Electrical measurements - folk.uio.no

1 KJM-MENA 4010. Electrical measurements Emphasising simple methods and instruments, materials aspects, electrochemistry, and impedance spectroscopy Truls Norby Department of Chemistry, University of Oslo FERMIO. Gaustadall en 21. NO-0349 Oslo, Norway 1. Welcome to KJM-MENA4010, Module 2; Electrical measurements In this module we will learn the most important principles of making Electrical measurements in general, , to obtain voltages and currents using the appropriate instruments and connections, and to understand and minimize sources of error. Furthermore, we will discuss selected Electrical measurement methods used to obtain chemical and physical information of liquids, solids, and interfaces. In addition to DC. methods we will focus on AC measurements and impedance spectroscopy. As practical skills we aim at the end of the course to - Be able to perform simple Electrical measurements of voltage, current, and resistance, as well as more sophisticated, scientific Electrical measurements , - master handheld and more accurate stationary multimeters and understand their differences, - have some knowledge of use of AC signals, AC generators, and an oscilloscope, - have some knowledge of use of a potentiostat/galvanostat, - have some knowledge of use of impedance spectrometers.

2 The course is considered passed when the student has fulfilled all of the following: - attended a major part of the lectures, - done all exercises, filled in the result forms, and had them accepted by the lecturer, - calculated the Electrical response of a hypothetical sample or a circuit as provided by the lecturer, and presented the result in a short (2-3 page) report, or deconvoluted an impedance spectrum measured by the student or provided by the lecturer using EQUIVCRT software. Supervision will be available during the exercises, calculations and deconvolutions. 2. Contents Electrical measurements .. 1. Welcome to KJM-MENA4010, Module 2; Electrical measurements .. 2. Contents .. 3. Some definitions relating to voltage and current .. 5. Voltage and 5. Mobility, conductance, resistance, Ohm's law .. 5. Direct and alternating current (DC and AC).

3 7. Electrical circuit elements and circuits .. 8. Passive Electrical circuit 8. Parallel and series connections .. 10. Active and non-linear Electrical circuit 11. Symbols for circuit 13. measurements of voltage, current and 13. 14. Current .. 15. Impedance basic principles and 15. AC 17. Error and accuracy .. 20. Thermal and other offsets .. 20. Noise .. 21. Accuracy .. 21. Parasitic impedances and admittances .. 22. Correction for sample geometry in impedance measurements .. 23. Grounding, guarding, 25. Floating and grounded 25. Guarding .. 26. Shielding .. 27. DC voltammetry and related techniques .. 29. Electrochemical processes at electrode-electrolyte interfaces .. 29. Semiconductor 33. Impedance spectroscopy .. 34. General .. 34. Generation and representation of example model spectra .. 34. Physical systems and equivalent circuits.

4 36. Deconvolution and fitting of measured spectra .. 42. Further considerations of data from impedance 43. Some specialties of advanced impedance spectrometers .. 44. Combining impedance spectrometers with other units; electrochemical interfaces, boosters, dielectric 45. Some related techniques .. 46. Selected special 46. Seebeck 46. 3. Concentration cells and transport number 46. measurements of conductivity etc. on thin films .. 46. Coulometric 46. High frequency measurements and use of transmission 46. Exercises .. 47. Equipment .. 47. Exercise 1: Simple instruments, measurements , and terms .. 1. Identify and check 1. Measure DC 1. Measure DC current .. 1. Measure resistance .. 2. Exercise 2: 2. Exercise 3: Diodes and transistors .. 3. Exercise 4: Input and output 4. Exercise 5: AC voltage and current .. 4. Exercise 6: Impedance measurements ; 2 and 4 wires, 2 and 4 electrodes.

5 5. Exercise 7: AC impedance measurements .. 6. Series circuit; AC 6. Parallel circuit; AC 6. Parallel circuit represented as impedance .. 7. Exercise 8: Error sources .. 7. Contact potentials and contact 7. Thermal offsets .. 8. Static charging and noise .. 8. Parasitics .. 9. Exercise 9: Grounding, guarding, 10. Grounding .. 10. Guarding .. 11. Shielding .. 11. (Optional) Exercise 10: 12. Voltammetry (chronovoltammetry) .. 12. Exercise 11: Impedance 13. Generate a 13. Deconvolute the 13. Deconvolute a given 14. Calculate the Electrical response of a given 14. 4. Some definitions relating to voltage and current Voltage and current Voltage, U, is the difference in Electrical potential, , between two locations: U = =. 2 - 1. The unit for voltage U is V (volt). Electrical field, E, is the negative of the gradient in Electrical potential, it is defined to be directed from positive to negative pole: E = -d /dx.

