C. Estimating the Total Charge in the Diffusive Layer

Reexpressing it via the Debye length,

leads to the following expression:

This equation can be rewritten by applying the following identity:

Substituting (7.24) into (7.23) leads to a first order differential euqation:

(7.25) can be solved via separation of variables. Under the condition of a vanishing electric field for the following solution can be derived:

(7.26) |

Exploiting the identity , the expression for can be formulated as:

(7.27) |

In the last calculation step Gauß's law is utilized to express the total charge per unit area in the Gouy-Chapman layer:

T. Windbacher: Engineering Gate Stacks for Field-Effect Transistors