Indian Institute of Technology Roorkee

Department of Metallurgical and Materials Engineering

MT­201 Electrical and Electronic Materials

Tutorial 1

1. i. Consider a multicomponent alloy containing N elements. If w1, w2, w3,…..,wN are

the weight fractions of the components 1, 2, 3, …..,N in the alloy and M1, M2, M3,……..,MN are the respective atomic masses of the elements, show that the atomic fraction of the ith component is given by, ni = wi ∕ Mi

­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­ w1 ∕M1+w2 ∕M2+­­­­­­­­­­­­+wN ∕MN

ii. Consider the semiconducting II­VI compound cadmium selenide, CdSe. Given the atomic masses of Cd and Se, find the weight fraction of Cd and Se in the compound and grams of Cd and Se needed to make 100 grams of CdSe.

2. Explain the general bonding principle of atoms to form a crystalline solid with the help of energy verses inter­atomic distance plot.

3. i. State various physical and mechanical properties of materials.

ii. Explain how the bonding type affect the above properties. Give examples.

4. i. ii. iii. iv. v. vi.

Define and explain the following with the help of suitable diagrams Space lattice Unit cell and lattice parameters Crystal systems Bravais lattice and their classification Origin for the creation of FCC Bravais lattice from a primitive cubic lattice Crystal voids and their coordinates

5. Calculate the following: i.

ii. iii. iv. v. vi. vii. viii.

Effective number of atoms in SC, BCC, FCC, HCP unit cells Relationship between the size of the unit cell and atomic diameter in SC, BCC, FCC, HCP unit cells Packing factors of BCC, FCC, HCP unit cells Packing factor of a diamond cubic crystal structure Coordination numbers of BCC, FCC, HCP crystal lattice c/a ratio for an ideal HCP unit cell Size of largest sphere that can fit into the tetrahedral & octahedral interstitial sites of a close packed structures without distorting the unit cell. Volume of unit cell of germanium in cubic meters, the atomic radius of Ge having Diamond Cubic structure being 1.223 Ao

6. i. ii. iii. iv. v. vi.

Show with the help of neat sketches the following: Planes whose Miller indices are (111), (210), (010), (0 Ī Ī), (002), (130), (212) and(3 Ī 2). Directions whose Miller indices are [111], [110], [1Ī0], [122], [301], [201] and [2 Ī 3]. [1210], [01 Ī0], [Ī011] directions and (1210), (Ī Ī 22), (1230) planes (Miller Bravais Index) in HCP unit cell In a cubic unit cell the (hkl) & [hkl] are perpendicular to each other Miller index of the direction that is common to both planes(110) and (111) inside the unit cell of a cubic crystal. 3 parallel planes of belonging to 111 inside a cubic unit cell (may be touching the UC). 6 direction <110> on any one 111

7. i.

Given the Si lattice parameter a=0.543 nm. Calculate the number of Si atoms per unit volume, in nm­3.

ii. Calculate the number of atoms per m2 and per nm2 on the (100), (110), and (111) planes in the Si crystal as shown in above figure. Which plane has the maximum number of atoms per unit area?

iii. The density of SiO2 is 2.27 g cm­3 . Given that its structure is amorphous, calculate the number of molecules per unit volume, in nm­3 . Compare your result with (i) and comment on what happens when the surface of a Si crystal oxidizes. The atomic masses of Si and O are 28.09 and 16, respectively.

8. In device fabrication, Si is frequently doped by the diffusion of impurities (dopants) at high temperatures , typically 950­12000C. The energy of vacancy formation in the Si crystal is about 3.6eV. What is the equilibrium concentration of vacancies in a Si crystal at 10000C ? Neglect the change in the density with temperature which is less than 1 percent in this case.

9 i. Describe with neat sketches, the 3 types of line defects and relate b, Burgers vector with dislocation line.

ii. Describe planar defects ; grain boundaries and surface defects

iii. How do the defects affect the electrical conductivity of the materials?

10.

i. What are the allotropically different forms of carbon?

ii. Give neat sketches of their crystal structures.

iii. How do you classify these materials in terms of electrical conductivity?

11.

i. Why single crystals are used for electronic applications? Explain methods of bulk single crystal growth.

ii. What is epitaxial growth? Explain with one example each of growth for; binary, ternary and quaternary semiconductor compounds, with the help of Eg vs lattice parameter of the crystal plot.

iii. What is the significance of ‘ distribution coefficient’ in zone refining?

12.

i. How amorphous semiconductors are prepared? Give an example.

ii. Explain how the nonstoichiometeric, ZnO crystal with excess Zn at the interstitial sites contribute free electron for conduction.

13.

i.

Consider 50% Pb­ 50% Sn solder alloy:

Sketch the microstructure of the alloy at various stages as it is cooled from the melt. What is the importance of this alloy in electrical applications?

ii. At what temperature does the solid melt? What is the significance of this temperature?

iii. What is the temperature range over which the alloy is a mixture of melt and solid? what is the micro structure of the solid ?

iv. Consider the solder at room temperature following cooling from 1830C. Assume that the rate of cooling from 1830C to room temperature is faster than the atomic diffusion rates needed to change the compositions of the α and β phases in the solid. Assuming the alloy is 1 kg. Calculate the masses of the following components in the solid.

a) The primary α ( proeutectic), b) α in the whole alloy, c) α in the eutectic solid and

d) β in the alloy ( where is the β phase?)

e) For Pb­40Sn, find the degree of freedom at,

i) liquid region, ii) liquidus, iii) two phase mushy region, iv) solidus and v )at room temperature.