# Low Current Measurements

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1 Number 1671 pplication Note Series Low Current Measurements Basic Current Measurements n a typical circuit (see Figure 1a), a source causes a current () to flow through the circuit. The goal of any electrical current measurement is to insert an ammeter in series with the circuit so that the current measured on the ammeter is identical to the current originally flowing through the circuit. To do so, the circuit is broken between points and B, and the meter is connected as shown in Figure 1b. n the ideal case, the meter would have absolutely no effect on the circuit. For practical measurements, however, several error sources may be present. These error sources can result in substantial uncertainty in the measurement, as we will now discuss. ny ammeter can be modeled to consist of the three separate circuit elements shown in Figure 1b: a shunt resistance (H ) caused by the input cable connected to the meter; a generator of unwanted current ( C ), which represents mainly currents generated by interconnections; and an internal resistance (R M ), which includes series cable resistance. Note that R M is in series with an ideal ammeter (M ), having no resistance or current source of its own. Figure 1a: source causes a current () to flow through a wire between and B. = B ndicated Current S Cable Shunt Resistance Circuit Under Test Equivalent Circuit = Current to be Measured H SH C M SH C ± U M oltage Burden Error Generated Currents mmeter Equivalent Circuit Shunt Current Error M Generated Current Error Meter and nternal Resistance R M M Meter Uncertainty Figure 1b: When an ammeter and connecting cable are used in place of a wire, a voltage burden ( M ) is developed, which forces a shunt current ( SH ) through the shunt resistance (H ) of the cable. Unwanted error currents (E) are also generated due to various phenomena discussed in the text. When the ammeter is connected in the circuit to be measured, the current indicated on the meter is equal to the current that would flow through the circuit without the ammeter inserted in the circuit, less errors caused by elements in the circuit model. These errors consist of current flowing through the model shunt resistance, currents generated by the interconnections, errors induced by the voltage burden (or drop) across the entire ammeter model, and the uncertainty of the meter itself. With measurements of currents in the normal range (typically >1m), errors caused by ammeter voltage burden, shunt currents, and noise current are often small enough to be ignored. n these cases, the displayed current reading is simply equal to the actual current plus or minus inherent meter uncertainty, (U M ). Meters designed to measure these normal currents generally consist of a voltmeter circuit that measures the voltage drop across a shunt resistor inserted in the series with the circuit being measured. (See the discussion on shunt ammeters that follows.) The reading provided by the voltmeter is thus directly proportional to the current flow. Unfortunately, the voltage burden (input voltage drop) produced by such meters usually ranges from 200m to about 2. This voltage drop is sufficient to cause errors with current measurements below the normal range. To avoid such large voltage drops, picoammeters and electrometers use a high gain amplifier with negative feedback for the input stage. s a result, the voltage burden is greatly reduced on the order of 200µ or less. This low voltage burden reduces both measurement errors and the minimum shunt cable resistance that must be maintained to provide a given meter accuracy. Consequently, no special measures need be taken to obtain unusually high cable resistance. Typical picoammeters or electrometers that employ feedback ammeters generally provide sensitivities to 1f (10 15 ) or less and typical accuracy of 0.1% to 3%. Shunt vs. Feedback mmeters There are two basic techniques for making low current measurements: the shunt method, and the feedback ammeter technique. The shunt configuration is used primarily in DMMs (digital multimeters) and in older electrometers where cable capacitance causes problems in the feedback mode. Picoammeters and newer electrometers use only the feedback ammeter configuration. The major difference between picoammeters and electrometers is that electrometers are multifunction instruments, while picoammeters measure only current. lso, a typical electrometer may have several decades better current sensitivity than the typical picoammeter. Shunt Picoammeter Shunting the input of an electrometer voltmeter with a resistor forms a shunt ammeter, as shown in Figure 2. The input current ( N ) develops an input voltage EN across the shunt resistance (HUNT ) as follows:

2 N R nput N E N R F Output HUNT E N R B = N R F Figure 3: Feedback ammeter Figure 2: Shunt ammeter = N HUNT E N = N HUNT Note that the voltage sensitivity of the circuit is controlled both by the value of HUNT and the relative values of R and R B. Thus, the output voltage ( ) is given by: ( R B ) R R B R B ( R B ) R R B R R E B OUT = E N = N R SHUNT lthough it might appear advantageous to use a larger value for HUNT, there are actually several good reasons why HUNT should be made as small as possible. First, low value resistors have better time and temperature stability, and a better voltage coefficient than high value resistors. Second, low resistor values reduce the input time constant and result in faster instrument response times. Finally, for circuit loading considerations, the input resistance HUNT of an ammeter should be small to reduce the voltage burden E N. However, using an electrometer (or any voltmeter) on its most sensitive range introduces noise and zero drift into the measurement. n contrast, Johnson noise current decreases as the value of HUNT increases. Thus, some compromise between these two opposing requirements is usually necessary. Choosing a 1 2 full-scale sensitivity and the appropriate shunt resistance value is often a good compromise. Feedback Picoammeter Figure 3 shows the general configuration of a feedback type ammeter. n this configuration, the input current ( N ) flows into the input terminal of the amplifier (), and it also flows through the feedback resistor (R F ). The low offset current of the amplifier changes the current ( N ) by a negligible amount. Thus, the output voltage is a measure of the input current, and sensitivity is determined by the feedback resistor (R F ). The low voltage burden (E N ) and corresponding fast rise time are achieved by the high gain operational amplifier, which forces E N to be nearly zero. Thus, Circuit analysis shows that: E OUT N R F = E N = E N, and E N = N R F = Since >>1, = N R F and E N = << Note that the amplifier gain can be changed as in the voltmeter circuit, using the combination shown in Figure 4. n this case, resistors R and R B are added to the feedback loop, forming a multiplier. The gain of the circuit is determined by the feedback resistor and by the relative values of R and RB and is given as follows: R R E B OUT = N R F ( R B ) and again, E N = E N N R F R R B = R F (1 R R B ) Figure 4: Feedback ammeter with selectable voltage gain Sources of Current Errors Errors in current-measuring instruments arise from extraneous currents flowing through various circuit elements. n the model circuit of Figure 5, the current ( ), indicated on the meter, is

3 S 1 1 = S SH E SE CE H RE E M Frictional motion at boundary due to cable motion nsulation nner Conductor Current Source E = SE CE RE E S = Source current SE = Source noise current CE = nterconnection noise current H RE E = = = Shunt resistance Shunt resistance noise nstrument error current Coaxial Cable Outer Jacket Outer Shield Conductive lubricant in low noise cable Figure 5: Sources of current errors actually equal to the current ( 1 ) through the meter, plus additional meter uncertainty (U M ). 1 is the signal current ( S ), less shunt current ( SH ) and the sum of all generated currents ( E ). The circuit model shown in Figure 5 identifies various noise and error currents generated during a typical current measurement. The SE current generator represents noise currents generated within the source itself. These currents could arise due to leakage, piezoelectric, or triboelectric effects, or through dielectric absorption. Similarly, the CE current generator represents currents generated in the interconnection between the meter and the source circuit. The same sources that generate noise currents in the circuit under test may produce noise in the interconnection. RE is generated by the thermal activity of the shunt resistance and the rms value of the noise current and is given by: RE = 4kTf/H where: k = Boltzman s constant ( J/K) T = absolute temperature in K f = noise bandwidth in Hz H = resistance in ohms Since peak-to-peak noise is about five times the rms value, the noise current can be ignored when measuring currents above Finally, E is the specified sum of error currents in the measuring instrument. Noise Currents The noise current generators CE, SE, and E in the above model represent unwanted currents generated at a particular point in the circuit. These currents may arise from triboelectric, piezoelectric, and electrochemical effects, or from resistive leakage or dielectric absorption. Triboelectric currents (shown in Figure 6) are generated by charges created at the interface between a conductor and an insulator due to friction. Here, free electrons rub off the conductor and create a charge imbalance that causes a current flow. typical example would be electrical currents generated by insulators and conductors rubbing together in a coaxial cable. Special Figure 6: Triboelectric effect pplied Force Piezoelectric nsulator Figure 7: Piezoelectric effect Figure 8: Electrochemical effects Printed Wiring Metal Terminal Flux or other chemical track and moisture low noise coax and triax cables are available to minimize this problem. Piezoelectric currents (Figure 7) are generated when mechanical stress is applied to certain insulating materials. These currents are generated in ceramics and other crystalline materials used for insulating terminals and interconnecting hardware. Similar stored charge effects occur in many plastics. Noise currents also arise from electrochemical effects, which are shown in Figure 8. Here, chemicals cause weak batteries between two conductors on a circuit board. For example, commonly used epoxy printed circuit boards can generate currents Conductive Plate Epoxy Printed Circuit Board

