lecture3

# lecture3 - 6.720J/3.43J Integrated Microelectronic Devices...

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Unformatted text preview: 6.720J/3.43J- Integrated Microelectronic Devices- Spring 2007 Lecture 3-1 Lecture 3- Carrier Statistics in Equilibrium (cont.) February 9, 2007 Contents: 1. Equilibrium electron concentration 2. Equilibrium hole concentration 3. np product in equilibrium 4. Location of Fermi level Reading assignment: del Alamo, Ch. 2, §§ 2.4-2.6 Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.720J/3.43J- Integrated Microelectronic Devices- Spring 2007 Lecture 3-2 Key questions • How many electrons and holes are there in thermal equilibrium in a given semiconductor? • How does the equilibrium electron (hole) distribution in the con- duction (valence) band look like? • How can one compute n i ? • Where is the Fermi level in a given semiconductor? How does its location depend on doping level? Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.720J/3.43J- Integrated Microelectronic Devices- Spring 2007 Lecture 3-3 Carrier statistics in equilibrium Question: how many electrons and holes are there in TE in a given semiconductor? Answer: rigorous model exploiting energy view of semiconductors and concept of Fermi level. Strategy to answer question: 1. derive relationship between n o and E F 2. derive relationship between p o and E F 3. derive expressions for n o p o and n i 4. figure out location of E F from additional arguments (such as charge neutrality) Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.720J/3.43J- Integrated Microelectronic Devices- Spring 2007 Lecture 3-4 1. Equilibrium electron concentration • Q: How many electrons are there in a semiconductor in TE? A: It depends on location of E F . • Why? Because E F defines probability that states are occupied by electrons. • The closer E F is to the conduction band edge, the more electrons there are in the conduction band. E E c E F n o (E) f(E) g c (E-E c ) E c E • If E F is not too close to the conduction band edge, what is the relationship between the location of E F and n o ? E F − E c n o ∝ exp kT Because high energy tail of Fermi-Dirac distribution function is ex- ponential with kT as characteristics energy. Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007....
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lecture3 - 6.720J/3.43J Integrated Microelectronic Devices...

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