Design of a Resistivity Measurement System for Conductive Polymer Films

0 Introduction
The electrical properties of conductive polymer materials are changed by controlling their resistivity through doping. Therefore, it is of great significance to accurately measure the resistivity of conductive polymers. In the semiconductor industry, four-probe measuring instruments are commonly used to measure the resistivity of inorganic semiconductor materials. However, conductive polymers belong to organic semiconductor materials, with different conduction mechanisms and a large resistivity range (10-3~1010Ω·cm). The use of four-probe measuring instruments cannot meet the application requirements. At present, when measuring higher resistivity, the measurement circuit can be built according to the national standard (GB3048.3-83). However, this method has strict requirements on the shape of the sample, and the circuit construction is time-consuming and labor-intensive; the excitation voltage is difficult to control, and the voltage is too small to affect the measurement accuracy. The voltage is too large to cause a large current, which may affect the characteristics of the sample, and the excessive voltage is very dangerous. In order to avoid pre-treatment processes such as tableting and molding, and to accurately and safely measure over a wide range, necessary improvements are made here.

1 Measurement principle
1.1 Four-probe resistance measurement method
The four-probe method can reduce the influence of contact resistance and wire resistance. A constant voltage excitation signal Vs is used to replace the original constant current signal between probes 1 and 4, as shown in Figure 1.

Current passing through the sample:

Where: Rw is the wire resistance; Rct is the contact resistance of pins (1, 4); R14 is the sample resistance. In order to obtain the sample current I, it is necessary to obtain the total resistance Rx through other means. Here, the ratio measurement method is introduced. As shown in Figure 2. Where: Vin is the input reference voltage (corresponding to Vs in Figure 2); Vout is the output voltage of the amplifier circuit; Rf is the feedback resistor. 1.2 Resolution of measurement Theoretical resolution of resistance measurement: When Vin and Rf are constant, the resolution decreases sharply as the resistivity of the sample to be measured increases. Maintaining a high resolution over the full range is achieved by the following methods: (1) Allocating a larger Rf when measuring a larger Rx; (2) Changing the voltage value of the excitation signal. Through programmable amplification technology, different gears are designed according to the resistance value range, and different excitation signal voltage values ​​are selected for the gears. The corresponding relationship is shown in Table 1. [page]

1.3 Current Limitation
When measuring the resistivity of semiconductor materials, there are relatively strict requirements on the current flowing through the sample:
(1) The current cannot be too small to ensure that the voltage between the inner probes can be measured;
(2) The current cannot be too large to reduce the influence of thermal effects on the resistivity of the sample;
(3) When measuring samples with larger resistivity, the injection current should be reduced to reduce the influence of minority carrier injection.
The circulating current affects the resistivity value
of the sample, but usually the range in which the resistivity is not affected by the current is very wide. According to the limit of this range, the safe operating current can be obtained. The current flowing through the test sample in this method is:


2 System Design
The system uses the LPC2148 ARM7 chip as the core unit for mathematical operations and control. The system structure is shown in Figure 3.

2.1 Control processing unit
The control processing unit includes LCD display circuit, keyboard input circuit, serial communication circuit, feedback control circuit 1 and 2 and microcontroller. The preset current limiting resistor Rc is used to limit the current passing through when measuring low resistivity materials. The current flowing can be calculated by formula (9). The measurement current can be guaranteed to be less than 2 mA within the full range. The parameters and gears are shown in Table 1.

2.2 Signal conditioning unit
It includes controllable constant voltage generation circuit, differential amplifier circuit, ratio measurement circuit and analog-to-digital (A/D) conversion circuit. The constant voltage source uses ADR01 to generate a 10 V reference voltage output, and further obtains 0.1 V and 0.01 V reference signals; the voltage between the two inner probes in Figure 2 is measured using the AD620 differential amplifier circuit and the high-precision operational amplifier AD546, and the amplitude of the output signal is changed by adjusting the gain resistor RG through the feedback control circuit 2; the analog/digital conversion circuit uses the 16-bit ∑-△ type AD7705, and the measurement resolution reaches 52μV/LSB when using a 3.401V reference voltage. As shown in Figure 4.

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2.3 Resistance Prejudgment Circuit
The introduction of the resistance prediction mechanism is due to the use of a 3-position constant voltage excitation signal. In order to prevent excessive current injection when measuring unknown resistance, the resistance value of the sample must be predicted, and then the appropriate position and excitation signal are selected. The circuit is built based on the Whittons bridge. As shown in Figure 5.

3 Program Design
According to formula (1), formula (3), and formula (10), the final calculation formula for the resistance to be measured is:

Where: R1, R2, and Rf are known gain resistors; Rc is the current limiting resistor; Vg is the voltage between the two probes of the internal measurement; Vo is the output voltage value of the ratio measurement circuit; and C is the probe coefficient of the probe platform. The main program flow chart is shown in Figure 6.

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4 System Test
4.1 Measurement Range and Accuracy
The effective measurement range and accuracy limit of the system are examined by measuring standard precision resistors. The precision E24 series resistors with a relative accuracy of 0.01% are selected, and the measurement results are
shown in Table 3.

The effective resistance measurement range of the test is 10 Ω～1 000 MΩ. When the probe coefficient C is 0.628 cm, the resistivity measurement range is: 6.28～6.28×108Ω·cm, and the relative error is less than 1%.
4.2 Comparative experiment
The measurement circuit is built according to the national standard GB3048.3-83 method. The sample is a carbon black-polypyrrole composite film with different doping concentrations grown on a plexiglass substrate. The resistivity range of the sample is controlled to be 102～105Ω·cm. 20 samples were randomly selected for comparative testing, and the results are shown in Figure 7. The comparison shows that the measured values ​​obtained using this system are in good agreement with the values ​​measured using the standard method.

4.3 Measurement precision
Three samples with different concentration ranges were selected, and each sample was measured 20 times. The measurement precision of the system was investigated to obtain the results in Figure 8.
After 20 measurements, the average resistivity of sample A was 11254.44Ω·cm, with a standard deviation of 9.77; the average resistivity of sample B was 6485.34Ω·cm, with a standard deviation of 8.54; the average resistivity of sample C was 895.47 Ω·cm, with a standard deviation of 1.45.

5 Conclusion
A method combining four-probe and ratio measurement method was proposed to measure the resistivity of conductive polymer film materials; a resistivity measurement system for conductive polymer film materials was designed and implemented; finally, a measurement experiment was carried out using standard resistors and film samples. The experiment showed that the effective resistivity measurement range of the system was 6.28~6.28×108Ω·cm; the relative error of measurement was less than 1%; the system had high precision, and the ratio of the standard deviation of multiple measurements of a single sample to the average value was less than one thousandth. Compared with the national standard method, the system has the advantages of simple operation and high safety factor. It can directly measure the conductive polymer film materials prepared during the experiment and improve the experimental efficiency.