EECS 105 Fall 2003 Lecture 6 Lecture 6 Integrated Circuit Resistors Prof Niknejad Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 6 Prof A Niknejad Lecture Outline z z z z z z z z z z Department of EECS Semiconductors Si Diamond Structure Bond Model Intrinsic Carrier Concentration Doping by Ion Implantation Drift Velocity Saturation IC Process Flow Resistor Layout Diffusion University of California Berkeley EECS 105 Fall 2003 Lecture 6 Prof A Niknejad Resistivity for a Few Materials z z z z z z Pure copper 273K Pure copper 373 K Pure germanium 273 K Pure germanium 500 K Pure water 291 K Seawater 1 56 10 6 ohm cm 2 24 10 6 ohm cm 200 ohm cm 12 ohm cm 2 5 107 ohm cm 25 ohm cm What gives rise to this enormous range Why are some materials semi conductive Why the strong temp dependence Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 6 Prof A Niknejad Electronic Properties of Silicon z Silicon is in Group IV z 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 Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 6 Prof A Niknejad Periodic Table of Elements Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 6 Prof A Niknejad The Diamond Structure 3sp tetrahedral bond o 2 35 A o 5 43 A Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 6 Prof A Niknejad States of an Atom Energy E3 E2 Forbidden Band Gap E1 z z z Allowed Energy Levels Atomic Spacing Lattice Constant Quantum Mechanics The allowed energy levels for an atom are discrete 2 electrons can occupy a state since with opposite spin 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 Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 6 Prof A Niknejad Energy Band Diagram z z 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 z Insulator large band gap 8 eV band gap Valence Band z Semiconductor medium sized gap 1 eV Electrons can gain energy from lattice phonon or photon to become free Department of EECS eeUniversity of California Berkeley EECS 105 Fall 2003 Lecture 6 Prof A Niknejad Model for Good Conductor z z z 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 Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 6 Prof A Niknejad Bond Model for Silicon T 0K Silicon Ion 4 q Four Valence Electrons Contributed by each ion 4 q Department of EECS 2 electrons in each bond University of California Berkeley EECS 105 Fall 2003 Lecture 6 Prof A Niknejad Bond Model for Silicon T 0K z z Some bond are broken free electron Leave behind a positive ion or trap a hole Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 6 Prof A Niknejad Holes z z z 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 Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 6 Prof A Niknejad Yes Holes z z z z The hole represents the void after a bond is broken Since it is energetically favorable for nearby electrons to fill this void the hole is quickly filled But this leaves a new void since it is more likely that a valence band electron fills the void much larger density that conduction band electrons The net motion of many electrons in the valence band can be equivalently represented as the motion of a hole J vb q vi vb J vb Filled Band q v i Empty States q v i Empty States Department of EECS q vi qv i Empty States University of California Berkeley EECS 105 Fall 2003 Lecture 6 Prof A Niknejad More About Holes z z z 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 Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 6 Prof A Niknejad Thermal Equilibrium Pure Si z z 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 2 n p Gth T k ni T ni T 1010 cm 3 at 300 K Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 6 Prof A Niknejad Doping with Group V Elements z P As group 5 extra bonding electron lost to crystal at room temperature Immobile Charge Left Behind Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 6 Prof A Niknejad Donor Accounting z z 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 z Free Holes Ions Immobile 2 By Mass Action Law n p ni T ni2 qn0 q qN d 0 n0 qn02 qni2 qN d n0 0 Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 6 Prof A Niknejad Donor Accounting cont z Solve quadratic n02 N d n0 ni2 0 N d N d2 4ni2 n0 2 z Only positive root is physically valid N d N d2 4ni2 n0 2 z For most practical situations N d ni 2 Nd Nd n0 Department of EECS ni 1 4 Nd Nd N Nd 2 2 2 University of California Berkeley EECS 105 Fall 2003 Lecture 6 Prof A Niknejad Doping with Group III Elements z z Boron 3 bonding electrons one bond is unsaturated Only free hole negative ion is immobile Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 6 Prof A Niknejad Mass Action Law z Balance between generation and recombination po no ni N type case 2 T 300 K ni 1010 cm 3 d n0 N N d P type case p0 N a N a Department of EECS ni2 n0 Nd ni2 p0 Na University of California Berkeley EECS 105 Fall 2003 Lecture 6 Prof A Niknejad Compensation z Dope with both donors and acceptors Create free electron and hole Department of EECS University of California Berkeley EECS
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