Lecture 15 OUTLINE The MOS Capacitor Energy band

Lecture 15 OUTLINE • The MOS Capacitor – Energy band diagrams Reading: Pierret 16. 1 -16. 2, 18. 1; Hu 5. 1

MOS Capacitor Structure MOS capacitor (cross-sectional view) GATE VG + _ Semiconductor EE 130/230 M Spring 2013 • MOS devices today employ: o degenerately doped polycrystalline Si (“poly-Si”) film as the gateelectrode material - n+-type for “n-channel” transistors xo - p+-type, for “p-channel” transistors o Si. O 2 as the gate dielectric - band gap = 9 e. V - er, Si. O 2 = 3. 9 o Si as the semiconductor material - p-type, for “n-channel” transistors - n-type, for “p-channel” transistors Lecture 15, Slide 2

MOS Equilibrium Band Diagram metal oxide semiconductor n+ poly-Si Si. O 2 p-type Si EC EC=EFM EV EE 130/230 M Spring 2013 Lecture 15, Slide 3 EFS EV

MOS Band Diagrams: Guidelines • Fermi level EF is flat (constant with x) within the semiconductor – Since no current flows in the x direction, we can assume that equilibrium conditions prevail • Band bending is linear within the oxide – No charge in the oxide => d. E/dx = 0 so E is constant => d. Ec/dx is constant • From Gauss’ Law, we know that the electric field strength in the Si at the surface, ESi, is related to the electric field strength in the oxide, Eox: E EE 130/230 M Spring 2013 E E Lecture 15, Slide 4

MOS Band Diagram Guidelines (cont’d) • The barrier height for conduction-band electron flow from the Si into Si. O 2 is 3. 1 e. V – This is equal to the electron-affinity difference (c. Si and c. Si. O 2) • The barrier height for valence-band hole flow from the Si into Si. O 2 is 4. 8 e. V • The vertical distance between the Fermi level in the metal, EFM, and the Fermi level in the Si, EFS, is equal to the applied gate voltage: EE 130/230 M Spring 2013 Lecture 15, Slide 5

Special Case: Equal Work Functions FM = FS EE 130/230 M Spring 2013 Lecture 15, Slide 6

General Case: Different Work Functions E 0 E 0 EE 130/230 M Spring 2013 Lecture 15, Slide 7

Flat-Band Condition EE 130/230 M Spring 2013 Lecture 15, Slide 8