Tester Theory

 

All Precision testers operate by measuring the electrical charge (µC) stimulated at one electrode of the sample under test by a voltage stimulus applied to the opposite electrode. This is compared to the more traditional Sawyer Tower method below. In the Precision tester the charge is captured at the RETURN port, passed through an amplification stage and into an integrator whose voltage output relates directly to the charge input. A simplified diagram is shown in Figure 1.

 

 

The circuit is called "Virtual Ground" because the Sample Charge (µC) Signal enters the Transimpedance Amplifier at zero Volts. This will be an important consideration in comparing Virtual Ground measurements to Sawyer Tower measurements.

 

An earlier standard for measuring the response of a non-linear sample under test - and one still taught to students - is the Sawyer Tower Circuit. In this much simpler circuit the voltage drop across a Sense Capacitor that is in series with the sample under test is measured. This voltage drop can then be directly related to the voltage drop across the sample under test. Here, then, the voltage across the sample, rather than the current through the sample, is measured. The simple circuit is shown in Figure 2.

 

 

The Sawyer Tower circuit has the advantage of simplicity. There, however, the advantages end. There are three main problems with the Sawyer Tower technique:

 

The Sense Capacitor is the critical element in the circuit. It must be a capacitor whose value is very precisely known. Furthermore the Sense Capacitor should be approximately ten times the capacitance of the Sample Under Test. That means that the sample capacitance needs to be well-estimated in constructing the Sawyer Tower circuit. The 10 X size ratio of the Sense Capacitor to the Sample Under Test is chosen to reduce Back Voltage. The Virtual Ground circuit uses a fixed, precisely-known integrating capacitor that is designed to measure samples with a wide range of capacitances. The value of the capacitor does not need to be selected by, or known to, the user.

 

As the Drive Voltage Signal peaks and begins to return to zero Volts during a Hysteresis measurement, the charge accumulated by the Sense Capacitor will create a back voltage at the sample electrode opposite the the Drive Voltage Signal (Figure 3). The effect of this Back Voltage combines with the influence of the Drive Voltage Signal to distort the sample's voltage response.

 

 

With the sample response held at 0.0 Volts at the RETURN port, the Virtual Ground circuitry allows for no Back Voltage to be applied to the sample RETURN electrode and does not distort the measurement.

 

All electronic circuits have capacitance. In the case of the Sawyer Tower circuit this capacitance can be modeled as a single constant capacitor in parallel with the Sense Capacitor (Figure 4). The parasitic capacitance sums with the Sense Capacitor, increasing its total capacitance. Since the parasitic capacitance is constant the contribution of this capacitance to error varies with the size of the Sense Capacitor. The contribution, as a percentage of the total, is larger for smaller Sense Capacitors.

 

 

Virtual Ground circuitry also has parasitic capacitance. However, on the RETURN signal side of the circuit, the capacitance is modeled between the zero-Volt Virtual Ground input of the circuit and earth ground. (Figure 5.) With no voltage across the parasitic capacitance the capacitor model introduces no contribution to the measured signal.

 

 

Note that the Transimpedance Amplifier, the Charge Integrator and other tester circuitry also add parasitic capacitance that does affect the measured data beyond the RETURN port. Normally this capacitance is insignificant with respect to the strength of the measured signal and can be ignored. For measurements on very small capacitors that return very low measured signals, Vision provides tools to characterize and remove tester parasitic capacitance contributions to the data.

 

The Hysteresis - or PE (Polarization Vs Field) - measurement is the primary non-linear characterization measurement made, within Vision, by the Precision Tester. Several measurements are derived directly from the Hysteresis measurement. In Vision, the basic Hysteresis measurement is performed using the Hysteresis Task. This is a discussion of the process involved in making the Hysteresis measurement. This discussion is heavily simplified.

