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. This will be in exchange for lecture slot in May that will be used 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 2007 Lecture 1-2 Key questions • What makes semiconductors so special? • How do electrons arrange themselves (in energy) in an electronic system? • What is the formal definition of thermal equilibrium? What are some 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 2007 Lecture 1-3 1. Semiconductors as solids � Semiconductors are crystalline solids Crystalline 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−3 Semiconductors held together by covalent bonding 4 valence elec-⇒trons shared with 4 neighbours low energy situation. ⇒IIIA IVA VA VIA IIB B 5 C 6 N 7 O 8 Al 13 Si 14 P 15 S 16 30 31 32 33 34 Zn Ga Ge As Se 48 49 50 51 52 Cd In Sn Sb Te 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 1-4 � Solid is electronic system with periodic potential Fundamental result of solid-state physics: quantum states cluster in bands leaving bandgaps (regions without allowed states) in between. E 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 1-5 � Electronic structure of semiconductors There are many more quantum states than electrons in a solid. Quantum states filled with one electron per state starting from lowest energy state (Pauli exclusion principle). Different solids have different band structures. At 0 K: Eg WM Eg � Eo Eo Eo Eg=0 a) metal b) insulator c) semiconductor Distinct feature of semiconductors: At 0 K, filling ends up with full band separated by 1− 3 eV bandgap from 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 2007 Lecture 1-6 Why is this significant? Eg WM Eg � Eo Eo Eo Eg=0 a) metal b) insulator c) semiconductor No conduction is p ossible 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 a function of energy and temp erature? 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 2. Electron statistics At finite temperature, state occupation probability by electron de termined by Fermi-Dirac distribution function: EF --Ferrni energg -energy for which occupation probability is 50% k -Boltxrnann constant = 8.62x lop5 eV/K kT -thermal energy = 25.9meV 0300 K Maxwell-Boltzmann Cite 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 2007 Properties of Fermi-Dirac distribution function: -10 -8 -6 -4 -2 0 2 4 6 8 10 (E-EF)I~T(no units) for E << EF:f (E)-Y I for E >> EF:f(E)-0 width of transition around EF r" 3kT (20% criterium) symmetry: f (EF+ El) = I -f (EF-El) Maxwell-Boltzmann approximation: For E -EF >> kT: E-EF f (E)r" exp -kT For E -EF << kT: E-EF f (E)-Y I -exp kT Cite 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 2007 Lecture 1-9 Temperature dependence of Fermi-Dirac distribution function: 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 f(E) T=1000 K 300 1001 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 E-EF (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 2007 Lecture 1-10 3. Thermal equilibrium A 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 zero hυ δ<θ> δt =0 Thermal equilibrium important because all systems evolve towards TE after having been perturbed. In order to know how a system evolves, it is essential to know where it is going. Cite as: Jesús del