1 / 13

Lecture #7

Lecture #7. OUTLINE Carrier diffusion Diffusion current Einstein relationship Read: Section 3.2. Diffusion. Particles diffuse from regions of higher concentration to regions of lower concentration region, due to random thermal motion. 1-D Diffusion Example.

fagan
Download Presentation

Lecture #7

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 #7 OUTLINE Carrier diffusion Diffusion current Einstein relationship Read: Section 3.2

  2. Diffusion Particles diffuse from regions of higher concentration to regions of lower concentration region, due to random thermal motion. EE130 Lecture 7, Slide 2

  3. 1-D Diffusion Example • Thermal motion causes particles to move into an adjacent compartment every t seconds • Each particle has an equal probability of jumping to the left and to the right. EE130 Lecture 7, Slide 3

  4. Diffusion Current x x D is the diffusion constant, or diffusivity. EE130 Lecture 7, Slide 4

  5. Total Current J= JN + JP JN = JN,drift + JN,diff = qnne+ JP = JP,drift + JP,diff = qppe– EE130 Lecture 7, Slide 5

  6. The position of EF relative to the band edges is determined by the carrier concentrations, which is determined by the dopant concentrations. In equilibrium, EF is constant; therefore, the band energies vary with position: Non-Uniformly-Doped Semiconductor Ec(x) EF Ev(x) EE130 Lecture 7, Slide 6

  7. In equilibrium, there is no net flow of electrons or holes  The drift and diffusion current components must balance each other exactly. (A built-in electric field exists, such that the drift current exactly cancels out the diffusion current due to the concentration gradient.) JN = 0 and JP = 0 e dn = + = m J qn qD 0 N n N dx EE130 Lecture 7, Slide 7

  8. Consider a piece of a non-uniformly doped semiconductor: Ec(x) EF n e = - q kT Ev(x) EE130 Lecture 7, Slide 8

  9. Einstein Relationship between D and m Under equilibrium conditions,JN = 0 andJP = 0 e dn = + = m J qn qD 0 N n N dx qD e e = - m N 0 qn qn n kT Similarly, Note: The Einstein relationship is valid for a non-degenerate semiconductor, even under non-equilibrium conditions EE130 Lecture 7, Slide 9

  10. Example: Diffusion Constant What is the hole diffusion constant in a sample of silicon with p = 410 cm2 / V s ? Solution: Remember: kT/q = 26 mVat room temperature. EE130 Lecture 7, Slide 10

  11. The ratio of carrier densities (n, p) at two points depends exponentially on the potential difference between these points: Potential Difference due to n(x), p(x) EE130 Lecture 7, Slide 11

  12. Quasi-Neutrality Approximation • If the dopant concentration profile varies gradually with position, then the majority-carrier concentration distribution does not differ much from the dopant concentration distribution. • n-type material: • p-type material: • in n-type material EE130 Lecture 7, Slide 12

  13. Summary • Electron/hole concentration gradient  diffusion • Current flowing in a semiconductor is comprised of drift & diffusion components for electrons & holes • In equilibrium, JN = JN,drift + JN,diff = 0 • The characteristic constants of drift and diffusion are related: J= JN,drift + JN,diff + JP,drift + JP,diff EE130 Lecture 7, Slide 13

More Related