MSE 510 - Applications Using Band Diagrams and Fermi Energy Level Applications to Devices – Physics Homojunctions Heterojunctions metal-metal junctions metal-s/c junctions & Thermocouples p-n junctions diodes p-n-p Bipolar transistors p-n-p junction Light Emitting Devices MOS capacitors MOS transistors NVM Metal-oxide-semiconductor junction Knowlton MSE 510 & 1 Part 1: Metal-Metal Contacts Pt (a) (Pt) = 5.36 eV Flat band Vacuum Mo Vacuum Fermi level Fermi level (Mo) = 4.20 eV - Workfunction Differences - Electrons Evac’s aligned Electrons (b) Vacuum Fermi level 4.20 eV Equilibrium 5.36 eV (Pt) - (Mo) = 1.16 eV = eV Vacuum Ef’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. Knowlton From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002) http://Materials.Usask.Ca 2 1 MSE 510 Workfunctions of Various Metals Workfunction Equation as Determined by Mehrotra & Mahanty ao = Bohr radius p = plasmon frequency = numerical value for integral = (1/3)0.5 vf vf = Fermi velocity ro = 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. Knowlton 3 MSE 510 Image Potential = Schottky Effect work Evacuum EF Applied PE Image PE EF + Image Force Potential Energy: EF + EF + eff Evacuum Vimage (r ) Evacuum Ef 0 x e2 er 16 r x x Vapplied (r ) er electric field 2 e 16 r VTotal (r ) Evacuum e2 16 r an e- a distance r from a metal surface that has a potential energy, Vimage. Vimage (r ) Net PE (a) (b) VTotal (r ) 0 r r rmin (c) To find eff: Need to find maximum: •Take derivative and set = 0 •Find rmin. •Substitute rmin back into equation and solve for eff. 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. Vmax eeff From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002) http://Materials.Usask.Ca p. 287-288 Knowlton Ng, p. 608-609 4 2 MSE 510 Field Emission & Image Force PE(x) EF + eff Vo e- Vmax eeff EF EF (a) 0 Metal 0 xF x x = 0 x = xF (b) Vacuum Field-Assisted Thermionic Emission Grid or Anode J e Cathode e E Vmax kT eeff kT where: (c) HV V e3 eeff e 4 o 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. From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002) http://Materials.Usask.Ca Knowlton 5 MSE 510 Metal-Metal Contacts – Seebeck Effect Seebeck effect (thermoelectric power) Built-in potential difference, ΔV, across a material due to a temperature difference, ΔT, across it S Knowlton V T Sign of S: potential of the cold side with respect to the hot side; Thus, neg. if e-’s have accumulated in the cold side. Kasap, Electronic Materials & Devices (McGraw-Hill, 2006) Ch. 4 6 3 MSE 510 Seebeck Effect Density of States = Low at Ef Phonon Scattering will have a greater effect on electrons Lhot < Lcold (L = e- mean free path) + + + + - e.g.: Cu, Li, Au Density of States = High at Ef Phonon Scattering will have a lesser effect on electrons Lhot > Lcold (L = e- mean free path) e.g.: Ni, Pt, Al, Pd Fig 4.61 Knowlton - + + + + From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) MSE 510 7 Metal-Metal Contacts – Seebeck Effect Application = Thermocouple Metal Metal type A Hot Cold Hot o o 100 C Cold o 100 C 0 C 0 Metal V Metal o 0 C 0 Metal type B V Metal type B (b) (a) Number of Carriers Diffusing to Hot Region will differ in each metal, thus voltage difference occurs 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 VAB SA SB dT SABdT To Knowlton To From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) 4 MSE 510 Metal-S/C Contacts: Schottky & Ohmic Contacts Flat band Knowlton MSE 510 R.F. Pierret, Semiconductor Device Fundamentals (Addison-Wesley, 1996) Ch. 14 9 Metal-S/C Contacts: Schottky & Ohmic Contacts Flat band Flat band Equilibrium Equilibrium Knowlton R.F. Pierret, Semiconductor Device Fundamentals (Addison-Wesley, 1996) Ch. 14 10 5 MSE 510 Metal-S/C Contacts: Schottky & Ohmic Contacts Band-Bending Where does it come from? q p N D n N A d dx where o R d 2V d dx 2 dx Poisson's Equation R.F. Pierret, Semiconductor Device Fundamentals (Addison-Wesley, 1996) Ch. 14 Knowlton 11 MSE 510 Metal-S/C Contacts: Schottky & Ohmic Contacts Biasing Effects R.F. Pierret, Semiconductor Device Fundamentals (Addison-Wesley, 1996) Ch. 14 Knowlton 12 6 MSE 510 Metal-S/C Contacts: Schottky & Ohmic Contacts Doping Effects Equilibrium Knowlton MSE 510 R.F. Pierret, Semiconductor Device Fundamentals (Addison-Wesley, 1996) Ch. 14 13 Metal-S/C Contacts: Schottky & Ohmic Contacts Overview Note: Blocking = Schottky Equilibrium Knowlton Muller & Kamins, Device Electronics for Integrated Circuits, 3rd Ed. (Wiley, 1996) Ch. 3 14 7