The Periodic Table III IV V EE40 Spring 2008 Slide 1 Venkat Anantharam Electronic Bonds in Silicon 2 D picture of perfect crystal of pure silicon double line is a Si Si bond with each line representing an electron Si ion charge 4 q Two electrons in each bond Actual structure is 3 dimensional tetrahedral just like carbon bonding in organic and inorganic materials Very few conduction electrons semiconductor EE40 Spring 2008 Slide 2 Venkat Anantharam How to get conduction in Si We must either 1 Chemically modify the Si to produce free carriers permanent or 2 Electrically induce them by the field effect switchable For the first approach controlled impurities dopants are added to Si Add group V elements 5 bonding electrons vs four for Si such as phosphorus or arsenic Extra electrons produce free electrons for conduction or Add group III elements 3 bonding electrons such as boron Deficiency of electrons results in free holes EE40 Spring 2008 Slide 3 Venkat Anantharam Doping Silicon with Donors n type Donors donate mobile electrons and thus n type silicon Example add arsenic As to the silicon crystal Mobile electron donated by As ion As Immobile stuck positively charged arsenic ion after 5th electron left The extra electron with As breaks free and becomes a free electron for conduction EE40 Spring 2008 Slide 4 Venkat Anantharam Doping with Acceptors p type Group III element boron typically is added to the crystal Immobile stuck negative boron ion after accepting electron from neighboring bond Mobile hole contributed by B ion and later path B The hole which is a missing bonding electron breaks free from the B acceptor and becomes a roaming positive charge free to carry current in the semiconductor It is positively charged EE40 Spring 2008 Slide 5 Venkat Anantharam Doping Typical doping densities 1016 1019 cm 3 Atomic density for Si 5 x 1022 atoms cm3 1018 cm 3 is 1 in 50 000 two persons in all of Berkeley wearing green hats EE40 Spring 2008 Slide 6 Venkat Anantharam Shockley s Parking Garage Analogy for Conduction in Si Two story parking garage on a hill If the lower floor is full and top one is empty no traffic is possible Analog of an insulator All electrons are locked up EE40 Spring 2008 Slide 7 Venkat Anantharam Shockley s Parking Garage Analogy for Conduction in Si Two story parking garage on a hill If one car is moved upstairs it can move AND THE HOLE ON THE LOWER FLOOR CAN MOVE Conduction is possible Analog to warmed up semiconductor Some electrons get free and leave holes behind EE40 Spring 2008 Slide 8 Venkat Anantharam Shockley s Parking Garage Analogy for Conduction in Si Two story parking garage on a hill If an extra car is donated to the upper floor it can move Conduction is possible Analog to N type semiconductor An electron donor is added to the crystal creating free electrons EE40 Spring 2008 Slide 9 Venkat Anantharam Shockley s Parking Garage Analogy for Conduction in Si Two story parking garage on a hill If a car is removed from the lower floor it leaves a HOLE which can move Conduction is possible Analog to P type semiconductor Acceptors are added to the crystal consuming bonding electrons creating free holes EE40 Spring 2008 Slide 10 Venkat Anantharam Summary of n and p type silicon Pure silicon is an insulator At high temperatures it conducts weakly If we add an impurity with extra electrons e g arsenic phosphorus these extra electrons are set free and we have a pretty good conductor n type silicon If we add an impurity with a deficit of electrons e g boron then bonding electrons are missing holes and the resulting holes can move around again a pretty good conductor p type silicon Now what is really interesting is when we join n type and p type silicon that is make a pn junction It has interesting electrical properties EE40 Spring 2008 Slide 11 Venkat Anantharam 1 Consider a sample of material of cross section A with an electric field E applied in the x direction Conduction electrons and holes can move under the influence of an electric field Electrons move in a direction opposite to that of the applied field while holes move in the same direction as the field In either case the resulting current is in the direction of the field Because the electrons and holes collide with and scatter off the ions in the lattice impurities and other crystal defects the force they are subject to due to the electric field can be thought of as working only during the free flight of the electrons or holes between collisions which is of the order of 10 13 seconds 1 The effect of the electric field is therefore to produce a net drift of electrons or holes which results in a current in the same direction as the electric field called the drift current This is written as Jndr qn n E 1 in the case of electrons and Jpdr qp p E in the case of holes Here q denotes the charge of the proton roughly 1 6 10 19 coulombs E the applied electric field in Volts m n the density of conduction electrons in m 3 and p the density of holes in the valence band in m 3 n and p are coefficients called the mobility of electrons and the mobility of holes respectively these relate to the details of the scattering process and are measured in m2 Volt sec Jndr is the current density of electrons measured in amps m2 and likewise Jpdr is the current density of holes The mobilities depend strongly on temperature and on the doping concentration at room temperature and moderate doping levels ballpark figures are 1000 cm2 Volt sec for n and 400 cm2 Volt sec for p 1 The electrons and holes themselves move at about 105 m sec at room temperature in a random fashion so that there is no net velocity on the average The mean distance between collisions is therefore about 10 8 m 1
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