Use Ramo's Theorem

http://scitation.aip.org/content/aip/journal/apl/72/7/10.1063/1.120895

This is the reference paper.But I could not understand how weigting potential is calculated for Plan virtual frisch grid.

Dear Abhinav,

For any weighting potential calculation, the best method is to solve LaPlace’s equation. For the one dimensional case,

d2V/dx2 = 0 ;

where the output conductive contact is normalized to one (unity) and all other contacts are grounded. This method is described by Shockley (1938). Note that the method is actually derived from Green’s theorem, although over the years it has been named Ramo’s theorem, Shockley-Ramo theorem, and so on. However, the core solution was derived from Green’s theorem, or the from the reciprocal Green’s theorem.

For the one dimensional case of a planar detector, the solution is quite simple. Suppose you have a detector of width W, with one contact at location x = 0 and the other contact at x = W.  Because the potential you are solving for is from a single point charge placed on the output electrode, space charge is not considered in the calculation (Gauss Law). That point charge is normalized to one (1) to simplify the derivation. LaPlace’s equation becomes,

d2V/dx2 = 0 ;

which can be solved to produce,

V(x) = C1x + C2.

Suppose you attach your preamplifier to the output at x = W; hence, the potential at W is normalized to unity and the potential at x = 0 is zero, as stated earlier. The solution is

V(x) = x/W  .

To determine the induced charge, insert the starting and ending locations into the solution. For instance, suppose that a positive voltage is applied to the contact at W. If an event produces No electron-hole pairs at x0, where the holes drift to x1 and the electrons drift in the opposite direction to x2, then,

Delta (Q) = Q0(x2 - x1)/W = qN0(x2 - x1)/W   .

From this simple example, we see that the induced charge is a linear function of the charge carrier drift distance, a result often named Ramo’s theorem from his 1939 paper. Obviously if (x2 - x1) = W, then Delta(Q) = Q0. Simple geometries such as cylindrical and spherical detectors can be solved in the same manner by adopting appropriate coordinates and using the proper form of LaPlace’s equation.

As for complex geometries with multi-terminal devices, I used a finite difference program to solve LaPlace’s equation. Some of my papers showing the results are listed below.

There are many good software packages that can be used to solve for the weighting potential, such as “Coulomb” and “Lorentz”, or you can write your own. When solving, just remember to assign V = 1 to the output contact (where the preamplifier is attached) and V = 0 to all other conductive contacts. Here are a few references that should get you on your way:

• A. Kargar, A.C. Brooks, M.J. Harrison, K.T. Kohman, R.B. Lowell, R.C. Keyes,  H. Chen, G. Bindley, D.S. McGregor, IEEE Trans. Nucl. Sci., NS-56 (2009) pp. 824-831.
• D.S. McGregor, Z. He, H.A. Seifert, R.A. Rojeski and D.K. Wehe, IEEE Trans. Nucl. Sci., NS-45 (1998) pp. 443-449.
• D.S. McGregor and R.A. Rojeski, IEEE Trans. Nucl. Sci., NS-46 (1999) pp. 250-259.
• V. Radeka, Ann. Rev. Nucl. Part. Sci., 38 (1988) pp. 217-277.
• W. Shockley, J. Appl. Phys., (1938) pp. 635-636.
• S. Ramo, Proc. IRE, 27 (1939) pp. 584-585.
• G. Cavelleri, G. Fabri, E. Gatti, V. Svelto, Nucl. Instrum. Meth., 92 (1971) pp. 137-140.

Enjoy, and have fun with it.

Sincerely,

Douglas

thank you, sir

regards