This project is a related to my graduate school research that I carry out in my university. I have decided to share it with everybody to help others understand or build similar devices. I will try to touch upon several subtopics that could be useful in understanding the subject of studying adsorption using surface potentials.
To describe the underlying phenomenon in simple words: Metals contain a cloud of free electrons inside them that posses particular energies. The energies of a number of electrons in vicinity of the surface could be affected locally by a, let’s say, some molecule adsorbed on the surface. The effect within the metal depends on the electronic characteristics (i.e. dipole moment) of the molecule. Therefore, if there was a way to detect this change in energy one could say something about the adsorbed molecule.
Contact Potential Difference (CPD) phenomenon
Every metal contains free electrons that are in constant random motion throughout the metal. The potential energies of these electrons are dictated by the atomic structure and could be described by the Fermi level/energy on the energy diagram. Fermi energy may be seen as the maximum energy level that electrons could posses in a metal at the absolute zero temperature. In other words, because of different atomic structures different metals have electrons with different potential energies.
When two dissimilar metals are brought close to each other the electrons in one of the metals will essentially be described by higher energy states in comparison with the other metal. If the metals are not electrically connected, or there is no mean for the electron exchange, the metal’s surface potentials will see no changes. However, once such mean appears a portion of electrons from a metal with higher electronic states will move to the second metal thus creating a transient current. The driving force for this migration is described by the metal electronic cloud cross-talking. The electrons with higher potential energies would gladly migrate to the states with lower energies. Once electrons started moving to another metal it charges negatively whereas the donor metal charges positively. The developed field in the gap between metals characterized by a potential difference is called the Contact Potential Difference. Once again this process has a transient nature - once the electrons re-distribute between the metals there is no net current flowing from one metal to another.
Measurement Technique
The transient nature of the CPD current makes the potential measurement troublesome at the first glance. The charge is trapped in the gap between two metals and the rest of the metal’s potential is unaffected. A simple voltmeter measurement will bring no result as the charges are concentrated in the gap and have absolutely no incentive to come out of there and, therefore, voltmeter will give exactly 0V measurement. However, let’s look at the following equation of electrostatics: Q=CU. It shows that the amount of charge is proportional to the capacitance between the metals. Thus, if we can change the capacitance of the system we can alter the equilibrium in it causing the charge to change. Moreover, if we introduce a periodic change in the capacitance of the system we will start generating an alternating current flowing back and forth between the metals. This current, in turn, is detectable.
So now, when we have understood what we needed to do to make the current flow through the external circuitry, let’s see how we can measure the contact potential difference between the metals.
Lets assume we have two dissimilar metallic plates that form a parallel plate capacitor. Let’s fix in space one plate and vibrate the second one while both plates are connected through a current detector. Of course the shape of the current depends on the type of oscillation - for instance, sinusoidal vibration will cause sinusoidal current. Now, let’s connect a battery to the static plate and start applying the external potential to it. If we apply different voltages in a several volt range we can notice that at some value the current that was previously flowing through the external circuit disappears. What happened?! The externally applied potential compensated the CPD between the metals and now both of the surfaces are at the same potential. In other words, the applied potential in absolute value equal to the contact potential difference between the metals. This method of the CPD detection is known as Kelvin-Zisman method.
Lock-in Amplifier Basic Theory
Lock-in amplifiers are generally used to extract useful signals from the inputs that are subjects to big noise values or measurements with very small signal to noise ratios.
The idea behind this technique is in the fact that the useful signal is characterized not only by amplitude but as well by the phase. It is hard to encounter a situation when the noise in the system has the same phase and frequency as the signal of interest, unless the system is poorly designed.
