PHYS208 - spring 2010 - page 1 PHYS208 – Solid state physics SPRING 2010 Part 2 Lectures from Thursday 18. February 2010 to Wednesday 21 th April 2010.

PHYS208 - spring 2010 - page 1 PHYS208 – Solid state physics SPRING 2010 Part 2 Lectures from Thursday 18. February 2010 to Wednesday 21 th April 2010 From Electrons in Metals, Fermi Gas To Bloch States, Energy Bands Semiconductors and P-N-junction (start) 210 pages

PHYS208 - spring 2010 - page 2 PHYS208 - Lecture Thursday 18. February 2010 Electrons in Metals Drude Lorenz Fermi Fermi Gas Comment:PLEASE READ THE DISCREPANCY STORY This text needs some more comments - to be added Includes: Slides from 2007 and 2008 The strange discrepancy between textbooks – Lorenz Number

PHYS208 - spring 2010 - page 3

PHYS208 - spring 2010 - page 6 Solid State Physics [3C25] Tony Harker, Chiranijib Mitra and Andrew Horsfield (pages 117) Slides from 2007 and 2008 The strange discrepancy between textbooks

PHYS208 - spring 2010 - page 7 There are the following groups: 1. Kittel's book -> Wikipedia -> Hyperphysics -> Tony Harker et al -> some new textbooks factor 2 ( i.e. 2 pi 2 /9 ) larger than our derivation 2. Ashcroft&Mermin -> Burns -> Hemmer -> our derivation The difference is in the value of "average velocity". Wikipedia gives (2007) a nice review of the three velocities: Most probable, Average speed and Root Mean Square. The "Physical" is the root mean square, clearly, it relates to average energy. If we assume thet all particles have the velocity, this assumption must at least conserve the total energy! (It might be possible to argue for the average speed too.....) http://en.wikipedia.org/wiki/Maxwell-Boltzmann_distribution Slides from 2007 and 2008 The strange discrepancy between textbooks

PHYS208 - spring 2010 - page 8 The difference is in the value of "average velocity". Wikipedia gives (2007) a nice review of the three velocities: Most probable, Average speed and Root Mean Square. The "Physical" is the root mean square, clearly, it relates to average energy. If we assume thet all particles have the velocity, this assumption must at least conserve the total energy! (But it might be possible to argue for the average speed too.....) http://en.wikipedia.org/wiki/Maxwell-Boltzmann_distribution Slides from 2007 and 2008 The strange discrepancy between textbooks

PHYS208 - spring 2010 - page 9 Slides from 2007 and 2008 The strange discrepancy between textbooks

PHYS208 - spring 2010 - page 12 And Kittel - with the factor 2 result Slides from 2007 and 2008 The strange discrepancy between textbooks

PHYS208 - spring 2010 - page 13 And Kittel - with the factor 2 result ________________________________________________________________ Slides from 2007 and 2008 The strange discrepancy between textbooks

PHYS208 - spring 2010 - page 14 BACK TO 2010 Identity of particles -> phasefact=+1 or -1 + -> boson behaviour... they like to be crowded - -> psi a,a is identically zero Identity of particles -> Pauli exclusion «principle» Pauli exclusion «principle» -> Identity of particles ??

PHYS208 - spring 2010 - page 20 SUMMARY Identity of particles -> phasefact=+1 or -1 + -> boson behaviour... they like to be crowded - -> psi a,a is identically zero therefore from Identity of particles follows Pauli exclusion «principle» Bose Einstein: Einstein invented that before quantum theory (photon behaviour - stimulated emission) Identity of particles -> Pauli exclusion «principle» Pauli exclusion «principle» -> Identity of particles ?? IN EACH (SPACE-based) STATE ONLY 2 PARTICLES (one in each spin state)

PHYS208 - spring 2010 - page 22 The following is the two-parts of the scanned handwritten note on Fermi Gas The SUM to INTEGRAL transition is a major part of the derivation of the density in K space

PHYS208 - spring 2010 - page 25 The lower part with today's comments

PHYS208 - spring 2010 - page 29 PHYS208 Lecture Wednesday 24. February 2010 Lecture Thursday 25. February 2010 Electrons in Metals Fermi Gas We have discussed the texts on thermal properties Fermi Gas; Somerfeld's method to evaluate the integrals Fermi Gas heat capacity for Electrons Boltzmann Distribution – Boltzmann Factor – Fremi-Dirac Distribution This text needs adding links and adding the details of evaluations

