review depletion region recombination l.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Review: Depletion Region Recombination PowerPoint Presentation
Download Presentation
Review: Depletion Region Recombination

Loading in 2 Seconds...

play fullscreen
1 / 19

Review: Depletion Region Recombination - PowerPoint PPT Presentation


  • 920 Views
  • Uploaded on

Review: Depletion Region Recombination Flat Quasi-Fermi Level (QFL)  Requires rate limiting recombination is slow compared to thermal diffusion Assuming: k n ~k p = σ v , Flat QFL  We get for recombination in the bulk at position x, Note, Vapp < 0 here

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Review: Depletion Region Recombination' - Audrey


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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
review depletion region recombination
Review: Depletion Region Recombination

Flat Quasi-Fermi Level (QFL)

 Requires rate limiting recombination is slow compared to thermal diffusion

Assuming: kn~kp = σ v , Flat QFL

We get for recombination in the bulk at position x,

Note, Vapp < 0 here

review depletion region recombination2
Review: Depletion Region Recombination

-Substitute definitions and divide top and bottom by

review depletion region recombination3
Review: Depletion Region Recombination

Maximum occurs when n(x) = p(x)

new material recall we desire u total
New Material: Recall we desire UTOTAL

Continue with Udr,max, recalling we want to solve for UTOTAL, as

We need definition for n(x) and p(x)

You can show that

Nm = concentration of e- for max U,

n(xm)=p(xm)

Xm= position where n=nm

In region 1, x<xm Exp (-) so n(x)<n(xm)

 More band bending

In region 2, x>xm Exp (+) so n(x)>n(xm)

 Less band bending

calculating u total back to math
Calculating UTOTAL: Back to Math

Substituting in for n(x) and p(x)

calculating u total
Calculating UTOTAL

For normally doped Si with Kn~Kp (assumed)

UMAX is strongly peaked away from W, so we can

extend the integral from W’ ∞.

calculating u total7
Calculating UTOTAL

After a change of variables,

Recognizing that:

u total
UTOTAL

Substituting for UMAX , we obtain

A = 2: There are e- s and h+s recombining. It is as if you

lose half of the voltage to the other carrier.

u total everyone does it differently
UTOTAL: Everyone Does it Differently

Note: Nate and Mary quote a different value.

quasi neutral region
Quasi-Neutral Region

Ionized donor atoms neutralized

by injection of electrons into CB.

p(x) has not changed: before injection of

electrons, p(w)<p(w’) despite flat bands

Concentration gradient causing holes to diffuse away from W’ into the bulk.

Need to understand Diffusion/Recombination/Generation equations

 Assume No Generation

diffusion recombination
Diffusion-Recombination

Diffusion:

Putting it together:

Need Boundary Conditions

diffusion recombination12
Diffusion-Recombination

Assume no recombination in D.R. or at S.S.

diffusion recombination13
Diffusion-Recombination

After the math:

You tell me.

diffusion recombination14
Diffusion-Recombination

We only have p(x), so lets take

region where flux only due to

holes: at x=W’

Evaluate at x=W’

schockley read hall
Schockley-Read-Hall

Trapped states can be caused

by metal impurities, oxygen,

or dopants

schockley read hall17
Schockley-Read-Hall

LLI: Lower Level Injection of

Electrons and holes from photons

For n-type:

HLI: Generate more electrons and holes than

We had in our lattice:

schockley read hall18
Schockley-Read-Hall

Assuming LLI of n-type

Leaving us with :

schockley read hall19
Schockley-Read-Hall

Solving yields:

For HLI, same assumptions:

HLI decays twice as slowly

LLI: Wait for hole carriers to recombine

HLI: hole & e- carriers must recombine  twice as long