At threshold voltage Vt the surface potential is Given this condition threshold voltage is: ….the 3rd term is V=Q/C Reorganizing terms: Substituting the identity for Es: Substituting for the body effect factor identity gamma: ….this is the same as equation 2.1.63 of CMOS Analog Design Using All Region MOSFET Modeling Equation 2.1.59 Read more…
which is Poisson's equation. Substitute the depletion region charge density at the surface far from the surface Subtracting: Depletion Derivation Line Inversion Derivation Line right hand side evaluated 0 to Identity Table
​ In the calculation of depletion region width and depletion capacitance the space charges could not move and the holes were largely already relatively negligible and thus modification of charge density due to Vg was not necessary in the first order. The inversion channel is formed using mobile electron carriers and therefore Read more…
​ Substitute for depletion region width from identity table: Now breaking down the identities to show the same form as the book: ….this is almost the same as equation 2.1.27 of CMOS Analog Design Using All Region MOSFET Modeling If you want to include the linear term of depletion Read more…
​ Definition of n is: Substituting: Using the depletion width from table: Which can be simplified quickly to the following when needed: ….this is almost the same as equation 2.1.58 of CMOS Analog Design Using All Region MOSFET Modeling If you want to include the linear term of depletion region electric field Read more…
(1)When voltage is first applied it is too low to attract many additional carrier electrons. As the voltage rises hole carriers flee the gate exposing more fixed negative charges to balance out the charge on the gate. A circle with – is a fixed acceptor dopant atom with Read more…
The source and body may not be at the same potential. The curve represented as EFi is the Fermi level from the p substrate through the reverse biased source–substrate junction to the source contact. The space charge region width under the oxide increases from the original xd @ threshold value when Read more…