00:00:03
when current goes from the drain to the
00:00:05
source it has to go through the channel
00:00:08
and the channel has a certain amount of
00:00:10
resistance which is just going to be
00:00:12
there because there's resistivity of the
00:00:14
channel material but the current also
00:00:17
has to pass to the drain and the source
00:00:21
which are end type for a nfet or P type
00:00:24
for p fet they contribute additional
00:00:27
resistance which we actually need to go
00:00:30
through some effort to
00:00:32
minimize Channel resistance is regarded
00:00:35
as the kind of intrinsic resistance of
00:00:37
the mosfet but the drain and Source
00:00:40
resistance are referred to as parasitic
00:00:43
resistances they are not necessarily
00:00:46
things that Aid the performance of the
00:00:48
device current is going to go from the
00:00:51
drain to the source through the channel
00:00:53
but it you know it has to go through
00:00:55
these extra resistances R sub CH is the
00:00:59
channel resistance distance it's
00:01:01
typically a few hundred ohms at least in
00:01:03
the example I'm going to give you which
00:01:05
I uses some realistic numbers that where
00:01:07
it is channel resistance is not
00:01:09
parasitic resistance it's intrinsic
00:01:12
resistance it belongs in the device and
00:01:14
the device's performance is based upon
00:01:16
the channel resistance but the parasitic
00:01:19
resistance will be something else the
00:01:22
parasitic resistance has the effect of
00:01:24
slowing down the circuit because it
00:01:25
raises the resistor capacitor time
00:01:28
constant which is kind of defined by the
00:01:30
channel resistance and the oxide gate
00:01:33
capacitance and that time constant
00:01:36
dictates how fast the mosfet can operate
00:01:40
a high frequency signal needs to be able
00:01:42
to fluctuate at its frequency while the
00:01:45
mosfet keeps up with it as it charges
00:01:47
and discharges that's impacted by the
00:01:51
extra resistance of the source in the
00:01:53
drain the inside the source and inside
00:01:55
the drain is where that parasitic
00:01:56
resistance resides it's between the
00:02:00
pads of the source and drain and the
00:02:02
metallurgical Junction which is the
00:02:04
place where the n and p type doping
00:02:07
change dominance let's go ahead then and
00:02:10
look at a resistor model of the
00:02:13
parasitic resistance which accounts for
00:02:16
the resistance inside the pad we'll just
00:02:18
look at the the drain contact pad which
00:02:20
has four different sources of parasitic
00:02:22
resistance I we'll go through each one
00:02:24
of them the contact the sheet the
00:02:27
spreading resistance accumulation
00:02:29
resistance and remember R sub CH is
00:02:31
inside the channel so it's on the other
00:02:33
side of the metallurgical
00:02:36
Junction pause the video for a minute
00:02:38
and look at the specifications on this
00:02:44
mosfet so you pause the video you've got
00:02:47
a gate source of 3 volts a threshold
00:02:50
voltage 1 volt the mosfet is 25 microns
00:02:53
wide in that two-dimensional cutaway
00:02:55
view of a mosfet that's the depth into
00:02:57
the screen that mosfet length which is
00:03:00
the distance basically from the source
00:03:01
to the drain is 1 and a half microns
00:03:03
that's kind of large compared to the the
00:03:04
record small gate lengths that we have
00:03:07
today the oxide thickness is 10 nanom
00:03:11
that's equivalent to knowing the
00:03:12
capacitance of the oxide thickness is
00:03:15
the primitivity divided by the
00:03:17
capacitance or rather C is Epsilon area
00:03:20
over distance and we always talk about
00:03:23
capacitance per area that's what Big C
00:03:26
is we will think body effect will be
00:03:29
zero for some licity and now this is
00:03:31
important we're looking in the linear
00:03:33
regime so we want to find the resistance
00:03:35
of the channel in the linear regime that
00:03:38
is we're not at a super high drain
00:03:41
Source voltage where we will enter into
00:03:43
saturation we're at a lower drain Source
00:03:46
voltage that this will be a constant
00:03:48
