Chapter 1, Crystal Properties and Growth of Semiconductors Video Solutions, Solid State Electronic Devices

Problem 1

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 $E_{g}$ ? Is there a noticeable pattern in the band gap energy of III-V compounds related to the column III element?

Suzanne W.

Numerade Educator

02:41

Problem 2

For a bcc lattice structure with a lattice constant of $3 \AA$, calculate the separating distance between the nearest atoms, the radius, and the volume of each atoms. Also find the maximum packing fraction.

Lottie Adams

Numerade Educator

04:57

Problem 3

Label the planes illustrated in Fig. P1-3.

Joanna Quigley

Numerade Educator

02:41

Problem 4

Sketch a bcc unit cell with a monoatomic basis. If the atomic density is $1.6 \times 10^{22} \mathrm{~cm}^{-3}$, calculate the lattice constant. What is the atomic density per unit area on the (110) plane? What is the radius of each atom? What are interstitials and vacancies?

Dr. Satish Ingale

Numerade Educator

01:30

Problem 5

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 $\mathrm{Si}, \mathrm{Ga}$, and $\mathrm{As}$ are $28.1,69.7$, and 74.9, respectively.

Adriano Chikande

Numerade Educator

02:53

Problem 6

The atomic radius of Ga and As are $136 \mathrm{pm}$ and $114 \mathrm{pm}$, respectively. Using hard sphere approximation, find the lattice constant of GaAs and the volume of the primitive cell. $\left[1 \ A^{\circ}=100 \mathrm{pm}\right]$

Bin Chen

Numerade Educator

05:43

Problem 7

Sketch an fcc lattice unit cell (lattice constant $=5 \AA$ ) with a monoatomic basis, and calculate the atomic density per unit area on (110) planes. What is the atomic density per unit volume? Indicate an interstitial defect in this cell.

Tianyu Li

Numerade Educator

00:16

Problem 8

Sketch a view down a $\langle 110\rangle$ direction of a diamond lattice, using Fig. $1-9$ as a guide. Include lines connecting nearest neighbors.

Amrita Bhasin

Numerade Educator

01:22

Problem 9

Show by a sketch that the bcc lattice can be represented by two interpenetrating sc lattices. To simplify the sketch, show a $\langle 100\rangle$ view of the lattice.

Penny Riley

Numerade Educator

01:49

Problem 10

(a) Find the number of atoms/cm $^{2}$ on the (100) surface of a Si wafer.
(b) What is the distance (in $\AA$ ) between nearest In neighbors in InP.

Penny Riley

Numerade Educator

View

Problem 11

The ionic radii of $\mathrm{Na}^{+}$ (atomic weight 23 ) and $\mathrm{Cl}^{-}$ (atomic weight $35.5$ ) are $1.0 \ A$ and $1.8 \ A$, respectively. Treating the ions as hard spheres, calculate the density of NaCl. Compare this with the measured density of $2.17 \mathrm{~g} / \mathrm{cm}^{3}$.

Vipin Singh

Numerade Educator

03:11

Problem 12

Sketch an sc unit cell with lattice constant $\mathbf{a}=4 \ A^{\circ}$, whose diatomic basis of atom $\mathrm{A}$ is located at the lattice sites, and with atom B displaced by $(\mathbf{a} / 2,0,0)$. 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 $\mathrm{B}$ atoms per unit volume,
(iii) the number of $\mathrm{A}$ atoms per unit area on (100) planes.

Chai Santi

Numerade Educator

02:17

Problem 13

How many atoms are found inside a unit cell of an sc, a bcc, and an fcc crystal? How far apart in terms of lattice constant $a$ are the nearest neighbor atoms in each case, measured from center to center?

Tianyu Li

Numerade Educator

02:26

Problem 14

Draw a cube such as Fig. $1-7$, and show four $\{111\}$ planes with different orientations. Repeat for $\{110\}$ planes.

Harshita Goel

Numerade Educator

02:44

Problem 15

Find the maximum fractions of the unit cell volume that can be filled by hard spheres in the sc, fcc, and diamond lattices.

Narayan Hari

Numerade Educator

01:30

Problem 16

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.

Adriano Chikande

Numerade Educator

01:06

Problem 17

Beginning with a sketch of an fcc lattice, add atoms at $\left(\frac{1}{4}, \frac{1}{4}, \frac{1}{4}\right)$ from each fcc atom to obtain the diamond lattice. Show that only the four added atoms in Fig. 1-8a appear in the diamond unit cell.

Narayan Hari

Numerade Educator

01:45

Problem 18

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 $\mathrm{AlSb}_{x} \mathrm{As}_{1-x}$ is lattice-matched to InP? What composition of $\operatorname{In}_{x} \mathrm{Ga}_{1-x} \mathrm{P}$ is lattice-matched to GaAs? What is the band gap energy in each case?

Aadit Sharma

Numerade Educator

01:11

Problem 19

(a) Find the composition of $\operatorname{In}_{1 \cdot x} \mathrm{Ga}_{\mathrm{x}}$ As grown lattice-matched on $\operatorname{InP}$ substrate. The lattice constants are: $a(\operatorname{InAs})=6.0584 \ A, a(\mathrm{GaAs})=5.6533 \ A$, and $a (\operatorname{In} P)=5.8688 \ = A$ A.
(b) An alloy of $\operatorname{In}_{0.2} \mathrm{Ga}_{0.8}$ As is grown pseudomorphically on a GaAs substrate. Determine the maximum thickness of the grown layer.

Chai Santi

Numerade Educator