# vlsi numericals ```VLSI DESIGN (numerical problems on MOSFET current and Threshold voltage)
Ex 1:
An NMOS transistor with device transconductance
K = 20&micro;A/V2 and threshold voltage of 1.5 V is operated at
VGS = 5V and ID = 100 &micro;A. Find VDS.
Solution :- Let us assume that the MOSFET is operating in Saturation,
ID sat = K/2 ( VGS – VTH )2
= 20/2 ( 5 – 1.5 )2
= 122.5 &micro;A
For device in saturation, the ID 122.5 &micro;A but ID of device is
Given as 100 &micro;A which is less than ID sat hence the device is not
In saturation but in linear region. ---------------------- ( 2 Marks )
ID linear = K/2 { 2 ( VGS – VTH ) VDS – VDS2 }
100 &micro;A = 20/2 { 2 ( 5 – 1.5 ) VDS – VDS2 }
10 = 7VDS – VDS2
VDS2 – 7VDS + 10 = 0
( VDS – 5 ) ( VDS – 2 ) =
VDS = 5 or VDS = 2
For linear region, VDS &lt; ( VGS – VTH )
i.e. VDS &lt; ( 5 – 1.5 )
i.e. VDS &lt; 3.5V
Hence VDS = 2V
----------------------- ( 3 Marks )
1
Ex 2:-
Solution :-
Calculate the zero-bias threshold voltage for an NMOS Silicongate transistor that has well doping = 5 &times; 10&sup1;⁵ cm⁻&sup3;, gate doping
= ND =10&sup2;⁰ cm⁻&sup3; , gate- oxide thickness = 100 A⁰ , and 3 &times; 10&sup1;⁰ /
cm&sup2; singly charged positive ions at the oxide-Silicon interface.
Also calculate the ion- implant doses needed to achieve a
threshold voltage of -1 V.
VT = ΦSG - 2 ΦF sub – QBO/COX – QOX/COX
---------( 1 Mark )
ΦF sub = -VT
= -0.02
-------------------------------- ( 1 Mark )
= -0.331V
ΦF GATE = VT
= 0.02
= 0.589V
----------------------------------- ( 1 Mark )
ΦSG = ΦF sub - ΦF GATE = -0.331 – 0.589 = -0.92V
εox = 3.97 x ε₀ = 3.97 x 8.854 &times; 10⁻&sup1;⁴ F/cm = 3.515 &times; 10⁻&sup1;3 F/cm
----------------------------- (1 Mark )
= 351.5 &times; 10-9 F/cm2
QBO = –
= – 33.12 &times; 10-9 C/cm2 -- ( 1 Mark )
= –0.0942 V --------------------- ( 1 Mark )
2
--------------------------------- ( 1 Mark )
VT = - 0.92 +0.662 +0.0942 – 0.01365 = - 0.17745 V ---( 1 Mark )
NI =
=
For -1 V ,
= 0.82255 V
NI = 1.8 x 1012 Donor ions / cm2
-------------------(2 Mark )
-----------------------------------------------------------------------------------------------------
3
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