also means that we can take out drain
00:03:51
Source voltage from our expression that
00:03:53
we came up with the other day the drain
00:03:56
Source current versus drain Source
00:03:59
voltage s and everything that multiplies
00:04:01
VDS is one over the channel resistance
00:04:04
because current is voltage over
00:04:06
resistance this bit of the expression is
00:04:09
one over the channel resistance first
00:04:11
thing we're going to need to do is find
00:04:12
the mobility everything else seems to be
00:04:15
given but we need to find the mobility
00:04:17
let's work on that for a minute here
00:04:18
that's surface mobility and look at what
00:04:21
we are told we're given the gate Source
00:04:24
voltage and the threshold voltage and
00:04:26
the oxide thickness so we can go ahead
00:04:29
and use figure 69 on page 203 so pause
00:04:34
the video until you turn to page 203 and
00:04:36
you have this figure in front of
00:04:40
you okay so now you have figure 69 in
00:04:43
front of you there are two horizontal
00:04:46
axes the bottom horizontal axis is for
00:04:49
the P type and the top horizontal axis
00:04:51
is for the N type and they are labeled
00:04:53
with the different formula you calculate
00:04:55
the value on those axes with these
00:04:57
formulas this is for the top axis so
00:05:00
it's for an N type V gate Source plus v
00:05:02
threshold plus2 over six oxide thickness
00:05:06
and so you plug in the numbers were
00:05:07
given and you get 7 megga volts per
00:05:09
centimeter 700,000 volts per CM go to
00:05:13
the graph and you read 340 cm squ per
00:05:16
volt second for the surface mobility and
00:05:19
then everything else is a given
00:05:20
including oxide capacitance which is
00:05:23
permitivity of silicon dioxide divided
00:05:26
by the thickness of silicon dioxide so
00:05:30
let's put that together then W was 25
00:05:33
microns permitivity of silicon dioxide
00:05:36
is the relative primitivity of 3.6 *
00:05:40
Epsilon KN in fads per centimeter and so
00:05:42
I'm doing all this in centimeters you
00:05:44
could do all this in meters and you you
00:05:46
might feel compelled to use all mkss
00:05:48
units here but if you converted all
00:05:50
these centimeters to meters the
00:05:52
conversion would cancel so I don't
00:05:54
bother there are our 10 nanom 10- 6 cm
00:05:58
thickness mobility of 340 we said and
00:06:03
difference in gap source and theral
00:06:04
voltage there is our Channel length of 1
00:06:06
and2 microns you find out that the
00:06:09
channel resistance is 280 ohms now one
00:06:12
quick thing I want to point out to you
00:06:14
is the channel resistance which is in
00:06:17
the denominator on the left is equal to
00:06:19
an expression which has the channel
00:06:21
length in the denominator on the right
00:06:23
in other words you double the channel
00:06:25
length you double the channel resistance
00:06:26
that makes sense resistance is row L
00:06:28
over a
00:06:30
so for a really long Channel you have a
00:06:32
really high Channel resistance for a
00:06:36
really short Channel you have a really
00:06:37
small Channel resistance and that's when
00:06:40
the parasitic resistance will start to
00:06:42
show up because parasitic resistance is
00:06:45
in series with the channel so when the
00:06:47
channel resistance is low the parasitic
00:06:50
resistance has an opportunity to exert
00:06:53
itself to be noticeable parasitic
00:06:55
resistance is what you would call a
00:06:58
short sh Channel effect because it is
00:07:02
more pronounced when channels are
00:07:04
short let's look at each one of these
00:07:06
resistances the r subac is the
00:07:09
accumulation layer resistance now that's
00:07:11
the resistance that will produce this
00:07:13
Delta L that you'll find in equation
00:07:17
61.1 there's RSP which is due to current
00:07:20
spreading so current comes out of the
00:07:21
drain and then it sort of fans out
00:07:24
throughout the junction it's the current
00:07:26
spreading effect and so you can imagine
00:07:27
it's going to have something to do with
00:07:28
the depth of the The Junction next Toby
00:07:31
and how deep the inversion layer is
00:07:33
