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# Introduction to Solid State Devices EEE 3396

FIU

GPA 3.8

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This 14 page Class Notes was uploaded by Geoffrey Schneider on Monday October 12, 2015. The Class Notes belongs to EEE 3396 at Florida International University taught by Staff in Fall. Since its upload, it has received 37 views. For similar materials see /class/221800/eee-3396-florida-international-university in Electrical Engineering at Florida International University.

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Date Created: 10/12/15

Chapter 2 Atoms and Electrons NexihPaia npaia uedu ch24 What and Why We will investigate Electronic structure of atoms Interaction of atoms and electrons with excitation such as absorption and emission of light Because it would be difficult to understand how an electron is transported through seniieonduetordeviee without some knowiedge of the electron and its interaction with the crystal lattice NexihPaia npaia uedu ch27 2 Roadmap Atoms and electrons A Before we can understand electricity we have to know some thing 6 about atoms At the core of all atoms is the nucleus The nucleus NW NW contains one or more protons and may also contain neutrons TR 39 quotquot 39 Protons have a positive charged and neutrons have no charge at p mmfm all Orbiting around the nucleus is one or more electrons 3 gt Electrons have a negative charge and are vew small compared to J E quot protons and neutrons The hydrogen atom has one proton and one electron A hydrogen proton has a mass of approximately 1850 imes the mass its an electron Elements are classified by the number of protons they have This is the atomic number This is what differentiates the basic elements The atomic weight is the total number of protons and neutrons an atom contains Normally an atom has the same number of electrons as it has protons When the number of electrons equals the number of protons the atom39s total electrical charge is balanced or neutralized If the atom loses an electron it has more protons than electrons and therefore its total charge is positive If the atom gains an extra electron it contains more electrons than protons and has an overall negative electrical charge When an atom has an imbalance of electrons and protons it is said to be ionized o Nezih Pala npalafiu edu 555 3396 r w r n The electromagnetic spectrum THE ELECTROMAGNETIC SPECTRUM mummy in ID ID I m ifquot m39 m mquot mquot cm met rl l mquot m39 mquot w mquot l 39r y i l quot wA quotx m a h i c wankHulk H w Enmnmn Hum m M n equwnry lwam nu sunmll mu mp mm W m 390 mi mu m rqm Margy a m lihnlnn rlnrrmn mm H Nezih Pala npalafiu edu EEE 3396 39 quotJ 39 quot 39 ChZ 5 Visible light waves lo 10quot IO393 4x10quot7gtltl1quot Itr4 10392 I 7 IOquot Gamma X Ulu39axiolel Infrared 39 Radloumcs raw r FM Shorlwuvc 1I 4x107 5x10 7 6x107 7x10 Visible light waves are the only electromagnetic waves we can see We see these waves as the colors of the rainbow Each color has a different wavelength Red has the longest wavelength and violet has the shortest wavelength When all the waves are seen together they make white light o Nezih Pala npalafiu edu 555 3396 r m r n Scientific Method The main effort of science is to describe what happens in nature in as complete and concise a form as possible When a new physical phenomenon is obsened it is necessary to nd out how it ts into the established models and laws of physics When a set of obsenations cannot be described in terms of existing theories it is necessary to develop models which are based as far as possible on existing laws but which contain new aspects arising from the new phenomena This was what happened in early 1900s Nezih Pala npalafiu edu EEE 3396 39 quotJ 39 quot 39 ChZ 7 New observations About the turn of the century there were many