# How to calculate Carrier Concentration vs. Depth from a CV measurement?

• Black Nova
In summary, to obtain the free carrier concentration vs depth profile from CV measurements of a normally-on HEMT, equations 16 and 17 can be used, but it is important to consider the assumptions and potential sources of error.
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TL;DR Summary
I'm trying to obtain the carrier concentration vs depth profile from the CV (capacitance-voltage) measurements of a normally-on HEMT, but I´'m confused about how to extract the values for depth.
I'm trying to obtain the free carrier concentration vs depth profile from the CV (capacitance-voltage) measurements of a normally-on HEMT with the expressions used for a Schottky barrier, but I´'m confused about how to extract the values for depth. I found in textbooks and articles that the formula W(V) = ε/C(V) can be used:

However, I don't know if using those equations, (16) and (17), is enough or I should make any additional considerations.

Thanks

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Yes, using equations 16 and 17 is enough to extract the free carrier concentration vs depth profile from the CV measurements of a normally-on HEMT. However, it is important to note that these equations assume the depletion region of the Schottky barrier is uniform and that the surface potential is known. If either of these assumptions are not valid, then the extracted profile may be inaccurate. Additionally, the profile may be affected by the presence of surface states or other material effects. It is thus important to ensure that the measured CV data is accurate before attempting to extract the profile.

## 1. How do I calculate carrier concentration from a CV measurement?

Carrier concentration can be calculated using the following formula:
n = εε0VTmax / qxdmax
Where n is the carrier concentration, ε is the dielectric constant, ε0 is the permittivity of free space, V is the applied voltage, Tmax is the maximum capacitance, q is the elementary charge, and dmax is the maximum depletion width.

## 2. What is the relationship between carrier concentration and depth in a CV measurement?

The carrier concentration is inversely proportional to the depth in a CV measurement. This means that as the depth increases, the carrier concentration decreases. This relationship is due to the fact that the majority carriers are depleted as the depth increases, resulting in a decrease in carrier concentration.

## 3. How do I calculate the depth from a CV measurement?

The depth can be calculated using the following formula:
d = εε0VTmax / qn
Where d is the depth, ε is the dielectric constant, ε0 is the permittivity of free space, V is the applied voltage, Tmax is the maximum capacitance, q is the elementary charge, and n is the carrier concentration.

## 4. What is the significance of calculating carrier concentration vs. depth from a CV measurement?

Calculating carrier concentration vs. depth from a CV measurement is important in understanding the electrical properties of a material. It can provide information about the type and concentration of majority carriers, as well as the depth of the depletion region. This information is crucial in designing and optimizing electronic devices.

## 5. Are there any limitations to calculating carrier concentration vs. depth from a CV measurement?

Yes, there are some limitations to this calculation. One major limitation is that it assumes a uniform doping profile, which may not always be the case in real materials. Additionally, it does not take into account the effects of surface states or interface traps, which can significantly affect the measured capacitance. It is important to carefully consider these limitations when interpreting the results of a CV measurement.

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