ECE 4370/6370 Homework 1

1 ECE 4370/6370 Homework 1 Due Jan. 21, 2016 1. (A lot of room at the bottom – scaling practice) (a) To store 1016 bits, if each bit is recorded in an area size of 50nm50nm, what is the area required, assuming I/O peripheral devices will occupy about 20% of the total area? If each bit is recorded in a volume of 5nm5nm5nm, what is the total volume required, assuming I/O devices about 40% of the total volume? If this amount of information is transferred serially in a 1Gbit modem, how long is required to finish the transfer? (5 pts) (b) In a biological DNA structure, each bit of information is stored by an average of 50 atoms. If the DNA structure needs to carry 33 billion bits, what is the approximate volume required? Assuming the average atomic radius is 1.2A and the packing density of DNA strands is 30%. (5 pts) (c) A good color picture has 1200 dots per inch with 10-bit color resolution for red-green-blue (RGB) each. For pixels defined by solid state light-emitting-diodes (LED), what is the area available for each single-color LED that can be assembled to picture-quality display? Assume the color resolution will be achieved through time division and not related to area. (5 pts) (d) Five hundred piece of 20-lb paper is about 4cm thick, what is the thickness of a piece of paper? How many times thick is a sheet of paper to a 2m-thick MEMS beam? (3 pts) (e) Calculate the weight of a 2m-thick MEMS membrane with an area of 200m5m. The MEMS membrane is made by poly-Si with a density of 2.33 g/cm3 . (2 pts) (f) For a water bubble of 5cm diameter, the weight is about 20mg, assume the membrane is homogeneous (in reality, they are affected by gravity), what is the thickness of the membrane? How does it compare with a 2m-thick MEMS membrane? (3 pts) 2. (Applications and transducer actions) Give practical examples that can use energy transducers in a small size (less than 1cm): (a) from thermal to electrical (3 pts) (b) from chemical to electrical (3 pts) (c) from electrical to mechanical force (3 pts) (d) from velocity to electrical (3 pts) (e) from acceleration to optical (3 pts) 3. (Units, units) Give the unit and an operating definition (in a simple formula or equation that matches with the unit) of the following physical quantity: dielectric constant (one that you can directly use in estimating capacitance), metal resistivity, electron mobility, diffusivity, dielectric breakdown field, specific heat, thermal conductivity, thermal expansion coefficient, Young’s modulus, Poisson ratio, shear modulus, yield strength, piezoresistive coefficient, and piezoelectric constant. (13 items). (26 pts) 4. (Comparison of materials in MEMS applications) Regardless of manufacturing issues, comment on the following material difference in the specific transducer applications (in terms of sensitivity and operational range, and qualitative description is good enough): 2 (a) Si and SiC moving beam by thermal expansion for thermal and mechanical transducers (3 pts) (b) Si and SiO2 substrate for building devices with high power ratings (3 pts) (c) SiO2 and Si3N4 for moving beam containing insulators to transduce mechanical movement to electrical signals (3 pts) 5. (Crystal orientation) In a face-center-cubic lattice (FCC), (a) Draw the (100), (011) and (111) planes in separate cubes. (3 pts) (b) Find all of the equivalent plane representation of (100), (011) and (111). Use 1 to represent -1. (4 pts) (c) Find all possible intersection angles between equivalent (100) and (111) planes. (4 pts) (d) What is the minimal atomic site distance in the (100) plane? What is the atomic density (atoms/cm2 ) in the (111) plane? (4 pts) x y z a

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