Читать книгу The ESD Control Program Handbook - Jeremy M. Smallwood - Страница 51

The resistance and capacitance form a resistor‐capacitor (RC) network that has a characteristic time constant τ.

In a time τ, the voltage will decay to about 37% of its initial value.

In the example, if the charge current is suddenly halted at time t = 0 with initial voltage V₀, the voltage V on the capacitor reduces as

An electrostatic field meter monitoring the material surface would measure this exponential decay of voltage. The product of a material's resistivity ρ and permittivity ɛ₀ ɛ_r gives a physical time constant for the material.

This behavior has important practical implications. If we consider a situation in which the capacitance is fixed at 100 pF (the order of magnitude of capacitance of a person) and the charging current 100 nA, we can consider the effect of different resistances. With a resistance of 1 GΩ, the voltage generated is only 100 V, and on cessation of the current, the voltage will fall to 37% of its initial value within 10⁹ × 10⁻¹⁰ = 0.1 seconds. The effect of a short duration charging current of this magnitude is unlikely to be noticed.

Figure 2.3 Charge or voltage decay curve.

If the resistance is increased 10 GΩ, not only is the voltage generated increased to 1 kV, but on cessation of the current, the voltage will take 10¹⁰ × 10⁻¹⁰ = 1 seconds to fall to 37% of its initial value. The presence of this voltage may or may not be noticeable or cause a problem, depending on the circumstance.

If the resistance is increased 100 GΩ, not only is the voltage generated increased to 10 kV, but on cessation of the current, the voltage will take 10 seconds to fall to 37% of its initial value. The presence of this voltage for such a long time could lead to the person experiencing shocks on touching something or discharging to cause some problem.

In ESD control, a different definition of charge decay time is usually used in standard measurements, and often the time for charge to reduce to one‐tenth of its initial value is measured (Figure 2.3). This value is theoretically equal to 2.3τ.

In practice, the charge decay time is often measured from the starting voltage down to a certain threshold voltage, e.g. 100 V. Polymers may have time constants of many tens or hundreds of seconds, or even days under clean dry conditions.

In practice, the simple model does not always correspond well with material behavior. Measured charge decay curve may depart considerably from the ideal exponential, and the measured time “constant” varies with measurement conditions. Often with high resistance materials the decay time lengthens as the surface voltage drops and may become very long at low voltages.