# Femtoamp (fA) measurements

-May 01, 2002

For most current measurements, DMMs simply pass the unknown current through a known resistance (either an internal or external current shunt) and measure the voltage developed. For example, a DMM's 1-mA range might pass an input of 1 mA through a 1-kΩ shunt to develop 1 V (Figure 1).

This simple arrangement has limitations, however, and one limit occurs when you try to measure current at the femtoamp (fA, 10-15) level. 1 fA through 1 kΩ would develop only 1 µV, which is clearly too small for any digital voltmeter (DVM) to measure. Even increasing the current shunt resistance to a maximum practical value of 1 GΩ develops only 1 μV. Thermal emfs alone in a DVM's input circuit can easily exceed several microvolts, which would still mask the input signal. Equally, a 1-GΩ resistor has inherent Johnson noise of several microvolts peak-to-peak, even in a 1-Hz noise bandwidth.

## How it works

To avoid these limitations, femtoammeters measure femtoamps with an integrator circuit (Figure 2). Now, the femtoamp input develops a charge (Q = I x t) on a capacitor, and the charge translates to a voltage (V = Q/C) for measurement by a DVM. Effectively, the new arrangement overcomes the limitation of the DMM method by replacing a noisy high-value resistance shunt with a capacitor that has no inherent noise.

By measuring the voltage at the integrator's output at preset time inter vals ( δt), you can calibrate this circuit so the corresponding integrator output voltage steps ( δv) are proportional to the unknown input femtoamp. As an example, a 1-fA input, a 100-µF integrator capacitor, and a 100-s measurement time now develop a 100-μV output—100 times greater than the shunt method.

The circuit can reset the charge on C to 0 before each measurement or continue to measure δV at equal time intervals as the capacitor charges up. Different δt settings provide the femtoammeter with different femtoamp input ranges.

Theory aside, this integrator setup still requires careful design. First, transporting the unknown femtoamp source to the integrator requires extensive guarding and isolation. Clearly, any stray currents from the instrument's internal circuitry that leak into or from the input terminal will immediately invalidate the measurement. Equally significant, triboelectrical effects when cables flex can easily generate picoamp peak-to-peak noise. Piezoelectrical effects in Teflon or ceramic insulators can also generate tens of femtoamps peak-to-peak noise. Running input signals across pc boards is also a non-starter. These designs use sapphire standoffs to transport input signals. The op amp, or electrometer, is also not an off-the-shelf design. Any femtoamp drift in its input bias current, for example, directly affects measurement performance. Ambient temperature and humidity stability are further prerequisites.

With precautions such as these, 51/2-digit femtoammeters offer ranges down to 1.00000 pA (resolution of 0.01 fA or 10 attoamps). Bear in mind that accuracy on this range could be around ±1% ±10 fA, which equates to an uncertainty of ±2000 digits of the scale.