Research and development of high-precision DC microresistance tester

This chapter mainly studies the relevant basic theories of high-precision micro-resistance testers.

Resistors can be divided into high resistance (above 100k), medium resistance (1 to l00k) and micro-resistance (below 1) according to their size. This topic mainly studies the resistance measurement of micro-ohm resistors.

Resistance measurement usually uses the method of adding current and measuring voltage, and the method of micro-resistance measurement is no exception. Considering that the resistance of microelectronics is very small, in addition to precisely controlling the test current and accurately measuring the weak voltage on the resistor to be measured, it is also necessary to consider eliminating the influence of wire resistance on the measured value and reducing the system error to a minimum, so as to achieve the purpose of high-precision measurement of micro-resistance.

2.1 Basic principles of resistance measurement

The basic principle of resistance measurement is very simple, that is, using the voltammetry method (as shown in Figure 2.1), with a given current I passing through the resistor R, measuring the voltage U between the two sections of R, and the resistance value can be obtained according to Ohm's law R=u/I.

However, due to the influence of wire resistance, contact potential, temperature difference potential and electrochemical potential in the detection circuit, these influences can be ignored when the resistance value is relatively large. If the resistance value is extremely small, the absolute value of the error caused by these influences may even exceed the resistance to be measured by several orders of magnitude. It is necessary to study where these errors come from, how to reduce or even eliminate them, so that the resistance value of the micro-resistor can be measured with higher accuracy.

2.2 Error analysis of DC micro-resistance measurement

When measuring resistance using the voltammetry method, a DC current source is used; and a small resistance value corresponds to a weak signal. Therefore, it is necessary to first study the noise in weak DC signal detection in a general sense, and then specifically study the error sources in DC microresistance measurement.

2.2.1 Noise theory for weak DC signal detection

Generally, interference noise can be defined from two perspectives. One is from the perspective of the circuit, which is the noise manifested by the random fluctuation of voltage or current caused by the random movement of charge carriers; the other is from the perspective of signal analysis, the unwanted signals that pollute or interfere with useful signals are called noise.

There are many types of interference noise, and different detection methods should be adopted for different types of interference noise signals. Before performing signal detection, the nature of the signal should be deeply analyzed and the object of detection should be clarified in order to determine the detection principle, method and instrument, etc.

2.2.1.1 Detection of inherent noise sources inside the circuit

The noise generated inside the detection circuit element is called intrinsic noise, which is caused by the random movement of charge carriers.

1. Thermal noise of the conductor itself Thermal noise of the conductor

It means that any conductor will show noise voltage fluctuations at both ends even if it is not connected to a power source and no current passes through it. Thermal noise is generated by the random and irregular thermal motion of electrons inside the resistor. Its amplitude depends on the temperature. The higher the temperature, the more intense the thermal motion of free electrons in the conductor, and the higher the noise voltage. Once the temperature drops, the thermal noise will decrease. Its amplitude is also related to the resistance value of the conductor. For large resistors, the influence of the thermal noise of the conductor is relatively small, while for micro resistors, its influence is very large. For systems that detect weak signals at the level of nanovolts or even nanovolts, the adverse effect of thermal noise on the measurement accuracy of resistance cannot be ignored.

2. Contact noise between conductors: Acoustic contact noise is also called 1/f noise. It is caused by the random fluctuation of the conductivity at the contact point of two conductors. Any device with imperfect conductor contact has contact noise. The amplitude distribution of 1/f noise current is Gaussian, and its power spectrum density function Sf(f) is proportional to the inverse of the operating frequency f. Sf(f) can be expressed as:

Since Sf(f) is proportional to 1, the lower the frequency, the greater the power spectrum density of this noise. In the low frequency band, the amplitude of 1/f noise may be very large. The excess noise generated by the fluctuation of resistance value inside the resistor is also a kind of 1/f noise. The following are the effective values ​​of excess noise voltage of several resistors (measured in the range of 10 times the frequency for every 1V voltage across the resistor):

Pure carbon resistor: 0.1-3.0uv

Carbon film resistor: 0.05-0.3uv

Metal film resistor: 0.02-0.2uv

Therefore, in order to effectively measure weak signals, the measurement bandwidth should be reduced as much as possible. [page]

3. Burst noise
The cause of burst noise is that impurities in the semiconductor (generally metal impurities) randomly emit or capture carriers in the PN junction. Burst noise is usually composed of a series of random current pulses with different widths but basically the same amplitude. The pulse width is generally on the order of a few microseconds to 0.15, and the pulse amplitude is generally 0.01"A to 0.001 forest A. The probability of its occurrence is less than a few hundred Hz. The burst noise depends on the manufacturing process of the conductor and the impurity conditions in the conductor material. If the burst noise is amplified and sent to a speaker, a sound similar to popcorn can be heard. Since the burst noise is a current-type noise, the resistance of the relevant resistors in the circuit should be reduced as much as possible, and filtering measures should be adopted.

