The basic formula for calculating built-in potential is:

Vbi = VT ln(NAND/ni2)

But in SILVACO software and some research papers the formula used for finding built-in potential is:

Vbi = VT ln(NS/D/ni)

Can someone explain which of these two are correct and how?

http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=1217247&newsearch=true&queryText=physical%20short%20channel%20threshold%20voltage%20model%20for%20undoped%20symmetric%20dg%20mos&fname=&mname=&lname=&title=&volume=&issue=&spage=

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