Dear Vimal Kumar Singh Yadav,

It depends on what you want to study. The actual doping profiles may turn out to be essential in studying contact phenomena, linear and non-linear spectrographic effects, etc. If all you need is just a concentration of free carriers at a room temperature, when all shallow donors are ionized - just average out the concentration of the donors. All of that makes sense, if the level of doping is within typical in electronics ~10^13 - 10^15 cm^-3, and the concentration of compensating defects/impurities is already defined and can be taken into account, or just insignificant.

Thank you Len Leonid Mizrah sir.

Another technique, somehow similar to SIMS, could be Atom Probe Tomography (APT). It may yield the atomic distribution in 3D, but (1) it is not a very widespread technique (2) it works with high dopant densities, higher than 1E18 cm-3.

Vimal Kumar Singh Yadav

There are two main types of nonhomogeneous dopings :

- One case where the inhomogeneities are randomly distributed in the bulk of the material. This can be dealt with as bulk disorder phenomenon with related effects on material's properties and consequences on material's conductivity through bandgap energy tails and related carrier localization induced by disorder. Here the conductivity decreases sometimes very strongly with respect to corresponding pure nondisordered homogeneous materials.

-The other case you seem to indicate, where the inhomogeneity is not ''lateral'' but ''transverse'' i.e. along the direction normal to the growth plane or to the doping plane. Impurity concentrations are distributed less ramdomly than in the former case but they tend to increase with decreasing the distance with respect to the surface of the sample. Impurity concentrations are higher at the surface than in the bulk. Here you can consider a system of two adjacent sub-materials:

a) one very thin surface layer (few monolayers) with quasi-metallic high doping, and,

b) a bulk layer with much smaller impurity concentrations.

In many real cases of planar devices, most of the contribution comes from the surface layer not from the bulk one, except in some very marginal working conditions as at very high frequencies, high electric fields, ...

How to detect it?

I agree with Martin Stutzmann 's arguments who already gave interesting methods to do so.

But there is a very nice and efficient experimental methods to do so, e.g., for instance, by performing simulateneously conductivity and Hall effect measurements as a function temperature in the 4.2K-300K range (for example).

If your system is a two adjacent layers system as I described above, then in some temperature interval only the metallic surface layer may dominate the conduction and in some other very different temperature interval, the bulk layer will dominate, and in between, there will be hybrid conduction with contributions from both layers.

Moreover, here thanks to simultaneous measurements of Hall effect and conductivity, you can directly access impurity concentrations through Hall and conductivity free carrier concentrations.

Hope this may help you,

Best regards,

Professor A. Kadri

Thank you all for your time and really helpful answers.

These two Ref. May help

Doping Profile Measurements in Silicon Using Terahertz Domain Spectroscopy (THz-TDS) Via Electrochemical Anodic Oxidation - RIT Scholar Works

by G Tulsyan ·

https://scholarworks.rit.edu/cgi/viewcontent.cgi?article=9926&context=theses

Determination of Doping Profiles in Silicon from Resistivity Measurements via the Four-Point Probe in combination with Layer Str http://unsworks.unsw.edu.au/fapi/datastream/unsworks:45581/SOURCE01?view=true

Dear Vimal Kumar Singh Yadav ,

Adding to the colleagues above,

One can look at the dopant distribution with depth measured for surface from an other point of view. It is how one produces such doping profiles, It is the doping technology. There is the epitaxial deposition where one normally produce layers with homogeneous doping. On can also grade the doping by controlling the doping atoms dose during the deposition. There is also the solid sate diffusion technology which results either in complementary error function dopant distribution or Gaussian distribution. There is also the ion implantation where the dopants are Gaussian around the pentation range of the implanted atoms.

These are the possible doping profiles according to their production method.

It is so that there are secondary factors which may slightly later the above theoretical distributions such as the presence of the crystallographic defects at high doping or the presence of the grain boundary.

You can find the analysis methods in the book of S.M.Sze VLSI technology.

Best wishes

It is usually determined by the process, temperature, and the source you are using. We can work with both solid and liquid sources. We need to use a liquid dopant source if we want a uniform profile. After that, we typically use four probes to characterise the data.

Dr. Thomas, can you put some light on how liquid dopant will be controlled?