1. Spring 2007EE130 Lecture 29, Slide 1 Lecture #29 ANNOUNCEMENTS Reminder: Quiz #4 on Wednesday 4/4 No Office Hour or Coffee Hour on Wednesday Tsu-Jae will hold office hour tomorrow (4/3) 11-12 OUTLINE The MOS Capacitor: Structure Energy band diagram Reading: Chapter 16.1-16.2

2. Spring 2007EE130 Lecture 29, Slide 2 MOS Capacitor Structure Typical MOS capacitors and transistors in ICs today employ –heavily doped polycrystalline Si (“poly-Si”) film as the gate- electrode material n + -type, for “n-channel” transistors (NMOS) p + -type, for “p-channel” transistors (PMOS) –SiO 2 as the gate dielectric band gap = 9 eV  r,SiO2 = 3.9 –Si as the semiconductor material p-type, for “n-channel” transistors (NMOS) n-type, for “p-channel” transistors (PMOS) Si + _ GATE xoxo VGVG MOS capacitor (cross-sectional view)

3. Spring 2007EE130 Lecture 29, Slide 3 MOS Equilibrium Energy-Band Diagram n+ poly-Si SiO 2 p-type Si E FS E C =E FM ECEC EVEV EVEV metaloxide semiconductor

4. Spring 2007EE130 Lecture 29, Slide 4 Guidelines for Drawing MOS Band Diagrams Fermi level E F is flat (constant with distance x) in the Si –Since no current flows in the x direction, we can assume that equilibrium conditions prevail Band bending is linear in the oxide –No charge in the oxide => dE/dx = 0 so E is constant => dE c /dx is constant From Gauss’ Law, we know that the electric field strength in the Si at the surface, E Si, is related to the electric field strength in the oxide, E ox : EEE

5. Spring 2007EE130 Lecture 29, Slide 5 MOS Band-Diagram Guidelines (cont.) The barrier height for conduction-band electron flow from the Si into SiO 2 is 3.1 eV –This is equal to the electron-affinity difference (  Si and  SiO2 ) The barrier height for valence-band hole flow from the Si into SiO 2 is 4.8 eV The vertical distance between the Fermi level in the metal, E FM, and the Fermi level in the Si, E FS, is equal to the applied gate voltage:

6. Spring 2007EE130 Lecture 29, Slide 6 Special Case: Equal Work Functions  M =  S

7. Spring 2007EE130 Lecture 29, Slide 7 General Case: Different Work Functions E0E0 E0E0 E0E0 E0E0

8. Spring 2007EE130 Lecture 29, Slide 8 Flat-Band Condition