experimental and natural phenomena that could not be explained by classical Newtonian mechanics 1 The frequency spectrum of black body radiation Max Planck Nobel Prize 1918 2 Photoelectric effect Photoemission of electrons from metals waves acting like particles A Einstein Nobel Prize 1921 3 The characteristic line spectra of atoms Niels Bohr Nobel Prize 1922 4 Particles like billiard balls could behave like waves interference diffraction DavisonGermer experiment T Number nfSrnlrued a cor 177quot 11quot 3a 950 l Nezih Pala npalafiu edu EEE 3396 39 quotJ 39 quot 39 ChZ 8 Black body radiation Max Planck applied quantization to the tiny oscillators that were thought to exist in the walls of the cavity He assumed that the H energy of these oscillators was limited to a 1 set of discrete integer multiples of a m fundamental unit of energy E proportional 2 3 f e uency v sow x timid weary 000 w to the oscillation r quot u mm m He derived a Srrhc 1 W W 7 uT u exkr 1 mmmm Nezih Pala npalafiu edu EEE 3396 39 quotJ 39 quot 39 ChZ 9 Photoelectric effect Consider monochromatic light is incident on the surface limitl of a metal plate in a vacuum The electrons in the metal absorb energy from the light and some of the electrons receive enough energy to be ejected from the metal surface into the vacuum lI39u39IL39Ll The maximum energy of electrons Em can be found by quot quot quot39quotquotquot quot placing another electrode to create an electric field in valnun between The potential necessary to retard all electron flow between the plates gives the energy Em Amman Em h u qCD Ituucry h Planck constant 663x10 34 J s414x10 15 eVs Ephomn hv 1 frequency mm a egmwg V 5 q electron charge 16x10 19 coulomb 17 27513 WMZQGX me x metal work function Joules or e 93911quot 399 actmns quot quot Nezih Pala n alafiu edu EEE 3396 Solid Sate Devices Ch2 IO Photoelectric effect For a particular frequency of light incident on the sample a maximum energy Em is observed for the emitted electrons The resulting plot of Em vs v is linear with a slope equal to Planck s constant If Em 2 hi qCD Slope l1 Planck was right Light energy is contained in discrete units rather than in a continuous distribution of energies The quantized units of light energy can be considered 4 as localized packets of energy called photons Einstein s interpretation of photoelectric based on Planck s hypothesis is considered to be the birth of Quantum Mechanics Nezih Pala n alafiu edu EEE 3396 Solid Sate Devices Ch2 I l Work function Work Function Work Function Metal eV Metal IeV Ag silver 426 Cr Chromium 46 Al aluminum 428 Mb Molybdenum 437 Au gold 51 Stainless Steel 44 Cs cesium 214 Ni Nickel 501 Cu copper 465 Pt Platinum 635 Li lithium 29 Zn Zinc 43 Pb lead 425 Fe Iron 45 Sn tin 442 Mg Magnesium 368 Nezih Pala nEalafiu edu EEE 3396 Solid Sate Devices Ch2 12 Photoelectric effect Example The work function of Cesium is 214 eV What retarding potential will be required to reduce the photocurrent to zero in a photoelectric experiment with Cs electrodes if the incident light is blue with the wavelength of 4500 A Find the fre uenc of the light c 3x108 m u 6 67x10 Hz 1 4500x10 m By using Em huq E 414x10 15ev sgtlt6 67 gtlt10m1s7214eV 2 767 2 14 0 62 eV 2 v0 0 62V Nezih Pala npalafiu edu EEE 3396 quot quot 39 ChZ 13 De Broglie hypothesis LouisVictorPierreRaymond 7th duc de Broglie 1892 1987 was a French physicist and a Nobel laureate He proposed that particles of matter such as electrons could manifest a wave character in certain experiments just like light manifested the discrete units of energy called photons His hypothesis completed the concept of duality deyBrogliawayelength 39 mv Remembering 0tf Ehfk2 t a22 f and h h27r Nezih Pala npalafiu edu EEE 3396 quot quot 39 ChZ 14 Dispersion relation For photons Ed39rfelec trdns quot quot Nezih Pala npalafiu edu EEE 3396 quot quot 39 ChZ 15 