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Field Effect

Field effect is a principle that refers to the modulation of conductance of a material through the use of an external electric field.

Overview[edit]

In an insulator, most atoms hold on to their electrons tightly. Contrary to an insulator, in a conductor, the valence electrons of the atoms are loosely bound and are free to roam through the lattice of the material. Those free electrons are always in random and ccontinuous motion due to the thermal energy of the conductor.

free electron in a conductor.gif

As they travel in random motion, free electrons collide with each other. In between collisions, electrons acquire relatively high velocity. However, due to their random motion, those charge carriers continue to suffer collisions so frequently that the net flow in any particular direction is roughly zero. That is, those electrons do not go anywhere.

The average distance traveled by those free electrons between any two successive collisions, or the mean free path ( Equation lamda , [cm]), can be calculated as the product of the time between collisions ( Equation tau Subscript upper C , [s]) and the thermal velocity ( Equation upper V Subscript th , [cm/s]). For example, silicon at ambient temperature (somewhere around Equation upper V Subscript th = 10^7 cm/s) with Equation tau Subscript upper C = 0.1ps would mean the average distance traveled is 10nm.

When an external electric field is applied to the conductor, that is when some potential difference is applied across the semiconductor, each of the free electrons in the conductor now experience a force in the direction opposite to the direction of the electric field.

free electron in a conductor with electric field.gif

That is, when under the effect of an electric field, the free electrons now flow in the a direction that is opposite to the direction of the electric field, in addition to their thermal velocities.

Theory[edit]

Below is a rectangular conductor with length Equation upper L Subscript c , width Equation upper W Subscript c , and tickness Equation t Subscript c .

field effect rect conductor.svg

In this conductor, the valence electrons of the atoms are loosely bound and are free to roam around. There are Equation n free electrons per cubic meter of this material, each with have an elementary charge Equation q .

We will call this conductor a channel. Applying a electric field Equation upper E [V/cm] across the channel will result in a net force on the carriers.

Equation upper F equals plus-or-minus q upper E

That is, in between their collisions, charge carriers will acquire a new average velocity.

Equation v Subscript d Baseline equals plus-or-minus mu Subscript n comma p Baseline upper E

Where the carrier mobility ( Equation mu Subscript n comma p [cm2/Vs]) refers to the ease of carrier drift. Note that for electrons, Equation mu Subscript n is positive, therefore the direction of Equation v opposes the direction of Equation upper E .

Equation v Subscript d n Baseline equals minus mu Subscript n Baseline upper E

Likewise, for holes, the mobility Equation mu Subscript p is positive.

Equation v Subscript d p Baseline equals mu Subscript p Baseline upper E

The drift current density is the net velocity of charged particles. That is, the total current density is the product of the mobile charge density and the average carrier velocity.

Equation upper J Subscript n Superscript drift Baseline equals minus q n v Subscript d n Baseline equals q n mu Subscript n Baseline upper E
Equation upper J Subscript p Superscript drift Baseline equals q p v Subscript d p Baseline equals q p mu Subscript p Baseline upper E

The total drift current density is the sum of the two drift current densities.

Gate[edit]

Suppose a gate electrode is now situated above the channel and is physically separated by an insulator of thickness Equation t Subscript ins .

field effect rect conductor - gate.svg

A change in the voltage of the gate Equation upper V Subscript g will affect the total drift current density in the channel. Therefore a change in the gate voltage will change the gate charge.

Equation normal upper Delta upper Q Subscript g Baseline equals upper C Subscript g Baseline normal upper Delta upper V Subscript g

That is,

Equation upper C Subscript g Baseline normal upper Delta upper V Subscript g Baseline equals upper W upper L t Subscript c Baseline normal upper Delta rho