Section 3.1 · Worked examples · 4 of 4
Worked example 3.1.4: An electrostatic discharge (ESD) event
About the worked examples of Section 3.1
Four short numerical calculations, covering four of the applications of Section 3.1.4. Each one starts from Coulomb's law and . Worked example 3.1.1 uses the line-charge result of Problem 3.1.1 directly, and Worked example 3.1.4 additionally borrows and from circuit theory. The best way to use them is to write down the given quantities, derive the formula yourself, and only then put the numbers in. Numerical constants used throughout (with as in Eq. (1.4.2) of Chapter 1):
An electrostatic discharge (ESD) event
#cf. Application 3.1.6
Given. A person modelled by the human-body model: charged to , discharging through into an IC pin. The gate oxide inside is thick and breaks down at about .
Find. the charge, the number of electrons, the stored energy, the peak current and the time constant, and then compare with what the oxide can survive.
The charged body is a capacitor, and the discharge is that capacitor emptying through a resistor. Only circuit relations are needed (, , Ohm's law, the time constant), and the gate oxide is a thin insulating layer whose breakdown voltage is its breakdown field times its thickness.
The current starts at its largest value and decays exponentially:
The power dissipated is , with peak value . Integrating gives , as it must, and of it is delivered within the first .
The largest voltage the oxide can stand is
A fifth of a microcoulomb, released in a discharge at or below the threshold of perception (about , and at nothing is felt at all), arrives as more than an ampere and kilowatts of peak power, while the oxide it reaches can withstand only a few volts. All ESD protection (on-chip clamp circuits, wrist straps, dissipative floors, ionisers) follows from comparing these two numbers.