Atoms and electrons Atoms are so small that even today direct visual inspection is all but impossible Our model of the atom changes as our experimental ability improves Todays atomic theory tries to explain the observations made with accelerators The current quotquark modelquot of the atom is a hypothesis based on current atomic theory v n The Greek Model 5 Democritus400 BC concluded that matter could not be divided Sb into smaller and smaller 7 ieces forever Eventuall the smallest 8 piece of matter would be found He used the word atomos to describe the smallest possible piece of matter Demokril The Dalton Model I Points of Dalton39s Theory 1803 252 1 All elements are composed of indivisible particles 3 2 Atoms of the same element are exactly alike 3 Atoms of different elements are different 4 Compounds are formed by joining atoms of two or more Dangquot elements Nezih Pala n alafiu edu EEE 3396 Solid Sate Devices Ch2 16 Atoms and electrons The Thomson Model a J J Thomson English scientist who discovered a 6 electrons in 1897 3 I 6 Mmquot Sometimes called the quotplum puddingquot model a 6 g 6 3 Thomson thought of an atom as being composed o of a positively charged material with the negatively charged electrons scattered through it The Ruther ord Model Ernest Rutherford British physicist who discovered the nucleus in 1908 Rutherford39s model proposed that an atom is mostly empty space There is a small positive Rm39w39fmd nucleus with the negative electrons scattered around the outside edge Size of atom 10quot m Nezih Pala nEalafiu edu EEE 3396 Solid Sate Devices Ch2 17 Atoms and electrons The Bohr model Bohr model created by Niels Bohr depicts the atom as a small positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus similar in structure to the solar system but with electrostatic forces providing attraction rather than gravity This was an improvement on the earlier plum pudding model 1904 and the Rutherford model 1911 Since the Bohr model is a quantum physicsbased modification of the Rutherford model sometimes it is referred Rutherford Bohr model Nezih Pala nEalafiu edu EEE 3396 Solid Sate Devices Ch2 18 Visible light Wslhla ngm Raglan ol lhe Eeclromagnellc Speclruln m ulnvmm When white light shines through a prism or through water vapor like this rainbow the white light is broken apartinto the colors of the visible light spectrum Nezih Pala npala u edu EEE 3396 39 quotJ 39 ChZ 19 Spectrum of hydrogen Light Bulb l Hydrogen Lamp 9 h A mm Lv m Ah My Nezih Pala npala u edu EEE 3396 39 quotJ 39 CM 23 Spectrum of hydrogen High voltage suppr Eyepiece to excite atoms to observe lines Diffraction gratthy to separate light Nezih Pala npala u edu EEE 3396 39 quotJ 39 ChZ 21 Emission spectrum of gases mm n x l39 l Ilmumndx u Hg l H lllll o Nezih Pala npalafiu edu EEE 339s Solid Sate Devices CM 22 Electron tranSItions in hydrogen atom n 7 5 I Fi l n 4 E ESL l I lm39licn n J I mum n 2 L Hullquot n 1 The series in the hydrogen spectrum follow empirical forms as 1 1 Lyman ucR1 27n 2 n234 Rydbeg commquot R 1097X1071m Balmer ucRi27i2 n345 2 quot Speed oflight Paschen waggizj n456 C 3 X 108 InS n o Nezih Pala npalafiu edu EEE 339s Solid Sate Devices CM 23 23 Bohr Model CM 24 EEE 3396 Solid Sate Devices Nezih Pala npalafiu edu Bohr s model of atom Niels Henrik David Bohr was 71952 wa a Danuh physicist r wha made fundamental cuntributiun ta undentandrng atomic tru re a d turn echanic hr en an cullaburated with rnany at the tap phyrcrt at the century at hi intr ut m Cup uhr ha decrib d f e enhagen B the meat influential phyicit at the 20th century quantum theary Planck in a way that accuunted quantitatively ra rnaye from one orbit ta anathen ha a frequency prapartmnal tn the energ difference ufthe two main Buhr work an atomic tructure wa recugnized by the 1922 Nabel Prize in Phyic Nexih Pals npala u eau chz 725 Bohr s