You need DHE (differential Hall effect) technique methods, including the conventional DHE or CAOT/DHE, to measure mobility profiles in substrate. Please read, Shu Qin, Y. Jeff Hu, Allen McTeer, Si Prussin, Jason Reyes, “Study of Carrier Mobility of Low Energy High Dose Ion Implantations”, IEEE Trans. on Plasma Science, vol. 39, no. 1, pp. 587-592, January 2011.

Thank you Sir, But I want know about theoretically

DHE method:

1. Etch to make van der Pauw structure

2. Anodic oxide layer dx by electrolyte under room temperature

3. Etched dx by HF, and rinse/dry

4. Put sample under test, and probe

5. Measure ρ and µ by I-V & Hall effect

then repeat 2-5 until etch down to xj, to get profiles of ρ(x), µ(x), and carrier (x)

If you need theory of Hall effect to get Hall mobility, then drift mobility, please read text books

Are you interested in the theory of a multiple-layer hall effect? Or that of multiple hall mobility spectrum?

For the former, it is quite a simple extrapolation of a single-layer hall effect theory into a multi-layer where each layer has a given unknown mobility. The problem is that the equations become transcendental and cannot be solved analytically to find the mobility within each region when given the hall voltage as-measured. You need to either fit it with theory-guided simulations, have a good first guess on the layers you expect, or attempt to solve the multi-layer equations iteratively

If it is the latter, there is a suite of papers regarding 'quantitative mobility spectrum analysis' or QMSA. This method looks at the different possible carriers and their relative mobilities when extracted from temperature and magnetic field dependent measurements.

The density of trap states are different within the bulk and on the surface, as a consequence the surface mobility and bulk mobility are different.

For bulk mobility, I have used Time of Flight (TOF) measurement since my material had slow electron and hole mobilities in the order of 0.1 or 0.003 Cm2/V.s. If you are interested to know more about TOF, please let me know.

@ Shu Qin Thank you for your great description, and I need to measure Field dependent mobility and field dependent mobility can you suggest me

@ Christopher Buurma I would like to know multiple layer of mobility, not hall mobility

@Shiva Abbaszadeh, yes I want to know about TOF, please give me full details and general theory also

Which materials will you look at and what is the purpose of the exercise - i.e., once you have these values, what weill you conclude ?

@Wilhelm Graupner, Rightnow I am using Organic semiconductors, I want to measure the surface of the thin film and bulk material of organic materials and want to know the difference between them.

So basically you will determine the properties of the "defect free" bulk and those of the surface which depend on the surface states / defects. Take a look here http://www.physics.rutgers.edu/A62D03EE-FA78-4BF8-B5AA-90A5D9049D28/FinalDownload/DownloadId-1FB6FD6F8E04C61864C6C8285405C2C1/A62D03EE-FA78-4BF8-B5AA-90A5D9049D28/~podzorov/first_proofs.pdf

Hi I was also following your nice discussion but @Wilhelm Graupner your suggested web page unfortunately is not supported anymore. could you put that pdf other web page please.

@Gökhan Yilmaz , same for me also

@Wilhelm Graupner, Sir please send me once again, I could not get that PDF

I downloaded the file from the internet - here it is :-)

Enjoy.

Thank you very much for this nice share.

@ wilhelm graupner thank you

Dear Ajaya,

Here is a paper describing the method I used for TOF measurement, Please let me know if you have any questions.

@ Shiva Abbaszadeh Thank you, If i have any doubt will contact you

You can use hall measurement to measure bulk mobility of material. However the surface mobility is a mobility in thin film transistor, which the carrier flow is on the channel surface. So measure the current in thin film transistor, and then use formula to calculate surface mobility.

Thank you Jun-dar Hwang, But I would like to measure the sandwich cell surface mobility.If you know the process or theory let me know please