Lecture6

Lecture6 - ECE 124A VLSI Principles Lecture 6 Prof Kaustav Banerjee Electrical and Computer Engineering University of California Santa Barbara

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Lecture 6, ECE 124A, VLSI Principles Kaustav Banerjee ECE 124A VLSI Principles Lecture 6 Prof. Kaustav Banerjee Electrical and Computer Engineering University of California, Santa Barbara E-mail: [email protected]
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Lecture 6, ECE 124A, VLSI Principles Kaustav Banerjee Semiconductors/Metals/Insulators Energy band diagrams – metal/semi/insulator Fermi level E F Intrinsic semiconductors n 0 = p 0 Intrinsic Fermi level E i ~ ½ (E V + E C ) Extrinsic Semiconductors – Doping n-doped semi: Donor Levels p-doped semi: Acceptor Levels Current in Semiconductors
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Lecture 6, ECE 124A, VLSI Principles Kaustav Banerjee Bond Model Completed or broken electronic bonds…used to describe behavior of electrons and holes Consider the diamond-type crystal lattice (for Si and Ge)
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Lecture 6, ECE 124A, VLSI Principles Kaustav Banerjee Each atom has covalent bonds with its four nearest neighbors Two tightly bound electrons associated with each bond ---one from each atom At absolute zero temperature, all electrons are held in these bonds, none are free to move At higher temperatures, thermal energy breaks some of the bonds and creates nearly free electrons Bond Model…for Si
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Lecture 6, ECE 124A, VLSI Principles Kaustav Banerjee Band Model of Solids An electron acted on by the Coulomb potential of an atomic nucleus can have only certain allowed states below a reference energy taken as E = 0 2 2 2 0 4 0 2 8 n h q m Z E n E n E 3 E 2 E 1 E = 0 Pauli Exclusion Principle (PEP) : at most 2 electrons (of opposite spins) can occupy an energy level
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Lecture 6, ECE 124A, VLSI Principles Kaustav Banerjee Band Model of Solids Now consider the electron in the highest occupied energy level ( E n ) when two atoms are separated by a large distance , electron associated with each atom has energy E n If the atoms approach one another , atomic core of first atom exerts a force on the second electron, changing the potential that determines the energy levels of the electron All allowed energy levels for the electron are consequently modified …. Considering PEP for the two-atom system: an energy level E n can contain at most 2 electrons ----so when two atoms are brought close together--- need to find distinct energy levels for the 4 electrons ! Energy level E n of the isolated atom must split into two with slightly differing energies to accommodate the 4 electrons If N atoms are brought together, E n will split into N different levels …forming an energy BAND ….that can contain at most 2N electrons
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Lecture 6, ECE 124A, VLSI Principles Kaustav Banerjee Band Model of Solids (Cont’d) Number of atoms in a crystal is large : of the order of 10 22 atoms/cm -3 and the total extent of the energy band is of the order of a few electron volts (eV) Hence, separation between the N different energy levels within a band is much smaller than the thermal energy (kT/q = ~1/40 eV) possessed by an electron at room temperature----therefore the
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This note was uploaded on 11/28/2011 for the course ECE 124A taught by Professor Benerjee during the Fall '08 term at UCSB.

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Lecture6 - ECE 124A VLSI Principles Lecture 6 Prof Kaustav Banerjee Electrical and Computer Engineering University of California Santa Barbara

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