The Periodic TableElectronic Bonds in SiliconHow to get conduction in Si?Doping Silicon with Donors (n-type)Doping with Acceptors (p-type)DopingSlide 1EE40 Spring 2008 Venkat AnantharamThe Periodic TableIII IV VSlide 2EE40 Spring 2008 Venkat AnantharamElectronic Bonds in Silicon2-D picture of perfect crystal of pure silicon; double line is a Si-Si bond with each line representing an electronTwo electrons in each bondSi ion(charge+4 q)Actual structure is 3-dimensional tetrahedral- just like carbon bonding in organic and inorganic materials.Very few conduction electrons: semiconductorSlide 3EE40 Spring 2008 Venkat AnantharamHow to get conduction in Si?We must either:1) Chemically modify the Si to produce free carriers (permanent) or2) Electrically “induce” them by the field effect (switchable)For the first approach controlled impurities, “dopants”, are added to Si:or(Extra electrons produce “free electrons” for conduction.)Add group V elements (5 bonding electrons vs four for Si), such as phosphorus or arsenicDeficiency of electrons results in “free holes”Add group III elements (3 bonding electrons), such as boronSlide 4EE40 Spring 2008 Venkat AnantharamDoping Silicon with Donors (n-type)Donors donate mobile electrons (and thus “n-type” silicon)Example: add arsenic (As) to the silicon crystal:Immobile (stuck) positively charged arsenic ion after 5th electron leftAsMobile electrondonated by As ionThe extra electron with As, “breaks free” and becomes a free electron for conductionSlide 5EE40 Spring 2008 Venkat AnantharamDoping with Acceptors (p-type)Group III element (boron, typically) is added to the crystal BMobile hole con-tributed by B ionand later pathImmobile (stuck) negative boron ion after accepting electron from neighboring bondThe “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.Slide 6EE40 Spring 2008 Venkat AnantharamDoping• Typical doping densities: 1016~1019cm-3• Atomic density for Si: 5 x 1022atoms/cm3 •1018cm-3is 1 in 50,000– two persons in all of Berkeley wearing green hatsSlide 7EE40 Spring 2008 Venkat AnantharamShockley’s Parking Garage Analogy for Conduction in SiTwo-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.Slide 8EE40 Spring 2008 Venkat AnantharamShockley’s Parking Garage Analogy for Conduction in SiTwo-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).Slide 9EE40 Spring 2008 Venkat AnantharamShockley’s Parking Garage Analogy for Conduction in SiTwo-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).Slide 10EE40 Spring 2008 Venkat AnantharamShockley’s Parking Garage Analogy for Conduction in SiTwo-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).Slide 11EE40 Spring 2008 Venkat AnantharamSummary of n- and p-type siliconPure 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.1Consider a sample of material of cross section A with an electric field Eapplied in the x-direction. Conduction electrons (and holes) can move underthe influence of an electric field. Electrons move in a direction opposite tothat 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. Becausethe 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 theelectric field can b e thought of as working only during the free flight of theelectrons (or holes) betwe en collisions, which is of the order of 10−13seconds.1The 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 electricfield, called the drift current. This is written asJdrn= qnµnE (1)in the case of electrons, andJdrp= qpµpEin the case of holes. Here q denotes the charge of the proton (roughly1.6 × 10−19coulombs), E the applied electric field in Volts/m, n the den-sity of conduction electrons in m−3and p the density of holes in the valenceband in m−3. µnand µpare coefficients called the mobility of electrons andthe mobility of holes respectively; these relate to the details of the scatteringprocess and are measured in m2/Volt-sec. Jdrnis the current density of elec-trons, measured in amps/m2, and likewise Jdrpis the current density of holes.The mobilities depend strongly on temperature and on the doping concen-tration; at room temperature and moderate doping levels ballpark figures are1000 cm2/Volt-sec for µnand 400 cm2/Volt-sec for µp.1The electrons (and holes) themselves move at about 105m/sec at room temperature,in a random fashion so that there is no net velocity on the average. The mean distancebetween collisions is therefore about
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