1. l

2. فیزیک الکترونیک Semiconductor devices Physics and Technology
Energy Bands and Carrier Concentration in Thermal Equilibrium

3. SEMICONDUCTOR MATERIALS
Solid-state materials can be grouped into three classes
1. Conductors Semiconductors Insulators

4. Semiconductor types Element semiconductors Compound semiconductors
Alloy semiconductors

5. Element semiconductors
Composed of single species of atoms
silicon (Si), germanium (Ge), and tin (Sn) in column IV
selenium (Se) and tellurium (Te) in column VI
Si Semiconductor
Silicon devices exhibit better properties at room temperature
High-quality silicon dioxide can be grown thermally
Device-grade silicon costs much less than any other semiconductor material.
Silicon in the form of silica and silicates comprises 25% of the Earth’s crust, and silicon is second only to oxygen in abundance.
Currently, silicon is one of the most studied elements in the periodic table, and silicon technology is by far the most advanced among all semiconductor technologies.

6. Compound semiconductors
Two element semiconductors
III-V : GaAs, AlP, AlAs, GaN, InP, …
II-VI : ZnS, CdTe, …

7. Alloy semiconductors III-V : (AlxGa1-x)As, (GaxIn1-x)(AsyP1-y), …
II-VI : (HgxCd1-x)Te

9. 3 Types of Solids

10. 3 Types of Solids

11. Crystal Versus Lattice
Crystal: Periodic arrangement of atoms in space.
Lattice: Periodic arrangement of points in space.
Basis(or Motif): an atom or group of atoms associated with each lattice point in crystal.
Crystal = Lattice + Basis

12. Semiconductors as solids
Unit cell: representative of the entire lattice, regularly repeated
Primitive cell: smallest unit cell that can be repeated to form lattice

13. Semiconductors as solids
Primitive cell: smallest unit cell that can be repeated to form lattice

14. Translation Vector
The relationship between the primitive cell and the lattice is characterized by three vectors a, b, and c.
m, n, p are integers.
a, b, c  basis vectors
In general
There is no need to be perpendicular to each other.
Can have different lengths

15. Two dimensional lattices
Oblique
Centered rectangular
(Orthorhombic)
Rectangular
(Orthorhombic)
Square
(Tetragonal)
Hexagonal

16. 3D lattices
There are 14 different 3D lattice.
In general

17. 3 Types of Cubic Lattice Structure

18. Simple Cubic (SC) a is lattice constant Each point has
6 nearest neighbor with distance of a
12 second nearest neighbor with distance of 𝑎√2

19. Packing factor of SC lattice
Sphere atoms per unit cell = 8× 1 8 =1 Nearest neighbor distance = a Radius of each sphere = 𝑎 2 Volume of unit cell = 𝑎 3 Volume of each sphere = 4 3 𝜋 𝑟 3 = 4 3 𝜋 𝑎 3 8 Packing factor = 1× 4 3 𝜋 𝑎 3 8 𝑎 3 = 𝜋 6 =0.523

20. Body Centered Cubic(BCC)
Each point has
8 nearest neighbor with distance of 𝑎 3 /2
6 second nearest neighbor with distance of 𝑎

21. Packing factor of BCC lattice
Sphere atoms per unit cell = 8× =2 Nearest neighbor distance = 𝑎 3 /2 Radius of each sphere = 𝑎 3 4 Volume of unit cell = 𝑎 3 Volume of each sphere = 4 3 𝜋 𝑟 3 =𝜋 3 𝑎 3 16 Packing factor = 2×𝜋 3 𝑎 3 16 𝑎 3 = 𝜋 3 8 =0.68

22. Face Centered Cubic(FCC)
Each point has
12 nearest neighbor with distance of 𝑎 2 /2
6 second nearest neighbor with distance of 𝑎

23. Packing factor of FCC lattice
Sphere atoms per unit cell = 8× × 1 2 =4 Nearest neighbor distance = 𝑎 2 /2 Radius of each sphere = 𝑎 2 4 Volume of unit cell = 𝑎 3 Volume of each sphere = 4 3 𝜋 𝑟 3 =𝜋 2 𝑎 3 3×8 Packing factor = 4×𝜋 2 𝑎 3 3×8 𝑎 3 = 𝜋 2 6 =0.74

24. Diamond lattice structure

25. Diamond lattice structure

26. Diamond lattice structure

27. Diamond lattice structure
Each point has
4 nearest neighbor with distance of 𝑎 3 /4
12 second nearest neighbor with distance of 𝑎 2 /2

28. Packing factor of Diamond lattice
Sphere atoms per unit cell = 8× × =8 Nearest neighbor distance = 𝑎 3 /4 Radius of each sphere = 𝑎 3 8 Volume of unit cell = 𝑎 3 Volume of each sphere = 4 3 𝜋 𝑟 3 =𝜋 3 𝑎 3 64×2 Packing factor = 8×𝜋 3 𝑎 3 64×2 𝑎 3 = 𝜋 3 16 =0.34

29. Silicon

30. Example
At 300 K the lattice constant for silicon is 5.43 Å. Calculate the number of silicon atoms per cubic centimeter and the density of silicon at room temperature.( silicon atomic weight is 28.1 gr/mol) Solution: There are eight atoms per unit cell. 8 𝑎 3 = 8 (5.43× 10 −8 ) 3 =5× atom/cm3 number of atoms per mol = Avogadro’s number(6.02× ) 𝑑𝑒𝑛𝑠𝑖𝑡𝑦=𝑛𝑜. 𝑜𝑓𝑎𝑡𝑜𝑚𝑠/ 𝑐𝑚 3 ×𝑤𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑒𝑎𝑐ℎ 𝑎𝑡𝑜𝑚

31. Zincblende structure zincblende (sphalerite)
Sphalerite: Sulfide mineral
((Zn, Fe)S)

32. Example: Calculate the densities of GaAs from the lattice constants.
GaAs: a=5.6510-8cm, atomic weight Ga:6.7gr/mol, As:74.9 gr/mol
4 Ga,As atoms/cell
4/a3= 2.221022atoms/cm3

33. Miller Indices Four atoms in the ABCD plane
Five atoms in the ACEF plane
The number of atoms and spacing between them is different in different planes
Therefore, the crystal properties along different planes are different, and the electrical and other device characteristics can be dependent on the crystal orientation.
defining the various planes in a crystal by Miller indices

34. Miller Indices h: inverse x-intercept k: inverse y-intercept
l: inverse z-intercept
(Intercept values are in multiples of the lattice constant;
h, k and l are reduced to 3 integers having the same ratio.)

35. Miller Indices

36. Miller Indices

37. Miller Indices