Before we broke in the last video, we were talking about MEMS accelerometers.
And we had figured out how to make an accelerometer which could
measure acceleration around the x and along the y direction.
And the main concept was to use this proof mass which could move
along the x direction.
And it's another proof mass, which is perpendicular to the first one,
which is confined and is free to move along the y direction.
And we thought, you know, we could lay these out to together on one single chip,
as is shown over here with a set of fingers and fixed plates.
Which would measure the acceleration in the x direction and the perpendicularly
laid set of, fins and plates which would measure it along the y direction.
The next question was how to make a three axis accelerometer for
which we would need to measure acceleration along the z-axis.
So one way to go about it would be essentially to take this chip and
just flip it 90 degrees.
Okay.
So one of these fins, which was you know, one of these moving mass, which had fins.
Which was maybe, which was maybe measuring acceleration along the y direction.
Would be now facing up and it could now measure acceleration along the z-axis.
While this is theoretically certainly possible,
there are many problems in taking approach like that.
We can think about how to make up contacts on
how to connect to this MEMS chip which is perpendicular.
And that would become very challenging.
Also how to over all package these two
chips into one monolithic package would become increasingly difficult if this
chip is you know, standing perpendicular with respect to the ground.
So even though this might sound like a cool thing to do,
it's not a very practical approach.
So the practical approach, which is most commonly used to make
three axis accelerometer are to enable measurement of acceleration
along the z-axis, is this concept of this mass.
Which is suspended using what's called the torsion bar or a torsion spring.
And the idea is pretty simple.
So the idea is you have large set of area which
is dedicated to this upper capacitor plate.
Which is suspended above the substrate using this torsion bar.
And the main idea is that the moment of this upper capacitor plate are unevenly
distributed, are unevenly distributed with respect to this access of the torsion bar.
So as you can see in this picture over here.
This upper capacitor plate has much more mass located towards the right
as compared to the mass it has located towards the left of the plate.
So whenever there's an acceleration along the z-axis,
there'll be a imbalance of the moments along these torsion bar.
And that would result in one part of the plate going down and
accordingly another part of the plate lifting up.
So to describe it more clearly, I will draw the cross section.
The side cross section.
So it I take a side cross section of this upper capacitor plate
it would look something like this.
Okay?
So I have this torsion bar over here.
And then I have these two masses unequally distributed.
So whenever I have an acceleration, this will essentially bend like this, okay?
So the part which has higher mass will go down and
the part which has lower mass will go up.
And I can use that to my leverage to measure the acceleration.
If I design a capacitor by using this
upper capacitor plate and I would lay down on the ground like this.
Fixed ground planes which measure these two capacitances.
So now, I would have essentially one capacitance which is going,
up with this motion and another capacitance,
which is going down because this distance is increasing.
And again, I can sense the change in capacitance as this,
plate, bends around this, torsion mark.
Okay.
So an important thing for
this to happen is that this area of this top capacitor plate has to be significant.
So that I can have a significant change in the capacitance.
So you'll notice that in these three axis accelerometer, using this concept,
a lot of the area on the chip is dedicated to making this z-axis accelerometer.
So I'm showing here one of these pictures.
So on this picture, you can clearly see,
on the three sensors which are measuring acceleration along x, y, and z-axis.
So these set of fins would be, let's say, used for
measuring acceleration along the x-axis.
And then you would have a perpendicular set of fins and
fixed plates which would measure the acceleration along the y-axis.
And then you see that you have a large part of the chip which is dedicated to
measuring the acceleration along the z-axis.
So over here you see this torsion bar or
this torsion spring and you see that this mass is
asymmetrically this upper capacitor plate you can clearly see is asymmetric.
There is much more mass along this side of this torsion spring,
as compared to this side.
And a large fraction of the area on the chip is dedicated to
making this upper capacitor plate.
Such that that you can detect this change of
capacitance when this this capacitor plate moves.
Okay?
