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- Q#04. Calculate the number of atoms per unit area in (100), (110) and (111) planes of in bcc crystal with the lattice parameter of 2.5 angstrom.Assume that the mobility of electrons in silicon at T = 300 K is µ= 1300 cm²/V-s. Also assume that the mobility is mainly limited by lattice scattering. Determine the electron mobility(cm:/V-s) at T= 400 K. !! 484 864 854 8441)A Si crystal in the form of a cube of side 1.0 nm is at equilibrium at 300 K.The edge of the conduction band is Ec = -1.0 eVa) What is the energy of a conduction electron in the ground state (in eV) ?b) What is the energy of the conduction electron in the first excited state (in eV)?
- K: Estimate the ratio of the electron densities in the conduction bands of silicon (Eg 1.14 eV) and gallium arsenide (Eg = 1.42 eV) at 400 K.1 (a) The width of an infinite potential well for a free electron of an 1-D material is 10.5 A°. Determine the first four allowed energy levels in eV for this free electron. Also find E2-E1, E3-E2 and E4-E3 in eV. Comment on the separation between successive levels. n²n²h? En %3D 2mа? (b) Suppose for Fermi-Dirac probability distribution function, E-EF = 0.15 eV. Find the temperature at which (i) the ff(E) = 0.05 and (ii) the ff(E) = 0.095. Why at higher temperature, the probability of occupancy of a state E > EF is higher? %3D 1 fr (E) = E-EF 1+e kT1. (a) Compute the concentration of holes and electrons in an intrinsic sample of Si at room temperature. You may take me = 0.7m and mh = m. (b) Determine the position of the Fermi level under these conditions.
- Determine the distance between nearest (110) planes in a simple cubic lattice with a lattice constant of an = 4.83 Å. (Ỵ T' The lattice constant of a face-centered-cubicstructure is 4.75 Å. Calculate the surface density of atoms for (a)a (100) plane and (b) a (110) plane. (Ans. (a) 8.86 x 104 cm-2, (b) 6.27 x 1014 cm-?]Consider a Face Centered Cubic (FCC) lattice structured Nickel crystal. We are looking to find the surface energy of the new surface that is formed after it is sliced at the (100) plane. a- Find the value of R as function of the lattice constant a. 4R Oa = 2R Oa = 4R Oa = = 2/2R V2 Find the area A11 of (111) surface as function of R. 04R? O16R? O8R? OR? How many atoms lie on the plane (111) within the unit cell? N111 = atoms within the unit cell Find the number of atoms per unit surface area. 2 2 R2 8R2 16R? 4R? Which of the following represents the expression of the surface energt? ON BEPAconstant = 1. If 1 × 1015 boron atoms per cm³ are uniformly added to silicon (diamond structure, lattice 0.543 nm) as a substitutional impurity, determine what percentage of the silicon atoms are displaced in the single crystal lattice, i.e., the concentration of boron as an impurity in silicon.
- An abrupt silicon pn junction at zero bias has dopant concentrations of Nd = 5 X 1017 cm 3 and N₂ = 1 X 1017 cm-3 at T = a 300K. Determine the peak electric field for this junction for a reverse voltage of 5 V. Emax = O Emax O Emax 3.88 X 105 V/cm Emax 3.21 X 105 V/cm Emax = 1.70 X 105 V/cm 1.35 X 105 V/cm =Body-centered cubic structure. (a) Show that for BCC the lattice length a in terms of the atomic radius is 4R/√3. (b) Calculate the volume of a BCC unit cell in terms of the atomic radius R. (c) Show that the atomic packing factor for the BCC crystal structure is 0.68.A/The volume density of atoms for a simple cubic lattice is 3 x 1022 cm. Assume that the atoms are hard spheres with each atom touching its nearest neighbor. Determine the lattice constant and the radium of the atom and APF. 15 M B/A th 0 051 ig diff oli calt