Nano-Measurements Need Mega-Care

General-purpose test instruments such as picoammeters, lock-in amplifiers, and nanovoltmeters often are integrated into this equipment and used separately with tools such as probe stations and nanopositioners.

An integrated solution will include many of the precautions necessary when working with very small signals. Low-level signals will be kept as far as possible from large digital signals to reduce coupling. Capacitive coupling is further minimized by electrostatic shielding. Material thickness isn't as important as conductivity, copper being more effective than steel at very high frequencies.

Twisting a signal wire with its return wire minimizes the enclosed loop area, which reduces inductive coupling. Magnetic shielding to reduce inductive coupling requires either high-permeability material or a thicker shield if the permeability is lower. More shielding information can be found in Ron Brewer's February 2008 EE-Evaluation Engineering article “3,000 dB and Rising.”

Whether you use a test station or build your own test setup, noise will be a major consideration. Regardless of how well a test setup has been constructed, broadband Johnson noise cannot be avoided. This is thermal noise that every resistance generates. Some types of resistive materials develop noise in excess of Johnson noise levels. Typically, this and similar excess noise generated by semiconductors have a 1/f spectrum. This means that measurements made at low frequencies and DC will be more affected by noise.

Differential amplification is the preferred procedure for handling low-level signals. In a balanced differential circuit, the signal and return lines are treated identically. Both have the same input characteristics, not just for intentional signals but for unintentionally coupled noise as well.

Of course, real circuitry isn't perfect although the common mode rejection ratio (CMRR) can be high to a few hundred kilohertz. LeCroy's DA1855A Differential Amplifier is a good example, being specified out to 100 MHz and with typically 115 dB CMRR at 100 kHz and 10x gain.

A number of approaches have been developed to deal with low-level signals that often are buried in a much larger noise signal. The most common method is averaging. If the noise signal really is random, then its rms value will reduce as the square root of the number of averages. For example, with 100 averages, the noise will be 10x less.

That sounds like an easy way to recover small signals, but averaging isn't always appropriate. Noise levels can easily be much greater than 10x the desired signal so a great deal of averaging could be required and take a large amount of time. During that time, the desired signal also is being averaged. Ideally, it shouldn't change from acquisition to acquisition.

Another way to minimize noise is to reduce bandwidth through filtering or some means other than averaging. The amount of Johnson noise is directly proportional to the square root of bandwidth, and a very small signal bandwidth is the key to the operation of lock-in amplifiers that routinely measure nanovolt signals. However, because of the way they work, lock-in amplifiers achieve that bandwidth anywhere within a wide frequency range—not just near DC.

At very low frequencies, thermal drift is a problem. The purpose of many experiments is to measure resistance, which generally is temperature sensitive. In addition, some materials act like current or voltage sources at a very low level so these effects must be separated from the voltage developed by the test current.

To eliminate the effects of self-generated currents or voltages, it has become common practice to average successive pairs of measurements, one made with current applied in the forward direction and the other with the current reversed. A further refinement uses three measurements to provide very good thermal drift cancellation.

When making these measurements, it's important to minimize the temperature change from one measurement to the next. Because of this, the speed with which a current source can be reversed or a nanovolt-level signal measured has become important.

Lock-in Amplifier

Various datasheets refer to the development of lock-in amplifiers in the 1960's. They tend to be listed under electrophysical or electrochemical equipment rather than as a general-purpose electronic measuring device.

The operating principle is elegant in its simplicity. If the experiment is excited by a very pure sinewave at a single frequency, the output can be measured by a phase-sensitive detector at precisely that frequency. Equation 1 explains the process mathematically.

In general, the output frequency is exactly the same as the exciting frequency so the cosine of the frequency difference equals 1.0. The frequency sum term is at twice the reference frequency and easily filtered and eliminated. The term that remains is proportional to the experiment output signal amplitude and phase difference.

A lock-in amplifier with two detectors—a dual-phase lock-in—has two references in quadrature and determines both the cosine of the phase difference as well as a separate sine term. In other words, it computes an in-phase and a quadrature component of the output.

From these values, the resultant magnitude R can be derived. These instruments label outputs X for the real or in-phase axis, Y for the quadrature component that is 90? out of phase, and R.