PHYS208 - spring 2010 - page 30 Slides from 2007 and 2008 The strange discrepancy between te

PHYS208 - spring 2010 - page 32 Slides from 2007 and 2008 The strange discrepancy between te

PHYS208 - spring 2010 - page 35 Lecture Thursday 25. February 2010 Fermi Gas We have discussed the texts on thermal properties Fermi Gas; Somerfeld's method to evaluate the integrals Fermi Gas heat capacity for Electrons Boltzmann Distribution – Boltzmann Factor – Fremi-Dirac Distribution Which texts we used – we make copies here We have used the 2008 texts; Notes by Trygve Buanes (sorry, no drawings there) Boltzmann Distribution – Boltzmann Factor – Fremi-Dirac Distribution Here we first take the blackboard THE WOW Argument For Boltzmann

PHYS208 - spring 2010 - page 36 Boltzmann Factor revisited

PHYS208 - spring 2010 - page 37 Boltzmann revisited THIS IS THE WOW Argument CONSTANT

PHYS208 - spring 2010 - page 38 Fermi Derivation Just copied and modified Boltzmann Factor revisited slide

PHYS208 - spring 2010 - page 39 Fermi Derivation modified Boltzmann Factor slide

PHYS208 - spring 2010 - page 41 Fermi Energy

PHYS208 - spring 2010 - page 42 Today 2007, 2008 and Yesterday

PHYS208 - spring 2010 - page 43 EXAM 2008 TEXT metals_Ex_2008.pdf

PHYS208 - spring 2010 - page 44 Well, here they jumped over the evaluation. We have two handwritten notes Performing this in detail see LATER VERSION EXAM 2008 TEXT metals_Ex_2008.pdf

PHYS208 - spring 2010 - page 45 This is what we did today and yesterday We have two handwritten notes Performing this in detail - we must include them (they are on the web) see LATER VERSION of this text for Detail At the end of todays lecture WE STARTED THE NEXT TOPIC ELECTRONS IN PERIODIC STRUCTURES

PHYS208 - spring 2010 - page 46 ELECTRONS IN PERIODIC STRUCTURES

PHYS208 - spring 2010 - page 47 PHYS208 Lecture Wednesday 3. March 2010 Lecture Thursday 4. March 2010 Electrons in Periodic Potentials Bloch's Theorem etc The text to follow Bloch2008_PDFslides.pdf

PHYS208 - spring 2010 - page 48 ELECTRONS IN PERIODIC STRUCTURES

PHYS208 - spring 2010 - page 51 A wave of HIGH FREQUENCY can be modulated by a signal of lower frequency

PHYS208 - spring 2010 - page 53 The text to follow Bloch2008_PDFslides.pdf

PHYS208 - spring 2010 - page 54 Mathematician Physicist

PHYS208 - spring 2010 - page 55 Combination of These two pictures is missing in the texts

PHYS208 - spring 2010 - page 59 Look at the continuation in the text.... THURSDAY This is the representation Of the operator H=T+U As discussed below

PHYS208 - spring 2010 - page 60 PHYS208 Lecture Thursday 4. March 2010 Electrons in Periodic Potentials Expansions in plane waves

PHYS208 - spring 2010 - page 61 We use expansions in eigenstates of the T – kinetic energy Expansions Fourier Series Linear vector space Operators Projection Operator All very simply Illustrated here

PHYS208 - spring 2010 - page 62 Insert The unit Operator i.e. the sum Of projection operators This is how operators become matrices And the functions (states) become Column vectors

PHYS208 - spring 2010 - page 63 Insert The unit Operator i.e. the sum Of projection operators This is how operators become matrices And the functions (states) become Column vectors

PHYS208 - spring 2010 - page 64 This is how operators become matrices And the functions (states) become Column vectors

PHYS208 - spring 2010 - page 65 This is how operators become matrices And the functions (states) become Column vectors

PHYS208 - spring 2010 - page 68 The properties Of H=T+U Following from The text to follow: Bloch2008_PDFslides.pdf

PHYS208 - spring 2010 - page 69 Brillouin zone -  /a to  /a Expanding the wavefunction – all possible k-values; The distance between k-values – from periodicity on L=N a (many =N atoms with a between neighbours) Large L -> small k Expanding the potential – all possible K-values; The distance between k-values – from periodicity on a (over 1 atom with a to the neighbour) Small a -> large K (G=2  /a steps) 22 __ a G = The text to follow: Bloch2008_PDFslides.pdf

