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Homework #1 ECE 3450 “Semiconductor Devices” Dr. John D. Cressler Due Date: Wednesday, 9/2/15 (in my hands by 5:00 pm) Topical Coverage: Review material from ECE 3040 [1] Which semiconductor would you expect to make the best visible LED: GaAs (Eg = 1.43 eV), Si (1.12 eV), or GaP (2.1 eV)? For credit you must carefully defend your answer (you will need some simple calculations). [2] At the 90 nm CMOS technology node, estimate how many CMOS transistors will fit into one wavelength of red light? For credit you must carefully defend how you got to your answer. [3] It is known that the capacitor storage cell of a 4Gbit DRAM memory chip is 5.0 fF. If the operating voltage of the DRAM is 1.5V, calculate the number of electrons needed to store a “1” or a “0” bit. [4] If you know that light travels 2.8 mm (in vacuum) during the time it takes a CMOS inverter to switch from a logical “1” to a logical “0,” calculate how fast the logic gate is switching (in picoseconds). [5] a) Calculate the resistivity (in Ω-cm) of a slab of Si of cross-sectional area 1.5 μm2 and length 4 μm, if you know that it has a measured resistance of 20kΩ. b) If one applies 20V across the ends of the sample, what is the magnitude of the electric field present (in V/cm)? c) Would this value of electric field be considered “large” or “small” in the context of semiconductors? Hint: Think about what defines large vs small in the context of electric field in semiconductors. [6] Draw a cubic unit cell and sketch the (111) and (211) planes. Also indicate the [110] direction. [7] The lattice constants of Si and GaAs are 5.43 and 5.65 Angstroms, respectively. The atomic weights of Si, Ga, and As are 28.1, 69.7, and 74.9, resepectively. Avagadro’s number is 6.02x1023. Calculate the densities of Si and GaAs. Hint: Si has 8 atoms per unit cell, and GaAs has 4 Ga atoms and 4 As atoms per unit cell. [8] a) Using correct terminology, label all of the equivalent <111> directions in a cubic crystal system. b) Using correct terminology, label all of the equivalent {100} planes in a cubic crystal system. [9] Consider a sample of Si at 300 K which is doped with 2.0x1016 cm-3 of B, and 1.0x1016 cm-3 of As. a) which carrier is majority carrier, and which is the minority carrier? b) calculate the majority carrier density (cm-3). Use correct notation for it. c) calculate the minority carrier density (cm-3). Use correct notation for it. d) calculate the position of the Fermi level w.r.t. EC (in eV) e) Sketch the energy band diagram [10] Consider an electron in Si at 300K. You have any means at your disposal to manipulate the electron without violating the laws of physics, but you need to move that electron from Atlanta to San Francisco and back again in the fastest possible time, assuming it travels that entire distance entirely within the Si (it’s a thought experiment!). Estimate the fastest possible time for the electron to travel from Atlanta to San Francisco and back (in sec).