l
فیزیک الکترونیک Semiconductor devices Physics and Technology Energy Bands and Carrier Concentration in Thermal Equilibrium
SEMICONDUCTOR MATERIALS Solid-state materials can be grouped into three classes 1. Conductors 2. Semiconductors 3. Insulators
Semiconductor types Element semiconductors Compound semiconductors Alloy semiconductors
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.
Compound semiconductors Two element semiconductors III-V : GaAs, AlP, AlAs, GaN, InP, … II-VI : ZnS, CdTe, …
Alloy semiconductors III-V : (AlxGa1-x)As, (GaxIn1-x)(AsyP1-y), … II-VI : (HgxCd1-x)Te
3 Types of Solids
3 Types of Solids
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
Semiconductors as solids Unit cell: representative of the entire lattice, regularly repeated Primitive cell: smallest unit cell that can be repeated to form lattice
Semiconductors as solids Primitive cell: smallest unit cell that can be repeated to form lattice
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
Two dimensional lattices Oblique Centered rectangular (Orthorhombic) Rectangular (Orthorhombic) Square (Tetragonal) Hexagonal
3D lattices There are 14 different 3D lattice. In general
3 Types of Cubic Lattice Structure
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
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
Body Centered Cubic(BCC) Each point has 8 nearest neighbor with distance of 𝑎 3 /2 6 second nearest neighbor with distance of 𝑎
Packing factor of BCC lattice Sphere atoms per unit cell = 8× 1 8 +1=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
Face Centered Cubic(FCC) Each point has 12 nearest neighbor with distance of 𝑎 2 /2 6 second nearest neighbor with distance of 𝑎
Packing factor of FCC lattice Sphere atoms per unit cell = 8× 1 8 +6× 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
Diamond lattice structure
Diamond lattice structure
Diamond lattice structure
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
Packing factor of Diamond lattice Sphere atoms per unit cell = 8× 1 8 +6× 1 2 +4=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
Silicon
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× 10 22 atom/cm3 number of atoms per mol = Avogadro’s number(6.02× 10 23 ) 𝑑𝑒𝑛𝑠𝑖𝑡𝑦=𝑛𝑜. 𝑜𝑓𝑎𝑡𝑜𝑚𝑠/ 𝑐𝑚 3 ×𝑤𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑒𝑎𝑐ℎ 𝑎𝑡𝑜𝑚
Zincblende structure zincblende (sphalerite) Sphalerite: Sulfide mineral ((Zn, Fe)S)
Example: Calculate the densities of GaAs from the lattice constants. GaAs: a=5.6510-8cm, atomic weight Ga:6.7gr/mol, As:74.9 gr/mol 4 Ga,As atoms/cell 4/a3= 2.221022atoms/cm3
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
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.)
Miller Indices
Miller Indices
Miller Indices