PHYS208 - spring 2010 - page 70 Text

PHYS208 - spring 2010 - page 71 These pictures can be really understood most easily from the Fourier Analysis (English Notes.... )

PHYS208 - spring 2010 - page 72 Text Rearranging band matrices A band matrix can be transformed BY REARRANGING THE BASIS i.e. just changing the order of the basis states The diagonalization: the two slosest states are pushed away from each other a=b case – 'degenerate' and a,b, different

PHYS208 - spring 2010 - page 73 BAND THEORY Where are the BANDS?

PHYS208 - spring 2010 - page 74 View the transformation of the matrix by rearrangement in the text on Bloch states Bloch2008_PDFslides.pdf

PHYS208 - spring 2010 - page 75 Text View the transformation of the matrix by rearrangement in the text on Bloch states Bloch2008_PDFslides.pdf

PHYS208 - spring 2010 - page 76 Rearrangement leads to BLOCK matrices – they consists of nonzero blocks and rest zeros everywhere

PHYS208 - spring 2010 - page 77 LCAO Linear Combination of Atomic Orbitals NEXT TOPIC – BAND THEORY from a different perspective

PHYS208 - spring 2010 - page 78 LCAO Linear Combination of Atomic Orbitals Tight Binding Model (opposite to the weak coupling)

PHYS208 - spring 2010 - page 79 PHYS208 Lecture Wednesday 17. March 2010 Lecture Thursday 18. March 2010 Electrons in Periodic Potentials Beyond Bloch Theorem The texts to follow finishing: http://web.ift.uib.no/AMOS/PHYS208/TEXT2008/Bloch2008_PDFslides.pdf started: http://web.ift.uib.no/AMOS/PHYS208/3dimband/3dim.pdf Starting next time: web.ift.uib.no/AMOS/PHYS208/TEXT2008/EffectiveMass2008_SLIDES.pdf

PHYS208 - spring 2010 - page 80 The properties Of H=T+U Following from The text to follow: Bloch2008_PDFslides.pdf

PHYS208 - spring 2010 - page 83 View the transformation of the matrix by rearrangement in the text on Bloch states Bloch2008_PDFslides.pdf

PHYS208 - spring 2010 - page 85 Text

PHYS208 - spring 2010 - page 86 Rearranging band matrices A band matrix can be transformed BY REARRANGING THE BASIS i.e. just changing the order of the basis states The diagonalization: the two slosest states are pushed away from each other a=b case – 'degenerate' and a,b, different

PHYS208 - spring 2010 - page 90 BAND THEORY Where are the BANDS?

PHYS208 - spring 2010 - page 91 ELECTRONS IN PERIODIC STRUCTURES Is this picture «correct» ?? We have used the expansion in eigenstates of the T – kinetic energy A wave of HIGH FREQUENCY can be modulated by a signal of lower frequency

PHYS208 - spring 2010 - page 92 Rearrangement leads to BLOCK matrices – they consists of nonzero blocks and rest zeros everywhere

PHYS208 - spring 2010 - page 93 LCAO Linear Combination of Atomic Orbitals – already discussed This week's TOPIC BAND THEORY from a different perspective

PHYS208 - spring 2010 - page 94 We have used the expansion in eigenstates of the T – kinetic energy Now → LCAO Linear Combination of Atomic Orbitals

PHYS208 - spring 2010 - page 98 http://web.ift.uib.no/AMOS/PHYS208/3dimband/3dim.pdf

PHYS208 - spring 2010 - page 100 The texts to follow finishing: http://web.ift.uib.no/AMOS/PHYS208/TEXT2008/Bloch2008_PDFslides.pdf started: http://web.ift.uib.no/AMOS/PHYS208/3dimband/3dim.pdf Starting next time: http://web.ift.uib.no/AMOS/PHYS208/TEXT2008/EffectiveMass2008_SLIDES.pdf In the lecture we also played with matrices http://web.ift.uib.no/AMOS/matrix/notes.pdf http://web.ift.uib.no/AMOS/matrix/Dirac-notation.pdf SOURCES are found in http://web.ift.uib.no/AMOS/matrix/

PHYS208 - spring 2010 - page 101 PHYS208 VERY Preliminary Lecture Thursday 18. March 2010 Electrons in Periodic Potentials Beyond Bloch Theorem – 3 dim band The texts to follow http://web.ift.uib.no/AMOS/PHYS208/3dimband/3dim.pdf http://web.ift.uib.no/AMOS/PHYS208/TEXT2010/Band-3-dim.pdf Started: web.ift.uib.no/AMOS/PHYS208/TEXT2008/EffectiveMass2008_SLIDES.pdf

PHYS208 - spring 2010 - page 102 LCAO Linear Combination of Atomic Orbitals – already discussed This week's TOPIC BAND THEORY from a different perspective

PHYS208 - spring 2010 - page 109 http://web.ift.uib.no/AMOS/PHYS208/TEXT2010/Band-3-dim.pdf

PHYS208 - spring 2010 - page 117 , 2 terms Zero, 12 terms ,other atom 2 terms One atom 3 terms ,other atom 4 terms  4 terms

PHYS208 - spring 2010 - page 118 PHYS208 Lecture Wednesday 24. March 2010 Lecture Thursday 25. March 2010 Motion of electrons The texts to follow web.ift.uib.no/AMOS/PHYS208/TEXT2010/EffectiveMass2008_corrected.pdf

PHYS208 - spring 2010 - page 119 Group velocity http://web.ift.uib.no/AMOS/WAVE/

PHYS208 - spring 2010 - page 121 There is no FORCE in quantum mechanics Only potentials

PHYS208 - spring 2010 - page 122 PHYS208 Lecture Wednesday 7 th April 2010 Lecture Thursday 8 th April 2010 Semiconductors Introduction Semiconductor Equation The Law of mass action

PHYS208 - spring 2010 - page 123 We have gone through http://web.ift.uib.no/AMOS/PHYS208/2008/2008_04_02_Start_Semiconductors.pdf Wednesday 2. April 2008 and Thursday 3. April 2008 SEMICONDUCTORS intro

PHYS208 - spring 2010 - page 130 Next time Density of states in band Fermi distribution Product of Density of states and Fermi distribution

PHYS208 - spring 2010 - page 131 Next time Density of states in band Fermi distribution Product of Density of states and Fermi distribution

PHYS208 - spring 2010 - page 132 Why is the Law of Mass Action important - basis for doping of semiconductors Law of Mass Action n. p = const p-h factor Miners town and textile workers town examples

PHYS208 - spring 2010 - page 133 http://www.elmhurst.edu/~chm/vchembook/184ph.htm l

PHYS208 - spring 2010 - page 134 p-h factor From 2008 notes http://web.ift.uib.no/AMOS/PHYS208/phys208- 2005.04.06/index0.html

PHYS208 - spring 2010 - page 135 Lecture Thursday 8 th April 2010 Semiconductors Semiconductor Equation The Law of mass action

PHYS208 - spring 2010 - page 136 The task here is to arrive at the semiconductor equation, which leads to obtaining a product of n electrons times n holes as a function of temperature n electrons n holes

PHYS208 - spring 2010 - page 137 With suitable approximations we transform both calculations to evaluation of the integral It has got a bit confused at the lecture It is indeed a standard integral Its evaluation is quite nice collection of tricks

PHYS208 - spring 2010 - page 138 Electrons and holes 2008 SLIDE NOTE

PHYS208 - spring 2010 - page 139 Electrons and holes When we reverse energy, the holes take the same role as electrons  note the – sign on  2008 SLIDE NOTE

PHYS208 - spring 2010 - page 140 The task here was to arrive at the semiconductor equation, which leads to obtaining a product of n electrons times n holes as a function of temperature Taking a product,  gets eliminated

PHYS208 - spring 2010 - page 146 PHYS208 Lecture Wednesday 14 th April 2010 Semiconductors Impurities - doping

PHYS208 - spring 2010 - page 147 We have gone through We have gone through: http://web.ift.uib.no/AMOS/PHYS208/2008/2008_04_09_Semiconductor-impurity.pdf We have also used parts of (exam presentation) http://web.ift.uib.no/AMOS/PHYS208/TEXT2010/Exam_2008_LATEX/pn_junction_Ex_2008.pdf We started to discuss thursday's and following week's text (handwritten notes) http://web.ift.uib.no/AMOS/PHYS208/2008/2008_P-N-junction.pdf ( to be used together with the above pn_junction_Ex_2008.pdf Some of the formalism is nicely discussed also in (mainly coming lectures material) http://web.ift.uib.no/AMOS/PHYS208/TEXT2008/phys208_Trygve_SLIDES.pdf

