in nature. These properties determined the major industrial applications of diamond, in addition to jewels, as cutting and polishing tools and for mechanical testing standard as indenter tip [3]. Given the difficulties of using other material as tool to measure the intrinsic strength of diamond, researchers developed various kinds of methods to measure the mechanical properties of bulk diamond, such as the hydraulic pressure strategy developed by Field et al. in 1980s [39]. In general, the tensile strength of natural diamond is around 1 GPa [1]. For synthesized diamond, its fracture strength is commonly known as 0.8-1.4 GPa, depending on the quality and crystallinity [1]. The strength of chemical vapor deposition (CVD)-synthesized diamond can reach to ~1 GPa with a Young’s modulus of ~1TPa [40, 41] by the pressurization tests, fairly close to natural diamond. The disparity in fracture strength between natural and CVD synthesized diamond can be ascribed to the higher defect density and residual stresses introduced during the CVD procedure [42]. Other than CVD method, researchers also synthesized bulk diamonds with nanocrystalline features by high pressure and high temperature (HPHT) graphite conversion strategy [43]. Such nanopolycrystalline diamonds can exhibit much higher hardness than other synthesized mono- and poly-crystalline diamond [44, 45]. In 2014, Tian et al. reported the HPHT synthesis of nanotwinned diamond with average twin thickness ~2-10 nm, with an unprecedented Vicker hardness and thermal stability [46]. Instead of introducing nanostructures into bulk diamonds, to reduce the volume size of diamond can also increase their strength to ~10 GPa [47, 48]. With the rapid development of microfabrication techniques, such as focus ion beam (FIB) and reactive ion etching (RIE) of diamond films, researchers fabricated diamond pillars with controlled sizes and crystalline orientations for better quantifying their size-dependent mechanical properties at micro and nanoscales [49]. Results showed the measured strengths for microscale diamonds are nearly ten times higher than that measured on bulk diamond [47]. Nevertheless, the mechanics research for nanosized diamonds was extremely challenging and rare due to the availability of suitable sample materials and nanomechanical approaches, despite their increased interests in biomedical and photonics fields [50, 51]. Recently, by working with materials scientists who fabricated nanoscale diamond needles by plasma-induced etching of CVD diamond thin films [52], we performed quantitative nanomechanical characterization of nanodiamonds by developing a “push-to-bend” strategy through conventional nanoindentation test [53]. As shown in Figure 1 below, the diamond nanoneedle was bent through the vertical indentation loading from a cube-corner diamond nanoindenter side surface. Coupled with finite element analysis (FEA) and in situ SEM imaging, we were able to precisely quantify the sample strain distribution, which shows a max elastic strain of ~9% and stress of ~95 GPa on the tensile side of the specimen, approaching to their theoretical elastic limit [25]. The ultralarge elasticity discovered in nanoscale diamonds will not only enhance their performance in ultrastrength nanostructures and composites, but also benefit their functional applications like strain-mediated nanomechanical resonators [54], drug delivery [52] and optomechanical devices [55].

Figure 1. Experiment and simulation of a diamond nanoneedle being bent by the side surface of a nanoindenter tip, showing ultralarge and reversible elastic deformation. [53]

 

Concluding remarks

Even though with limited deformability at bulk status, considerably enhanced strength and elasticity have been unambiguously revealed in these networked covalent crystals (Si, Ge and diamond) when their critical characteristic sizes reduced to micro-/nanoscale domain. The nanomechanical properties of other covalent crystalline solids, such as cubic boron nitride (BN) and silicon carbide (SiC), shall be also of great interest and attract more research efforts due to their important industrial applications as well as the emerging applications at micro-/nanoscales. To further investigate their mechanics at the relevant dimensions and length scales [56], innovative nanomechanical characterization strategies need to be developed to uncover those unprecedent properties such as the “deep ultra-strength” reported for nanoscale diamond and silicon here. So “there is still plenty of room” to investigate the solid mechanics of covalent crystalline solids at small scales [32, 57], and explore their novel applications such as in flexible electronics and bio-nano interfaces [15, 51, 58].

Beyond mechanics, the enhanced elasticity in covalent crystals could also drastically change the functional properties of their nanostructures, such as electronic structures of materials. In fact, semiconductor industries already use strained Si as important components given its considerably enhanced electron mobility and have achieved astonishing commercial success [59-62]. For nanoscale Si structures (thin films and nanowires), earlier computational works [26] and our recent DFT calculations [63] suggest that the bandgap structure of severely strained silicon could undergo revolutionary changes, even leading to the transition from semiconductor into metallic state. While for micro/nano-sized Ge, elastic strain-induced bandgap transition and enhanced light emission have been already experimentally demonstrated [38, 64]. Lastly, for diamond, in addition to its desired electronic and optical properties, it’s receiving more and more research interests nowadays as one of the most promising quantum information materials [65]. Thus, the unprecedent nanomechanical behavior of covalent crystals could open up new opportunities for the exciting and emerging functional applications, such as “elastic strain engineering” through the mechanical strategies [66, 67].

 

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