# Investigation of the Influence of Sublayer Thickness on Pairing of Metallic MEMS Shutter Blades
## 1 Introduction  
Three-dimensional self-assembled forms induced by movements and deformations in the systems due to stress relaxation can be observed in nature and living organisms. Self-assembly in nature can occur in the DNA of some bacteria [1], the curling of blooming lillies [2], components of plant cell walls [3], and hydro-actuated ice plants [4]. Various new technologies can be developed when it becomes possible to establish a controlled and reproducible process that enables the fabrication of 3D self-assembled elements inspired by nature. The stress for such 3D elements can originate from lattice mismatch, grain boundaries, material thermal expansion, and thin film properties. Much research has been conducted, such as the fabrication of nanocomposite origami and kirigami structures [5, 6]. The era of origami research opened a new door for 3D structuring and designs around 22 years ago [7, 8]. Since then, several 3D self-assembled microstructures and innovations have been created using different materials, layer systems, sacrificial layers, and releasing methodologies for specific corresponding applications and purposes. The sacrificial layers can be organic or non-organic ones. In some techniques, no sacrificial layers are used. The layer system of the 3D origami structures can have diverse designs and comprising materials, which can provide unique optical and electrical properties, enabling a widerange of applications and breakthroughs [9]. For our structure and design, metallic MEMS shutter blades have been constructed in a 3D Yin-Yang shape called paired shutters. Metallic MEMS shutters have been implemented for various applications, such as camera shutters [10], displays [11], smart glasses for daylight steering in buildings [12; 13], and space instruments [14]. Our 3D MEMS shutter arrays are metal-based and non-planar ones. These micro-shutter elements are curled/rolled up in the initial state and can be electrostatically actuated to un-roll. MEMS microstructures elevated in a gaseous environment often experience intentional or unintentional adhesion to the base plates or substrates. This stiction can either occur during the removal of sacrificial layers to release the structures or during the actuation of the movable MEMS structures. When the restoring forces within the structures are not enough to overcome the interfacial forces such as capillary, Van der Waals, or Casimir ones, the shutter blades remain stuck. Usually, stiction is undesirable when it comes to MEMS devices and applications. Much research has been conducted to overcome such a dilemma [15]. Recently, our group demonstrated a novel method for the 3D self-assembly of paired neighbouring MEMS shutter blades [16] using mainly Casimir forces to keep the elements tightly attached. The Casimir effect represents attraction or repulsion forces between two uncharged conducting plates at a very close distance depending on the materials of the plates, as well as the geometries. Figure 1 shows the case of attraction forces between two identical metal plates. In 1948, the Dutch physicist [PERSON] [17] first proposed the existence of Casimir forces, and it has been proven step by step experimentally over time [18; 19; 20; 21; 22; 23; 24; 25; 26]. Still, it is a cutting-edge topic, and currently, many questions remain unanswered, motivating researchers to fill that research gap. In the last decade, the Casimir effect was explored from many different points of view, e.g., considering different materials, geometries, and methodologies [19; 20]. Here, various geometries exploiting the Casimir force which have already been investigated in the existing literature are presented. We observed The molecular attraction force between a lens and a metal plate with a gap of between \(10^{-5}\) and \(10^{-4}\) cm was observed (Figure 2a) [21]. Crossed cylinders of mica (Figure 2b) at a thickness of 3 \(\upmu\)m with a separation distance of 15 nm were used to detect and calculate the Casimir force.