One of the necessary conditions that determines if this technique might be used or not in an experiment is the presence of a reference signal. If it is available the measurement can be performed as follows:
A signal acquired from the output of a device can be multiplied by a reference signal that is characterized by exactly same frequency but might have a different phase. The multiplication of two signals represented by a cos() function leads to a difference of the cos() functions - first with phases subtracted and the second with the phases summed. In other words, one of the cos() functions become a constant due to subtraction of equal frequencies, while the second cos() function will have a double frequency argument. The latter can be simply filtered out by a low pass filter. The DC voltage result after the filtration will be proportional to the amplitude of the harmonic of interest - the useful signal.
Other variations of the lock-in amplifiers exist.
Design of the setup
- Vibrating Plate Driver
One of the instability problems can arise when an unstable signal generator is used to drive the vibration of one of the plates: frequency instabilities can detune the lock-in amplifier causing incorrect measurement. The closer to ideal behavior show digital generators. Plus, a stable phase adjustment can be easily achieved using digital circuits.
All the described above, made me choose a mixed design to purely analog. I used a Atmega8 micro-controller from Atmel to generate a sine wave and a reference signal. I am aware of three different ways to generate a sine wave using micro-controllers:
- using a DAC and a simple filter
- using PWM (pulse width modulated signal) and a filter
- using delta-sigma approach with filter
As I the resources of my micro-controller were limited and the budget was not, I decided to go with the simple first option. A DAC with a SPI interface was chosen. A table with 512 points per period was created and fed into the DAC. During the operation of the generator, the phase reference signal is generated in parallel by triggering to two of the points within the 512 given points separated by half period. In other words, the phase of the reference signal can be adjusted within 360 degrees with a 360/512 degree resolution.
- Preamplifier
The signal in the CPD setup is the transient current flowing from one conductor to another. That suggests that a current-to-voltage converter (or a trans-impedance amplifier) to be used in this measurement. There are several advantages of that: 1) high input impedance of the amplifiers along with a high value resistor in the feedback allow for high impedance of the measurement input. 2) convenience of the bias application to one of the electrodes.
The bias can be applied in different ways:
- through a positive input of the operational amplifier only
- through a “phantom ground” - shifting the ground along with shifting the power supply potentials
The second approach gives better results as it allows for wider range bias adjustments. Plus, I have experienced strange amplifier behavior with approach 1 with high biases.
- Lock-in Amplifier
The idea behind the control circuit in this particular apparatus is to apply a bias to the measuring input (connected to the vibrating electrode) to make the CPD voltage zero and therefore reduce the current flowing between conductors to zero. Once this condition achieved the voltage applied to the electrode will be equal to the actual CPD developed between two metals.
The control circuit first amplifies the voltage put out by the current-to-voltage converter and then multiplies it by a reference signal that in this case is a square wave of same frequency. An analog switch is used for this purpose. The switch outputs two signals each of which are rectified cos() function one positive and second negative. In other words, it slices the signal along the time axis. Next, the signals are fed into a differential integrator that computes the difference of these two signals and integrates it. The result is further used as a bias voltage for the input electrode.
Let’s say the CPD developed between the electrodes is 0.5V. After the current-to-voltage conversion and amplification we get a cos() signal with amplitude let’s say 0.1V. Next this signal is integrated and let’s say the result is 0.2V. Now this voltage is being fed as a bias to the input causing the voltage difference between the metals to be (CPD-0.2V). Sequentially, the signal after the amplification is reduced due to this reduction. The integrated signal will be 0.2V+v. This process continues until the (CPD-V) voltage will be close to zero and will not cause the integrator to change its value. Finally, the integrator will hold the voltage equal to the Contact Potential Difference between the metals.
- Experimental Setup
The setup consists of a voice coil on a one-axis positioning stage and a sample table made out of aluminum. The vibrating electrode is made of gold. The voice coil is mounted upside down with the electrode on the top. The sample table hovers over the vibrating electrode and has a cut out window for the vibrating electrode to pass through. The sample metal and an optional dielectric are placed on the top of the sample table.
- Selected Results
Here are some stability test results in the laboratory environment over several days.
TBContinued …. Pictures and Figures to come
Tags: CPD, Kelvin Probe, research
