Week 1: Fundamental Exploration

Introduction

To make sure higher level research outcome, the basic properties of the material are essential, which are actually focused in this week, include the Type of substrate, relative permittivity (k or 𝜀₀ and equivalent oxide thicknesss (EOT).

Type of Substrate

Our team first focus on the type, we sketch a CV plot by Numbers with the given voltages and capacitances, as shown in the following.

Figure 1: The first version of CV plot

It's not the actual CV plot, since the voltages are sorted in descending order from positive to negative, which is the original order of given data, it leads an inversion in the Voltage axis (horizontal) and the corresponding graph.

Subsequently, it affect the results of analyze, we determined it as a n-type substrate in the early stage by mistake, and it took further impact to the process of the project. 

This version was changed when we found that the exceptions in the Voltage axis, we inverted the order and repainted the graph, then we get a better plot, but we were worried about its utility. Although we had got the proper CV plot of the given data, the plot is still confusing with the unclear and superfluous Voltage axis label, and the units of the Capacitance axis (vertical) should not be F. 

Therefore, we repainted it again with MATLAB, which has less labels in Voltage axis and more accurate plot, as shown in the Figure 2.

Figure 2: The later version of CV plot

According to the graph, it has a maximum 2999 pF and a minimum 48.2 pF, it is a p-type silicon substrate, the majority carrier (holes) will increase on the surface adjacent to the oxide when the gate voltage is negative in accumulation area.

Oxide Relative Permittivity

For any kinds of materials, the relative permittivity can be expressed as a ratio of its absolute permittivity with the vacuum permittivity. Permittivity is a material property that effects the Coulomb force between two point charges in the material.

 In the research process for this parameter, we misunderstood its concept and calculated the relative dielectric permittivity of the entire oxide, and use such a result in the subsequent process. 

However, after communication and discussion with the academic advisor, we realized that the required relative dielectric permittivity is for the doped portion instead of the entire oxide. The relative dielectric constant of the doped part needs to be calculated using the equations about the capacitance, which cost more time in this part.

The equation of the oxide relative permittivity can be expressed as:

Where C ≈ 3*10^3*10^(-12) F, d = t_high-k+t_SiOx = (3.2+1.6)*10^(-9) m, S = π*(0.29*10^(-3))^2. Then the result is:

Furthermore, k_high-k can also be obtained by:

Which will used in subsequent steps of the project.
Note: Both of the k and 𝜀 are represent relative dielectric permittivity.

Equivalent Oxide Thickness (EOT)

Figure 3: The p-type semiconductor

An equivalent oxide thickness is a distance, which indicates how thick a silicon oxide film would need to be to produce the same effect as the high-k material being used.

During the research in this property, the first trouble we faced was about equations. We found two different equations for calculating EOT:

Their results are completely different, this block our process for a long time, we ensure the correctness of the calculation and the previews steps, still can not find what the error is.

After careful research in this problem, we found that the previous equation are used to calculate the EOT of the entire and the another used to calculate the EOT of the doped part. 

The EOT can be obtained by the following equations:

 Plug in t_high-k= 3.2*10^(-9) m, k_SiO2 = 4.1 and k_high-k = 4.105. Then, 

Summary

Roma was Not Built in a Day

This is a huge project contains a series of works, it start with these basic but important tasks, we need to follow the plan, step by step to reach the final expected outcome gradually. 

Basic but not Easy

Despite the tasks in this week are more basic, there are still many barriers when proceeding the process. It is a team project which need every member to keep concentrating, and contributing to the work.