1 / 15

Lecture 9

dominique
Download Presentation

Lecture 9

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 #9 OUTLINE Continuity equations Minority carrier diffusion equations Minority carrier diffusion length Quasi-Fermi levels Read: Sections 3.4, 3.5

    2. EE130 Lecture 9, Slide 2 Derivation of Continuity Equation Consider carrier-flux into/out-of an infinitesimal volume:

    3. EE130 Lecture 9, Slide 3

    4. EE130 Lecture 9, Slide 4 Derivation of Minority Carrier Diffusion Equation The minority carrier diffusion equations are derived from the general continuity equations, and are applicable only for minority carriers. Simplifying assumptions: The electric field is small, such that in p-type material in n-type material n0 and p0 are independent of x (uniform doping) low-level injection conditions prevail

    5. EE130 Lecture 9, Slide 5 Starting with the continuity equation for electrons:

    6. EE130 Lecture 9, Slide 6 Carrier Concentration Notation The subscript “n” or “p” is used to explicitly denote n-type or p-type material, e.g. pn is the hole (minority-carrier) concentration in n-type material np is the electron (minority-carrier) concentration in n-type material Thus the minority carrier diffusion equations are

    7. EE130 Lecture 9, Slide 7 Simplifications (Special Cases) Steady state: No diffusion current: No R-G: No light:

    8. EE130 Lecture 9, Slide 8 Example Consider the special case: constant minority-carrier (hole) injection at x=0 steady state; no light absorption for x>0

    9. EE130 Lecture 9, Slide 9 The general solution to the equation is where A, B are constants determined by boundary conditions: Therefore, the solution is

    10. EE130 Lecture 9, Slide 10 Physically, LP and LN represent the average distance that minority carriers can diffuse into a sea of majority carriers before being annihilated. Example: ND=1016 cm-3; tp = 10-6 s Minority Carrier Diffusion Length

    11. EE130 Lecture 9, Slide 11 Whenever Dn = Dp ? 0, np ? ni2. However, we would like to preserve and use the relations: These equations imply np = ni2, however. The solution is to introduce two quasi-Fermi levels FN and FP such that Quasi-Fermi Levels

    12. EE130 Lecture 9, Slide 12 Example: Quasi-Fermi Levels

    13. EE130 Lecture 9, Slide 13 Find FN and FP :

    14. EE130 Lecture 9, Slide 14 Summary

    15. EE130 Lecture 9, Slide 15 The minority carrier diffusion length is the average distance that a minority carrier diffuses before it recombines with a majority carrier: The quasi-Fermi levels can be used to describe the carrier concentrations under non-equilibrium conditions:

More Related