6 If the gradient is linear and homogeneous, the voltage over a length L is U = -EL. Current, I, results from the flux of charged particles. The unit for current is A. (ampere). 1 A = 1 C/s (coulomb per second). There are 96485 C/mol of elemental charges ( electrons). Consequently 1 A corresponds to ca 10-5 mol/s (of charges). 1 A over a voltage of 1 V gives a power P = UI = 1 W (watt). 1 W for 1 s gives 1. J (joule) of energy. Figure 1. Schematic illustration of potential, voltage, field, current, and power in relation to current passing through a resistor. Mobility, conductance, resistance, Ohm's law In the following we derive some simple relationships between voltage and current valid for constant voltage and current in homogeneous media (conductors). If a particle has charge ze, it feels a force F = zeE in the Electrical field E.

7 This gives rise to a velocity v = BzeE, where B is the mechanical mobility of the particle. If we define a charge mobility u = Bze, then v = uE. The flux density of particles then becomes j = cv = cuE, where c is the volume concentration of particles. The current 5. density is obtained by multiplying the flux density by the particles' charge: i = zej =. zecuE. Current is then obtained by multiplying by the cross-sectional area A: I = iA. By replacing E with U/L we finally get I = zecuUA/L. The product of concentration x charge mobility x charge is called conductivity : = zecu (1.). and when multiplied with area and divided by length we get conductance G: G = A/L (2.). Conductance, G is a property that relates to a particular sample, and has unit S (siemens). while conductivity (often called specific conductivity) is a materials property with unit S/m.

8 Because samples typically are of sizes in the cm-range, tradition has made it common to use S/cm rather than the SI unit S/m. The inverse of conductance is resistance R = 1/G and the inverse of conductivity is resistivity = 1/ . Obviously, R = L/A. The unit for resistance is ohm (=1/S). We can now from the above equations and definitions express the current as I = UG = U/R (3.). known as Ohm's law. We have not said anything about the physical basis for mobility of charge carriers. It can be derived from various formalisms, diffusion or collisions, depending on the type of transport and the traditions in different fields of application and science. Moreover, we have not said anything about the concentration of charge carriers, which depends on materials, temperature and composition. While these are the interesting parameters for us as chemists, physicists or materials scientists, this course is not so much about that.

9 Instead it is about the methodology to measure Electrical properties as part of what may be needed to get hold of those parameters. Figure 2. Schematic illustration of terms relating to current and resistance 6. Direct and alternating current (DC and AC). The voltage and resulting current can be constant with time and are then referred to as DC. (from direct current ). The voltage can also be varied in numerous ways, referred to as sine, square or sawtooth waves, noise, etc. Most important, and the only we will treat here, is the sine voltage, resulting in sine current and thus referred to as AC (from alternating current ). The sine voltage is characterized by its frequency f and angular frequency = 2 f as well as its amplitude U0: U = U 0 sin t (4.). The amplitude can also be specified as the peak-to-peak voltage, Up-p = 2U0 or the root mean square (rms) voltage Urms = U0/ 2 = Up-p/(2 2).

10 The term t is called the phase angle. A sinusoidal AC current resulting from the applied AC voltage will have the same frequency as the voltage, but may have different amplitudes and phase angles: I = I 0 sin( t + ) (5.). The phase shift results from capacitive (non-ohmic) elements in the circuit. A sine AC voltage or current can be superimposed on a DC voltage Ub or current Ib. The DC part of the voltage or current is called bias, and shifts the AC curve off symmetry around zero voltage or current. Figure 3. Left: AC voltage and current. Right: Biased AC voltage. Sine waves can be troubled by harmonics (usually overharmonics; presence of voltage and current components that is a multiple of the fundamental frequency) or distorsion (deviations from ideal sinusoidal curve form). These are usually generated by the AC source itself or by non-ideal electronic components in the electric pathway.