Kelvin four-wire connection resistance test technology and its application

1 Introduction

In the semiconductor process, the important parameters and performance of many devices are related to the sheet resistance. In order to improve the production accuracy of thick and thin film integrated circuits and chip resistors, it is necessary to use equipment such as probe stations and laser resistor trimmers to test or adjust them. The measuring instruments or equipment generally used include connection, excitation, measurement and display units, and sometimes post-data processing units. Different measurement methods and different connection methods introduce different measurement errors, and the measurement accuracy obtained is also different. Usually, the closed resistance of the relay contact in the switch matrix is ​​about 1Ω, the resistance when the FET switch is turned on is more than ten ohms, and the lead resistance is several hundred milliohms. How to reduce the measurement error according to the needs is one of the keys to testing technology.

2 Basic principles of resistance testing

In resistance testing, we often use constant current voltage measurement method, Wheatstone bridge (single-arm bridge) and double-arm bridge method.

2.1 Constant current pressure measurement method

In Figure 1, r is the sum of the lead resistance and the contact resistance; I is a programmable constant current source; V is a voltmeter with extremely high input impedance, which does not shunt the constant current source. Apply a known constant current I through the measured resistor Rt, and then measure the voltage V across the resistor. When Rt>>r, the resistance value can be calculated according to the formula Rt=V/I.

2.2 Wheatstone Bridge Method

In Figure 2, V1 and V2 are programmable constant voltage sources; Rstd is a standard resistor; Rt is the resistor to be measured; and I is an ammeter. When the bridge is balanced, that is, the current flowing through the ammeter I is zero, V1 /V2=Rstd/Rt, from which Rt=Rstd×V2/V1 can be calculated.

2.3 Double-arm bridge method

The measurement range of a single-arm bridge is 10 to 106 Ω. When a single bridge measures a few ohms of low resistance, the lead resistance and contact resistance cannot be ignored. The double-arm bridge is suitable for measuring resistances of 10-6 to 102 Ω. It is an improved single-arm bridge, as shown in Figure 3. By changing the medium and low resistors Rt and R in the bridge to a four-terminal connection and adding two high-resistance resistors R3 and R4 in the bridge circuit, the influence of the lead resistance and contact resistance is greatly reduced. For a detailed introduction, see reference [1].

This article mainly introduces the constant current voltage measurement method. When the resistance of the resistor to be measured is much larger than the resistance of the test lead and the contact resistance between the test probe and the test point, the basic method of two-wire testing shown in Figure 1 is feasible and can also achieve a fairly high test accuracy. [page]

3 Kelvin connection test technology

When the resistance value of the measured resistor is less than a few ohms, the resistance of the test lead and the contact resistance between the probe and the test point are no longer negligible compared to the measured resistance. If the two-wire test method is still used, the test error will increase. At this time, the Kelvin connection method (or four-wire test method) can be used for testing, as shown in Figure 4.

There are two requirements for Kelvin connection: for each test point, there is an excitation line F and a detection line S, which are strictly separated and each constitutes an independent loop; at the same time, the S line must be connected to a test loop with extremely high input impedance so that the current flowing through the detection line S is extremely small, approximately zero.

In Figure 4, r represents the sum of the lead resistance and the contact resistance between the probe and the test point. Since the current flowing through the test loop is zero, the voltage drop on r3 and r4 is also zero, and the voltage drop of the excitation current I on r1 and r2 does not affect the voltage drop of I on the measured resistor, so the voltmeter can accurately measure the voltage value across Rt, thereby accurately measuring the resistance value of Rt. The test result has nothing to do with r, which effectively reduces the measurement error.

According to their functions and potentials, these four lines are respectively called high potential applying line (HF), low potential applying line (LF), high potential detection line (HS) and low potential detection line (LS).

4. Resistance Isolation Test Technology

When the applied constant excitation current can flow through the resistor under test, it is very simple to use the above method to test, such as testing a single resistor. However, we often encounter a situation where the resistor under test is connected in parallel with a resistor network. This resistor network will shunt the applied current, making it impossible to use the above method for testing. In this case, we must use the resistor isolation test technology, and the test circuit principle is shown in Figure 5.

