Determining the resistivity of intrinsic Germanium

In summary, the conversation discusses finding conductivity by taking the reciprocal of resistivity and using the formula ##\frac{1}{\sigma} = C(T)^{-3/2}e^{(\frac{-E_g}{2k_BT})}## to calculate it. The conversation also mentions that the constant C can be dropped out by taking the ratio of conductivities at two different temperatures. However, the conversation points out that the ratio may be undefined and suggests doing the ratio algebraically before plugging in numbers. It also brings up the importance of using correct units in calculations.
  • #1
jisbon
476
30
Homework Statement
At room temperature (300 K), the bandgap energy and resistivity of
intrinsic germanium is 0.67 eV and 0.455 ohm/m, respectively.
Determine the resistivity of the intrinsic germanium at 150 °C. Assume
that, at room temperature, the electron and hole mobilities are 0.14 and
0.05, respectively. The bandgap is insensitive to the temperature.
Relevant Equations
Shown below.
Hi.
Since,
1580648252211.png

I can find conductivity by taking the reciprocal of resistivity, in this case, 1/0.455
Hence, I will end up with:
##\frac{1}{0.455}=C(300)^{-3/2}e^{(\frac{-0.67}{2(1.38*10^{-23})(300)})}##
However, my C value seems to be invalid in this case.
May I know what may went wrong here? Thanks
 
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  • #2
take the ratio of the conductivities at the two twmperatures and the constant will drop out...
 
  • #3
Dr Transport said:
take the ratio of the conductivities at the two twmperatures and the constant will drop out...
The ratio seems to be undefined too:
1580650920626.png
 
  • #5
Not only that, but you should really do the ratio algebraically first before plugging in all those numbers. Give σ and T different subscripts, while everything else is common to both.

It is easier to deal with, and it is why we try to teach the students to do at the General Physics level.

Zz.
 
  • #6
Dr Transport said:
look at the magnitude of your exponent...
The formula states that it has a negative sign though. Is the formula wrong in this case..? Sorry
 
  • #7
jisbon said:
The formula states that it has a negative sign though. Is the formula wrong in this case..? Sorry
[itex] \approx 10^{23} [/itex]
 
  • #8
Isn't the boltzman constant 10 to the power of - 23?
Dr Transport said:
[itex] \approx 10^{23} [/itex]
 
  • #10
your Boltzmann constant is in [itex] JK^{-1}[/itex] and your band gap is in [itex] eV[/itex].
 

1. What is resistivity?

Resistivity is a measure of a material's resistance to the flow of electricity. It is typically denoted by the Greek letter rho (ρ) and has units of ohm-meters.

2. Why is it important to determine the resistivity of intrinsic Germanium?

Intrinsic Germanium is a semiconductor material commonly used in electronic devices. Its resistivity can provide valuable information about its electrical properties and how it can be used in various applications.

3. How is the resistivity of intrinsic Germanium determined?

The resistivity of intrinsic Germanium can be determined through a process called four-point probe measurement. This involves passing a known current through the material and measuring the voltage drop across four equally spaced points. The resistivity is then calculated using Ohm's Law.

4. What factors can affect the resistivity of intrinsic Germanium?

The resistivity of intrinsic Germanium can be affected by factors such as impurities, temperature, and crystal defects. These can alter the number of free charge carriers in the material, thereby changing its conductivity and resistivity.

5. How is the resistivity of intrinsic Germanium used in practical applications?

The resistivity of intrinsic Germanium is an important property in the design and development of electronic devices such as transistors, diodes, and solar cells. It can also be used in the manufacturing of sensors, infrared detectors, and other semiconductor-based technologies.

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