Using the Vander paaw method you measure a 30nm thick film t

Using the Vander paaw method you measure a 30nm thick film to have R(T) to be 7 ohms at 300K, 6 ohms at 250K, 5 ohms at 200K. a.) what is the resistivity at 300K? b.) what is the resistivity at 275K? c.) What is the conductivity at 300K? d.) What is the conductivity at 225K? e.) Calculate the residual resistivity.

Solution

solution:

1)let consider room temprature R0=5 ohm at To=200k

R1=7 ohm and T1=300 K

R2=6 ohm and T2=250 K

2) where resistance variation with temprature is given by

R=Ro(1+a(T-To))

where from above cases for resistance R1 and R2 we get coefficient of expansion as

a=4*10^-3

3) resistivity at 300Kby vander pauw method is given by

R=rho*(l/A)

A=l*t

assuming vary thin section

we get resistivity as

resistivity=rho=R*t

rho1=7*30*10^-9=2.1*10^-7 ohm m

4) conductivity is reciprocal of resistivity

C=1/rho1=1/2.1*10^-7=4761904.76 siemens/m

5) resistance at 275 K s given as

R=Ro(1+a(T-To))

putting value we get

R3=5(1+.004*(275-200))=6.5 ohm

resistivity=rho3=R3*t=6.5*30*10^-9=1.95*10^-7 ohm-m

6) resistance at T4=225 K is given by

R=Ro(1+a(T-To))

R4=5.5 ohm

where resistivity is

rho4=R4*t=1.65*10^-7 ohm m

conductivity=1/rho4=6060606.06 s/m

7)residual resistivity is ratio of resistivity at room temprature (for this case of 200K) to resistivity at 0 K

resistance at 0 k is

R=Ro(1+a(T-To))

R5=5(1+4*10^-3*(0-200))=1 ohm

residual resistivity=(rho at room temprature/rho at 0k)=Ro/R5=5/1=5 ohm m