In theory, a lock-in amplifier seems like a great idea. Today's digital versions actually perform very well, especially in comparison to earlier analog models. Almost all of the analog circuit areas cause problems because they simply are not as precise as needed.

For example, the sinewave reference generator may lack the required purity. This means that the phase detector will be sensitive to harmonics. In fact, some analog lock-in amplifiers use a square wave as the reference and are sensitive to all the odd harmonics of the fundamental. In contrast, a 20-bit digital sine generator might have harmonics as low as -120 dB.

Preceded by a suitable amount of low-noise analog amplification, a modern 18-b ADC introduces little noise on its own. In the Stanford Research Systems Model SR850 Digital Lock-in Amplifier, gain ahead of the ADC is high enough that the actual signal noise is larger than the ADC noise. The subsequent multiplication of the signal by the reference is almost perfect, being done digitally and with high resolution.

Very large noise levels must be accommodated while at the same time providing enough gain to get the needed sensitivity. The ratio of the largest permitted signal to the full-scale value of a particular range is called the dynamic reserve.

Digital lock-in amplifiers are more flexible in the way gain is distributed before and after the ADC and detector. Because the SR850 performs digital multiplication and filtering, large amounts of post-detector gain can be provided with few undesirable consequences.

Analog detectors have a limited dynamic range, and some lock-in amplifiers use tracking prefilters to reduce noise levels away from the reference frequency. Up to 20 dB greater noise can be handled in this way, but such filters add their own noise and contribute to phase error. Increased gain following the detector also is problematic because of detector DC offsets and drifts.

An important aspect of dynamic reserve is its behavior near the reference frequency. DSP-based filtering provides a totally stable low-pass characteristic with very steep skirts, which increases the dynamic reserve close to the reference. In effect, the detector bandwidth is narrower. A digital lock-in amplifier can have as much as 100 dB of dynamic reserve, where analog systems may be limited to about 60 dB.

In addition to basic performance benefits, digital designs typically include analysis functions such as curve fitting, statistics and calculations, and data smoothing algorithms. Multiple auxiliary channels may be available and often the input can be switched between a high-impedance for voltages or a low impedance for currents.

Several companies make lock-in amplifiers and the specifications vary widely. A 1-V maximum full-scale range is common, but the most sensitive range varies from 2 nV on the SR850 and Signal Recovery Model 7124 to 1 ?V on the Scitec Model 450S. The Signal Recovery instrument is unusual because it has a separate remote input chassis controlled by a fiber-optic link to avoid introducing digital noise into sensitive experiments.

It's also possible to assemble lock-in amplifiers from off-the-shelf building blocks. As described in a National Instruments (NI) case study, a Harvard University research team at The Department of Chemistry needed to make 128 simultaneous low-current measurements on nanowire FET sensors. They used NI's Model PXI-4472 Dynamic Signal Acquisition modules to sample all 128 channels and a software-based lock-in amplifier technique to extract the desired signals from the noise.

Picoammeters

Most commonly used ammeters and DMMs indicate current but actually measure the voltage drop, called the burden voltage, across a small shunt resistance. This method is low cost and sufficiently accurate for many applications. However, accuracy degrades when the shunt resistance approaches the signal source resistance and the burden voltage is no longer negligible.

In the extreme, a very large shunt is required for nanoamp currents, leading to long settling times and slow measurement rates. Instead, the feedback ammeter approach shown in Figure 1 is used. The input impedance of the operational amplifier must be very high, but with a suitable device, the equivalent burden voltage can be as low as a few tens of microvolts. Because an additional gain factor (R₂ + R₃)/R₃ is provided by the circuit, the values of the resistors can be relatively small even for nanoamp sensitivity, leading to faster measurements.

A Keithley Instruments Application Note discusses several noise and error sources encountered in low-current measurements.¹ In addition to the burden voltage, several other error sources become important at lower current levels. For example, leakage currents across or through insulation, noise current generated by triboelectric or piezoelectric effects, current associated with dielectric absorption, and electrochemical effects due to surface contamination can all contribute to measurement errors.

Some suggested solutions are obvious: secure connections so that they cannot move and create triboelectric or piezoelectric currents. Clean the PCB or material being measured so that electrochemical effects are minimized. Beyond these precautions, guarding is a very common means of reducing errors caused by leakage currents.

