1. ELECTRONICS II VLSI DESIGN FALL 2013 LECTURE 4 INSTRUCTOR: L.M. HEAD, PhD ELECTRICAL & COMPUTER ENGINEERING ROWAN UNIVERSITY

2. MOSFET Symbols

3. Cross-section used to identify capacitances.

4. Accumulation

5. Depletion – no channel poly SiO 2 P-type substrate GND V << V th Depletion region

6. Depletion – sub threshold channel

7. Inversion

8. Capacitance to ground

9. MOSFET Capacitance Model

10. Threshold Voltage

11. Calculating the Threshold Voltage 1. Develop the depletion region 2. Create a channel at the gate oxide/substrate interface 3. Account for any source to body voltage 4. Neutralize defect charge 5. Neutralize material dependent potential difference Begin with the definition of voltage due to a charge stored on a capacitor. +Q b ’ is the charge on the gate and -Q b ’ is the charge under the gate oxide.

12. Calculating the Threshold Voltage From these equations: If the surface potential, V s is equal to the electrostatic potential in the semiconductor bulk there is no charge stored in a depletion region. As V s increases, the depletion region grows. First, we determine the charge in the depletion region.

13. Next, we determine the additional charge due to the channel. V s increases with an increase in V GS. When V S reaches -V fp negative charge has accumulated at the oxide semiconductor interface. In fact, at that point the interface area (channel) is as n-type as the bulk semiconductor is p-type. Taking into consideration any source to body potential: If the body of the MOSFET is not tied to the source, the potential between the interface and the bulk is not only dependent upon V GS. Now the charge under the gate totals,

14. The total potential across the gate-oxide capacitance: Since the change in voltage to obtain the channel is: Then*, *Remember, V fp is a negative number! An additional source of charge is defects at the oxide interface:

15. And finally, there is the inherent potential difference between the gate and the substrate:

16. Combining these components to get the final version of the threshold voltage: Note error in equation 6.17

17. Now we come to the I-V Characteristics