PROBLEMS\ Notes: Use Matlab for all calculations and plotting.\ When choosing unspecified parameter values and plotting use reasonable values\ and scales that allow illustration of interesting behavior.\ Submitted results must be your own work done on an individual basis and include\ any code you have written.\ Problem 2.1 Sensitivity of Surface Height Measurement Using Scanning Tunneling\ Microscopy (STM) and Atomic Force Microscopy (AFM)\ You are considering the use of two different piezo-scanners in the construction of a\ scanning tunneling microscope. One is a PI PT230.24 tube scanner (see data sheet on\ website) having a wall of thickness h = 1.0 mm, an outer diameter of D = 10.0 mm and a\ length of l = 30.0 mm. The other is a linear tripod scanner with thickness h = 1.0 mm and\ length of l = 25.0 mm. (See piezo-positioner references on website.)\ (a) Calculate and compare the relative sensitivities (lateral and vertical) of the two\ types of scanner for reasonable voltages.\ (b) Assume you are to use a feedback loop (similar that shown in slide 2-28) with a\ loop bandwidth of B = 100kHz and the dominant thermal noise source is\ equivalent to a resistance of RN when referred to the output (i.e. at the piezo-\ actuator). Calculate the size of RN required to maintain sufficient accuracy to\ measure to atomic resolution (i.e. about 0.1 nm) at room temperature.\ (c) If instead of STM we chose to use atomic force microscopy (AFM) using the\ same measurement bandwidth in (b) with a cantilever quality factor of Q = 40,\ and force constant k = 1.0 N/m. What cantilever mass would be required to\ achieve atomic resolution at room temperature both at resonance and off\ resonance?