nanoHUB-U Principles of Nanobiosensors/Lecture 3.6: Potentiometric Sensors - How to beat Screening
========================================
>>
[Slide 1] Welcome back and we are talking about potentiometric sensors, as you might recall. And in last five lectures, or at least four lectures, I sort of gave you bad news about potentiometric sensors. Yes, it can be integrated, it can be made very small, and you can put hundreds of millions of them in parallel, in modern nanosensor -- nanobiosensor technology. But we saw that this salt was a tax collector, and a very bad one at that, and it was stealing significant amount of charge from the biomolecules, making potentiometric sensing difficult. We are engineers so last time, I told you how to beat the diffusion limit about -- through evaporation of the droplet or by putting many sensors in the solution so that in
[inaudible] approach you can detect the rear analyte relatively quickly. So therefore, we should look for an engineering solution. We'll again look at the physics deeply, that what is it that cause this screening and that will then, once we understand that, it will tell us also that how we can beat it. And it will turn out that an analogy with basketball will help you understand this very quickly. If you are -- if you play or watch basketball, then you know what I am talking about.
[Slide 2] So I have -- I'll start by explaining the challenge of charge screening. By now, I have told you enough times so I'll go quickly. And then, essentially, I will talk about two approaches, de-screening at high frequency and the Giant Nernst Sensor. And then, I will just briefly mention one -- another approach before I conclude.
[Slide 3] Very briefly, let me remind you what the issue was about DNA binding and salt. The idea was that when the DNA binds, by now you know that the repulsion is significant because, remember, if it's 100 nucleotide long, that pH is seven, charge is 138. And so, there is another 138 charges in here and they will have strong repulsion unless we have the sodium chloride in it -- potassium chloride in the system. And the sodium, positive ions will come into a drain and screen the interaction and allow them to stay together. Now, look at this. This immediately is telling us something, which will allow us to beat the sensing limit, for example. These almost looks like, you know, if you had listed five player in each basketball team, if you had many, it looks like that almost for every player of a team, there is an opposing player sitting in here. So you can immediately see that if you change things slowly, of course the screening, there -- it will be screened out. Everybody will be able to guard everybody else and essentially the whole charge systems, you cannot really -- will be able to penetrate through. So how do you beat it? The simplest way to beat it is to make a fast break. So do something so that the molecules cannot follow you. And if you can do that, then that can only happen at high frequency and we'll see what frequency to use so that you can beat the screening limit.
[Slide 4] Now, this screening limit is, again, to remind you that assume that you have 100 millimolar of salt solution and if you have been doing the homework, by now you would know that that gives you about a one nanometer sort of screening length, or divide length. So that, you can only see approximately three nucleotides because each turn is about 0.34 nanometer, 3.4 angstrom. In a nanometer, you see three. So you see just the fit of the biomolecule. And the trouble is that even when the blue target biomolecule has landed, if it doesn't land within that one nanometer, but sort of binds a little bit farther out, you wouldn't know because this biomolecule, this target biomolecule, will be lost in the fog of the salt. So therefore, nothing will be reflected on the sensor itself, the potentiometric sensor itself. Somehow, if you could make the screening length a little bit larger, so that it doesn't decay so fast, if you could do that, let's say somehow if you can increase it to five nanometer, then in that case, we'll be able to see much farther. And certainly, this part of the extra target molecule will become visible to the sensor itself. And in that way, we'll be able to detect the biomolecule even in the presence of strong salt concentration. Now, the question is how do you do it? You cannot just arbitrarily reduce and increase salt concentration in a fluid. How do you do it dynamically? That is what is -- I'll explain at -- that when you use an AC frequency, let's say about a megahertz, it will turn out that these salt molecules, the sodium and chloride, chlorine molecules, they will stay frozen. So the electric field from here, from the molecule, can directly penetrate the sensor surface and therefore, the molecule can be detected. And so, the essential difference between high frequency and low frequency is that at high frequency -- at low frequency, the decay is very strong, exponential. At low frequency, because as if the salt concentration is frozen, so the differential salt concentration, as if sort of gets reduced, and the potential can get farther out and therefore, your -- the "Debye length" gets much bigger. Let me explain that a little bit -- physically a little bit more.
