7. Electric Fields

by HobbyGenius VIP on October 3, 2014 at 10:17 am | 0 comments.


Introduction to Electric Fields

An Electric Field is a region in which a charged object will experience a force; similarly a magnetised object will experience a force within a Magnetic Field. In order to visualise this we use electric field lines, these lines have arrows that display the direction a positively charged object will move, these are evenly spaced and the closer they are together, the stronger the field strength (measured in  – Newtons per Coulomb).

Electric Field Lines

Electric Field Lines

There are 2 types of electric fields: uniform and radial. A uniform electric field will exist between any 2 objects which are at different electric potentials: for example, 2 parallel metal plates connected to a power supply will set up a potential difference across the plates and thus an electric field between them.

A radial field exists around a positively charged sphere or point charge, such as an electron, and will act outwards away from the centre of the sphere. The further away from the centre, the lines will get further apart and thus the field strength will decrease: therefore unlike a uniform electric field, the electric field strength will decrease exponentially making the calculations a little bit different (as we’ll find out later on).

Gauss’ Law

Gauss’ Law relates the distribution of electric charge within an electric field; it states:

“The electric flux through any closed surface is proportional to the enclosed electric charge”

This can be defined as:

  •  is the electric flux
  •  is the enclosed charge
  •  is the permittivity of free space – 
  •  is the relative permittivity of material (also known as dielectric constant)

Or to simplify:

  •  is the enclosed area

A charged object in a field will experience a force given by the equation by:

This object will accelerate due to the equation:

So we can calculate the acceleration by combining and rearranging:

  •  is the force
  •  is the charge on the object
  •  is the Electric Field Strength
  •  is acceleration
  •  is mass of the particle

Calculating Electric Potential

Electric-Fields-with-Particles

Uniform Electric Field

To calculate the electric field strength of a uniform electric field, we use the equation:

  • is the potential difference between the 2 points
  •  is the distance between the 2 points

The thing to remember in a uniform electric field is that the field strength is uniform (hence the name), so it is the same at any point between the 2 plates. Knowing this, we can calculate the field strength by knowing the potential difference between the 2 plates and knowing the distance apart they are. We can then use the field strength to calculate the potential of a particle at any distance from the 2 plates.

In this example, the charged particle is a distance of d away from the positive plate (which is at a voltage of 10V) and the positive and negative plate (which is at a voltage of 0V) are a distance of D apart. To calculate the electric field strength we use:

Now that we know the electric field strength, we can calculate the potential of the particle.

 
In this example, the values of d and D have not been provided but by simple substitution we can calculate E in the first part and therefore go on to find V in part 2 simply by substituting the value of E that we calculated and our distance from the 10V plate – .

Radial Electric Field

To calculate the electric field strength around a point charge, we use the equation:

  •  is the charge of the particle
  •  is the permittivity of free space – 
  •  is the relative permittivity of material (also known as dielectric constant)
  •   is the radius of the point

Note that for both equations, if we know the electric field strength we can easily calculate the electric potential of a charged particle in an electric field. We will use these equations later on to understand more about semiconductor devices and capacitors.

Conduction

In free space, a charge will accelerate to high velocities if there is a uniform electric field present. In a semiconductor, regular collisions will occur due to the surrounding crystal lattice keeping these velocities limited. The average velocity of an electron in an Electric Field can be calculated using:

  • is average velocity
  •  is the charge
  •  is the Electric Field Strength
  •  is the scattering time, this controls the electrical conductivity of a material
  •  is the mass of the carrier

We usually write the average velocity of charges within a semiconductor as:


  • is the mobility of the charges.

In a conductor, all of the mobile charge carriers are electrons and they all have the same scattering time. However in a semiconductor (pure or doped), the mobile charge carriers are either electrons or holes and they have different scattering times.

For example: Silicon has an electron mobility () of  () and has a hole mobility () of  (). These values are different for each semiconductor material.

Energy of Charges in an Electric Field

At every point within the electric field there is a potential, the difference between these 2 locations is called the Potential Difference: this is defined as the energy transferred per Coulomb of charge. In an electric field, the potential difference is the amount of kinetic energy gained/lost by the object as it moves between the 2 potentials. This can be shown by the equation:

  •  is the energy
  •  is the charge
  •  is the voltage difference

Now move onto the next tutorial to learn how we can apply all of this to semiconductor devices. We will be looking at the electric fields in capacitors and the carrier drift in semiconductors.