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Lecture 2

Lecture 2. OUTLINE Semiconductor Fundamentals (cont’d) Energy band model Band gap energy Density of states Doping Reading : Pierret 2.2-2.3, 3.1.5; Hu 1.3-1.4,1.6, 2.4. Potential Energy Profiles. 2 atoms. 1 atom. Discrete allowed energy levels.

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Lecture 2

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  1. Lecture 2 OUTLINE • Semiconductor Fundamentals (cont’d) • Energy band model • Band gap energy • Density of states • Doping Reading: Pierret 2.2-2.3, 3.1.5; Hu 1.3-1.4,1.6, 2.4

  2. Potential Energy Profiles 2 atoms 1 atom Discrete allowed energy levels V(r)1/ris mostly a coulombic potential btwn the positive nucleus & negative electrons. When two atoms are in close proximity, the upper energy levels are shifted to bonding and anti-bonding levels. N atoms many bonding/anti-bonding levels EE130/230A Fall 2013 Lecture 2, Slide 2

  3. Si: From Atom to Crystal • The highest nearly-filled band is the valence band • The lowest nearly-empty band is the conduction band R.F. Pierret, Semiconductor Fundamentals, Figure 2.5 Energy states in Si atom  energy bands in Si crystal EE130/230A Fall 2013 Lecture 2, Slide 3

  4. Energy Band Diagram • Simplified version of energy band model, showing only the bottom edge of the conduction band (Ec) and the top edge of the valence band (Ev) • Ec and Ev are separated by the band gap energy EG Ec electron energy Ev distance EE130/230A Fall 2013 Lecture 2, Slide 4

  5. Electrons and Holes (Band Model) • Conduction electron = occupied state in the conduction band • Hole = empty state in the valence band • Electrons &holes tend to seek lowest-energy positions  Electrons tend to fall and holes tend to float up (like bubbles in water) electron kinetic energy Ec represents the electron potential energy. Ec Increasing electron energy Increasing hole energy Ev hole kinetic energy EE130/230A Fall 2013 Lecture 2, Slide 5

  6. Electrostatic Potential, Vand Electric Field, E • The potential energy of a particle with charge -q is related to the electrostatic potential V(x): • Variation of Ec with position is called “band bending.” 0.7 eV EE130/230A Fall 2013 Lecture 2, Slide 6

  7. Measuring the Band Gap Energy • EG can be determined from the minimum energy of photons that are absorbed by the semiconductor Ec photon hn > EG Ev Band gap energies of selected semiconductors EE130/230A Fall 2013 Lecture 2, Slide 7

  8. Density of States E dE Ec Ec density of states, g(E) Ev Ev g(E)dE = number of states per cm3 in the energy range between E and E+dE Near the band edges: Electron and hole density-of-states effective masses for E Ec for EEv EE130/230A Fall 2013 Lecture 2, Slide 8

  9. Effective Mass, m* • When an electron is moving inside a solid material, the potential field will affect its movement. • For low kinetic energy where p is the crystal momentum i.e. a conduction electron behaves as a particle but with an effective mass m* Schrödinger equation: E : total energy Y: wave function ħ : reduced Planck constant EE130/230A Fall 2013 Lecture 2, Slide 9

  10. EG and Material Classification silicon dioxide silicon metal • Neither filled bands nor empty bands allow current flow • Insulators have large EG • Semiconductors have small EG • Metals have no band gap (conduction band is partially filled) Ec Ec Ev EG = 1.12 eV EG = ~ 9 eV Ev Ec Ev EE130/230A Fall 2013 Lecture 2, Slide 10

  11. Donors: P, As, Sb Acceptors: B, Al, Ga, In Doping • By substituting a Si atom with a special impurity atom (Column V or Column III element), a conduction electron or hole is created. ND ≡ ionized donor concentration (cm-3) NA ≡ ionized acceptor concentration (cm-3) http://inventors.about.com/library/inventors/blsolar5.htm EE130/230A Fall 2013 Lecture 2, Slide 11

  12. Doping Silicon with a Donor Example: Add arsenic (As) atom to the Si crystal Si Si Si Si As Si Si Si Si The loosely bound 5th valence electron of the As atom “breaks free” and becomes a mobile electron for current conduction. EE130/230A Fall 2013 Lecture 2, Slide 12

  13. Doping Silicon with an Acceptor Example: Add boron (B) atom to the Si crystal Si Si Si Si B Si Si Si Si The B atom accepts an electron from a neighboring Si atom, resulting in a missing bonding electron, or “hole”. The hole is free to roam around the Si lattice, carrying current as a positive charge. EE130/230A Fall 2013 Lecture 2, Slide 13

  14. Solid Solubility of Dopants in Si F. A. Trumbore, Bell Systems Technical Journal, 1960 Atoms per cubic centimeter EE130/230A Fall 2013 Lecture 2, Slide 14

  15. Doping (Band Model) Donor ionization energy Ec ED EA Ev Acceptor ionization energy Ionization energy of selected donors and acceptors in silicon EE130/230A Fall 2013 Lecture 2, Slide 15

  16. Dopant Ionization R.F. Pierret, Semiconductor Fundamentals, Figure 2.13 EE130/230A Fall 2013 Lecture 2, Slide 16

  17. Charge-Carrier Concentrations Charge neutrality condition: ND + p = NA + n At thermal equilibrium, np = ni2 (“Law of Mass Action”) Note: Carrier concentrations depend on net dopant concentration! EE130/230A Fall 2013 Lecture 2, Slide 17

  18. n-type Material (n > p) ND > NA(more specifically, ND – NA >> ni): EE130/230A Fall 2013 Lecture 2, Slide 18

  19. p-type Material (p > n) NA > ND(more specifically, NA – ND >> ni): EE130/230A Fall 2013 Lecture 2, Slide 19

  20. Carrier Concentration vs. Temperature R.F. Pierret, Semiconductor Fundamentals, Figure 2.22 EE130/230A Fall 2013 Lecture 2, Slide 20

  21. Terminology donor: impurity atom that increases n acceptor: impurity atom that increases p n-type material: contains more electrons than holes p-type material: contains more holes than electrons majority carrier: the most abundant carrier minority carrier: the least abundant carrier intrinsic semiconductor: n = p = ni extrinsic semiconductor: doped semiconductor such that majority carrier concentration = net dopant concentration EE130/230A Fall 2013 Lecture 2, Slide 21

  22. Summary • Allowed electron energy levels in an atom give rise to bands of allowed electron energy levels in a crystal. • The valence band is the highest nearly-filled band. • The conduction band is the lowest nearly-empty band. • The band gap energy is the energy required to free an electron from a covalent bond. • EG for Si at 300 K = 1.12 eV • Insulators have large EG; semiconductors have small EG EE130/230A Fall 2013 Lecture 2, Slide 22

  23. Summary (cont’d) • Ec represents the electron potential energy Variation in Ec(x)  variation in electric potential V Electric field • E - Ec represents the electron kinetic energy EE130/230A Fall 2013 Lecture 2, Slide 23

  24. Summary (cont’d) • Dopants in silicon: • Reside on lattice sites (substituting for Si) • Have relatively low ionization energies (<50 meV)  ionized at room temperature • Group-V elements contribute conduction electrons, and are called donors • Group-III elements contribute holes, and are called acceptors Dopant concentrations typically range from 1015 cm-3 to 1020 cm-3 EE130/230A Fall 2013 Lecture 2, Slide 24

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