Channel Current = Rate of Flow of Charge

1
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 ?ox
gate oxide permittivity W channel width Vt
threshold voltage
Channel Current Rate of Flow of Charge Ids
Q/tsd Derive transit time tsd tsd channel
length (L) / carrier velocity (v) v µEds Eds
Vds / L v µVds / L Thus tsd 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 ?ox / Tox Hence, drain current Ids W L ?ox
µVds (Vgs -Vt - Vds/2) / L2 x Tox
2
Basic MOSFET Model
In the non - saturated region where Vds lt Vgs -
Vt
K ?ox 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
3
Threshold Voltage
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
4
Transconductance
Transconductance expresses the relationship betwee
n 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