COMSOL 6.4 - Electrostatic Discharge

Electrostatic discharge (ESD) occurs when there is a sudden flow of electricity between two objects with different electrical potentials. This often happens when a charged object, like a human hand, comes into contact with a conductive material, such as metal. The process begins with the accumulation of static charge on the human body, typically due to frictional contact with various materials—like walking across a carpet or rubbing against certain fabrics. The human body can store this static electricity, leading to a significant voltage build-up.

As the charged hand approaches the metal object, the electric field between the two intensifies. Once the hand is close enough, the electric field becomes strong enough to ionize the air molecules between them, creating a conductive path. This allows the accumulated charge to rapidly discharge from the hand to the metal, resulting in a brief, high-current pulse—an ESD event. This discharge equalizes the potential difference between the hand and the metal, often producing a visible spark and potentially damaging sensitive electronic components.

To simulate this complex phenomenon, the model connects the Electrical Discharge interface with the Electrical Circuit interface. The Electrical Discharge interface is used to simulate the ionization and discharge process between the hand and the metal. Meanwhile, the Electrical Circuit interface represents the human body, modeling how it stores and releases the static charge. Together, these interfaces allow for a detailed simulation of how ESD current is generated and how it interacts with electrical circuits.

Model Definition

Field–Circuit Model

The human body is represented by a typical RLC circuit as shown in Figure 1. In this model, it is assumed that human body is charged to 8 kV and has a resistance, inductance, and capacitance of 300 Ω, 1.5 μH, and 150 pF, respectively. The Electrical Circuit interface is employed to model this circuit. The node names (0, 1, 2, 3) are also labeled in Figure 1. To integrate the circuit with the physical discharge model, the External U vs. I feature is used to establish the connection between the circuit and the discharge simulation.

Figure 1: The Field–Circuit Model.

Charge Transport Model

The spark discharge between human finger and metal is modeled using the built-in charge transport model in the Electric Discharge interface.

where

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e, p, n denote electrons, positive ions, and negative ions

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ni is the number density of the charge carrier (SI unit: 1/m3)

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E is the electric field (SI unit: V/m)

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zi denotes the carrier charge (SI unit: 1)

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μi denotes the carrier mobility (SI unit: m2/(V·s))

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wi is the drift velocity in the electric field (SI unit: m/s)

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Di is the diffusion coefficient (SI unit: m2/s)

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Ri is the reaction rate (SI unit: 1/(m3·s))

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α is the ionization coefficient (SI unit: 1/m)

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η is the attachment coefficient (SI unit: 1/m)

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βep is the electron–ion recombination coefficient (SI unit: m3/s)

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βpn is the ion–ion recombination coefficient (SI unit: m3/s)

The above transport equations are fully coupled with Poisson’s equation through the electric field and the space charge:

where e is the elementary charge.

Results and Discussion

Figure 2 plots the electric current density for several instants during the ESD simulation. Figure 3 compares the ESD current with and without the discharge gap.