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ECE216-Lecture-17-Metal-Gate-MOS-Capacitors

# ECE216-Lecture-17-Metal-Gate-MOS-Capacitors - ECE 216...

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ECE 216 DEVICE PHYSICS FOR INTEGRATED CIRCUITS Lecture 17 METAL-GATE MOS CAPACITORS Professor Hisham Z. Massoud Department of Electrical and Computer Engineering Fitzpatrick Building, Room 3521 Duke University, Durham, NC 27708–0291 [email protected] https://courses.duke.edu/webapps/portal/frameset.jsp ECE 216 Chapter 10 – Metal-Gate MOS Capacitors Lecture 17.1

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LECTURE 17 – TOPICS 10. Bias-Voltage Dependence of MOSCAP Variables 11. MOSCAP Small-Signal Capacitance-Voltage Characteristics ECE 216 Chapter 10 – Metal-Gate MOS Capacitors Lecture 17.2
10. BIAS-VOLTAGE DEPENDENCE OF MOSCAP VARIABLES The bias-voltage dependence of the MOSCAP variables can be obtained in the following way: 1. Start by selecting a value of V SC,B that corresponds to conditions of strong accumulation in the substrate. In a metal-gate MOSCAP fabricated on a p -type substrate, a starting value of V SC,B of - 1 . 0 V is a good choice. 2. Calculate Q SC,B using the Q SC,B ( V SC,B ) relationship. 3. Calculate E x,B (0 + , V GB ) from Q SC,B . 4. Calculate E x,OX (0 - , V GB ) from E x,B (0 + , V GB ), Q f , and Q it ( V GB ). 5. Calculate V OX ( V GB ) from E x,OX (0 - , V GB ), Q mi , and Q ot . 6. Calculate Q G ( V GB ) from the charge-conservation relationship. 7. Calculate V GB from the potential-distribution relationship. 8. Calculate ψ B ( x, V GB ) for the chosen value of V SC,B by numerical in- tegration. ECE 216 Chapter 10 – Metal-Gate MOS Capacitors Lecture 17.3

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10. BIAS-VOLTAGE DEPENDENCE OF MOSCAP VARIABLES 9. Calculate n B ( x, V GB ) from ψ B ( x, V GB ). 10. Calculate p B ( x, V GB ) from ψ B ( x, V GB ). 11. Calculate % B ( x, V GB ) from n B ( x, V GB ) and p B ( x, V GB ). 12. Calculate E x,B ( x, V GB ) from ψ B ( x, V GB ). 13. Change V SC,B to a new value V SC,B + δV SC,B where δV SC,B is a small increment. 14. Repeat steps 2 to 12. 15. Plot the variable of choice vs V GB . ECE 216 Chapter 10 – Metal-Gate MOS Capacitors Lecture 17.4
10. BIAS-VOLTAGE DEPENDENCE OF MOSCAP VARIABLES Q mi + Q ot Q f + Q it Q G E x,OX Q SC,B V SC,B V OX V GB ϕ PM ECE 216 Chapter 10 – Metal-Gate MOS Capacitors Lecture 17.5

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10. BIAS-VOLTAGE DEPENDENCE OF MOSCAP VARIABLES Gate-to-Bulk Voltage, V GB (V) Substrate Space-Charge Voltage, V SC,B (V) p -Si, 300 K, X ox = 20 nm N - a,B =4 . 0 × 10 15 cm - 3 ϕ PM = 0 V, Q f = Q it = 0 E v /q E i /q E c /q - 2 - 1 0 1 2 3 4 - 0.4 - 0.2 0 0.2 0.4 0.6 0.8 1.0 1.2 ECE 216 Chapter 10 – Metal-Gate MOS Capacitors Lecture 17.6
10. BIAS-VOLTAGE DEPENDENCE OF MOSCAP VARIABLES Gate-to-Bulk Voltage, V GB (V) Substrate Space-Charge Density, | Q SC,B | ( μ C/cm 2 ) Flat-band Depletion Strong Inversion Accumulation p -Si, 300 K, Q f = Q it = 0, ϕ PM = 0 N a,B = 4 . 0 × 10 15 cm - 3 , X ox = 20 nm - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 ECE 216 Chapter 10 – Metal-Gate MOS Capacitors Lecture 17.7

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10. BIAS-VOLTAGE DEPENDENCE OF MOSCAP VARIABLES Gate-to-Bulk Voltage, V GB (V) Substrate Space-Charge Density, | Q SC,B | (C/cm 2 ) Flat-band Depletion Accumulation Strong Inversion p -Si, 300 K, Q f = Q it = 0, ϕ PM = 0 N a,B = 4 . 0 × 10 15 cm - 3 , X ox = 20 nm - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 10 - 9 10 - 8 10 - 7 10 - 6 10 - 5 10 - 4 ECE 216 Chapter 10 – Metal-Gate MOS Capacitors Lecture 17.8
10. BIAS-VOLTAGE DEPENDENCE OF MOSCAP VARIABLES Gate-to-Bulk Voltage, V GB (V) Oxide Electric Field, |E x,OX ( V GB ) | (MV/cm) Flat-band

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