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DerivationMOSFET

# DerivationMOSFET - I D = μC ox(W/L(V GS-V th)V DS(1/2)V 2...

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Derivation of I-V relationship for a MOSFET: Ex. Adding a thin layer of P + alters the threshold. If V DS =0, Q d =WC ox (V GS -V th ) Total capacitance per unit length. If V DS >0 small: Q d (x) =WC ox (V GS -V(x)-V th ) where V(x) is the channel potential at x. Also I = Q d . v, where v is the velocity of the charge in meters/sec. So, I D = -WC ox [(V GS -V(x)-V th )]v negative sign indicates charge carriers are negative. v = μE, where μ is the charge mobility and E is the electric field. Also, E = -dV(x)/dx. So I D = WC ox [(V GS -V(x)-V th )] μdV(x)/dx with initial condition: V(0) =0 and V(L)= V DS Integrating both sides, results in:
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Unformatted text preview: I D = μC ox (W/L)[(V GS-V th )V DS- (1/2)V 2 DS ] where L is the effective channel length. A plot of this curve is what is known as the I-V characteristic of MOSFET. W/L is also known as "aspect ratio", V GS-Vth is the overdrive voltage. I D(max) =(1/2)μC ox (W/L)[(V GS-V th ) 2 ] If V DS <<2(V GS- V Th ), ** I D = μC ox (W/L)(V GS-V th )V DS Which is a linear function. R on = ) ( 1 th GS ox V V L W C-μ Under ** condition, MOSFET operates as a resistor whose value is controlled by the override voltage....
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