[Slide 5] You see what happens is that there is a -- if you start -- let's start with this biosensor and let's apply a certain frequency. There is a DC bias, but on top of it, let's use a slight AC bias on top of the DC bias. In that case, what will happen, that this will correspondingly cause oscillation in the biomolecule itself, as well as around all the salt. So this is really the liquid. This is the fit of the target biomolecule. So I'm representing it in this cartoon form. Now, if your frequency of modulation is low, then you'll get the green point, where the capacitance -- effective capacitance will be large. And if you look at the potential, the potential essentially will dive very quickly to the -- from the biomolecule. So therefore, the biomolecule is invisible to the sensor itself. So that's the green curve and that happens at low frequency. Now, at intermediate frequency what will happen, that the capacitance will begin to drop. How does capacitance drop? That means somehow, effectively, the screening is getting weaker. LD is getting bigger, as if the salt concentration is going down. Of course, in reality, the salt concentration cannot go down. It's just that it cannot follow the fast AC signal. So therefore, the capacitance is going down. And if you look at the potential, actually do this calculation, you will see that, indeed, now the potential drop is somewhat different. It doesn't drop off as quickly and a little bit of the biomolecule is now getting visible to the sensor surface. The best, of course, is use a little bit higher frequency and if you do that, at beyond a certain critical frequency, then what we'll see that the effect of screening is gone. The potential begins from the charge, goes all the way to the sensor, and therefore, it can immediately sense the presence of the biomolecule. So these are the essential features about how high frequency allows this type of screening free sensing for these molecules.
[Slide 6] Now, it turns out that you really don't have to do any sophisticated calculation. In order to get these basic facts right, all you need to know is something that we have already learned in the previous lecture. What is this capacitance? You remember, if you have a charge, if you have a salt, what is the capacitance called? Well, that's the double layer capacitance. Remember the salt screening? And therefore, you know the formula. The double layer formula for capacitance formula essentially goes the square root of the salt concentration and temperature and exponentially with voltage. Something that we have seen before. Now, something that we have not seen before is this conductance G of the salt. And that depends on, because remember, salt has the sodium and chlorine. So therefore, when you apply voltage, just like electrons and holes, they move in the opposite direction. And of course, if you change the polarity of the voltage, they will reverse direction and go in the other direction. And so therefore, there is this factor two in the conductivity, one accounting for sodium, the other for the chlorine. Now, I know their mobility is not exactly the same, which is here, but we are assuming it's about the same. Otherwise, you will say mu sodium plus mu chlorine and drop the two. And essentially, this is the number of salt molecules you have. So qN and the mu, that gives you the conductivity of this. If you have -- just know these two quantities, in fact you can find out what frequency should you operate so that the sensing becomes screening-free. So let's remind ourselves that this is the capacitance equivalent circuit network. Now, if you have taken a simple physics course, you know that when you have a RC circuit, then the resonant frequency or the critical frequency. The decay frequency, occurs at G divided by CDL. That is while it will begin to respond and what will happen, the capacitance will gradually begin to disappear. The effective of the capacitance will gradually begin to disappear at that point and there will be a linear voltage drop associated with the conductor. And so therefore, all we have to do for a given salt concentration, all we have to do is to calculate this ratio. As you can see, there is a salt concentration I naught here and then there is another salt concentration, square root of I naught . So this ratio will therefore be -- will be proportional to the square of the salt -- square root of the salt concentration. Now, this particular calculation was done for one millimolar salt concentration, relatively low. But remember that for physiological conditions, in order to keep the DNAs bound together. The salt concentration is about a factor of hundred millimolar. That tells us therefore that the frequency -- critical frequency at the reason and conditions will be about a factor of 10 larger. And so, if you operate the -- this detection steam at one megahertz, this is 0.1 megahertz, if you operate it one megahertz, you can be rest assured that there will not be any effect of screening on this sensing. Now, where is this oscillation going on? Remember, I said the basketball players are sort of staying frozen as you make the first break. Where is the mass in this whole picture? You don't see any mass anywhere else. Well actually, mass is hiding in mu. You may remember that mu is the mobility, which is Q tau over m sta
[phonetic]. Larger the mass, more difficult it is for it to get high velocity. And so, their fact that sodium and chlorine are big molecules, cannot move very easily, is reflected in small mu, and that small mu tells me that the G is small, relatively speaking, compared to a proton, for example. And that's what allows this critical frequency to be in a range, which is accessible to experiment the
[inaudible]. Had it been at a gigahertz, for example, this critical frequency? We would be out of luck. Who would put a gigahertz oscillator in the system in order to do biosensing? Especially for over the counter biosensors, you wouldn't really like this type of sophisticated instrumentation.
