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# Channel Current = Rate of Flow of Charge I ds = Q/τ sd Derive transit time τ sd - PowerPoint PPT Presentation

Basic MOSFET Model. Q = channel charge L = channel length v = carrier velocity µ = carrier mobility Eds = electric field Vds = drain - source voltage Cg = gate - channel capac. Tox = gate oxide thickness є ox = gate oxide permittivity W = channel width Vt = threshold voltage.

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## PowerPoint Slideshow about ' Channel Current = Rate of Flow of Charge I ds = Q/τ sd Derive transit time τ sd ' - zedekiah-louis

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Presentation Transcript

Q = channel charge

L = channel length

v = carrier velocity

µ = carrier mobility

Eds = electric field

Vds = drain - source voltage

Cg = gate - channel capac.

Tox = gate oxide thickness

єox = gate oxide permittivity

W = channel width

Vt = threshold voltage

Channel Current = Rate of Flow of Charge

Ids = Q/τsd

Derive transit time τsd

τsd = channel length (L) / carrier velocity (v)

v = µEds

Eds = Vds / L

v = µVds / L

Thus τsd = L2/µVds

Channel charge: charge appears in channel when gate voltage exceeds threshold.

Since gate and oxide form a capacitor:

Q = C x ( Vgc - Vt )

Q = C x ( Vgs - Vt ) source end

Q = C x ( Vgs - Vds -Vt) drain end

So, average channel charge Q = C x (Vgs -Vt - Vds/2)

Gate - channel capacitance is a parallel plate capacitor

Cg = W L єox / Tox

Hence, drain current

Ids = W L єox µVds (Vgs -Vt - Vds/2) / L2 x Tox

EE213 VLSI Design S Daniels

In the non - saturated region where Vds < Vgs - Vt

K = єox µ/Tox = process transconductance parameter

ß = KW/L = device transconductance parameter

Saturation begins when Vds = Vgs - Vt

In the saturated region where Vds = Vgs - Vt

These expressions are based on a very simple model. Real transistors will behave slightly differently

These expressions hold for both enhancement mode and depletion mode devices

EE213 VLSI Design S Daniels

VSB = substrate bias voltage

N = impurity concentration in the substrate

Vt(0) = the threshold voltage for VSB = 0

Increasing VSB causes the channel to be depleted of charge carriers

and thus the threshold voltage is raised

Change in Vt depends on VSB and a constant which

depends on substrate doping

EE213 VLSI Design S Daniels

Transconductance expresses the relationship

between output current Ids and input voltage Vgs

In saturation Vds = Vgs -Vt

An indication of frequency response can be given by:

This shows that switching speed is proportional to gate voltage above threshold and carrier mobility.

Speed is inversely proportional to the square of the length of the channel

Both gm and Vt are important FET characteristics which need to be tightly controlled

EE213 VLSI Design S Daniels