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- Question : 1P - Using Appendix III, which of the listed semiconductors in Table 1-1 has the largest band gap? The smallest? What are the corresponding wavelengths if light is emitted at the energy Egl Is there a noticeable pattern in the band gap energy of III-V compounds related to the column III element?
- Question : 2P - Find the fraction of the fee unit cell volume filled with hard spheres.
- Question : 3P - Label the planes illustrated in Fig. PI-3.
- Question : 4P - Calculate the densities of Si and GaAs from the lattice constants (Appendix III), atomic weights, and Avogadro's number. Compare the results with densities given in Appendix III. The atomic weights of Si, Ga, and As are 28.1,69.7, and 74.9, respectively
- Question : 5P - The atomic radii of In and Sb atoms are approximately 1.44 A and 1.36 A, respectively. Using the hard-sphere approximation, find the lattice constant of InSb (zinc blende structure), and the volume of the primitive cell. What is the atomic density on the (110) planes? (Hint: The volume of the primitive cell is one-fourth the fee unit cell volume.)
- Question : 6P - A crystal mth a simple cubic lattice and a monoatomic basis has an atomic radius of 2.5 A and an atomic weight of 5.42. Calculate its density, assuming that the atoms touch each other.
- Question : 7P - Sketch a view down a (110) direction of a diamond lattice, using Fig. 1-9 as a guide. Include lines connecting nearest neighbors
- Question : 8P - Show by a sketch that the bcc lattice can be represented by two interpenetrating sc lattices. To simplify the sketch, show a (100) view of the lattice.
- Question : 9P - (a) Find the number of atoms/cm2 on the (100) surface of a Si wafer, (b) What is the distance (in A) between nearest In neighbors in InP?
- Question : 10P - The ionic radii of Na+ (atomic weight 23) and Cl~ (atomic weight 35.5) are 1.0 and 1.8 A, respectively. Treating the ions as hard spheres, calculate the density of NaCl. Compare this with the measured density of 2.17 g/cm3.
- Question : 11P - Sketch an sc unit cell with lattice constant a = 4 A, whose diatomic basis of atom A is located at the lattice sites, and with atom B displaced by (a/2,0,0). Assume that both atoms have the same size and we have a close-packed structure (i.e., nearest neighbor atoms touch each other). Calculate (i) the packing fraction (i.e., fraction of the total volume occupied by atoms), (ii) the number of B atoms per unit volume, (iii) the number of A atoms per unit area on (100) planes.
- Question : 12P - How many atoms are found inside a unit cell of an sc, a bcc, and an fee crystal? How far apart in terms of lattice constant a are the nearest neighbor atoms in each case, measured from center to center?
- Question : 13P - Draw a cube such as Fig. 1-7, and show four {111] planes with different orientations. Repeat for {110] planes.
- Question : 14P - Find the maximum fractions of the unit cell volume that can be filled by hard spheres in the sc, fee, and diamond lattices.
- Question : 15P - Calculate the densities of Ge and InP from the lattice constants (Appendix III), atomic weights, and Avogadro's number. Compare the results with the densities given in Appendix III.
- Question : 16P - Beginning with a sketch of an fee lattice, add atoms at (\, \, \) from each fee atom to obtain the diamond lattice. Show that only the four added atoms in Fig. l-8a appear in the diamond unit cell.
- Question : 17P - Assuming that the lattice constant varies linearly with composition x for a ternary alloy (e.g., see the variation for InGaAs in Fig. 1-13), what composition of AlSbjAs^ is lattice-matched to InP? What composition of InrGa^P is lattice- matched to GaAs? What is the band gap energy in each case? (Note: Such linear variations of crystal properties (e.g., lattice constant and band gap) with mole fraction in alloys is known as Vegard's law. A secondorder polynomial or quadratic fit to the data is called the bowing parameter.)
- Question : 18P - An Si crystal is to be pulled from the melt and doped with arsenic (kd = 0.3). If the Si weighs 1 kg, how many grams of arsenic should be introduced to achieve 1015 cm-3 doping during the initial growth?
- Question : 1SQ - (a) Label the following planes using the correct notation for a cubic lattice of unit cell edge length a (shown within the unit cell). (b) Write out all of the equivalent (100) directions using the correct notation. (c) On the two following sets of axes, (1) sketch the [011] direction and (2) a (111) plane (for a cubic system with primitive vectors a, b, and c).
- Question : 2SQ - (a) Which of the following three unit cells are primitive cells for the two-dimensional lattice? Circle the correct combination in bold below. 1 / 2 / 3 / 1 and 2 / 1 and3 / 2 and3 / 1, 2, and3 The following planes (shown within the first quadrant for 0 < x,y,z < a only, with the dotted lines for reference only) are all from what one set of equivalent planes? Use correct notation Which of the following three planes (shown within the first quadrant only) is a (121) plane? Circle the correct diagram.
- Question : 3SQ - a) Diamond and zinc blende crystal structures are both composed of a Bravais lattice with a two-atom basis. Circle the correct unit cell for this Bravais lattice. (b) Which statement below is true? 1. GaAs has a diamond / zinc blende crystal structure. 2. Si has a diamond / zinc blende crystal structure.
- Question : 4SQ - Give some examples of zero-dimensional, one-dimensional, two-dimensional, and threedimensional defects in a semiconductor.
- Question : 5SQ - (a) What is the difference between a primitive cell and a unit cell? What is the utility of both concepts? (b) What is the difference between a lattice and a crystal? How many different 1-D lattices can you have?
- Question : 6SQ - Consider growing InAs on the following crystal substrates: InP, AlAs, GaAs, and GaP. For which case would the critical thickness of the InAs layer be greatest? You may use

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