[Slide 7] All right. So this is how it works experimentally. I'll be very brief. What you do in the beginning is apply an AC voltage, but modulate it. So this is the carrier frequency, but modulate it with a modulation frequency of omega M. So you have a big carrier wave, but just like a radio signal, AM radio signal, you modulate it with the extra frequency. That carries the information, omega M. Then what happens, that as a result, this voltage here sets up an oscillation. The salt molecules cannot move, but the electrons in the mod DNA itself, they can move just fine because they can oscillate. Their mass is smaller; they can oscillate much more easily. This oscillation, once it sets up, then this dipole, as you're going back and forth, you know, from the positive to negative, as is going back and forth, that changes, in turn gets reflected in the potential, again in oscillating potential. And you simply detect this as a result, the change in the corresponding current at this modulation frequency. And if you do that, you will see that, whether a molecule is present or not. Because this magnitude of the oscillation will change as individual biomolecules that you are landing on the sensor surface. I thought this is pretty neat. This is recent, like about two years ago this experiment came out, and I thought this was a very neat idea that addressed the problem in a simple and fundamental way. Of course, use of a high frequency, gigahertz or associate circuitries, something that's not desirable, but you can see fundamentally, it addresses the screening problem.
[Slide 8] Let me now tell you about the second approach.
[Slide 9] The second approach relies on device physics and it really doesn't solve the screening problem fundamentally, but it addresses the problem in a system perspective. I'll explain how. And the way it works, again it's a DC technique. There's no AC signal anywhere, so therefore, perhaps simpler. So this is how it works. I've already told you that if you had a certain MOSFET or an ion sensitive field effect transistor, then the maximum change that you can have is 59 millivolt by pH. Now, what does it mean? What it means is this. That if you change the pH by a -- by one, which is increase the concentration by one, let's say, the proton concentration by one, then its effect is equivalent to, in the ideal case, applying 59 millivolt of gate voltage. So if you had two devices, in ideal case, one where the pH has changed by one, in another where somebody has changed it by 59 millivolt, the gate voltage, you will not be able to tell them apart because that is the ideal limit. Now, it turns out that you can amplify this pH response. So there's a fundamental limit for single sensor. You can amplify it by using a double-gated MOSFET. So double-gated MOSFET actually has two gates. You have one gate on the top and another gate on the bottom. Most of the normal are other sensors that I had been talking about are the channel and a single gate. Now, we have added a second gate. Source and drain are on the left and right and salt and the pH are on the top electrode, let's say. Now, let's say you have changed the pH by one, if you have changed the pH by one, then the -- this will correspondingly induce charges on the top part of the channel and the current will be something like oxide capacitance multiplied by mu, how big the channel is, that mu over L, how much voltage you have applied on the channel, and delta VG is what is the corresponding change in the voltage? For a certain, pH -- change in pH, it will be equivalent to changing the voltage by a certain amount. Okay? That's -- that's my current on the top, top part of the channel. Now, I can also induce channel current on the bottom part of the channel also by using the back gate. And if I do that, I will write the same expression for the bottom channel, which is the blue, except that I will not change the mu because it's sharing the same material. I will not change the W over L because this is the same transistor; same width, same length. This shares the drain voltage. They would be the same. But of course, VG1 and VG2 could be very different, in principal, and also the oxide capacitance here on the top and the bottom could be very different. All right? I have a total amount of change in the current due to the extra gate voltage. Now, what I can do is essentially add the two current and see what the new drain current is. And change VG2 in a way, in a negative way, so that any increase in the rate current is compensated by corresponding decrease in the blue current so that the sum becomes equal to zero. There is no change. Right? You will have returned it back. And then, if you equate these two quantities, then you immediately see that the delta VG2 is actually equal to 59 millivolt by pH multiplied by this huge factor, the capacitance on the top oxide, and capacitance on the bottom oxide. You can physically see what's going on. What's going on is that here, the charge can couple easily with the oxide, easily with the channel, because the oxide is 10. Here, you need a much more larger voltage to induce the same channel current because it's so thick. This weaker coupling gives you this voltage amplification. 00:20:56,066 --> 00:20:58,576