4 of several nanoamps when not thoroughly cleaned of etching solution, flux, or other material. To prevent these error currents, all interconnecting circuitry should be thoroughly cleaned using a cleaning solvent such as methanol, and then be allowed to dry completely before use. Dielectric absorption can occur when a voltage applied across an insulator causes positive and negative charges within that insulator to polarize. When the voltage is removed, the separated charges generate a decaying current through external circuitry as they recombine. The effects of dielectric absorption can be minimized by avoiding the application of voltages more than a few volts to insulators to be used for sensitive current measurements. f this practice is unavoidable, it may take minutes or even hours in some cases for currents caused by dielectric absorption to dissipate. Figure 9 summarizes approximate magnitudes of the various current-generating effects. Typical Current Generated Guarding Standard cable Low noise cable Triboelectric Effects Teflon Clean surface High resistance paths between low current conductors and nearby voltage sources can cause significant leakage currents, which can be eliminated through guarding. Basically, guarding uses a conductor at the same potential as the sensitive current path to totally surround the input leads carrying the high impedance signals. This guard conductor is driven by a low impedance source, and maintaining the conductor at the same potential as the highimpedance source results in drastically reduced leakage currents from those leads. For example, assume that an ammeter is to be used to measure the reverse current D through the diode shown in Figure 10a. f the meter (a picoammeter or electrometer ammeter) is connected in series with the diode (Figure 10b), it will measure not only the diode current ( D ), but also the leakage current ( L ) that flows through the leakage resistance path (R L ). f R L has a value of 1GW (10 9 W, a reasonable value for many insulators), the leakage current ( L ) would be 15n (assuming a 15 potential across the circuit, as shown). Obviously, the large value of leakage current would obscure the actual diode reverse current ( D ), which is typically much Ceramics Mechanical Stress Effects Dirty surface Epoxy board Electrochemical Effects Current-Generating Phenomena Resistor noise in 1Hz bandwidth Figure 9: Typical magnitudes of currents generated by low current phenomena lower than 15n in modern diodes. One way to solve the problem is to increase the leakage resistance (R L ) to 1TW, reducing L to 15p, which still may be large compared to D. nother way to reduce the effects of leakage currents is to guard the connection between the diode and the picoammeter so that it is completely surrounded by a conductor connected to the same potential (15 in this example). The resulting configuration is shown in Figure 10c. Since a typical feedback picoammeter has a maximum voltage burden of only 200µ, the voltage across RL is reduced to that value, and the leakage current now becomes: 200µ L 1GW L (0.2p) Thus, L is reduced by four decades and is likely to be insignificant compared to D. The current flowing through R G is still 15n, but it is now supplied by the low impedance 15 source, and it does not present a problem since it is not measured by the ammeter. nother situation where guarding is beneficial is shown in Figure 11a. n this case, the leakage resistance of a coaxial cable whose shield is grounded will reduce the output voltage of a high resistance source, as shown in Figures 11a and 11b. Note that voltage actually measured by the high impedance voltmeter is attenuated by the voltage divider formed by the source resistance ( ) and the leakage resistance (R L ). Figure 10a: diode whose reverse current D is to be measured. R 1 R 2 15 D R 1 15 D R 1 R 2 R L = 1GΩ R G = 1GΩ Figure 10b: n ammeter measures both D and L, the leakage current. 15 D R 2 R L = 1GΩ = D L 0.2p GU RD 15 G = = 15n 1GΩ = D L 15 L = = 15n 1GΩ Figure 10c: By guarding the input to the picoammeter, L is greatly reduced, and the picoammeter measures D accurately.