PHYS208 - spring 2010 - page 148 Density of states in band Fermi distribution Product of Density of states and Fermi distribution

PHYS208 - spring 2010 - page 150 The task here was to arrive at the semiconductor equation, which leads to obtaining a product of n electrons times n holes as a function of temperature Taking a product,  gets eliminated

PHYS208 - spring 2010 - page 151 Once more about electrons and holes; Ferromagnetic fluid story once more Concept of holes

PHYS208 - spring 2010 - page 152 semiconductor equation, which leads to obtaining a product of n electrons times n holes - function of temperature. Taking a product,  eliminated Last time revisiting this (  evaluation is in the exam slides )

PHYS208 - spring 2010 - page 153 Starting Impurities Semiconductors might contain various impurities. However, only the type of impurities discussed below – DOPING by controlled impurities of one or other type P or N and the abrupt JUNCTION ( two types of doping in the same crystal structure with a sharp border ) appears to be useful for devices and instruments

PHYS208 - spring 2010 - page 154 Impurity atoms have 3 valence electrons Acceptor P-type (hole, positive charge carriers) Impurity atoms have 5 valence electrons Donor N-type (electron, negative charge carriers) PN

PHYS208 - spring 2010 - page 155 The atom-like states of impurities explained; Bohr-like 'atom' relations More details on the followin slide from 2008....

PHYS208 - spring 2010 - page 156 Impurity States – Donors from 2008 slide

PHYS208 - spring 2010 - page 157 Starting P-N junction

PHYS208 - spring 2010 - page 158 For work with P-N junction Exam presentation http://web.ift.uib.no/AMOS/PHYS208/TEXT2010/Exam_2008_LATEX/pn_junction_Ex_2008.pdf thursday's and following week's text (handwritten notes) http://web.ift.uib.no/AMOS/PHYS208/2008/2008_P-N-junction.pdf ( to be used together with the above pn_junction_Ex_2008.pdf ) Some of the formalism is nicely discussed also in http://web.ift.uib.no/AMOS/PHYS208/TEXT2008/phys208_Trygve_SLIDES.pdf

PHYS208 - spring 2010 - page 159 PHYS208 Lecture Thursday 15 th April 2010 P-N-Junction part 1 THE FIRST 18 pages – background from previous lectures 4 pages of new lecture calculations with comments

PHYS208 - spring 2010 - page 160 For work with P-N junction Exam presentation http://web.ift.uib.no/AMOS/PHYS208/TEXT2010/Exam_2008_LATEX/pn_junction_Ex_2008.pdf thursday's and following week's text (handwritten notes) http://web.ift.uib.no/AMOS/PHYS208/2008/2008_P-N-junction.pdf ( to be used together with the above pn_junction_Ex_2008.pdf ) Some of the formalism is nicely discussed also in http://web.ift.uib.no/AMOS/PHYS208/TEXT2008/phys208_Trygve_SLIDES.pdf THE FIRST 18 pages or so – background from previous lectures

PHYS208 - spring 2010 - page 162 Once more about electrons and holes; Ferromagnetic fluid story once more Concept of holes We have discussed one more illustration of holes: BUBBLES

PHYS208 - spring 2010 - page 163 Starting Impurities OLDER NOTE Semiconductors might contain various impurities. However, only the type of impurities discussed below – DOPING by controlled impurities of one or other type P or N and the abrupt JUNCTION ( two types of doping in the same crystal structure with a sharp border ) appears to be useful for devices and instruments COPY OF OLDER NOTE

PHYS208 - spring 2010 - page 164 Impurity atoms have 3 valence electrons Acceptor P-type (hole, positive charge carriers) Impurity atoms have 5 valence electrons Donor N-type (electron, negative charge carriers) PN COPY OF OLDER NOTE

PHYS208 - spring 2010 - page 165 The atom-like states of impurities explained; Bohr-like 'atom' relations More details on the following slide from 2008.... COPY OF OLDER NOTE

PHYS208 - spring 2010 - page 168 The following three slides show how the 'acceptor levels' Can be created ABOVE the valence band edge We start by showing how the 'donor levels' are created BELOW the conduction band edge

PHYS208 - spring 2010 - page 169 Impurity States - Donors

PHYS208 - spring 2010 - page 170 Impurity States - Acceptors

PHYS208 - spring 2010 - page 171 Impurity States - Acceptors Acceptor Bound State

PHYS208 - spring 2010 - page 172 Do these 'inclined bands' Look strange to you? We have used such picture before! And with a nice explanation - see the following 2 slides Picture from 1954 article on p-n-junction for solar cell Physical Review

PHYS208 - spring 2010 - page 173 Do the 'inclined bands'of previous slide look strange to you? We have used such picture before! – The forces on electrons Copy is here – and a copy of nice explanation on the following slide

PHYS208 - spring 2010 - page 174 'inclined bands' – The forces on electrons

PHYS208 - spring 2010 - page 175 We have discussed one more illustration of holes: BUBBLES And Helium-filled balloon And thus the whole story of Archimedes law and buoyancy – OPPDRIFT (norwegian) Any floating object displaces its own weight of fluid. – Archimedes of Syracuse We have discussed one more illustration of holes: BUBBLES Bubbles travel uppwads Stones are falling downwards

PHYS208 - spring 2010 - page 176 Riddle: Train accellerates. A lamp or rubber ball will hang as shown in the upper picture Helium-filled balloon in the same train: How will it place itself ?

PHYS208 - spring 2010 - page 177 A related riddle: how fast did you give the answer: A stone is placed on a toy boat. The stone is now moved to the water. What will happen? Result (A) or result (B) ? Will the level of water in the container rise or sink? And thus the whole story of Archimedes law and buoyancy – OPPDRIFT (norwegian) Any floating object displaces its own weight of fluid. – Archimedes of Syracuse (A) (B)

PHYS208 - spring 2010 - page 178 Diffusion, Fick's first law of diffusion, conductivity, Ohm's Law, drift velocity, mobility, Equillibrium as cancellation of currents

PHYS208 - spring 2010 - page 179 Equillibrium as cancellation of currents; Diffusion caused by gradient of density; what is 'Diffusion constant' D ? ELECTRIC FIELD IS GRADIENT OF ELECTROSTATIC POTENTIAL. Evaluate potential difference

PHYS208 - spring 2010 - page 180 Einstein – Nernst: Diffusion against force related to Boltzmann Use the same equation as before with different aim: Now the Field is known and constant

PHYS208 - spring 2010 - page 181 Einstein – Nernst: gives us the diffusion constant / mobility relation JUST IN THE FORM needed for the potential difference.

PHYS208 - spring 2010 - page 182 PHYS208 Lecture Thursday 15 th April 2010 Lecture Wednesday 21 th April 2010 P-N-Junction part 1+2 THE FIRST 18 pages – background from previous lectures 4 pages of new lecture calculations with comments -part 1 Part 2 – applying law of mass action

PHYS208 - spring 2010 - page 183 For work with P-N junction Exam presentation http://web.ift.uib.no/AMOS/PHYS208/TEXT2010/Exam_2008_LATEX/pn_junction_Ex_2008.pdf thursday's and following week's text (handwritten notes) http://web.ift.uib.no/AMOS/PHYS208/2008/2008_P-N-junction.pdf ( to be used together with the above pn_junction_Ex_2008.pdf ) Some of the formalism is nicely discussed also in http://web.ift.uib.no/AMOS/PHYS208/TEXT2008/phys208_Trygve_SLIDES.pdf THE FIRST 18 pages or so – background from previous lectures

PHYS208 - spring 2010 - page 185 Once more about electrons and holes; Ferromagnetic fluid story once more Concept of holes We have discussed one more illustration of holes: BUBBLES

PHYS208 - spring 2010 - page 186 Starting Impurities OLDER NOTE Semiconductors might contain various impurities. However, only the type of impurities discussed below – DOPING by controlled impurities of one or other type P or N and the abrupt JUNCTION ( two types of doping in the same crystal structure with a sharp border ) appears to be useful for devices and instruments COPY OF OLDER NOTE

PHYS208 - spring 2010 - page 187 Impurity atoms have 3 valence electrons Acceptor P-type (hole, positive charge carriers) Impurity atoms have 5 valence electrons Donor N-type (electron, negative charge carriers) PN COPY OF OLDER NOTE

