Question

A silicon (300 K) block has a Boron dopant density of OSE+17 per cm*3. The thickness of the Silicon region is 1 micro-meter (1E-6 m). (a) Calculate the resistivity (Hint: The thickness does not play any role in determining the resistivity) (b) What should the length and width of the silicon region be if I want to build a resistor with this silicon block that has a resistance of 20 kilo-Ohm. (Hint: There is more than one correct answer for this question. But you should provide one correct answer of your choice.)

Answer 1

Go through the solution given below.

Given? BORON Dopant cp-type) . NA = 0.5 X 101 cm-3 thickness IX20-fm = 1X10-4 cm (a) o pe un p= number demnity of hole 0.5X2017 cm3 e = Electric Charge = 1.6 X 10-19 C Mhz hole mobility 450 cm2 V-'s-1 at book in silicon conductivity P = 1 -Resistivity (0.5 X1017) x (1-6X10-19 19) x(450) 0.8 X10-2 X 450 3.6 = PO! P = 0.2778 21 cm و ا ے (b) Given : Resistance (R) - 20X1033 Length = ? Width =2 Is thickness R PL А A: Crom Dictional area Length

A= thickness & Width 20X103 = C0.2778) L (1810-4W → L (0.2778) X LOY 20 X 203 0.1389 IL w L :. Ratio of off width to length in 0.1389 if L=1cm then w=0.1389 cm