Only need answers A and B Consider a bar of N type silicon with cross-sectional

Question

Only need answers A and B

Consider a bar of N type silicon with cross-sectional area A = 100 mum Times 100mum) nin and concentration of lice electrons n0 = 1015 cm-3. Estimate the number of electrons that pass through a cross-sectional plane in only one direction each second. The temperature is 300 K, and the effective mass of electrons in silicon is m = 0.26m0. Express the flow of electrons, calculated in part as electric current in amperes. Based on the diffusion - current equation, determine the concentration gradient dn0/dx that corresponds to the diffusion current of I diff = 100 mA. Assuming linear concentration change, determine the distance Delta x that is needed for the concentration to change from n0 to 0. The diffusion constant for the electrons is Dn = 38 cm2/s. Based on the results obtained in parts (b) and (c), answer the following question: Can the diffusion current exceed the current value that corresponds to the flow of electrons in one direction only, which determined in part(b)

Explanation / Answer

Free electons from Si are assumed as an "electron gas". From the kinetic theory of gases (K is Boltzamnn constant)

Ek =(3/2)*KT

http://en.wikipedia.org/wiki/Kinetic_theory#Temperature_and_kinetic_energy

(1/2)m*V^2 =(3/2)*KT

Also from kinetic theory all 3 space directions are equivalent so that one can write

Vx^2 =(1/3)*(V^2)

The mean square speed in one direction is 1/3 of the total mean square speed.

Therefore for one direction we have

mVx^2 =KT

Vx =sqrt(KT/m) =sqrt(1.38*10^-23 *300/(0.26*9.1*10^-31) ) =1.32*10^5 m/s =1.32*10^7 cm/s

above m=0.26*m0

The above speed can be taken with +/- sigm since it was computed from an sqrt(). Half of electrons are traveling back and half are traveling forward.

Area S =100*100 (um^2) =10^4*(10^-4)^2 cm^2 = 10^-4 cm^2

(1 um =10^-4 cm)

Thus the number of free electrons passing in one direction in time unit is (n0 =10^15 (1/cm^3))

N/t =(1/2)*n0*(Vx*S) =(1/2)*10^15* 1.32*10^7* 10^-4 =6.6*10^ 17   (1/s)

The current is

I = eN/t = 1.6*10^-19*6.6*10^17 =0.1056 A

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