667f05hw6 - kinetics follows a thermal activation energy (E...

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ELEG 667–016; MSEG-667-016 - Solid State Nanoelectronics – Fall 2005 Homework #6 - due Thursday, 3 November 2005, in class 1. Molecular Beam Epitaxy: The evaporation of a material from a Knudsen cell is given by the Langmuir equation on p. 206 of the text (Waser). Assuming that the evaporated atoms travel ballistic trajectories, following a cosine distribution versus angle as shown in Figure, 13, calculate the flux of atoms striking a unit area of substrate per second at a distance L from the source. Using this equation, calculate the arrival rate of gallium (as in the growth of GaAs). For Ga, use the atomic mass of 70; length L = 15 cm; the area of the Knudsen orifice of 5 cm 2 ; and the equilibrium vapor pressure of Ga = 4x10 -3 Torr at T= 1000C. Estimate the corresponding growth rate in μm per hour. 2. Chemical Vapor Deposition: Analyze the two fundamental types of limitations to chemical deposition, using the nomenclature of the text (Waser). The rate j k due to chemical reaction
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Unformatted text preview: kinetics follows a thermal activation energy (E act ) such as: j k ~ exp[- E act / k B T] where k B is Boltzmanns constant and T is the absolute temperature. The growth rate limitation due to the mass transport of chemicals to the growing film follows a diffusion equation such as: j t ~ D / T where D is a diffusivity Using these equations, analyze the data of Figure 37 on page 214, for the growth of polysilicon. Estimate the activation energy E act , and the effective diffusivity D. Discuss in your own words the sensitivity of the growth rate to temperature in the two regimes of: (a) reaction kinetics -limited growth, and (b) mass transport -limited growth. Give the temperature ranges for the two growth rate limitations. Homework assignments will appear on the web at: http://www.ece.udel.edu/~kolodzey/courses/eleg667_016f05.html Note: On each homework and report submission, you must please give your name, the due date, assignment number and the course number....
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