Prove that (111) surface of a crystal with cubic lattice Intercepts (100) surfac

Question

Prove that (111) surface of a crystal with cubic lattice Intercepts (100) surface at an inclination angle of approximately 54.75 degree. Calculate surface density of atoms in (100), (110) and (111) crystal planes of a simple cubic lattice with a lattice constant a = 5 where 1 = 10-8 cm. OR Calculate the intrinsic electron concentration (n1) for undoped GaAs at room temperature (300K). The bandgap of GaAs is Eg = 1.424 ev. Effective mass of electrons mn* = 0.066 mg. Effective mass of holes is mp* = 0.52 m0 and m0 = 9.11 Times 10-11 kg. Determine hem far the Fermi energy level is from the middle of the bandgap of undoped GaAs at 300K. Lattice constant of GaAs crystal is 5.65 . Calculate nearest neighbor atom distance in GaAs. Write electronic structure of a silicon atom (Z = 14) in spectroscopic notation Silicon is a donor impurrty for GaAs crystal. A silicon atom substitutes a gallium atom in GaAs semiconductor crystal. Assume a hydrogen atom like model for silicon donor impurity atom in GaAs crystal, Write expressions for binding energy (E8) and radius (r8) of n=l orbit of the donor electron (ie., fourth valence electron of silicon that does not participate in bonding with other atoms in the GaAs crystal). Calculate the binding energy E8 of the donor. The dielectric constant of GaAs is K8 = 12.9 Effective mass of electrons mn* = 0.066 m0. Calculate the radius r8 of n = 1 orbit of the donor electron of silicon atom GaAs crystal. Determine the ratio of the radius of the n = 1 orbit of the donor electron of silicon dopant atom with the nearest neighbor atom distance of GaAs.

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This book provides the knowledge and understanding necessary to comprehend the operation of individual electronic devices that are found in modern micro-electronics. As a textbook, it is aimed at the third-year undergraduate curriculum in electrical engineering, in which the physical electronic properties are used to develop an introductory understanding to the semiconductor devices used in modern micro-electronics. The emphasis of the book is on providing detailed physical insight into the microscopic mechanisms that form the cornerstone for these technologies. Mathematical treatments are therefore kept to the minimum level necessary to achieve suitable rigor.

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