Week 3: Further Research

Introduction

The main tasks of this week are some important results include flatband voltage, midgap voltage and the oxide charge density at the flatband condition.

Flatband Voltage

Figure 1: The Energy Diagram of Flatband Condition

Debye length should be considered in this section, which is a measure of a charge carrier's net electrostatic effect in a solution and how far its electrostatic effect persists. It can be expressed as:

Then, C_D can be expressed as:

This is the final correct version of equation, but we have not multiply the area (A) initially, it leads a incorrect capacitance, we tried to find corresponding voltage on the CV plot for many times, but the voltages we got are never within the voltage domain, the missed area were added after some research.

Furthermore, C₁ has such a relationship with C_ox and C_D:

Then, C₁ = 3.105154057⨉10² pF. 

Midgap Voltage

Figure 2: Energy Diagram of Midgap Condition

As 𝜙_S = 𝜙_F, 

Because of C₂ connected wit C_ox in series, therefore:

Oxide Charge Density (Q_ox in C_cm^-2) at the Flatband Condition

Figure 3: Electrons in Oxide Layer

When at the flatband condition:

When at the mid-gap condition:

According to the CV plot which was sketched in the first week, V_mid-real = 1.2 V, so 𝛥V = 1.2 V - 0.4143507163 = 0.7856492835. 𝛥V can also support to sketch the ideal CV plot.

As for the oxide charge density in this condition:

Summary

The Last Leg of a Journey Marks the Halfway Point
As we have calculated all the required parameters and results, what we should do in next stage is to analyse the characteristic of high-k materials been used. The destination is approaching. However, we should not be too optimistic, since the requirement for the project is not only the result, but also the deeper algorithm behind the calculation.