1 / 24

Lecture 8: Capacitors and PN Junctions

Lecture 8: Capacitors and PN Junctions. Prof. Niknejad. Lecture Outline. Review of Electrostatics IC MIM Capacitors Non-Linear Capacitors PN Junctions Thermal Equilibrium. +++++++++++++++++++++. − − − − − − − − − − − − − − −. Electrostatics Review (1).

ruthpickett
Download Presentation

Lecture 8: Capacitors and PN Junctions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lecture 8: Capacitors and PN Junctions Prof. Niknejad

  2. Lecture Outline • Review of Electrostatics • IC MIM Capacitors • Non-Linear Capacitors • PN Junctions Thermal Equilibrium University of California, Berkeley

  3. +++++++++++++++++++++ − − − − − − − − − − − − − − − Electrostatics Review (1) • Electric field go from positive charge to negative charge (by convention) • Electric field lines diverge on charge • In words, if the electric field changes magnitude, there has to be charge involved! • Result: In a charge free region, the electric field must be constant! University of California, Berkeley

  4. +++++++++++++++++++++ − − − − − − − − − − − − − − − Electrostatics Review (2) • Gauss’ Law equivalently says that if there is a net electric field leaving a region, there has to be positive charge in that region: Electric Fields are Leaving This Box! Recall: University of California, Berkeley

  5. Electrostatics in 1D • Everything simplifies in 1-D • Consider a uniform charge distribution Zero field boundary condition University of California, Berkeley

  6. Electrostatic Potential • The electric field (force) is related to the potential (energy): • Negative sign says that field lines go from high potential points to lower potential points (negative slope) • Note: An electron should “float” to a high potential point: University of California, Berkeley

  7. More Potential • Integrating this basic relation, we have that the potential is the integral of the field: • In 1D, this is a simple integral: • Going the other way, we have Poisson’s equation in 1D: University of California, Berkeley

  8. Boundary Conditions • Potential must be a continuous function. If not, the fields (forces) would be infinite • Electric fields need not be continuous. We have already seen that the electric fields diverge on charges. In fact, across an interface we have: • Field discontiuity implies charge density at surface! University of California, Berkeley

  9. Top Plate Bottom Plate Bottom Plate Thin Oxide IC MIM Capacitor • By forming a thin oxide and metal (or polysilicon) plates, a capacitor is formed • Contacts are made to top and bottom plate • Parasitic capacitance exists between bottom plate and substrate Contacts University of California, Berkeley

  10. Vs + − Review of Capacitors • For an ideal metal, all charge must be at surface • Gauss’ law: Surface integral of electric field over closed surface equals charge inside volume +++++++++++++++++++++ − − − − − − − − − − − − − − − University of California, Berkeley

  11. +++++++++++++++++++++ − − − − − − − − − − − − − − − Capacitor Q-V Relation • Total charge is linearly related to voltage • Charge density is a delta function at surface (for perfect metals) University of California, Berkeley

  12. +++++++++++++++++++++ − − − − − − − − − − − − − − − A Non-Linear Capacitor • We’ll soon meet capacitors that have a non-linear Q-V relationship • If plates are not ideal metal, the charge density can penetrate into surface University of California, Berkeley

  13. What’s the Capacitance? • For a non-linear capacitor, we have • We can’t identify a capacitance • Imagine we apply a small signal on top of a bias voltage: • The incremental charge is therefore: Constant charge University of California, Berkeley

  14. Small Signal Capacitance • Break the equation for total charge into two terms: Incremental Charge Constant Charge University of California, Berkeley

  15. Example of Non-Linear Capacitor • Next lecture we’ll see that for a PN junction, the charge is a function of the reverse bias: • Small signal capacitance: Voltage Across NP Junction Charge At N Side of Junction Constants University of California, Berkeley

  16. Carrier Concentration and Potential • In thermal equilibrium, there are no external fields and we thus expect the electron and hole current densities to be zero: University of California, Berkeley

  17. Carrier Concentration and Potential (2) • We have an equation relating the potential to the carrier concentration • If we integrate the above equation we have • We define the potential reference to be intrinsic Si: University of California, Berkeley

  18. Carrier Concentration Versus Potential • The carrier concentration is thus a function of potential • Check that for zero potential, we have intrinsic carrier concentration (reference). • If we do a similar calculation for holes, we arrive at a similar equation • Note that the law of mass action is upheld University of California, Berkeley

  19. The Doping Changes Potential • Due to the log nature of the potential, the potential changes linearly for exponential increase in doping: • Quick calculation aid: For a p-type concentration of 1016 cm-3, the potential is -360 mV • N-type materials have a positive potential with respect to intrinsic Si University of California, Berkeley

  20. p-type NA ND n-type PN Junctions: Overview • The most important device is a junction between a p-type region and an n-type region • When the junction is first formed, due to the concentration gradient, mobile charges transfer near junction • Electrons leave n-type region and holes leave p-type region • These mobile carriers become minority carriers in new region (can’t penetrate far due to recombination) • Due to charge transfer, a voltage difference occurs between regions • This creates a field at the junction that causes drift currents to oppose the diffusion current • In thermal equilibrium, drift current and diffusion must balance − V + + + + + + − − − − − − − − − − − − + + + + + + + + + + − − − − − − University of California, Berkeley

  21. PN Junction Currents • Consider the PN junction in thermal equilibrium • Again, the currents have to be zero, so we have University of California, Berkeley

  22. p-type n-type ND NA – – + + Transition Region PN Junction Fields University of California, Berkeley

  23. Total Charge in Transition Region • To solve for the electric fields, we need to write down the charge density in the transition region: • In the p-side of the junction, there are very few electrons and only acceptors: • Since the hole concentration is decreasing on the p-side, the net charge is negative: University of California, Berkeley

  24. Charge on N-Side • Analogous to the p-side, the charge on the n-side is given by: • The net charge here is positive since: – – + + Transition Region University of California, Berkeley

More Related