THE MEMS HAMMER, A TOOL TO STUDY MICROFRACTURE

A MEMS actuator, dubbed the MEMS hammer, capable of storing and rapidly releasing mechanical energy has been designed, built and tested. The hammer is fabricated using a single mask silicon-on-insulator (SOI) process. These devices have been used to study fracture in both lateral and vertical regimes. The lateral tests have shown excellent agreement with shear fracture theory. Using either a mechanical or an electrostatic latching mechanism, the hammers are capable of storing energies up to 3. 3μJ. The hammers have been shown to displace up to 36μm, exert a maximum force of 240 mN, move at speeds exceeding 50m/s, and deliver at least 330 mW of mechanical power. INTRODUCTION The goal of this research is to create a microactuator capable of fracturing barriers made of silicon and silicon dioxide. At its core, the MEMS hammer is a device capable of storing and releasing mechanical energy. This system could be used for applications ranging from jumping microrobots [1] to needle-free delivery of drugs and vaccines [6]. In this work, the MEMS hammer is used as a tool to study fracture at the microscale. Additionally, we show promising steps towards creating a self-destructing sensor. MEMS devices are commonly used in energy harvesting applications to transduce mechanical energy into electrical energy, often using piezoelectric materials [11]. However, limited work has been done at the microscale to store energy in a mechanical state. One way to store energy mechanically is in tension in a beam. The maximum energy stored in a beam of length l, cross-sectional area A, and Young’s Modulus E is given by the following equation where εmax is the maximum strain the material can undergo before fracture Emax = 1 2 Fmaxxmax = 1 2 AlEεmax 2 (1) Bergbreiter et al [1,2] have successfully stored and released 100uJ of mechanical energy using polydimethylsiloxane (PDMS) as their energy storage medium. These devices were designed to work with micromechanical motors which have an output force of 10mN. This relatively small force was the driving factor for using an elastomer based energy storage system. To store large energies with a small applied force, large displacements had to be achievable. Rogers et al [3] created a mechanical energy storage and rapid release system in polysilicon using Sandia’s SUMMiT-V process. This device was capable of using microfabricated electrostatic motors coupled to a 20,000:1 gear reduction ratio to launch a projectile with 19nJ of energy. Both of the abovementioned systems were created with the intent of using a MEMS motor to store the initial mechanical energy, and the designs were constrained accordingly. These motors have an inherently low force output, so the researchers were forced to use a large mechanical advantage or a material with a low Young’s modulus. In this research, the initial mechanical energy is stored in the device in a post fabrication assembly step, allowing us the freedom to choose a simple design and a material more suitable for microfabrication. DESIGN The MEMS hammer is fabricated in a single mask SOI process Figure 1: The layout of a MEMS hammer capable of storing 0. 8μJ of energy. with a 40μm device layer, a 2μm buried oxide, and a 500μm handle wafer. The MEMS hammer, shown in Figure 1, is composed of three main components: a cylindrical impactor, energy storing beams and a latching mechanism. In standard operation, the lever arm is pushed towards the right using a probe tip. As the lever arm rotates about the pin, it catches the hammer and starts loading the beams. The mechanical latch is moved to the side to allow the lever arm to pass by. Finally, the mechanical latch is moved back into its resting position and the hammer is latched in a high energy state. A latched hammer can be seen in Figure 3b, left. To successfully build a device capable of fracturing silicon, it is crucial to identify and reinforce all load bearing features in the design. The beams are the main energy storing elements in this device; without filleting the interface between these springs and the anchoring silicon, they will fail at deflections of less than 15μm, as opposed to 40μm with the fillets. Additionally, the pin must be able to withstand the maximum force of the springs, which can be up to 240mN. The pin is anchored to the substrate via the buried oxide layer, and should theoretically fail when the shear stress induced by the hammer exceeds the fracture stress of the oxide. The literature on fracture stress of thinfilm silicon dioxide varies from 0.77 MPa [12] to 364 MPa [13]. In earlier versions of the MEMS hammer, a fracture stress of 364 MPa was used to design these pins. Every pin tested failed catastrophically. It was determined that a pin of radius 46μm can withstand forces up to ~300mN, putting the estimated fracture stress of our oxide at 54 MPa. It is important to make this pin radius as small as possible to keep the force required to latch the hammer low. The distance from the center of the pin to the end of the lever arm divided by the distance from the center of the pin to the hammer is roughly equal to the mechanical advantage scale factor seen by the mechanical and electrostatic latches. That is to say, the smaller the pin radius is, the easier it is for these latches to restrain the hammer. Therefore, the pin radius was optimized to allow for ease of latching while still being robust enough to withstand the high forces from the hammer. Lastly, the piece of the lever arm that catches and loads the hammer must be designed carefully. The first iterations of the hammer used square etch holes. These stress concentrations caused the lever arm to fracture at its contact point with the hammer. In the current design, this was mitigated by moving to circular etch holes. Figure 2: MEMS hammer force vs displacement data. The empirical force vs displacement data is fit to the theoretical curve given by equation 5 and is in agreement with Coventor FEA. Nonlinear Beam Model In many MEMS applications, small displacement approximations are made to simplify calculations. These approximations are valid if the angle of beam deflection is small, such that the small angle approximations hold [4]. In this small displacement regime, the force displacement relationship of a centrally loaded fixed-fixed beam can be described using standard Euler-Bernoulli beam theory: F(x) = 16 Ew3t l3 x (2) This equation accounts for the bending strain energy stored in the beam. The MEMS hammer design uses beams which are 1000μm long and deflect more than 35μm at their center. The angles reached are large enough that nonlinear beam theory must be used, which adds a third order term corresponding to the axial stretching of the beam. A simple derivation of this non-linear term is done by assuming the springs stretch linearly, like a rubber band. By ignoring the boundary conditions at the fixed and guided edges, the derivation becomes a simple geometry problem. The non-linear term can be shown to be: Fstretch(x) = 8 Ewt l3 x (4) Combining this with the linear force-displacement relation given by equation 2, we arrive at the following equation which approximates the force-displacement relation of a fixed-fixed beam F(x) = 16 Ew3t l3 x + 8 Ewt l3 x (5) This equation corresponds to the force output for a single beam. In most hammer designs, multiple beams are used in parallel to increase the maximum force output by the device. This manifests itself in equation 5 with the addition of a factor N, equal to the total number of beams, in front of both terms. The integral under this force curve is equal to the energy stored by the hammer. The energy storing characteristics of the beams used in this work were calibrated with a Dage 4000 multipurpose bondtester. This tool applies displacement at a fixed rate and measures the resulting reaction force. Figure 2 shows this data plotted against a finite element analysis (FEA) performed using Coventor. The data from the bondtester was then fit to equation 5 to determine how closely this simplified beam model describes our system. The coefficients of the best fit curve are 24.3 and 7.4 for the linear term and the third order term respectively. We see excellent agreement with our theory for the non-linear stretching term, and fairly poor agreement with the linear bending term. This is in part due to the inability of our bondtester to accurately measure forces of less than ~5mN. Figure 2 shows that not a single data point was acquired until the beams had displaced 12μm, well outside the linear range of these beams. Additionally, the critical region of operation is at high displacements where the most energy is stored. In this region, we see less than 5% deviation from theory and simulation.