Figure 2 shows a typical measurement set up with guarding. The basic idea is to divert the leakage current away from the measuring circuit. You can't stop a small amount of current from flowing through test set-up insulation, but you can control where it flows.

In the figure, the high-impedance node connecting the ammeter and diode has been enclosed in a metal box driven at 15 V. A 1-GΩ leakage resistance has been assumed that, without the guard, would cause an additional 15 nA to flow through the ammeter. With the guard, the 15 nA still flows, but from the very low-impedance 15-V supply rather than from the high-impedance ammeter-diode node. The measurement error caused by the leakage current has been reduced to 0.2 pA, corresponding to a 0.2-mV burden voltage.

Depending on the test setup, it may be more appropriate to drive the guard from a low-impedance buffered version of the measured output voltage. For example, the current leakage within a shielded cable driving a high-impedance voltmeter can be minimized through guarding. A buffered copy of the voltmeter output is used to drive the shield of the cable. Because the signal and the shield are at the same voltage, the leakage current is minimized.

Beyond these considerations, many picoammeters average successive readings to reduce noise. The Agilent Technologies Model 4339B High-Resistance Meter measures DC current from 60 fA to 100 ?A and resistance from 1,000 Ω to 1.6 x 10¹⁶ Ω, using source voltages from 0.1 V to 1,000 V. Measurement precision and time are, 3, 4, and 5 digits requiring 10 ms, 30 ms, and 390 ms, respectively.

Agilent also provides picoampere measurement capability in the Model B1500A Semiconductor Device Analyzer. This test platform has 10 slots that accept a range of source/monitor units, a multi-frequency capacitance measurement unit, a high-voltage pulse generator, and a waveform/fast measurement unit.

Pulsed measurements are very important in nanoelectronic work, primarily because the structures are so small that they cannot support significant currents and voltages at DC. Keithley's Model 4200 Semiconductor Characterization System has parametric test functionality similar to the Agilent B1500A covering precision DC and pulse measurements. In addition, Keithley offers a range of stand-alone picoammeters and electrometers as well as the production-oriented S600 Parametric Test System with DC through RF capabilities.

Agilent and Keithley have the largest selection of picoammeters and related low-level instruments such as source/measure units (SMUs), the Keithley equivalent to Agilent's source/monitor unit. With the addition of a remote preamplifier, Keithley's Model 6430 SMU provides a 1-pA full-scale range with 10-aA resolution. One attoamp is equivalent to six electrons per second.

This level of integration seems to have addressed a real need in the market as evidenced by the wide adoption of the SMU terminology. NI also offers an SMU, the Model PXI-4130, that can source, sink, and measure current to 1 nA.

Other picoammeters include the Model AH401 from Sincrotrone Trieste that features 20-b measurements with 50-aA resolution and integration times from 1 ms to 1 s for full-scale ranges of 50 pA to 350 nA. This compact, four-channel unit transfers data via USB 2.0 and is intended for applications such as photodiode current measurement.

According to NI's Travis White, product manager, precision DC measurements, “A sensitive picoammeter can be based on the NI PXI-4022 Current Amplifier Module, which implements a feedback ammeter with less than 20 ?V of burden voltage on its 100-nA current range. When combined with the NI PXI-4071 DMM to measure the output voltage, current measurement resolution of 0.5 pA results.”

Nanovoltmeters

Similar to the error currents that can affect low-current measurement accuracy, nanovolt measurements are subject to unintentional voltage drops. The most common solution to eliminate low-level voltage errors caused by the test set up is the use of four-wire or Kelvin connections.

One set of leads sources the exciting current and the other set measures the voltage drop caused by the current. In a simple two-wire Ohms measurement, error voltages are created because the test current flows through the measurement leads as well as the unknown resistance.

Additional voltages may be generated by thermoelectric effects and cause a measurement offset. Typically, your test setup will require two or more connections between wires and terminals of different materials. If there is a temperature difference between parts of the test setup, small voltages will be generated—certainly nanovolts and possibly microvolts.

The traditional way to minimize this effect is to make a voltage measurement with the current in one direction, then repeat the measurement with the current reversed. This technique gives the best results when the current can be reversed so quickly that the temperature has not changed between the two readings.

Of course, this is only an approximation to a constant temperature situation, and may not be accurate for very sensitive measurements. A better approach is the so-called delta method that uses three successive measurements. This technique approximates any change in voltage between successive readings as a linear function. Using the delta method provides more accurate measurements even if the current direction is switched quickly.

Agilent's Model 34420A NanoVolt/Micro-Ohm Meter is one of a few instruments with nanovolt sensitivity. This unit is interesting in several aspects. As with the company's 4339B Meter, resolution is traded against integration time. Here, DC readings with 5?-, 6?-, and 7?-digits resolution require 1, 20, or 200 power line cycles (plc), respectively. In a country with 60-Hz power, 200 cycles are equivalent to 3.33 s.

The specification is written in this way because the type of ADC used in the nanovoltmeter integrates an integer number of power line cycles to reduce power line noise. That this technique is effective can be seen from the 110-dB normal-mode rejection resulting from 200-plc integration. Integrating for one plc gives 60 dB.

The instrument has 0.1-nV resolution, but the most sensitive full-scale range is 1 mV. On the 1-mV range, the peak-peak noise observed during a 2-minute period was 8 nV. Over a 24-hour period, the peak-peak value increased to 12 nV. No doubt, the noise spectrum is limited by the instrument's bandwidth, but nevertheless the increase simply confirms the generally unbounded nature of Gaussian noise.

Keithley's Model 2182A Nanovoltmeter emphasizes both speed and sensitivity, making a 15-nV peak-to-peak measurement in 1 second. Slightly less sensitive 40-nV to 50-nV measurements take only 60 ms. The delta mode thermoelectric drift cancellation measurement scheme is built in.

The Model 2182A also is capable of operating synchronously with the Models 6220 or 6221 Current Sources. Both of these instruments can be operated in pulse mode and can switch current polarity at a 24-Hz rate.

A Keithley white paper discusses the improved performance represented by the combination of models 2182A and 6220 compared to a very good lock-in amplifier. Voltage noise is lower than the lock-in amplifier by a factor of 7.2.² This is important because lower noise supports a higher SNR with lower signal power. And, with nanoelectronics and nanomaterial research, it's always necessary to minimize test signal power.

DC noise performance is comparable to the Agilent figures, but expressed differently. For the Keithley 2182A, noise was observed for a 2-minute period after the meter had settled to an input step. The 10-mV range has 1-nV resolution, and on this range integrating for 5 plc and with a 75-reading digital filter, the peak-to-peak noise was 6 nV.

Summary

The ubiquitous 3-digit $49 DMM is a long way from coping with the scale of measurements required in nanoelectronics and nanomaterial research. Instead, much more specialized equipment is needed that has orders of magnitude higher input impedance and sensitivity. Many of the same kinds of measurements are made in semiconductor parameter testing, and the Keithley and Agilent test platforms are good examples of this type of product. In addition to the hardware, different test techniques are needed, and are supported in the newer test instruments.

Several companies are involved in building low-level test systems with a wide range of capabilities. For example, Charles Greenberg, senior product marketing manager at EADS North America Defense Test and Services, described a wafer probing application that required four-wire connections, pulsed operation to reduce device heating, and six-wire guarded Ohms measurements.

In addition, because many points needed to be tested, the good low-level performance had to be maintained when the instrumentation was switched among many channels. The company's new Model 1830 Test Platform combines switching with multiple SMUs and supports low-level measurements.

It's also apparent that even if a bench top DMM can't match the sensitivity of a picoammeter or nanovoltmeter, its capabilities are being extended in those directions. Fluke's marketing manager Hilton Hammond commented that with so many consumer products being battery powered, engineers need to make accurate low-level stand-by or leakage measurements during design and manufacturing. This is one reason that the Fluke Model 8808A uses a feedback amplifier-based current measurement circuit with higher accuracy and less loading at low currents.

Nanoelectronics and nanomaterial measurements have special needs. Help is available in the form of white papers, application notes, and a dedicated low-level measurement handbook.³ For this kind of work, understanding how a measurement must be approached to get the desired result is at least as important as having the right instruments.

References

1. “Low Current Measurements”, Keithley Instruments, Application Note Series, Number 100, 2007.
2. Daire, A., et al, “New Instruments Can Lock Out Lock-ins,” Keithley Instruments, white paper, 2005.
3. Nanotechnology Measurement Handbook, Keithley Instruments, 2007.