PHYS208 - spring 2010 - page 188 The atom-like states of impurities explained; Bohr-like 'atom' relations More details on the following slide from 2008.... COPY OF OLDER NOTE

PHYS208 - spring 2010 - page 191 The following three slides show how the 'acceptor levels' Can be created ABOVE the valence band edge We start by showing how the 'donor levels' are created BELOW the conduction band edge

PHYS208 - spring 2010 - page 192 Impurity States - Donors

PHYS208 - spring 2010 - page 193 Impurity States - Acceptors

PHYS208 - spring 2010 - page 194 Impurity States - Acceptors Acceptor Bound State

PHYS208 - spring 2010 - page 195 Do these 'inclined bands' Look strange to you? We have used such picture before! And with a nice explanation - see the following 2 slides Picture from 1954 article on p-n-junction for solar cell Physical Review

PHYS208 - spring 2010 - page 196 Do the 'inclined bands'of previous slide look strange to you? We have used such picture before! – The forces on electrons Copy is here – and a copy of nice explanation on the following slide

PHYS208 - spring 2010 - page 197 'inclined bands' – The forces on electrons

PHYS208 - spring 2010 - page 198 We have discussed one more illustration of holes: BUBBLES And Helium-filled balloon And thus the whole story of Archimedes law and buoyancy – OPPDRIFT (norwegian) Any floating object displaces its own weight of fluid. – Archimedes of Syracuse We have discussed one more illustration of holes: BUBBLES Bubbles travel uppwads Stones are falling downwards

PHYS208 - spring 2010 - page 199 Riddle: Train accellerates. A lamp or rubber ball will hang as shown in the upper picture Helium-filled balloon in the same train: How will it place itself ?

PHYS208 - spring 2010 - page 200 A related riddle: how fast did you give the answer: A stone is placed on a toy boat. The stone is now moved to the water. What will happen? Result (A) or result (B) ? Will the level of water in the container rise or sink? And thus the whole story of Archimedes law and buoyancy – OPPDRIFT (norwegian) Any floating object displaces its own weight of fluid. – Archimedes of Syracuse (A) (B)

PHYS208 - spring 2010 - page 201 Diffusion, Fick's first law of diffusion, conductivity, Ohm's Law, drift velocity, mobility, Equillibrium as cancellation of currents

PHYS208 - spring 2010 - page 202 Equillibrium as cancellation of currents; Diffusion caused by gradient of density; what is 'Diffusion constant' D ? ELECTRIC FIELD IS GRADIENT OF ELECTROSTATIC POTENTIAL. Evaluate potential difference

PHYS208 - spring 2010 - page 203 Einstein – Nernst: Diffusion against force related to Boltzmann Use the same equation as before with different aim: Now the Field is known and constant

PHYS208 - spring 2010 - page 204 Einstein – Nernst: gives us the diffusion constant / mobility relation JUST IN THE FORM needed for the potential difference.

PHYS208 - spring 2010 - page 205 PHYS208 Lecture Wednesday 21 th April 2010 P-N-Junction Continue – model depletion zone...... pages of new lecture calculations with comments

PHYS208 - spring 2010 - page 206 Einstein – Nernst: gives us the diffusion constant / mobility relation - potential difference.

PHYS208 - spring 2010 - page 208 We have shown that The potential difference generated in junction of typical doping degrees can be of the order of Volts

PHYS208 - spring 2010 - page 209 The drawing to left is showing the whole solution of the model of the charge depletion charge density, electric field and resulting potential difference. This will determine the SIZES OF DEPLETION REGIONS – Right – realistic shapes The potential difference is due to the opposite carrier densities. How are they positioned? MODEL:

PHYS208 - spring 2010 - page 210 The potential difference is due to the opposite carrier densities. How are they positioned? MODEL:

PHYS208 - spring 2010 - page 1 PHYS208 – Solid state physics SPRING 2010 Part 2 Lectures from Thursday 18. February 2010 to Wednesday 21 th April 2010.

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PHYS208 - spring 2010 - page 1 PHYS208 – Solid state physics SPRING 2010 Part 2 Lectures from Thursday 18. February 2010 to Wednesday 21 th April 2010.

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Presentation on theme: "PHYS208 - spring 2010 - page 1 PHYS208 – Solid state physics SPRING 2010 Part 2 Lectures from Thursday 18. February 2010 to Wednesday 21 th April 2010."— Presentation transcript:

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