5 Figure 11a: high resistance source is to be measured by a high impedance voltmeter. Source E S E S Figure 11b: Equivalent circuit of Figure 10a showing loading effect of the connecting cable resistance R L. R L G R G R L E G f instead, the shield is connected to a low impedance source of the same potential as the high resistance source, such as the unity-gain or preamp output of an electrometer voltmeter (Figure 11c), leakage from the center conductor to the shield will vanish, since there is essentially no potential across the insulator (R L ). Leakage current ( G ) from the outer guard shield to ground may be considerable, but it is of no consequence since the current is supplied by the low impedance preamp output rather than by the high impedance source. lthough the main advantage of guarding is in the reduction of leakage resistance effects, another is the reduction of effective input capacitance. Measurement rise time depends both on the equivalent source resistance and the effective meter input capacitance, which depends both on the electrometer input capacitance and the connecting cable capacitance. Thus, for high resistance measurements, even a small amount of cable capacitance can result in very long rise times. For example, an input capacitance of 1,000pF (including the input cable) and a resistance of 200GW results in a time constant (t = RC) of 200 seconds, and 1,000 seconds (more than 16 minutes) must be allowed for the measurement to settle to within 1% of final value. Modern electrometers, such as the Models 6514, 6517B, and 6430, have built-in provisions to take full advantage of guarding. n the guarded mode, the effective cable capacitance can be reduced to about 20pF, speeding up measurements by a factor of 50. E S E O H E O R L H H High mpedance oltmeter R L ER OS E O = RL Figure 11c: guarded configuration for the same measurement. No current flows through R L since E G = E O E S. E S Electr ometer oltmeter X1 or Preamp Output High Resistance Measurements When resistances >1GW must be measured, an electrometer is usually required. n electrometer may measure high resistance by either the constant voltage or the constant current method. Some electrometers allow the user to choose either method. The constant voltage method utilizes the electrometer ammeter and a voltage source, while the constant current method uses the electrometer voltmeter and a current source. description of these techniques follows. Constant oltage Method To make high resistance measurements using the constantvoltage method, an electrometer ammeter or picoammeter and a constant voltage source are required. Some electrometers and picoammeters have voltage sources built into the instrument and can automatically calculate the resistance. This section describes this method and ways to reduce the leakage resistance due to test fixturing when making these measurements. Basic Configuration The basic configuration of the constant voltage method is shown in Figure 12. n this method, a constant voltage source () is placed in series with the unknown resistor (R) and an electrometer ammeter ( ). Since the voltage drop across the ammeter is negligible, essentially all the voltage appears across R. The resulting current is measured by the ammeter and the resistance is calculated using Ohm s Law (R = /). Figure 12: Constant voltage method for measuring high resistance R Because high resistance is often a function of the applied voltage, this method is preferred compared to the constant current method. By testing at several voltages, a resistance vs. voltage curve can be developed and a voltage coefficient of resistance can be determined. Some of the applications that use this method include testing two-terminal high resistance devices, measuring insulation resistance, and determining the volume and surface resistivity of insulating materials. The constant voltage method requires using an electrometer ammeter, so all the techniques and errors sources apply to this method. One common error source when making high resistance measurements is due to the leakage resistance of the cables and fixturing. Two methods for eliminating fixture leakage are guarding and baseline suppression. H

6 Baseline Suppression lthough the constant voltage method is suitable for measuring very high resistance values and is quite fast, some care should be taken to suppress any leakage currents present in the system. Otherwise, any leakage current adds to the test current, reducing resistance measurement accuracy. Such leakage currents can be nulled out by using baseline suppression. Consider the test circuit shown in Figure 13. n this instance, the test resistance is removed from the system, and any leakage current flowing through R LEKGE is measured by the meter as LEKGE. t this point, the current suppression feature of the meter is enabled to null out the leakage current. S oltage Source R R LEKGE Without suppression: R M = S R LEKGE = S R R R LEKGE H LEKGE With suppression: R M = S LEKGE = S R R LEKGE H Figure 14: Baseline suppression cancels leakage current. S oltage Source Figure 13: Leakage resistance (R LEKGE ) causes a current ( LEKGE ) to flow. f we connect the DUT for measurement (Figure 14), the resistance can then be determined based on the present measured current and the suppressed leakage current previously determined: S = LEKGE Example: ssume that S = 10, = 11p, and LEKGE = 1p. Without suppression, the measured resistance is: 10 = = 909GW 11p With suppression, the measured resistance is: 10 = = 1TW 11p 1p Thus, we see that suppression eliminates an error of about 9% in this example. Guarding and Capacitive Effects To minimize shunt currents, most electrometer amplifiers include a guard connection to their amplifier outputs. Since the guard output is a unity-gain output, the voltage potential across insulators connected between the input terminal and guard is essentially zero. n general, the same techniques used to minimize leakage current in low current measuring situations can minimize these effects in high resistance measurements. One additional source of error in high resistance measurements is parasitic capacitance, normally associated with cables and connectors. t high resistance levels, even a few picofarads of stray capacitance can significantly affect circuit rise times and thus the settling time required for accurate measurements. For example, a 10TW (10 13 W) resistance and a cable capacitance of 100pF results in an RC time constant of 1,000 seconds. Since five time constants are required for the circuit to settle to within 1%, more than 80 minutes would be required for the circuit to settle adequately. Guarding a high resistance measurement reduces the effects of stray capacitance considerably. The effective capacitance is reduced by a factor equal to the open-loop gain of the amplifier typically from 10 4 to Low Current Measurement pplications pplication 1: Sub-Threshold oltage Characterization One important low-current application is characterizing the subthreshold voltage of a MOSFET. This test requires at least one picoammeter and two voltage sources. One voltage of the voltage sources sweeps a gate voltage, while the other provides a constant DC bias to the drain of the MOSFET. The drain current and (optionally) the gate current are measured for each gate bias voltage value. Figure 15 shows the connections for this test. oltage Source (1) nput (1) H (1) nput (1) H (2) nput (2) oltage Source (2) Figure 15. MOSFET sub-threshold voltage test using picoammeters and voltage sources (such as the Model 6482 Dual Channel Picoammeter/oltage Source).