 

 

 

 

The Hysteresis Task offers many DRIVE Voltage Profile options. Eleven automatic profiles and a custom profile are offered. In addition any profile may be shifted vertically by specifying a Hyst Bias. The user can completely specify a DRIVE Profile by selecting a DRIVE Profile Type, assigning a Max Voltage, specifying the Period (ms) and, perhaps, assigning a Hyst Bias. The period is the duration of the entire DRIVE profile in milliseconds. For bipolar profiles this is equivalent to 1000 / Frequency (Hz) => Frequency (Hz) = 1000 / Period (ms). For double-bipolar profiles, the factor is 2000 and for monopolar sequences the factor is 500. A final complexity is that the profile strength and offset may be specified in units of Electric Field (kV/cm). Here, Electric Field (kV/cm) is given by:

 

Electric Field (kV/cm) = Voltage / (1000 V/kV x Sample Thickness (µm) x 10^-4 cm/µm) (1)

 

 

 

Figure 10 shows two profile options. The figure is generated by clicking the Profile Preview button on the configuration dialog.

 

 

Each DRIVE Profile is composed of a sequence of discrete real-valued voltages. While the user completely specifies the profile with a DRIVE Profile Type selection, Max Voltage, Period (ms) and possibly Hyst DC Bias (V), the program takes these parameters and constructs the voltage list. For this example the default "Standard Bipolar" DRIVE Profile Type will be used with a Max Voltage of 10.0 V and a 10.0 ms Period (ms). Hyst DC Bias (V) is 0.0 V. The first point in the list is always 0.0 V. (The Hyst DC Bias (V) parameter is passed separately to the driver).

 

 

The Standard Bipolar profile starts at 0.0 V, rises linearly to +10.0 V, then falls linearly at the same rate to -10.0 V before rising again to a final value of 0.0 V. Note that the total magnitude of the voltage traversed is 4 x 10.0 V = 40.0 V.

 

The program begins by determining the number of points over which to space the voltages in the list. The number of points specified is the maximum possible number (always the highest-precision) given several conditions:

 

 

The DRIVE Profile list always begins and ends at 0.0 Volts. (Any Hyst Bias (V) is passed separately to the Vision Driver and applied to the waveform there.) For the Standard Bipolar profile of this example, each voltage is determined by incrementing or decrementing the previous voltage by a fixed magnitude of (4 x Max Voltage)/(Points - 1). For a 20001-point waveform this step voltage is given as (4 x 10)/20000 = 0.002 V. Figure 12 shows a partial list of the example DRIVE Profile voltages at 20001 points. This list was generated from the results of an actual measurement. The data do not represent the DRIVE Profile voltages requested by Vision. They represent the actual DRIVE voltages that were applied at each sample point as discussed in Step 9 of

Simplified Hysteresis Measurement Sequence

, above.

 

 

Figure 12 also lists the sample time (ms) for each point relative to the first-captured point. The sample time is captured by the driver at the time of the measurement. The list should increment time (ms) by a constant value that is very close to the ideal time of Period (ms)/(Points - 1). Here, 10.0 ms / 20000 = 0.0005 ms. The actual DRIVE Voltage, Charge (µC), Sample Time (ms), SENSOR 1 voltage and SENSOR 2 voltage parameters are captured at each point after the voltage at that point has been stable for the constant period.

 

 

In Figure 13, the DRIVE Profile represents actual measured DRIVE Voltage and Step Delay (ms) data. These differ from the ideal data of Figure 11.

 

With the exception of the Precision RT66C tester, all Precision model testers released since 2014 are capable of generating up to 32,000-point Hysteresis measurements. The Precision RT66C has an upper limit of 2000 points. (These numbers are approximate. The actual limit is somewhat higher.) Vision will always build the DRIVE Profile voltage waveform using the maximum number of points given the test conditions. For most testers the user can specify and upper bound on that number of points. To set the limit, go to Tools->Options->Measurement and Test Definition Execution and adjust the selection in Hysteresis-Based Task Point Limit. The selection becomes permanent between Vision program executions until it is changed.

 

 

The sample charge (µC) response to the DRIVE stimulus voltage is captured by the integrating circuit at the Precision tester RETURN port after passing through a variable amplification stage. The output of the amplifier/input to the integrator is in the ±5.0-Volt range A quality measurement will have a peak amplifier output that is within 5% and 95% the output range (±0.25 to ±4.75 Volts). If the signal is outside this range, then the amplification should be adjusted to boost or reduce the signal into the range. The user has three options for setting the amplification level: