Lecture6

Lecture6 - ECE ECE 124A VLSI Principles Lecture 6 Tutorial...

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CE 124A ECE 124A LSI Principles VLSI Principles ecture 6 Lecture 6 Tutorial on Basic Solid-State and Semiconductor Physics Prof. Kaustav Banerjee lectrical and Computer Engineering Electrical and Computer Engineering E-mail: kaustav@ece.ucsb.edu Lecture 6, ECE 124A, VLSI Principles Kaustav Banerjee
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reviously on 124A Previously on 124A • Switch level modeling of NMOS and PMOS • Using this model to build simple gates – NAND/NOR eneral Boolean F nctions – General Boolean Functions – Latches – Flip-Flops p p • Basics of Semiconductor Device Fabrication • IC Testing, Packaging and Assembly • Process Variations • Emerging Devices Lecture 6, ECE 124A, VLSI Principles Kaustav Banerjee
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Next Few Slides • Energy band diagrams – metal/semi/insulator ermi level E • Fermi level E F • Intrinsic semiconductors – n 0 = p 0 – Intrinsic Fermi level E i ~ ½ (E V + E C ) xtrinsic Semiconductors oping • Extrinsic Semiconductors – Doping – n-doped semi: Donor Levels - oped semi: Acceptor Levels p doped semi: Acceptor Levels • Carrier Concentration Equations Lecture 6, ECE 124A, VLSI Principles Kaustav Banerjee
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and Model of Solids 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 = 0 E 2 E Pauli Exclusion Principle (PEP) : at most 2 electrons (of opposite spins) Lecture 6, ECE 124A, VLSI Principles Kaustav Banerjee 1 can occupy an energy level
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and Model of Solids Band Model of Solids Now consider the electron in the highest occupied energy level – 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 ,g g p that determines the energy levels of the electron – All allowed energy levels for the electron are consequently modified…. onsidering PEP for the two- tom system: an energy level E 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 of the isolated atom must split into two with n 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 Lecture 6, ECE 124A, VLSI Principles Kaustav Banerjee
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and Model of Solids (Cont’d) Band Model of Solids (Cont d) Number of atoms in a crystal is large: of the order of 10 22 toms/cm - nd the total extent of the energy band is of the order 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 and is much smaller than the thermal energy (kT/q = ~1/40 eV) band is much smaller than the thermal energy (kT/q = ~1/40 eV)
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This note was uploaded on 12/04/2010 for the course ECE 134 taught by Professor York during the Fall '08 term at UCSB.

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Lecture6 - ECE ECE 124A VLSI Principles Lecture 6 Tutorial...

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