7 Electrometer/Picoammeter Selector Guide Model Features nput Connection Current oltage Resistance Charge B ½ digits. 0.4f p-p noise. oltage/current Sources with Measurement. EEE-488/RS-232 programmable. 6½ digits. utoranging. Low cost. nalog Output Source. EEE-488/RS-232 programmable. 6½ digits. Low cost. utoranging. nalog Output. EEE-488/RS-232 programmable. 6½ digits. 0.03p p-p noise. Dual-channel Picoammeter with dual /- 30 voltage sources. EEE-488/RS-232 programmable. 5½ digits. utoranging. Low cost. EEE-488/RS-232 programmable. 5½ digits. utoranging. 500 Source. EEE-488/RS-232 programmable. Banana, 3-lug Triax 50a 100m Source 10a 100m Measure 5µ 200 Source 1µ 200 Measure 10µW W 3-lug Triax 100a 20m 10µ µW W 10fC 2µC 3-lug Triax 100a 20m 10µ mW 200GW 10fC 20µC 3-lug Triax (BNC adapters provided for legacy applications) 1f 20m ±30 Source BNC 10f 20m ±500 Source 10W W 3-lug Triax 10f 20m When properly biased, the drain current of the MOSFET during the sub-threshold voltage test will vary from sub-p to 1µ or so. pplication 2: Photodiode Dark Current nother useful low current application is the characterization of the dark current of a photodiode. n this application, the photodiode is reverse biased by a swept voltage source while the current is measured for each change in voltage bias. The dark current of a photodiode can vary from a few hundred f to a few hundred p as the bias voltage is changed. These current levels require the use of an accurate picommeter or electrometer. Figure 16 shows the connections for this test. oltage Source nput H Light Shield Light shield and DUT connect to nput Figure 16. Dark current characterization of a photodiode using picoammeter and voltage source (such as the Model 6482.) Test System Safety Many electrical test systems or instruments are capable of measuring or sourcing hazardous voltage and power levels. t is also possible, under single fault conditions (e.g., a programming error or an instrument failure), to output hazardous levels even when the system indicates no hazard is present. These high voltage and power levels make it essential to protect operators from any of these hazards at all times. Protection methods include: Design test fixtures to prevent operator contact with any hazardous circuit. Make sure the device under test is fully enclosed to protect the operator from any flying debris. Double insulate all electrical connections that an operator could touch. Double insulation ensures the operator is still protected, even if one insulation layer fails. Use high-reliability, fail-safe interlock switches to disconnect power sources when a test fixture cover is opened. Where possible, use automated handlers so operators do not require access to the inside of the test fixture or have a need to open guards. Provide proper training to all users of the system so they understand all potential hazards and know how to protect themselves from injury. t is the responsibility of the test system designers, integrators, and installers to make sure operator and maintenance personnel protection is in place and effective.

8 Specifications are subject to change without notice. ll Keithley trademarks and trade names are the property of Keithley nstruments, nc. ll other trademarks and trade names are the property of their respective companies. Greater Measure of Confidence KETHLEY NSTRUMENTS, NC UROR RD. CLEELND, OH Fax: KETHLEY BELGUM Sint-Pieters-Leeuw Ph: Fax: CHN Beijing Ph: Fax: FRNCE Les Ulis Ph: Fax: GERMNY Germering Ph: Fax: ND Bangalore Ph: Fax: TLY Peschiera Borromeo (Mi) Ph: Fax: JPN Tokyo Ph: Fax: KORE Seoul Ph: Fax: MLYS Penang Ph: Fax: NETHERLNDS Son Ph: Fax: SNGPORE Singapore Ph: Fax: TWN Hsinchu Ph: Fax: UNTED KNGDOM Bracknell Ph: Fax: Copyright 2012 Keithley nstruments, nc. Printed in the U.S. No Rev

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