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by: Daron Kemmer IV


Daron Kemmer IV
GPA 3.63


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Class Notes
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This 4 page Class Notes was uploaded by Daron Kemmer IV on Thursday October 22, 2015. The Class Notes belongs to SPAN 100 at University of California Santa Barbara taught by Staff in Fall. Since its upload, it has received 23 views. For similar materials see /class/226850/span-100-university-of-california-santa-barbara in Spanish at University of California Santa Barbara.




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Date Created: 10/22/15
Materials 100A Class 11 Electrical Properties etc Ram Seshadri MRL 2031 x6129 seshadri mrliucsbiedu httpwwwimrliucsbleduNseshadriteachihtml This class tries to follow the twelfth chapter of Callister A little more on defects Grain Boundaries ln polycrystalline materials crystals are separated by grain boundaries that are typically several atomic layers wider One way of considering grain boundaries is to cut a crystal into two and then stick it back but not precisely along the same atomic rows along which it was cut The boundary so formed is a grain boundary One then considers whether it is a lowangle or highangle grain boundary depending on the angle by which the two new crystals are mismatchedi High angle grain boundaries are usually higher in energy less stable tool SUCK n Iogeiher om Ihe orysial o gram boundary Twin Boundaries or Twin Planes ln twin boundaries the atoms on the two sides of the boundary are symmetryrelated and can usually be considered as having been re ected by a mirror 000000 000000 000000 000000 twin plane Electrical resistance and Ohm39s Law if an electric current I units of A Ampere ows through a conductor with resistance R then the potential difference across the ends of the conductor V unit V Volts is given by Ohmls law V R or R K I and the units of resistance are 9 Ohms The resistance of a material is directly proportional to its length l and inversely proportional to the crosssectional area Al The proportionality constant is called the resistivity or the speci c resistance p and Materials 100A Class 11 Electrical Properties etc l R 7 3 A The unit of p are 9m though 9cm is also commonly used p is an important materialdependent property that is usually a function of temperature The value of p at room temperature is indicative of whether something is a metal p is of the order of 10 6 Qm or less an insulator p is of the order of 106 Qm or more Materials that are somewhere inbetween are called semiconductors The electrical conductivity 0 is the inverse of the electrical resistivity pi Usually the latter is used Never mix the two up l To add to the confusion the unit 9 1 has a name It is called S Siemeni Avoid its use l1 Measuring the resistance Usually the fourprobe technique is employed as depicted belowi M46 The resistance is measured using R VI and the resistivity is then obtained from a knowledge of A and ll Energy bands We have already introduced the H2 molecule and the notion that electrons are shared between atoms These electrons form bonding and antibonding energy levels In a crystal with typically Avogadro number of atoms the energy levels are smeared out into what are known as bands In the simplest picture in a covalent solid such as C diamond or Si Avogadro number of bonding levels form the valence band which is lled with electrons and Avogadro number of antibonding levels form the conduction band which is empty 1As William of Okham 1288 7 1347 pithin stated Pluralims non est ponenda sine necessitate Materials 100A Class 11 Electrical Properties etc SOlld molecule 7 gt cinductlon 9 D 7 C 6 1 LL band gap 4 4 7 H2 1 61S valence When in a materials such as C diamond or Si an electric eld is applied if an electron goes from the left to the right in the material this is compensated by an electron that goes from the right to the left There is therefore almost no electrical conduction and the electrical resistance is very high This is a characteristic of a materials where the valence band is completely lled The only current that is carried in the material is by electrons that are energetically promoted from the valence band to the empty conduction band Such promotion is called thermal activation and this in insulators decreases the resistivity ln insulators and semiconductors the resistivity often varies with temperature in the following manner E MT r30 exp2kBgT where p0 is a constant prefactor and Eg is the electronic band gap 7 the energy separation between the top of the valence band and the bottom of the conduction band as probed by electrical transport studies A plot of logp vs lT gives a slope which is equal to EgleB Eg for semiconductors is Si lill eV Ge 067 eV GaAs 142 eV and CdS 2 40 th The schematic 77 band structures77 of these is shown the next guret Metals have 77free77 electrons This means that Insulators semiconductors and metals instead of having all bonding states lled and all antibonding states empty they can have partially lled valence or conduction bandst insulator semiconductor metal metal 2Other techniques such as spectroscopy often yield different values so it is best to specify how the band gap is measured Energy Materials 100A Class 11 Electrical Properties etc Metals are formed when there is not a simple integral relation between the number of bonds and the number of valence electrons For example Al has 3 valence electrons shared in its fcc structure with twelve neighbors It is dif cult to make a clear separation between bonding and antibonding levelsl Si on the other hand has four valence electrons and four nearneighbors in the diamond structurel Each Si has a bond with its neighbor with 2 electrons and an antibond which is correspondingly emptyl So Al is a very good metal and Si is a very good semiconductorl Carbon diamond is similar to Si in its bonding and is one of the best insulatorsl In general compounds formed from atoms with halffilled or fully filled levels will be insulating or semiconducting whereas compounds formed from atoms that have some 77free77 electrons will be metallicl Anything with a stable electronic configuration noble gas do 10 etc usually forms an insulator Electron mobility Metals have 77free77 electrons and these are usually knocking around in in a random fashion much like atoms in a gas When en electric field is applied however the electrons start transporting a current In other words there is a net ow of electrons depending on the direction of the electric field The drift velocity vd describes the average velocity of the electrons in the direction of the electric field 5 The mobility Me of the electron is then obtained from 3900 Meg The conductivity 0 can then be expressed anmw where n is the number of electrons participating in the electrical transport process and lel is the magnitude of the electronic charge Electrical resistivity of metals Different processes in a metal can scatter electrons as they travel increasing the electrical resistivity The resistivity can be written as sum corresponding to the different processes Ptocal P Pi Pd where the subscripts on the RHS correspond to temperature impurities and deformations respectively This is called Matthiessen s ruler Electrons and holes and the Hall effect Depending on whether the conduction arises from a few electrons in the conduction band or some electrons having been removed at the top of the valence band the nature of charge carriers variesl In the former case the carriers are negatively Charged In the latter case the carriers effectively have positive charge 7 it is useful to the think of the the few electrons removed from the top of the valence band as having left behind positively charged llholeslll Electrons are indicated with n and holes with p o e vs electron conduction can be distinguished by the Hall experiment where the resistance of a conductor is measured in the presence and absence of a magnetic field IIIIII a


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