because that's that's over here it has
00:07:35
to get into the inversion layer over
00:07:37
here and it goes as the log of those two
00:07:40
ratios the sheet resistance is actually
00:07:44
uh fairly small in a well repared mosfet
00:07:47
and so we won't be in need of
00:07:49
considering it actually but I'll keep
00:07:51
writing it the contact resistance is the
00:07:54
resistance between the tight and depth
00:07:58
and the metallic contact pad so it's
00:08:01
contact resistance and depends on the
00:08:04
size of the pad and the resistivity of
00:08:06
the
00:08:07
contact so you put them all together all
00:08:09
four of them together and you have the
00:08:11
parasitic
00:08:13
resistance which is the resistance of
00:08:15
the source and the resistance of the
00:08:17
drain which will'll take to be identical
00:08:19
take them to be designed the same total
00:08:21
resistance from the source to the drain
00:08:22
is the resistance of the channel plus
00:08:24
the resistance of the drain plus that of
00:08:25
the source and the drain plus the source
00:08:28
resistance is what goes together to make
00:08:30
parasitic
00:08:31
ARA and again if you have a really long
00:08:34
Channel our Channel dominates you need a
00:08:36
short channel for the parasitics to
00:08:38
matter so there's short Channel effect
00:08:41
let's look at the effect on the drain
00:08:42
Source current and the saturation of the
00:08:45
drain Source current and then we're
00:08:46
going to explain where this mysterious
00:08:48
equation
00:08:49
6101 came from so we have two
00:08:52
considerations one with and one without
00:08:54
parasitics if you have a pristine
00:08:56
situation ideal situation where there
00:08:58
are no parasitic resistances the drain
00:09:01
Source saturation current is
00:09:03
proportional to the gate Source voltage
00:09:06
minus the threshold that's stated
00:09:07
clearly in equation
00:09:10
6914 with parasitics present that
00:09:13
saturation current is reduced and so
00:09:16
it's going to be reduced by iir of the
00:09:18
parasitic resistances and so we'll write
00:09:20
it this way it's going to be smaller by
00:09:23
resistance parasitic times that drain
00:09:26
saturation current that you would have
00:09:27
if the parasitics weren't there that's
00:09:29
our first order adjustment so given the
00:09:32
ratio of idat which is this longer
00:09:35
expression divide by idat ideal which is
00:09:38
the shorter expression simplify a little
00:09:41
bit make sure you follow that algebra
00:09:42
canceling out the vgs minus BT that's a
00:09:45
useful thing to know so you can put a
00:09:48
circle around this and save it and use
00:09:50
it how much the saturation current is
00:09:53
reduced from the ideal value when you
00:09:56
have parasitic resistance there's a
00:09:59
different expression in our textbook
00:10:00
let's take a look at that if I look at
00:10:03
some typical values for these quantities
00:10:06
like an ID set saturation drain Source
00:10:10
current of about a milliamp a parastic
00:10:12
resistance of less than 10 ohms it will
00:10:16
be typically 1 ohm uh the gate Source
00:10:20
voltage Min be threshold something on
00:10:22
the order of 1 volt well if these are
00:10:24
the values this expression right here is
00:10:27
0.01 and so that's a one % adjustment
00:10:30
with these typical values actually 10
00:10:32
ohm probably being a worst case I have a
00:10:36
uh adjustment on my drain Source
00:10:38
saturation current of about 1% you can
00:10:41
invoke the binomial expansion theorem
00:10:44
and rewrite it 1 minus a very small
00:10:47
number is 1 / 1 plus that very small
00:10:51
number I don't have a good reason for
00:10:53
doing that except that that's how
00:10:54
equation
00:10:55
6.1.1 is presented to us so I just
00:10:59
thought I would argue why that that's
00:11:01
okay to to have but again I go with
00:11:04
what's derived but you can use that as
00:11:06
well as long as these really do come out
00:11:10
to make a small number that's the
00:11:12
parasitic resistance its effect is to
00:11:15
reduce the saturation current uh
00:11:17
somewhat not a lot but it reduces it