2.2.1.2 Interference noise outside the detection circuit

The noise in the environment where the detection circuit is located is called external interference noise. This noise is determined by the environment, not caused by the internal circuit, and belongs to external environmental noise. A certain external interference source generates noise and couples the noise to the signal detection circuit through a certain path, thereby forming external interference noise to the detection system {7]. There are many types of external interference noise, such as 50Hz AC interference from the mains, AM broadcast signals from radio stations or switching spark interference from power supplies, broadband interference caused by pulsed lasers or radar emissions, cosmic rays, lightning, and mechanical vibration of components or parts to produce microphonic effects. Common external noise mainly includes ground potential noise and power frequency noise formed by ground loops.

Ground potential difference noise is the noise introduced by the ground loop formed when the signal source and the measuring instrument are connected to the same ground. There are many grounding points on the ground, and different grounding points have different potentials. A small potential difference at different points can form a large current in the circuit system and produce a considerable voltage drop. This noise has a greater impact on the measurement accuracy of small resistances. This external noise can be eliminated by isolating and grounding the entire measurement circuit system at the same point.

The influence of power frequency noise on DC signal measurement is quite obvious. Common power frequency interference sources include power frequency electric field and power frequency magnetic field generated by power lines, power frequency magnetic field generated by power lines and power transformers, harmonic interference generated by motor starters, etc. Power frequency noise has a greater impact on the microresistance measurement circuit. The impact

of environmental interference noise on the detection result is closely related to the layout and structure of the detection circuit. Its characteristics depend on both the characteristics of the interference source and the characteristics of the coupling path, and have nothing to do with the quality of the components in the circuit. The power of the interference noise source is much greater than the power of the useful signal in the detection circuit. After the coupling path, the noise power is greatly weakened, but it may still be considerable relative to the weak useful signal (9). Therefore, it is necessary to suppress the interference sources of the external environment to ensure the high precision requirements of the microresistance tester.

2.2.2 Sources of error in DC microresistance measurement

Based on the noise theory of weak DC signals, external interference noise exists in the environment and is not controlled by the detection circuit. Therefore, in DC microresistance measurement, the main research is how to reduce the impact of internal inherent noise sources on the measurement results. In

microresistance measurement, there are several sources of internal inherent noise errors: thermal noise inside the conductor will cause thermoelectric potential errors, contact noise between conductors will cause contact potential errors, and the combined effect of contact potential and thermoelectric potential will produce thermoelectric potential; electrochemical electromotive force errors will also be generated between the conductor and the environment due to electronic polarization; and the measurement circuit itself also has offset and temperature difference errors.

2.2.2.1 Thermoelectric potential

Thermoelectric potential is the most common error source in weak DC voltage measurement. Thermoelectric potential includes contact potential and temperature difference potential.

Contact potential is caused by the diffusion movement of electrons on the contact surface due to different electron densities inside two different conductors, and changes with temperature. In electronic measurement systems, there are many conductors, such as copper, gold, silver, tin, germanium, carbon, lead, copper oxide and other conductors, so there must be contact potential in the measurement system. The influence of contact potential inside the measurement system amplifier circuit can be eliminated by various technologies, but it is difficult to eliminate the influence of contact potential in the signal input circuit, so homogeneous materials should be used as much as possible for connection.

When the temperatures of the two ends of the same conductor are different, the electrons at the high temperature end migrate to the low temperature end, causing a temperature difference potential. This phenomenon is also called the Thomson effect. Obviously, there is a step-by-step uneven temperature field in the electronic measurement system: the temperature inside and outside the components is different, and the temperature of different areas of the same component is different, so there must be a temperature difference potential. Although the influence of the temperature difference potential inside the electronic measurement system can be eliminated, the influence of the contact potential of the signal input circuit is sometimes difficult to eliminate. In this case, the temperature field distribution of the measurement system should be kept as uniform as possible.

As mentioned above, the thermoelectric potential is caused by the contact of conductors of different materials and the difference in the temperature of the conductor nodes.

As shown in Figure 2.2:

A and B are two conductors of different materials, and the temperature of the contact point between the two conductors is:

Among them, , is the thermoelectric potential constant when conductors of different materials are in contact, and the unit is v/℃. The following are the values ​​of , when several metals are in contact:

From the above, it can be seen that although the thermoelectric potential generated by copper-copper contact is very small, if the copper material is poorly connected and there is oxidation, the thermoelectric potential will have a considerable impact on the measurement of weak DC signals.

