6.720J/3.43J - Integrated Microelectronic Devices - Spring Lecture
6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007Lecture 1-1Lecture 1 - Electronic structure ofsemiconductorsFebruary 7, 2007Contents:1. Electronic structure of semiconductors2. Electron statistics3. Thermal equilibriumReading assignment:del Alamo, Ch. 1Announcements:Tomorrow’s recitation slot will be used as lecture. Thiswill be in exchange for lecture slot in May that will beused as recitation.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 2007Lecture 1-2Key questions What makes semiconductors so special? How do electrons arrange themselves (in energy) in an electronicsystem? What is the formal definition of thermal equilibrium? What aresome of its consequences?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 2007Lecture 1-31. Semiconductors as solids Semiconductors are crystalline solidsCrystalline solid elemental atomic arrangement, or unit cell, re peated ad infinitum in space in three dimensions. Si lattice constant: 0.54 nm Si atomic spacing: 0.24 nm Si atomic density: 5.0 1022 cm 3Semiconductors held together by covalent bonding 4 valence elec trons shared with 4 neighbours low energy 87S3334Zn Ga Ge As Se48Cd49In505152Sn Sb TeCite 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 2007Lecture 1-4 Solid is electronic system with periodic potentialFundamental result of solid-state physics: quantum states cluster inbands leaving bandgaps (regions without allowed states) in between.ECite 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 2007Lecture 1-5 Electronic structure of semiconductorsThere are many more quantum states than electrons in a solid.Quantum states filled with one electron per state starting from lowestenergy state (Pauli exclusion principle).Different solids have different band structures. At 0 K:EoEoEoWMEg 0Ega) metalb) insulatorEg c) semiconductorDistinct feature of semiconductors:At 0 K, filling ends up with full band separated by 1 3 eV bandgapfrom next empty band.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 2007Lecture 1-6Why is this significant?EoEoEoWMEg 0Ega) metalb) insulatorEg c) semiconductorNo conduction is possible in a full band insulators and semicon ductors do not conduct at 0 K.Conduction requires a partially filled band metals conduct at 0 K.But in semiconductors at finite temperatures, some electrons popu late next band above bandgap conduction becomes possible.What is the law that regulates electron ocupation of states as afunction of energy and temperature?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 20072. Electron statisticsAt finite temperature, state occupation probability by electron d etermined by Fermi-Dirac distribution function:EF---- Ferrni energgkenergy for which occupation probability is 50%Boltxrnann constantkTthermal energy 8.62xlop5 e V / K25.9 m e V 0 300 KMaxwell-BoltzmannCite as: leslis del Alamo, course materials for 6.7201 Integrated Microelectronic Devices, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month W].
6.720J/3.43J-Integrated Microelectronic Devices-Spring 2007Properties of Fermi-Dirac distribution function:-10-8-6-4-20246810(E-EF)I T(no units)for E EF: f (E) -Y Ifor E EF: f ( E )- 0width of transition around EF r" 3 k T (20% criterium) symmetry: f (EF El) I-f (EF- El)Maxwell-Boltzmann approximation:For E - EF k T :f (E)r" exp -E-EFkTFor E - EF k T :f (E) -Y I-expE-EFkTCite as: leslis del Alamo, course materials for 6.7201 Integrated Microelectronic Devices, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month W].
6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007Lecture 1-9Temperature dependence of Fermi-Dirac distribution function:10.90.80.7f(E)0.60.50.4T 1000 F (eV)In general, EF function of T.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 2007Lecture 1-103. Thermal equilibriumA particle system is in thermal equilibrium if: it is closed: no energy flow through boundaries of system it is in steady-state: time derivatives of all ensemble averages(global and local) are zerohυδ θ 0δtThermal equilibrium important because all systems evolve towardsTE after having been perturbed.In order to know how a system evolves, it is essential to know whereit is going.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 2007Lecture 1-11 In thermal equilibrium, EF constant throughout systemhigh energy states occupiedlow energy states emptyEFEFCite 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 2007Lecture 1-12Key conclusions In solids, electron states cluster in bands separated by bandgaps. Distinct feature of semiconductors: at 0 K, quantum state fillingends up with full band separated from next empty band by 1 3 eV bandgap at around 300 K, some electrons populate nextband above bandgap. Occupation probability of quantum systems in thermal equilib rium governed by Fermi-Dirac distribution function:f (E) 11 exp E kTEF System in thermal equilibrium: isolated from outside world in steady state. In thermal equilibrium, EF is independent of position. Order of magnitude of key parameters:– atomic density of Si: NSi 5 1022 cm 3– bandgap of Si: Eg 1 eV– thermal energy: kT 26 meV @ 300KCite 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 2007Lecture 1-13Self-study Concept of blackbody radiation. Concept of vacuum energy. Concept of density of states. Understand how can the Fermi energy change with temperature. Maxwell-Boltzmann distribution function.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 1-1 Lecture 1 - Electronic structure of semiconductors February 7, 2007 Contents: 1. Electronic structure of semiconductors 2. Electron statistics 3. Thermal equilibrium Reading assignment: del Alamo, Ch. 1 Announcements: Tomorrow's recitation slot will be used as lecture .
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