EE105 Fall 2006 Microelectronic Devices and Circuits Prof Jan M Rabaey jan eecs Lecture 2 Semiconductor Basics Your EECS105 Week Mo Tu We Lab 353 Cory Lab 353 Cory Th Fr 9am 10am Lab 353 Cory 11am Discussion 293 Cory 12pm Office Hour Ryan Roberts 1pm 2pm Discussion 293 Cory Office Hour Nate Pletcher 3pm Discussion 293 Cory 4pm Office Hour Gerald Wang Lecture 203 McLaughlin Office Hours Prof Rabaey 511 Cory Office Hour Asako Toda Lecture 203 McLaughlin Lab 353 Cory 5pm 6pm 2 1 This week Discussion sessions and office hours starting this week Discussions 293 Cory Office Hours TAs 477 Cory Labs 353 Cory Make up Lecture Friday September 8 3 30 5pm 203 McLaughlin 3 At a glance Last class Intro and some recap of circuit analysis Today Review of Semiconductor Basics 4 2 Periodic Table of Elements 5 Electronic Properties of Silicon Silicon is in Group IV atomic number 14 Atom electronic structure 1s22s22p63s23p2 Crystal electronic structure 1s22s22p63 sp 4 Diamond lattice with 0 235 nm bond length Very poor conductor at room temperature why 1s 2 2s 2 2p 6 3sp 4 Hybridized State 6 3 The Diamond Structure 3sp tetrahedral bond o 2 35 A o 5 43 A 7 Energy States of an Atom E3 E2 Allowed Energy Levels Forbidden Band Gap E1 Atomic Spacing Lattice Constant Quantum Mechanics The allowed energy levels for an atom are discrete 2 electrons with opposite spin can occupy a state When atoms are brought into close contact these energy levels split If there are a large number of atoms the discrete energy levels form a continuous band 8 4 Energy Band Diagram The gap between the conduction and valence band determines the conductive properties of the material Metal Conduction Band negligible band gap or overlap Valence Band Conduction Band Insulator band gap large band gap 8 eV Valence Band Semiconductor e medium sized gap 1 eV e Electrons can gain energy from lattice phonon or photon to become free 9 Model for Good Conductor The atoms are all ionized and a sea of electrons can wander about crystal The electrons are the glue that holds the solid together Since they are free they respond to applied fields and give rise to conductions On time scale of electrons lattice looks stationary 10 5 Bond Model for Silicon T 0K Silicon Ion 4 q 2 electrons in each bond Four Valence Electrons Contributed by each ion 4 q 11 Bond Model for Silicon T 0K Some bond are broken free electron Leave behind a positive ion or trap a hole 12 6 Holes Notice that the vacancy hole left behind can be filled by a neighboring electron It looks like there is a positive charge traveling around Treat holes as legitimate particles 13 More About Holes When a conduction band electron encounters a hole the process is called recombination The electron and hole annihilate one another thus depleting the supply of carriers In thermal equilibrium a generation process counterbalances to produce a steady stream of carriers 14 7 Thermal Equilibrium Pure Si Balance between generation and recombination determines no po Strong function of temperature T 300 oK G Gth T Gopt R k n p G R k n p Gth T n p Gth T k ni T 2 Mass action law ni T 1010 cm 3 at 300 K 15 Doping with Group V Elements P As group 5 extra bonding electron lost to crystal at room temperature Immobile Charge Left Behind 16 8 Donor Accounting Each ionized donor will contribute an extra free electron The material is charge neutral so the total charge concentration must sum to zero qn0 qp0 qN d 0 Free Electrons Free Holes Ions Immobile n p ni T 2 By Mass Action Law ni2 qn0 q qN d 0 n0 qn02 qni2 qN d n0 0 17 Donor Accounting cont n02 N d n0 ni2 0 Solve quadratic n0 N d N d2 4ni2 2 Only positive root is physically valid n0 N d N d2 4ni2 2 For most practical situations N d ni 2 n N d N d 1 4 i N N N n0 d d Nd 2 2 2 18 9 Doping with Group III Elements Boron 3 bonding electrons one bond is unsaturated Only free hole negative ion is immobile 19 Mass Action Law Balance between generation and recombination po no ni N type case P type case 2 T 300 K ni 1010 cm 3 n0 N d N d p0 N a N a p0 ni2 Nd n0 ni2 Na 20 10 Compensation Dope with both donors and acceptors Create free electron and hole 21 Compensation cont More donors than acceptors Nd Na no N d N a ni po n i2 Nd Na More acceptors than donors Na Nd po N a N d ni no n 2i Na Nd 22 11 Disturbing the Equilibrium Rapid random motion of holes and electrons at thermal velocity vth 107 cm s with collisions every c 10 13 s 2 1 1 2 mn vth 2 kT Apply an electric field E and charge carriers accelerate for c seconds vth c zero E field 107 cm s 10 13 s 10 6 cm mean free path 10 nm v th positive E a c hole case vth x 23 Drift Velocity and Mobility For holes F qE c q c E vdr a c e c m m m p p p vdr p E For electrons F vdr a c e mn qE q c c m c m n n E vdr n E 24 12 Mobility vs Doping in Silicon at 300K default values p 400 n 1000 25 Speed Limit Velocity Saturation c 3 1010 m s Thermal Velocity 10 4 V V cm V 10 4 1 4 cm cm 10 m m The field strength to cause velocity saturation may seem very large but it s only a few volts in a modern transistor 26 13 Drift Current Density Holes Hole case drift velocity is in same direction as E hole drift current density Jpdr vdp E x The hole drift current density is Jp dr q p p E 27 Drift Current Density Electrons Electron case drift velocity is in opposite direction as E electron drift current density Jndr vdn E J ndr q n n E qn n E x The electron drift current density is Jndr q n vdn units C s cm2 A cm2 J J pdr J ndr qp p qn n E 28 14 Resistivity Bulk silicon uniform doping concentration away from surfaces n type example in equilibrium no Nd When we apply an electric field n Nd J n q n nE q n N d E Conductivity n q n N d eff q n N d N a Resistivity n 1 n 1 q n N d eff cm 29 Ohm s Law I JA J tW t W E t W R V tW V V L L R 1 L L tW t W 30 15 Sheet Resistance Rs IC resistors have a specified thickness not …
View Full Document
Unlocking...