Ultra-flat bismuth films for diamagnetic levitation by template-stripping

a r t i c l e i n f o Keywords: Bismuth Template stripping Surface roughness Crystal structure Young's modulus In this paper we present a method to deposit thin films of bismuth with sub-nanometer surface roughness for application to diamagnetic levitation. Evaporated films of bismuth have a high surface roughness with peak to peak values in excess of 100 nm and average values on the order of 20 nm. We expose the smooth backside of the films using a template stripping method, resulting in a great reduction of the average surface roughness, to 0.8 nm. Atomic force microscope and X-ray diffraction measurements show that the films have a polycrystalline texture with preferential c-axis orientation. On the back side of the film, fine grains are grouped into larger clusters. Cantilever resonance shift measurements indicate that the Young's modulus of the films is on the order of 20 GPa. Diamagnets possess the fascinating property that they can be stably positioned in non-uniform magnetic fields, without dissipation of energy [1]. Superconductors for instance are diamagnets with magnetic susceptibility of − 1, and find important applications in, for example, levitated trains [2]. Here, even though no energy is required for stable levitation, energy is dissipated to maintain the superconducting temperature. Room temperature diamagnets have much smaller diamagnetic constants. Silicon has a susceptibility of − 3.4 · 10 − 6 , water has a susceptibility of − 10 −6 , and even the highest known room-temperature diamagnets have susceptibilities only on the order of −10 −4 [3]. Thus, in room temperature levitation, the levitating forces are orders of magnitude lower than in a superconducting train. As a consequence, room temperature levitation at dimensions in the meter range is not possible. Room temperature levitation is possible however if we shrink the dimensions. The diamagnetic force density f d is proportional to the gradient of the magnetic field H [4], f d ¼ μ 0 χ H j j∇ H j j ð Þ ð1Þ where μ 0 is the permeability of free space and χ is the volume magnetic susceptibility of the material. The gradient is inversely proportional to the dimensions of the system. Consequently, the smaller the system, the larger the gradient and the larger the diamagnetic force densities. The development of high-field permanent magnets has enabled dissipation-free levitation of millimeter-sized objects. Today, one can buy toys where a thin highly-oriented pyrolytic graphite …