Question

JEE3370 Class To: DLR FROM: Homework #1 SUBJECT: a) A bar-shaped piece of silicon at room temperature is one inch in length and has a 100 m2 cross-sectional area (i.e. 10x10 um). It is doped with phosphorous to a concentration of 1017/cm3. Find the electrical current through the bar when a voltage of 10 V is applied across the one-inch dimension. b) How long does it take an average electron to drift from one end of the bar to the other? c) Suppose now that we operate in the high-field regime and apply a voltage of 250 kV. What is the electrical current and how long does it take an average electron to drift from one end of the bar to the other? /mi

Answer 1

As we know that current density J = sigma E where sigma is conductivity, sigma = e mu N_D where e = 1.6 times 10^- 19 c mu is mobility of e^- in silicon = 1300 cm^2/v sec N_D is doped concentration = 10^17/cm^3 and E is Electric field, E = V/d where v is voltage and d is length across this voltage is applied Hence sigma = (1.6 times 10^- 19) (1300) (10^17) = 20.8 /cm E = 10/2.54 = 3.93 volt/cm [1 inch = 2.54 cm) So J = (20.8) (2.54) = 52.832 Amp/cm^2 And current I = A.J A is cross sectional Areal I = (10 times 10 times 10^- 4 times 10^- 4) (52.832) I = 52.832 mu A (b) Drift velocity (V_D) V_d = mu E V_d = (1300) (3.93) V_d = 5109 cm/sec time taken t = 1 inch/V_d = 2.54cm/5109 t = 4.97 times 10^- 4 sec \r\n (c) Given E = v/d