2.2.2.2 Chemical electromotive force

The electrochemical effect is another major source of error in weak DC voltage measurement. It is essentially a weak battery effect produced by the electrochemical effect between two electrodes. For example, the commonly used epoxy resin printed circuit board may produce an error current of the order of nA if it is not cleaned enough and has some contamination or flux. If the temperature is high or contaminated, the insulation resistance of the material will be greatly reduced. High humidity can cause the material to deform or absorb moisture, while contamination may come from human body oil, salt or solder, etc. Contamination first reduces the insulation resistance. If high humidity is added, a conductive path will be formed, and even a chemical battery with a large series resistance will be formed. This type of battery may produce an error current of the order of PA to nA. Like thermoelectric potential, the influence of the chemical potential within the system can be eliminated, but the influence of the electrochemical potential of the signal input circuit is sometimes difficult to eliminate.

2.3 Error processing method for DC micro-resistance measurement

When the test current flows through a weak resistor, the main reason why the weak voltage signal at both ends cannot be accurately measured is the influence of DC error sources. These error sources mainly include: thermoelectric potential, electrochemical potential, offset and temperature drift of the amplifier circuit itself, etc. Under normal circumstances, the amplitude of the error signal is much larger than the voltage signal to be measured, thereby drowning it out. Amplifying the signal to be measured will also amplify the error signal. The measurement is meaningful only when the amplification is performed while eliminating or reducing the error source. For the thermoelectric potential error, chemical electromotive force error and offset error of the measurement circuit itself in the DC microresistance measurement mentioned in the previous section, first of all, it can be solved by physical means, and secondly, the current reverse three-time measurement method can be used to eliminate the error. Finally, the appropriate circuit wiring method can be selected to minimize the interference of errors on the microresistance voltage value measurement.

2.3.1 Physical means to eliminate errors

In order to reduce the error of thermoelectric potential, homogeneous measuring wires should be selected as much as possible when designing the circuit, and the temperature difference between the measuring end and the measuring environment should be minimized as much as possible. All nodes in the instrument circuit should be placed close to each other, and the ventilation inside the test instrument should be kept good, and the temperature of each component should be kept consistent as much as possible; the instrument should be preheated for a period of time before measurement to make the temperature inside the measuring instrument as close to the ambient temperature as possible, so that the measurement error is as small as possible.

In order to reduce the influence of chemical electromotive force, non-absorbent materials should be selected, and at the same time, attention should be paid to keeping the insulator clean and hygienic, and not be attached by dirt or dust. If dirt is found on the insulator, it should be cleaned in time. This is a physical means to eliminate and reduce the error of chemical electromotive force.

We can only eliminate part of the errors by physical means. Errors such as thermoelectric potential, electrochemical potential, and measurement circuit imbalance cannot be completely eliminated by physical means, and they always exist partially. Next, we will explore the method of eliminating errors from the circuit wiring method and the secondary measurement method. [page]

2.3.2 Circuit wiring method design

There are generally four common resistance measurement wiring methods. According to the number of feeders used for measurement, they can be divided into two-wire method, three-wire method and four-wire method. In addition, there is another common bridge method for measuring resistance.

Let's look at the principles and advantages and disadvantages of the two-wire method, three-wire method, bridge method and four-wire method.

2.3.2.1 Principle of two-wire method for measuring resistance

The circuit diagram of the two-wire method for measuring resistance is shown in Figure 2.3:

Among them, the resistance to be measured is 1, and the measured contact resistance and lead resistance are represented by 1 and 2 respectively. It can be seen from the figure that the resistance value of the unknown resistance 2 will be the sum of the resistance values ​​of 2, 1 and 2. Therefore, this method can only be used when the resistance to be measured is large. If the resistance to be measured is small, or even smaller than the resistance of the measuring wire, then this method will produce a large error. Therefore, the two-wire method is not suitable for measuring micro-resistance with very small resistance value. It is only suitable for measuring wiring with larger resistance.

2.3.2.2 Principle of three-wire method for measuring resistance

The wiring for measuring resistance using the three-wire method is to connect the resistor to be measured to the ground wire. The principle is shown in Figure 2.4.

In the figure, one end of the resistance circuit to be measured is grounded through a wire, and the other end is connected to the op amps Al and AZ through two wires. The resistance of the three wires is required to be the same, all of which are 1. When the current I is passed through, the output voltages and K of the two op amps are: (the gains of the three op amps are all 1)

From the above formula, we can see that no matter what the value of the measured resistance is, the error caused by the wire resistance can be compensated. In this compensation method for measuring micro-resistance circuits, the factor that ensures measurement accuracy is mainly whether the resistance values ​​of the three wires are consistent. Therefore, when using this method to measure a resistor with a smaller resistance value, special attention should be paid to the fact that the resistance values ​​of the three wires connected to the resistor to be measured must be equal to ensure the accuracy of the measurement.

This three-wire method of measuring resistance is widely used in practice. As long as the resistance values ​​of the three wires are equal, a certain accuracy requirement can basically be achieved. However, the three-wire resistance measurement method can only eliminate the influence of the isoline resistance, but cannot eliminate the influence of the contact resistance. The length of the measuring wire cannot be completely equal. Therefore, the three-wire method cannot meet the high-precision requirements of micro-resistance measurement.