- #1
PhysicsTest
- 238
- 26
- Homework Statement
- Consider intrinsic germanium at room temperature 300 Degree K. By what percent does the conductivity increase per degree rise in temperature?
- Relevant Equations
- ##n_i^2 = A_0T^3\exp\frac{-E_{G0}} {kT} ##
The intrinsic concentration ##n_i## varies with T as
##n_i^2 = A_0T^3e^{\frac{-E_{G0}} {kT}} ## ---> eq1
The mobility ##\mu## varies as ##T^{-m}## over a temperature range of 100 to 400K. For Germanium, m = 1.66 (2.33) for electrons (holes) as per book.
The conductivity is given by ##\sigma = (n\mu_n + p\mu_p)q## ---> eq2
Step1: Calculate ##n_i## at 300K, 400K
Step2: Calculate the ##\mu_n, \mu_p## at 300K, 400K
Step3: Calculate the desired parameter.
When i perform Step1 i get a different value for ##n_i## than the standard value mentioned in the book for Ge ##2.5*10^{13}##
Calculating ##n_i## at 300K by substituting in eq1
##n_i^2 = A_0T^3e^{\frac{-E_{G0}} {kT}} ##
##A_0 = 6.022 * 10^{23} ##
##T = 300 ##
##E_{G0} = 0.785 ##
##k = 1.38 * 10^{-23} ##
##n_i^2 = 6.022*10^{23} * 300^3 * e^\frac{-0.785} {1.38*10^{-23}*300}##
##n_i = 6.6*10^{15} ## What is the mistake, it differs from the standard value?
Step2:
##\mu## varies as ##T^{-m} ##
##m = 1.66 = m_{e300} \text{ electrons} ; m=2.33\text{ holes}=m_{n300}##
As per the standard in the book ## \mu_n = 3800=\mu_{n300}; \mu_p=1800=\mu_{p300} ## at 300K
##\mu_{e300} = K_e*T_{300}^{-m_{e300}}## ->eq3
##\mu_{n300} = K_n*T_{300}^{-m_{n300}}## -> eq4
##K_e = \frac{\mu_{e300}} {T_{300}^{-m_{e300}}}## --> eq5
##K_n = \frac{\mu_{n300}} {T_{300}^{-m_{n300}}}## --> eq6
At 400K
##\mu_{e400} = K_e*T_{400}^{-m_{e400}}## -> eq7
##\mu_{n400} = K_n*T_{400}^{-m_{n400}}## -> eq8
Are the eq(7), eq(8) correct?
##n_i^2 = A_0T^3e^{\frac{-E_{G0}} {kT}} ## ---> eq1
The mobility ##\mu## varies as ##T^{-m}## over a temperature range of 100 to 400K. For Germanium, m = 1.66 (2.33) for electrons (holes) as per book.
The conductivity is given by ##\sigma = (n\mu_n + p\mu_p)q## ---> eq2
Step1: Calculate ##n_i## at 300K, 400K
Step2: Calculate the ##\mu_n, \mu_p## at 300K, 400K
Step3: Calculate the desired parameter.
When i perform Step1 i get a different value for ##n_i## than the standard value mentioned in the book for Ge ##2.5*10^{13}##
Calculating ##n_i## at 300K by substituting in eq1
##n_i^2 = A_0T^3e^{\frac{-E_{G0}} {kT}} ##
##A_0 = 6.022 * 10^{23} ##
##T = 300 ##
##E_{G0} = 0.785 ##
##k = 1.38 * 10^{-23} ##
##n_i^2 = 6.022*10^{23} * 300^3 * e^\frac{-0.785} {1.38*10^{-23}*300}##
##n_i = 6.6*10^{15} ## What is the mistake, it differs from the standard value?
Step2:
##\mu## varies as ##T^{-m} ##
##m = 1.66 = m_{e300} \text{ electrons} ; m=2.33\text{ holes}=m_{n300}##
As per the standard in the book ## \mu_n = 3800=\mu_{n300}; \mu_p=1800=\mu_{p300} ## at 300K
##\mu_{e300} = K_e*T_{300}^{-m_{e300}}## ->eq3
##\mu_{n300} = K_n*T_{300}^{-m_{n300}}## -> eq4
##K_e = \frac{\mu_{e300}} {T_{300}^{-m_{e300}}}## --> eq5
##K_n = \frac{\mu_{n300}} {T_{300}^{-m_{n300}}}## --> eq6
At 400K
##\mu_{e400} = K_e*T_{400}^{-m_{e400}}## -> eq7
##\mu_{n400} = K_n*T_{400}^{-m_{n400}}## -> eq8
Are the eq(7), eq(8) correct?