[Slide 10] And if you are right, if the same have -- the top and the bottom oxide have the same dielectric constant, so epsilon naught A over T, then correspondingly, you can see that the gate voltage, the pH sensitivity of this combined system, would be proportional to the thickness of the bottom oxide divided by the thickness of the top oxide. It could be a huge number, 100, 150, 200, for example. And in that case, you will get a huge amplification of the pH sensitivity. Remember, I still have screening and other issues, but it is sort of allowing me to get around it. And indeed, if you do different oxide thicknesses as a function of pH, remember this pH on the top gate is like equivalent to changing the gate bias, top gate bias, and these three curves are for three different bottom gate oxide. The thicker the bottom gate, higher is the response. And instead of 59 millivolts pH, you can begin to have a significantly larger number associated, and experimental data does support this conclusion, that indeed there is this significant amplification of the original Nernst response. In fact, it turns out you can do better if you use a slightly -- you're willing to use a slightly different geometry. For example, in this case, instead of sharing the same channel on the top side and the bottom side, sort of, on the second floor and the first floor, but sharing the same footprint in the same building, what you can do is to have a nanoplate, essentially an elongated plate, like transistor, and control it with, negate this current with, with a second nanowire transistor so that any change in the current associated with the first transistor, due to pH, is counter balanced by the change in the current associated with the nanowire. Now, you can see that this is very small compared to this. Therefore, you need much bigger voltage in order to compensate this current and hence, VG2 would be large and the pH sensitivity will be amplified. You can immediately see the first transistor, let's say this is the nanoplate transistor, and the key difference is here. You see, I don't have to have mu1 and mu2 the same. The first transistor could be made of silicon; the second could be made of Gallium arsenide. It is not even seeing the salt and the fluid environment. So I can use any other material that has higher mobility. I can have two different W over L ratio, two different voltages, and therefore, it gives me significant freedom in order to amplify the signal. So therefore not only I have the oxide ratios, but I have the material ratios, voltage, and as geometric ratio, which can give me voltage responses of 10s of volts as a function of pH, part pH, not this tiny 59 millivolt, but actually more than 10 volts response associated with this.
[Slide 11] And -- but before I go any further, I want to specify one thing very clearly. You see, by itself, it doesn't beat the sensor response because, you see, anytime you balance the current like this, so let's say this is the original noise of the sensor, and this one is the original signal, and let's say you need approximately three times more than the noise in order to detect the signal. So this was your original one and this is after amplification, through this transistor after amplification. Your signal is much bigger, so it has gotten larger by, let's say, a factor of two. Unfortunately, in the process you have also amplified the noise. And so, if you look at the signal to noise ratio, they have not changed at all. And so, actually, you haven't really solved any problem with this. But what makes life easier, because anything that is unresolved in this -- in ideal case. Anything that's unresolved in the original sensor cannot be resolved by amplification. Signal to noise ratio will change. However, the real advantage of this type of system comes from the fact that if you have a system noise not determined by the individual sensors, but by the measurement equipment itself. In that case, you see a larger sensor. It may have a very small noise, but the system noise will essentially prevent it, detection, this signal to noise ratio. The signal to noise ratio would rather be this flat line with the top of this peak. On the other hand, even after the noise had been amplified, the signal to noise ratio would be much larger, and this, of course, would be the case if the equipment noise is larger than both of the noises. This would be the signal to noise ratio for the original scheme. This would be the signal to noise ratio for the amplified scheme. So under certain conditions, this can and do significant amplification of the original signal.
[Slide 12] This is an experimental demonstration. For example, the instrument noise in this -- this is the original single sensor, pH sensor, and you can see the noise is very low because it's a big sensor. And after amplification, it goes significantly larger, but the instrument noise is somewhere here. And so, your signal to noise ratio is relatively poor. On the other hand, even after -- in the amplified scheme, even after the noise has gotten bigger, from 10 to the power five to 10 to the power four, a factor of 10. The signal correspondingly gets bigger also, but the instrument noise is here. So that gives you a significant gain compared to the original signal. It's only in that sense the circuit can help address the screening limits.
[Slide 13] So let me conclude. So I said that the screening is a troublemaker and -- because it's sort of reduced the sensitivity quite a bit, logarithmic dependence, it created the logarithmic dependence. But at high frequency, the signals stay put and they cannot -- the salt ions stay put and therefore you can now see the sensors and now see the biomolecules through the salt. That was the essential point. Now, the Giant Nernst Response is another scheme, but in this particular scheme, it turned out that you can get -- enhanced signal to noise ratio only if the instrument noise is larger than the minimum noise floor associated with the original sensor. If you have that, then you can get significant enhancement. But you see, there is a problem with high frequencies in general you don't want to use in simple biosensors, nanobiosensors, high frequency circuits, because it makes life complicated, especially when you have hundreds and millions of them. See, how are you going to synchronize all these frequencies and keep them separate so that they don't interfere with each other? So therefore, often people get away from the potentiometric sensor for this screening limit and then, turn to amperometric or cantilever sensors, because they don't have any screening, as I'll explain. And those would be the topic for next six lectures and -- three for amperometric and three for cantilever sensors.