The resistance R of a sample of semiconductor material of le

The resistance R of a sample of semiconductor material of length L, with width and thickness t is given by R = rho 1/wt = rho 1/A, A = wt rho = resistivity of the material. If the I = w, a square material R_Square= rho/t (Ohms/Square) Write the resistance formula as R = R_Square x (l/w) = R_Square x Sigma (li/wl) Find the R_square for the layout below.

Solution

1)    Lets consider   first piece                          

which is 1 x 1 piece

R =   R_{square 1} x ( L / W )

R =   R_{square 1} x ( 1 /  1 )

R_{square 1}    = R..............................1)

2)

Consider Second piece of   It which Is 2 x 3 x 3 , which is 18 square of Same value of R we considered ,

So now   As Area is increased R decreased,length increased R will increase.

So R_{square 2}    = 2R/9   ( because araay of 18 same Cubes)

R_{square 3}    = 1.5R/25   ( same way we considered Cubes of 1x1 25 cubes in 5X5 array)

R_{square 4}    = 2.5R/4

total will be   R_square1    +   R_{square2    +}    R_{square3     +}   R_square4

R_square =      R +   2R/9  + 1.5R/25 +   2.5R/4

          = R ( 1 + 2/9   +   1.5/25   + 2.5/4 )

    R square       = 1.9072 (R )          

But Hear R is considered AS R of    1X 1 X 1 piece , which is first in the fidure

So value of R of Piece 1x1x1 is   Rho ( Resistivity, )

So ,

  R square       = 1.9072 ( )   

     

R _square        =