Understanding PN Junction & MOS Capacitors

1. Lecture 10: PN Junction & MOS Capacitors Prof. Niknejad

2. Lecture Outline • Review: PN Junctions Thermal Equilibrium • PN Junctions with Reverse Bias (3.3-3.6) • MOS Capacitors (3.7-3.9): • Accumulation, Depletion, Inversion • Threshold Voltage • CV Curve University of California, Berkeley

3. Results of MT #1 • Good Job! • This is only 17% of your grade Homework 15% Laboratory 20% Midterm #1 17% Midterm #2 18% Final 30% University of California, Berkeley

4. PN Junction in Thermal Equilibrium • Contact potential develops between P and N region • Diffusion current balanced by drift current • Depletion region is a “space-charge” region where the concentration of free carriers is low • The depletion region is charged due to the immobile background ions (donors and acceptors) • Used the “Depletion Approximation” to estimate the charge density  calculate the electric fields and potential variation using electrostatics in 1D University of California, Berkeley

5. ? Have we invented a battery? • Can we harness the PN junction and turn it into a battery? • Numerical example: University of California, Berkeley

6. + − n p Contact Potential • The contact between a PN junction creates a potential difference • Likewise, the contact between two dissimilar metals creates a potential difference (proportional to the difference between the work functions) • When a metal semiconductor junction is formed, a contact potential forms as well • If we short a PN junction, the sum of the voltages around the loop must be zero: University of California, Berkeley

7. PN Junction Capacitor • Under thermal equilibrium, the PN junction does not draw any current • But notice that a PN junction stores charge in the space charge region (transition region) • Since the device is storing charge, it’s acting like a capacitor • Positive charge is stored in the n-region, and negative charge is in the p-region: University of California, Berkeley

8. + − Reverse Biased PN Junction • What happens if we “reverse-bias” the PN junction? • Since no current is flowing, the entire reverse biased potential is dropped across the transition region • To accommodate the extra potential, the charge in these regions must increase • If no current is flowing, the only way for the charge to increase is to grow (shrink) the depletion regions University of California, Berkeley

9. + − Current Under Reverse Bias • Under thermal equilibrium current is zero • If we apply a reverse bias, we are increasing the barrier against diffusion current • Drift current is low since the field only moves minority carriers across junction • In fact, current is not zero but very small since the minority carrier concentration is low. Minority carriers within one diffusion length of junction can contribute to a reverse bias current. This is more or less independent of the applied bias n p University of California, Berkeley

10. Voltage Dependence of Depletion Width • Can redo the math but in the end we realize that the equations are the same except we replace the built-in potential with the effective reverse bias: University of California, Berkeley

11. Charge Versus Bias • As we increase the reverse bias, the depletion region grows to accommodate more charge • Charge is not a linear function of voltage • This is a non-linear capacitor • We can define a small signal capacitance for small signals by breaking up the charge into two terms University of California, Berkeley

12. Derivation of Small Signal Capacitance • From last lecture we found • Notice that University of California, Berkeley

13. Physical Interpretation of Depletion Cap • Notice that the expression on the right-hand-side is just the depletion width in thermal equilibrium • This looks like a parallel plate capacitor! University of California, Berkeley

14. A Variable Capacitor (Varactor) • Capacitance varies versus bias: • Application: Radio Tuner University of California, Berkeley

15. Oxide N-type Diffusion Region P-type Si Substrate “Diffusion” Resistor • Resistor is capacitively isolation from substrate • Must Reverse Bias PN Junction! • PN Junction creates a distributed capacitance with substrate (RC transmission line) University of California, Berkeley

16. Gate (n+ poly) Body (p-type substrate) MOS Capacitor • MOS = Metal Oxide Silicon • Sandwich of conductors separated by an insulator • “Metal” is more commonly a heavily doped polysilicon layer n+ or p+ layer • NMOS  p-type substrate, PMOS  n-type substrate Oxide (SiO2) Very Thin! University of California, Berkeley

17. Gate (n+ poly) Body (p-type substrate) P-I-N Junction • Under thermal equilibrium, the n-type poly gate is at a higher potential than the p-type substrate • No current can flow because of the insulator but this potential difference is accompanied with an electric field • Fields terminate on charge! University of California, Berkeley

18. + − + − Body (p-type substrate) − − − − − − − − − − − − − − − − − − − − − − − − − − Fields and Charge at Equilibrium • At equilibrium there is an electric field from the gate to the body. The charges on the gate are positive. The negative charges in the body come from a depletion region ++++++++++++++++++ University of California, Berkeley

19. Body (p-type substrate) + − Good Place to Sleep: Flat Band • If we apply a bias, we can compensate for this built-in potential • In this case the charge on the gate goes to zero and the depletion region disappears • In solid-state physics lingo, the energy bands are “flat” under this condition University of California, Berkeley

20. − + Body (p-type substrate) Accumulation • If we further decrease the potential beyond the “flat-band” condition, we essentially have a parallel plate capacitor • Plenty of holes and electrons are available to charge up the plates • Negative bias attracts holes under gate −−−−−−−−−−−−−−−−−− ++++++++++++++++++ University of California, Berkeley

21. − − − − − − − − − Body (p-type substrate) − − − − − − − − + − Depletion • Similar to equilibrium, the potential in the gate is higher than the body • Body charge is made up of the depletion region ions • Potential drop across the body and depletion region + + + + + + + + + + University of California, Berkeley

22. − − − − − − − − − Body (p-type substrate) − − − − − − − − + − Inversion • As we further increase the gate voltage, eventually the surface potential increases to a point where the electron density at the surface equals the background ion density • At this point, the depletion region stops growing and the extra charge is provided by the inversion charge at surface + + + + + + + + + + University of California, Berkeley

23. Threshold Voltage • The threshold voltage is defined as the gate-body voltage that causes the surface to change from p-type to n-type • For this condition, the surface potential has to equal the negative of the p-type potential • We’ll derive that this voltage is equal to: University of California, Berkeley

24. Inversion Stops Depletion • A simple approximation is to assume that once inversion happens, the depletion region stops growing • This is a good assumption since the inversion charge is an exponential function of the surface potential • Under this condition: University of California, Berkeley

25. Q-V Curve for MOS Capacitor • In accumulation, the charge is simply proportional to the applies gate-body bias • In inversion, the same is true • In depletion, the charge grows slower since the voltage is applied over a depletion region inversion depletion accumulation University of California, Berkeley

26. Numerical Example • MOS Capacitor with p-type substrate: • Calculate flat-band: • Calculate threshold voltage: University of California, Berkeley

27. Num Example: Electric Field in Oxide • Apply a gate-to-body voltage: • Device is in accumulation • The entire voltage drop is across the oxide: • The charge in the substrate (body) consist of holes: University of California, Berkeley

28. Numerical Example: Depletion Region • In inversion, what’s the depletion region width and charge? University of California, Berkeley