postulates To develop the model of atom Bohr made several postu 1 Electrons exist in certain stable circular orbits about the nucleus without radiation of light 2 The electron mat shift to an orbit of higher or lower energy with gaining or losing energy equal to the difference in the energy levels by absorption or emission of a photon of energy hv 3The angular momentum p8 of the electron in an orbit is always an integer multiple of Planck39s constant divided by Zn hZn h pe nh where n 1 2 3 4 Nexih Pals npala u eau chz 726 Bohr s postulates Thus according to Bohr electron in the atom obeys the following rules 1 angular momentum is quantized ie cannot have just any value 2 angular momentum is restricted to values for which n is a posI ve nte er 3 angular momentum can change only by discrete amounts ie integral multiples of hZn Nexih Pals npala u eau chz 727 Bohr s model 1 Electron orbits and transitions in the Bohr s model of the hydrogen atom Nezih Pala npalafiu edu 555 3396 r w r n ChZ 28 Bohr s model 2 From Newton s third law quot Elem electrostatic force between nucleus and electron in orbital model must be equal to centrifugal force Proton 2 2 i x 61 m V l 2 V 4722901 r q charge m mass V velocity r radius 80 dielectric constant For simplicity we can replace constant 47I80 K Nezih Pala npala u edu EEE3396quotquot39 quot 39 CM 23 Bohr s model 3 From Bohr s postulate 3 Radius r may have discrete values only r1 r2 rm indicating nth orbit Let s find radius of the nth orbit Nezih Pala npala u edu EEE3396quotquot39 quot 39 ChZ 30 Bohr s model 4 From Bohr s postulate 3 angular momentum of the electron is P5 where r1 r2 v is equation can be modi ed rli z2merz szz n radii of the allowed orbits quot2722 2 To eliminate velocity from the equation let s plug this into equation for the force actingbetween proton and electron qz 7 sz KrZ r cnz 731 Nexih Pals npala u edu Bohr s model 5 Farce equatiun 2 2 n h 2 Frum prevluu llde ubmtute i m V2 Nexih Pals npala u edu cnz 732 Bohr s model 6 Let s find energyof an electron on nth orbits Tatalenergy Em Em Em 2 tantialenergy Em 7L Pa uf an electan an new urblt KI w anhz Rememberequation for the radius r 2 mt lgtotential energy of an electron on nth orbit qu 7 Kinth cnz has Nexih Pals npala u edu Bohr s model 7 2 Kinetic energy Eh MV W Z 2 2 Velocity of an electron can be found using equation mzyz g nh 39n V m7 Using equation for the radius 2amp2 eNezinPala npalaonueuu EEEaa abrsblmSateDemoes ohm Bohr s model 8 Let s find energy difference between orbits in and n2 4 E 7 m1 728an quot1 21871912 E E miq miq Zl ngn 216th if mq 1 7 1 2m n gen spectrum farlymanwherer234 farBalmenwherert31415 farPaxchemwhererFAYSYSi Nexih Pals npala u edu cnz 735 Bohr s model 9 If an electrons drops from higher orbit to lower one it emits light a photon Transition of an electron from lower orbit to the higher is possible when it absorbs a photon Energy of emitted photon is E hv Frequency of emitted light when electron drops from higher orbit to lower one 4 Ehu quot14 iii UEh ZKZhZh n quot12 K4Il u U Nexih Pals npala u edu cnz 736 Energy levels of Hydrogen atom mq4 7136 EH 7 ev 24713980 nh 2 rt2 n1 2 3 Nezih Pala npalafiu edu EEE 3396 quot M 37 Atomic excitation Atomic excitation Atomic relaxation E firk Nezih Pala npalafiu edu EEE 3396 quot hZ 38 Shortcomings of the Bohr model Bohr model can not explain the experimentally observed splitting of levels in addition to the levels predicted by the theory It is difficult to extend the model to atoms more complicated than hydrogen Amonee0impr hensive thiedry wasne39eded However partial success of the Bohr model was an important step toward the eventual development of the quantum theory Nezih Pala npalafiu edu EEE 3396 quot M 39 13 Spectrum of light emitted by hydrogen atom Nexvh Pals npalaQ u edu chz an

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