How does an electrometer measure high resistance greater than 1GΩ using the constant voltage method?

The constant voltage method[1] for measuring high resistance requires an instrument capable of measuring low currents and a DC constant voltage source. Some electrometers and picoammeters[2] have built-in voltage sources that automatically calculate the unknown resistance. The
basic circuit configuration for the constant voltage method using an electrometer and picoammeter is shown in Figure 2-30a. Figure 2-30b shows the constant voltage method for high resistance measurements using an SMU[3].
In this method, a constant voltage source (V) is connected in series with the unknown resistance (R) and an ammeter (IM). Since the voltage drop across the ammeter is negligible, all of the test voltage appears across the resistor R. The resulting current is measured by the ammeter, and the resistance is calculated using Ohm's law (R = V/I).
High resistance is usually a function of applied voltage, so the constant voltage method is superior to the constant current method. By measuring at a selected voltage, a resistance vs. voltage curve can be obtained, and the "voltage coefficient of resistance" can be determined.
Applications using this method include testing two-terminal high resistance devices, measuring insulation resistance, and determining the bulk and surface resistivity of insulating materials.
The constant voltage method requires measuring low currents, so the various techniques and error sources described in Section 2.3 (low current measurements [4]) apply to this method. The two most common sources of error when measuring high resistances are electrostatic interference and leakage current. Shielding high impedance circuits can minimize the effects of electrostatic interference, as described in Section 2.6.2. The effects of leakage current can be controlled using the protection techniques described in Section 2.3.1.