• We may consider this deficiency as a particle similar to an electron. • This fictitious particle is called hole
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Energy levels of isolated atoms
• For an isolated, the electron an have discrete energy level
– Ex: an isolated hydrogen atom are given by the Bohr model
E H m o q / 8 o h n 13 . 6 / n eV
– Find the intercepts of the plane on the three Cartesian coordinates in terms of the lattice constant – Take the reciprocals of these numbers and reduce them to the smallest three integers having the same ratio – Enclose the result in parentheses (hkl) as the miller indices for a single plane
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Compound semiconductors
Wen Chang HuangΒιβλιοθήκη chapter 25
Basic crystal structure
• Single crystal
– The atoms are arranged in three dimensional periodic fashion
• The element semiconductors
– Silicon and germanium – Belongs to fcc crystal family
• Two interpenetrating fcc sublattices with one sublattice displaced from the other by one-quarter of the distance along the body diagonal of the cubic • A displacement of a 3 / 4
• SiC+SiO2(sand)→Si(solid)+Si O(gas)+CO(gas)
– 98% pure
• Si(solid)+3HCl(gas)→SiHCl3( gas)+H2(gas) • SiHCl3(gas)+H2(gas)→Si(solid )+3HCl(gas)
– Polycrystalline silicon
• Body centered cubic
– Additional an atom at the center – Each atom has eight nearestneighbor atoms – Sodium, tungsten
• Face-centered cubic
– Additional an atom at each face – Each atom has 12 nearestneighbor atoms – Aluminum, copper, gold and platinum
– Zincblende lattice
• One fcc sublattice fas column III atoms and the other has column V atoms
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Example 2
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– A unit cell of a diamond lattice consists of a tetrahedron
• Each atom is surrounded by four equidistant nearest neighbors
• III-V compound semiconductor
Wen Chang Huang chapter 2 20
Isolated silicon atom
• Has 14 electrons
– 10 electrons occupy deeplying energy level – The four remaining valence electron
• • • • • • • Semiconductor materials Basic crystal structure Basic crystal growth technique Valence bands Energy bands Intrinsic carrier concentration Donors and acceptors
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Example 3
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Miller indices, some other convention
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Basic crystal growth technique
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Unit cell
• R=na+nb+pc • R: lattice point
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Basic cubic-unit cells
• Simple cubic
– Has an atom at each corner – Each atom has six equidistant nearest-neighbor atoms – Lattice constant: a – Polonium 釙
• As N isolated atoms are brought together to form a solid
– N separate but closely spaced level are formed – As N is large continuous band of energy – The parameter a: the equilibrium interatomic distance of the crystal
Chapter 2
Energy bands and carrier concentration in thermal equilibrium
Wen Chang Huang chapter 2 1
Energy bands and carrier concentration in thermal equilibrium
Conduction electron and hole
• At low temperature
– Not available for conduction
• At higher temperature
– Thermal vibrations break the covalent bonds a free electron results participle in current conduction – A electron deficiency is left in the covalent bond
• Weakly bound • Involved in chemical reactions • The 3s sushell has two allowed quantum states per atom
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Simple cubic
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FCC
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example1
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The diamond structures
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Crystal planes and miller indices
• The crystal properties along different planes are different • The electrical and other device characteristics can be dependent on the crystal orientation • Miller indices
• Lattice
– The periodic arrangement of atoms in a crystal – In a crystal, an atom never strays far from a single, fixed position
• Unit cell
– Is representative of the entire lattice
4 2 2 2 2
– The discrete energy level
• Consider two identical atoms
– Far apart
• Both atoms have the same energy
– Brought closer
• The doubly degenerate energy levels will spilt into two level by the interaction between the atoms