Results 1 to 5 of 5

Math Help - Derivation of relationship between carrier density and current

  1. #1
    Newbie
    Joined
    Mar 2011
    Posts
    3

    Derivation of relationship between carrier density and current

    Hi there,

    I'm new here so I'm not sure if this is in the best section, but here goes...

    I'm trying to establish how a formula (relating the carrier lifetime in a semiconductor active region with the injected current) from a paper I have read has been derived. The formula is:

    n=\frac{1}{qV} \int_0^I{\tau} dI (1)

    where n is the carrier density, q is the elementary charge, V is the volume of the semiconductor active area.

    From another source (textbook) I have:

    \frac{1}{\tau} = \frac{\partial R}{\partial n} (2)

    where

    R(n) = An + Bn^2 + Cn^3 (3)

    and also the injected current I is related to n as follows:

    I = qVR(n) (4)

    I have a complete mental block on how whether I can derive the first equation from the following three - any help would be appreciated!
    -----

    Also, in the textbook, it uses equations 2,3 and 4 above to define the relationship between \tau and I as being:

    \frac {1}{\tau^2} = A^2 + \frac{4B}{qV}I} (5)

    I just keep going round in circles when I try to derive this from equations 2,3 and 4
    -----

    Any help in how to derive (1) or (5) would be appreciated! I realise that this is a 'physicsy" type question being asked on a math forum, but I hope someone can give me some pointers. Cheers!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Mar 2010
    Posts
    280
    From (4):

    <br />
\displaylist<br />
dI=qV \ \frac{dR}{dn}dn=qV \ \frac{1}{\tau} \ dn<br />

    <br />
\displaylist<br />
dn=\frac{1}{qV} \ \tau dI<br />

    and integrating dn from 0 to n
    dI from 0 to I
    gives (1).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2011
    Posts
    3
    Quote Originally Posted by zzzoak View Post
    From (4):

    <br />
\displaylist<br />
dI=qV \ \frac{dR}{dn}dn=qV \ \frac{1}{\tau} \ dn<br />

    <br />
\displaylist<br />
dn=\frac{1}{qV} \ \tau dI<br />

    and integrating dn from 0 to n
    dI from 0 to I
    gives (1).
    Hey, thanks for your reply. I can sort of follow what you've done, in that I'm not sure how you made the first step, but I can follow it on after that...

    Can you explain how you went from (4) to dI=qV \ \frac{dR}{dn}dn

    Did you differentiate (4) w.r.t. dn?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Mar 2010
    Posts
    280
    If we have function <br />
f(x)<br />

    then its differential is

    <br />
\displaystyle<br />
df=f'(x)dx= \frac{df}{dx}dx<br />
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Mar 2011
    Posts
    3
    Thanks - you've been a big help
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Derivation and Jordan derivation
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: May 8th 2011, 09:22 PM
  2. Finding Marrginal Density Fcn From Join Density Fcn
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: October 26th 2010, 08:25 PM
  3. How do carrier waves work
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: June 24th 2010, 12:19 PM
  4. Disease carrier problem with binomial dist.
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: October 9th 2009, 09:49 PM
  5. marginal density, conditional density, and probability
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: March 24th 2008, 06:50 PM

Search Tags


/mathhelpforum @mathhelpforum