Applications Using Band Diagrams and Fermi Energy Level Applications to Devices Physics Physics Homojunctions Heterojunctions pn junction metals/c junctions diodes pnp junction pnp Bipolar transistors & Light Emitting Devices Metaloxidesemiconductor junction MOS capacitors MOS transistors 1 1
Part 1: MetalMetal Contacts Workfunction Differences Flat band (a) (Pt) = 5.36 ev Pt Vacuum Fermi level Electrons Mo Vacuum Fermi level Electrons (Mo) = 4.20 ev E vac s aligned (Pt) (Mo) = 1.16 ev = ev Vacuum Equilibrium (b) 5.36 ev Fermi level Vacuum 4.20 ev E f s aligned Fig. 4.28: When two metals are brought together, there is a contact potential, V. (a) Electrons are more energetic in Mo so they tunnel to the surface of Pt. (b) Equilibrium is reached when the Fermi levels are lined up. From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap ( McGrawHill, 2002) http://materials.usask.ca 2 2
Workfunctions of Various Metals Workfunction Equation as Determined by Mehrotra & Mahanty a o = Bohr radius p = plasmon frequency = numerical value for integral = (1/3) 0.5 v f v f = Fermi velocity r o = radius of equilibrium density distribution of free electrons Mehrotra & Mahanty, Free electron contribution to the workfunction of metals, J. Phys. C: Solid State Phys., Vol. 11, 1978. 3 3
Workfunctions of Various Metals CRC?; http://public.wsu.edu/~pchemlab/documents/workfunctionvalues.pdf 4 4
Image Potential = Schottky Effect E E work vacuum F Image PE E F E vacuum Applied PE Net PE E F E F eff 2 e VTotal () r E vacuum er 16 r Image Force Potential Energy: an e a distance r from a metal surface that has a potential energy, V image. V image 2 e () r 16r E f 0 V () r E image x vacuum 2 e 16r (a) (b) (c) Fig. 4.36: (a) PE of the electron near the surface of a conductor, (b) Electron PE due to an applied field e.g. between cathode and anode (c) The overall PE is the sum. V x Vapplied () r er electric field VTotal () r r rrmin 0 x To find eff : Need to find maximum: Take derivative and set = 0 Find r min. Substitute r min back into equation and solve for eff. max e eff From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap ( McGrawHill, 2002) http://materials.usask.ca p. 287288 Ng, p. 608609 5 5
Field Emission & Image Force PE(x) E F eff V o (a) E F V max e eff e E F 0 0 x F Metal Vacuum (c) x Cathode x = 0 x = x F From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap ( McGrawHill, 2002) http://materials.usask.ca E (b) Grid or Anode FieldAssisted Thermionic Emission J e where: 3 e e eff e 4 o HV V electric field Fig. 4.37 (a) Field emission is the tunneling of an electron at an energy EF through the narrow PE barrier induced by a large applied field. (b) For simplicity we take the barrier to be rectangular. (c) A sharp point cathode has the maximumfield at the tip where the fieldemission of electrons occurs. e Vmax kt eeff kt 6 6
MetalMetal Contacts Seebeck Effect Seebeck effect (thermoelectric power) Builtin potential difference, ΔV, across a material due to a temperature difference, ΔT, across it S V T Sign of S: potential of the cold side with respect to the hot side; neg. if e s have accumulated in the cold side. Kasap, Electronic Materials & Devices (McGrawHill, 2006) Ch. 4 7 7
Seebeck Effect e.g.: Cu, Li, Au Density of States = Low at E f Phonon Scattering will have a greater effect on electrons L hot < L cold (L = e mean free path) Density of States = High at E f Phonon Scattering will have a lesser effect on electrons L hot > L cold (L = e mean free path) e.g.: Ni, Pt, Al, Pd Fig 4.61 From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap ( McGrawHill, 2005) 8 8
Hot MetalMetal Contacts Seebeck Effect Application = Thermocouple Metal Cold Hot Metal type A Cold Metal 100 o C 0 V 0 o C Metal Metal type B 100 o C 0 o C 0 V Metal type B (a) Fig 4.32 (a) If same metal wires are used to measure the Seebeck voltage across the metal rod, then the net emf is zero. (b)the thermocouple from two different metals, type A and B. The cold end is maintained at 0 C which is the reference temperature. The other junction is used to sense the temperature. In this example it is heated to 100 C. T T V AB T o SA SBdT From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap ( McGrawHill, 2005) T o S AB (b) Number of Carriers Diffusing to Hot Region will differ in each metal, thus voltage difference occurs dt 9 9
MSE 410ECE 340 MetalS/C Contacts: Schottky & Ohmic Contacts Flat band R.F. Pierret, Semiconductor Device Fundamentals (AddisonWesley, 1996) Ch. 14 10 10
MetalS/C Contacts: Schottky & Ohmic Contacts Flat band Flat band Equilibrium Equilibrium R.F. Pierret, Semiconductor Device Fundamentals (AddisonWesley, 1996) Ch. 14 11 11
MetalS/C Contacts: Schottky & Ohmic Contacts BandBending Where does it come from? D A q pn nn d dx where o R 2 dv dx 2 d dx Poisson's Equation R.F. Pierret, Semiconductor Device Fundamentals (AddisonWesley, 1996) Ch. 14 12 12
MetalS/C Contacts: Schottky & Ohmic Contacts Biasing Effects R.F. Pierret, Semiconductor Device Fundamentals (AddisonWesley, 1996) Ch. 14 13 13
MetalS/C Contacts: Schottky & Ohmic Contacts Doping Effects Equilibrium R.F. Pierret, Semiconductor Device Fundamentals (AddisonWesley, 1996) Ch. 14 14 14
Overview Equilibrium MetalS/C Contacts: Schottky & Ohmic Contacts Note: Blocking = Schottky Muller & Kamins, Device Electronics for Integrated Circuits, 3 rd Ed. (Wiley, 1996) Ch. 3 15 15