In the figure, Rt is the resistance to be measured, R1 and R2 are connected in series and then in parallel with Rt; A1 and A2 are high input impedance and high precision operational amplifiers; DVA is a high input impedance and high precision differential voltage programmable amplifier for multipliers, and its output is connected to the digital-to-analog converter ADC; DAC is a current output digital-to-analog converter, and DAC and A1 constitute a programmable constant current source; according to computer control, DAC outputs different constant currents If.

A2 forms a voltage follower circuit to make Vc = Vb, so I1 = 0. Therefore, the computer controls the current It flowing through the measured resistor Rt by setting If through the 16-bit current output DAC, and then the voltage across Rt is tested by the voltage detection circuit composed of DVA and ADC to calculate the resistance value of Rt.

This method is equivalent to disconnecting R1 and isolating the resistor to be tested separately, so it is called resistor isolation test technology. [page]

5 minute Darwin connection test resistor

The resistor isolation test is applicable to most complex resistor networks, but some problems will arise when it is applied to a very small number of resistor networks with extremely large resistance ratios. As shown in Figure 6, R2/R1=6000, R3/R1=4000, if the resistor R3 is tested according to the connection in Figure 5 (i.e., the connection in Figure 6-(a)), the facility current It is 200μA, then an 8V voltage drop will be generated across R3. Since R2 is isolated, the voltage across its two ends is zero, so an 8V voltage will inevitably be generated across R1, resulting in R2's power consumption of V2/R1=6.4W, which is obviously not allowed. If the HP and LP positions are interchanged, since A2 is not an ideal device, there is a certain offset voltage Vos, even if it is as small as 20μV, a 2μA current will be generated on R1, causing the current flowing through R3 to have a 1% deviation, resulting in a significant decrease in test accuracy.

In this case, a modified Kelvin connection method can be used for testing, and the isolation method is no longer used. It still uses four wires, but one or two pairs of F and S wires are separated and connected to different points as needed for testing. This method is called a separated Kelvin connection method. In this example, the three resistors need to be tested four times to calculate their resistance values. The connection methods of the four tests are shown in the table in Figure 6, where points 1, 2, and 3 are connection points. The connection method of Figure 6-(b) can directly measure the value of R1; Figure 6-(c) can measure the parallel value R p of R2 and R3; Figure 6-(d) and Figure 6-(e) measure the resistance values ​​R2′ and R3′ respectively. Analysis shows that

R2′/R 3′=R2/R3, 1/Rp=1/R2+1/R3; from this we can solve R2 =Rp×(1+R2′/R3′), R3=R 2×R3′/R2 ′.

In testing, it is often encountered that there are no test points at both ends of the measured resistor, and it is hidden in the resistor network, such as R-2R network. In this case, it is also necessary to use separate Darwin connections for testing.

6 Measurement technology of minimum value resistance

The circuit shown in Figure 7 can be used to measure resistance in a very small resistance range. It can measure resistances of 10 to 80 mΩ. The weak voltage signal generated by the measured resistor is amplified 100 times through the differential operational amplifier circuit, so the actual resistance value is the measured value divided by 100. The operational amplifier UI in the figure uses a low-noise, high-speed, precision operational amplifier, such as OP-37EJ, AD645 or MAX400. The resistor R1 connected in series with the high-potential application line (HF) is used to match the optimal output load of the current application module. R2 to R5 use high-precision and high-stability resistors to ensure the stability of the differential amplifier circuit gain, which determines the accuracy and repeatability of the measurement. In order to ensure accuracy, the power supply voltage of the operational amplifier is very high. The installation position of the circuit should be as close to the measured resistor as possible, all probes should be as short as possible, and C2 and C3 should be as close to the operational amplifier as possible.

7 Conclusion

Since the resistance to be tested needs to be constantly changed during automatic testing, and the test method and connection method need to be flexibly selected according to the situation, in actual production, a probe card is used to connect the circuit to be tested to the system, and the switch matrix composed of relays or FET switches is appropriately switched by the software to improve the test speed and production efficiency. At the same time, different probe connection methods are used in different measurements, such as the straight four-probe method and the square four-probe method, which can overcome the influence of various factors and optimize the measurement results [2]. As mentioned above, as long as we combine the specific situation of the resistance to be tested and flexibly and reasonably apply the test technology introduced above, we can get satisfactory test results. High-quality thick and thin film integrated circuits and chip resistors are manufactured.