Another thing to keep in mind, that this z-axis sensor, the properties of that
that is the stiffness of this spring as well as the stiffness as well as the mask.
The proof mask of this spring is going to
be different as compared to these x and y sensor.
Okay?
So many a times this mask ends up being larger as compared
to the mass that you have, the proof mass that you have for x and y direction.
As a result of that, the resonant frequency that you get along the z
direction could be different as our you know, usually lower than the resonant
frequency that you get along the x and, the y direction.
So what I would encourage you to do is go check out the data sheets for
some of these three axis accelerometer.
Which lists out what is the bandwidth, what is the frequency.
and, some of the other properties allowing x, y, and z direction.
And you will notice that the properties along the z direction are different
as compared to what you have along the x and y direction.
So that's, good, in that,
you know it's indicating that the sensor has been made using this approach.
So I like to end with this final note, which is around scaling since
we have studied a lot about scaling in a lot of other videos on this channel.
What I would like to also mention is how the MEMS accelerometer has
scaled over the years.
So this is zero drawing this line along the other function of years.
And what you see is clearly the size of the MEMS accelerometer has
decrease this significantly in these last over the span of last four years.
And now you are getting accelerometers, three axis accelerometer with the,
the overall [INAUDIBLE] dimension nearing close to mm squared.
And it started all the way back in
2007 where the dimension of this was around 9mm squared.
And you might think why this is a big steal because you
know 9mm squared is 3mm by 3mm.
As compared to a lot of the accelerometers today are like 2mm by 2mm,
and increasingly they are approaching 1mm by 1mm here.
So, remember the picture that I showed you which showed the these
MEM accelerometers and also the gyroscopes in the first video.
So, there are two things, once you have your printed circuit board on a phone.
You have only an area of typically like 80mm
squared available on your primary circuit board.
And if you do reduce the size it does matter a lot.
So if you have a chip, which is 3mm by 3mm.
Okay?
Versus if you have a chip which is 1mm by 1mm.
The routing on this printed circuit board are the options which are available for
placing this 1mm by 1mm chip are usually, you know, 300 or 400 times.
Much better the number of options you have placing a smaller chip
as compared to the number of options you have placing a larger chip.
And this, as you can imagine,
would become even more significant once you go to variable devices.
Where, again, the amount of area which is available for
placing the chips is, again, much smaller.
So, especially for mobile, and even especially for variable applications,
the reduction in the die size from 9mm squared to 1mm squared
gives you a lot of flexibility in terms of where you can place the chip.
You'll notice that the consumer electronic based devices,
they have reduced this, this area of the accelerometer much more
aggressively as compared to what have been done in these automobile applications.
Because in an automobile you're not as constrained with space as you are in
consumer electronic application.
Okay? The other benefit that you do get as
you reduce the size.
Okay?
Is this cost reduction.
Okay?
So you get tremendous amount of cost reduction so
when these accelerometers were first introduced,
they used to cost more than $0.10 for a three axis accelerometer.
Now you can get something in the range of $0.03 for a three axis accelerometer.
Or that is around $0.01 for measuring acceleration along each of these axis.
And again, that's, you know, a huge,
that makes a huge impact in terms of the volume shipments for these accelerometers.
And [UNKNOWN] enough penetration that they have in your phones and
all of your consumer electronics.
So, as a result of scaling the size of these accelerometers,
it has further enabled the adoption of these things in all sorts of devices.
So I'd like to leave you with a final thought.
We have talked about scaling with respect to transistor.
We have seen the performance of the transistor.
It improves as you scale down the area of transistor,
as you scale down the lateral dimension of each transisitor.
The final food of thought that I want to leave you with is think
about what would happen to the performance of a MEMS accelerometer as you
scale down it's area of size.
You can think the proof mass will decrease or
the dimensions in that capacitor assembly that we talked about will decrease.
So think about what would happen to the performance, or
the specs of a accelerometer as you scale down its dimensions.
And we'll come, and touch base on this topic in the subsequent questions and in,
in other videos.
Thanks