Micro and Nanoelectronics
ELL732
Lecture 2
Dhiman Mallick
Department of Electrical Engineering, IIT Delhi
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Semester I – 2024 - 2025
The Periodic Table
Semiconductor Materials
Semiconductors are a group of materials having conductivities between those of metals and
insulators.
❖ Elemental
❖ Compound
❖ Binary
❖ Ternary
Types of Solids
Amorphous, polycrystalline, and single crystals are the three general types of solids.
❖ Each type is characterized by the size of an ordered region within the material.
❖ An ordered region is a spatial volume in which atoms or molecules have a regular geometric
arrangement or periodicity.
Types of Solids
❖ Amorphous materials have order only within a few atomic or molecular dimensions.
❖ Polycrystalline materials have a high degree of order over many atomic or molecular dimensions.
❖ These ordered or single-crystal regions, vary in size and orientation with respect to one another.
❖ The single-crystal regions are called grains and are separated from one another by grain boundaries.
❖ Single-crystal materials, ideally, have a high degree of order, or regular geometric periodicity, throughout
the entire volume of the material.
❖ The advantage of a single-crystal material is that, in general, its electrical properties are superior to those
of a non-single-crystal material.
❖ Since grain boundaries tend to degrade the electrical characteristics.
Lattice and Unit Cell
❖ A representative unit, or a group of atoms, is repeated at regular intervals in each of the three
dimensions to form the single crystal.
❖ The periodic arrangement of atoms in the crystal is called the lattice.
Lattice point
❖ A unit cell is a small volume of the crystal that can be used to reproduce the entire crystal.
❖ A unit cell is not a unique entity.
Lattice and Unit Cell
The relationship between the cell and the lattice is characterized by
three vectors 𝑎,
Ԧ 𝑏, 𝑐Ԧ which need not be perpendicular, and which may or
may not be equal in length.
Every equivalent lattice point in the three-dimensional crystal can be
found using the vector
𝑟Ԧ = 𝑝𝑎Ԧ + 𝑞𝑏 + 𝑠𝑐Ԧ
where p , q , and s are integers.
As the location of the origin is arbitrary, p , q , and s are positive integers
for simplicity.
A generalized three-dimensional unit cell
The magnitudes of the vectors 𝑎,
Ԧ 𝑏, 𝑐Ԧ are the lattice constants of the unit
cell.
Basic Crystal Structures
Three lattice types: (a) simple cubic, (b) body-centered cubic (bcc), (c) face-centered cubic (fcc).
The lattice constant of each unit cell is a.
Find the volume density of atoms in a crystal.
Crystal Planes and Miller Indices
Three lattice planes: (a) (100) plane, (b) (110) plane, (c) (111) plane.
Miller Indices:
i. Find axes intercepts, ii. Take reciprocals, iii. Write integers within parentheses to denote the crystal plane
Crystal Planes and Miller Indices
Crystal Planes and Miller Indices
Calculation of distance and angle between crystal planes
❖ Two useful relationships in terms of Miller indices describe the distance between planes and angles
between directions.
❖ The distance d between two adjacent planes labeled (hkl) is given in terms of the lattice constant, a, as
❖ The angle θ between two different Miller index directions is given by
Calculate the surface density of atoms on a particular plane in a crystal.
Crystal Directions
Three lattice directions and planes: (a) (100) plane and [100] direction, (b) (110) plane and [110]direction, (c)
(111) plane and [111] direction.
Impurities in Solids
Lattice vibrations – thermally induced imperfections
A vacancy and interstitial may be in close enough
proximity to exhibit an interaction between the two-
point defects.
This vacancy–interstitial defect, also known as a Frenkel
defect.
Line Dislocation
Impurities in Solids
(a) a substitutional impurity and (b) an intersitital impurity.
Impurities in Solids
Diffusion Ion Implantation
Final concentration of diffused impurities into the Final concentration of ion-implanted boron into
surface of a semiconductor. silicon.
Packing Density
References
• Semiconductor Physics and Devices- Basic Principles by
Donald A. Neamen
• Solid State Electronic Devices by Ben G. Streetman and
Sanjay Kumar Banerjee
• Physics of Semiconductor Devices by S.M. Sze and Kwok K.
Ng
• State-of-the-art Research Papers
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