© 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.pss-rapid.com pss Phys. Status Solidi RRL 6, No. 3, 99–101 (2012) / DOI 10.1002/pssr.201105541 Strength of metals at the Fermi length scale Jason N. Armstrong, Susan Z. Hua, and Harsh Deep Chopra * Laboratory for Quantum Devices, Materials Program, Mechanical and Aerospace Engineering Department, The State University of New York at Buffalo, Buffalo, NY 14260, USA Received 21 November 2011, revised 8 December 2011, accepted 12 December 2011 Published online 14 December 2011 Keywords yield strength, Fermi length scale, Sharvin length scale, surface energy, atomic force microscope * Corresponding author: e-mail hchopra@buffalo.edu, Phone: +1 716 645 1415, Fax: +1 716 645 2883 © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1 Introduction The use of scanning probes to study atomic-sized samples has led to basic insight into mechani- cal forces, quantum properties, and their interplay [1–8]. For example, isomorphous Ag and Au have nearly identi- cal bond length and lattice constant. Being monovalent, conductance across a single-atom Au or Ag bridge be- comes indistinguishable, equal to one quantum of conduc- tance, G 0 = 2e 2 /h. Recent studies reveal new ‘markers’ for their chemical identity at atomic level based on differences in the transition from tunneling to contact [8]. As another example, we have reported a modulus enhancement in Au at the Fermi length scale [7]. In addition to the modulus, strength is another property of interest (stress at which ma- terial yields). Here, for the first time, we measure the strength of metals at the Fermi and Sharvin length scales. 2 Experimental details A modified atomic force microscope (AFM) was used to simultaneously measure force – deformation and conductance traces across atomic- sized samples; the experimental setup is described in detail elsewhere [6, 7]. Measurements were made at room tem- perature in inert atmosphere. The AFM assembly consists of a dual piezo [6, 7]. With this configuration, the noise band is 5 pm (peak-to-peak), and its center line can be shifted by a minimum step of 4 pm. Conductance for Ag and Au was recorded at 100 mV and 250 mV, respectively. Increased instability was seen in Ag at higher voltages, possibly due to electro-migration away from ballistic con- tacts. Hence a lower voltage for Ag is used. Piezo was re- tracted at a rate of 5 nm/s. Silver and gold films (200 nm thick) were magnetron sputtered (30 W) on Si substrates and cantilevers in Ar atmosphere with partial pressure of 3 mTorr in a UHV chamber with base pressure of ~10 –8 – 10 –9 Torr. The sputtering targets were 99.999% pure. 3 Results and discussion Figure 1 shows an exam- ple of simultaneously measured force and conductance across atomic-sized Ag samples, where piezo retraction Using silver and gold, we have measured the size-dependence of the yield strength of atomic-sized samples as small as a single-atom bridge, with pico-level resolution in the applied force and displacement. The strength approaches theoretical values as the diameter of the sample becomes comparable to the Fermi wavelength of electrons (~0.5 nm); in the limit of a single-atom bridge, the strength is over four orders of magni- tude higher than in bulk single crystals. Results provide direct evidence for Pauling’s prediction of bond stiffening with re- duced atomic coordination. Beginning with a single-atom bridge, strength evolves in a staircase manner in Ag, instead of the intuitively assumed continuous approach to a saturating bulk value. 0 1 2 3 0 50 100 150 Yield Strength (GPa) Cross-section area ( nm 2 ) Strain e ≅ a/2a; Ideal strength t= e*E a t t t t 2a Measured strength approaching theoretical (ideal) values at the Fermi length scale, corresponding to a sample made of a single-atom Au bridge.