Electrical conductivity of a semiconductor

In summary, the electrical conductivity of silicon doped with 3 x 1024 per meter cubed of aluminum atoms at 135°C can be estimated using the equation σ=|e|*nh*μh, where σ is the conductivity, e is the elementary charge, nh is the number of holes, and μh is the hole mobility. Assuming values of 0.03 m2/V-s for electron mobility and 0.007 m2/V-s for hole mobility, the resulting conductivity is 3360 (Ωm)-1.
  • #1
Plasmosis1
17
0

Homework Statement



Estimate the electrical conductivity, at 135°C, of silicon that has been doped with 3 x 1024 per meter cubed of aluminum atoms. Assume values for electron and hole mobilities of 0.03 and 0.007 m2/V-s, respectively.

Homework Equations



σ=|e|(ne*μe+nh*μh)

σ=conductivity
e=1.6*10-19
ne=number of free electrons
μe=electron mobility
nh=number of holes
μh=hole mobility

The Attempt at a Solution



So far I have this:
σ=1.6*10-19*(ne*0.03+3*1024*0.007)

I don't know how to find ne. Is it the same value of nh?
 
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  • #2
Plasmosis1 said:
I don't know how to find ne. Is it the same value of nh?
Then doping would be pointless - no.
You should have some formula relating those two numbers (it also includes the temperature). Then the density of aluminium atoms (which type of doping is that?) allows to determine both.

So far I have this:
σ=1.6*10-19*(ne*0.03+3*1024*0.007)
Don't forget the units.
 
  • #3
The only other formula that I can think of is n=n0exp(-Eg/2kT)
But I can't use that because I don't know n0 or Eg.
 
Last edited:
  • #4
ne*nh = ?

You will have to look up at least one material constant of silicon.
 
  • #5
Is the equation
ne*nh=(1.5x1010cm-3)2
where ni=1.5x1010cm-3

So ne=1.5*1010*1003m-3/(3*1024)=1.5*1016m-3
∴ σ=1.6*10-19*(1.5*1016*0.03+3*1024*0.007)=3360 (Ωm)-1

Is that right?
 
  • #6
Where does the first equation come from?

The other equations look good (apart from formatting issues).
 
  • #7
No one actually said this but because ne<<nh you can just neglect ne.

The original equation becomes:
σ=|e|*nh*μh
=1.6*10-19*3*1024*.007
=3360 (Ωm)-1
 

Related to Electrical conductivity of a semiconductor

1) What is the difference between a conductor and a semiconductor?

A conductor is a material that allows electricity to easily flow through it, while a semiconductor only allows some electricity to flow through it. In conductors, the outermost electrons are loosely bound and can move freely, whereas in semiconductors, the outermost electrons are more tightly bound and require additional energy to move. This difference in electron mobility is what distinguishes conductors from semiconductors.

2) How is the electrical conductivity of a semiconductor determined?

The electrical conductivity of a semiconductor is determined by its band gap, which is the energy difference between the highest occupied energy level (valence band) and the lowest unoccupied energy level (conduction band). A smaller band gap means there is less energy required for electrons to move from the valence band to the conduction band, making the material more conductive. Additionally, the number of free electrons (or lack thereof) also affects the conductivity of a semiconductor.

3) What factors affect the electrical conductivity of a semiconductor?

The electrical conductivity of a semiconductor is affected by several factors, including temperature, impurities, and doping. Higher temperatures can increase the conductivity as it provides more energy for electrons to move. Impurities can also alter the conductivity, with certain impurities creating more free electrons and making the material more conductive. Doping, which involves intentionally adding specific impurities, can also greatly alter the conductivity of a semiconductor.

4) What are some common applications of semiconductors?

Semiconductors have a wide range of applications, including in electronic devices such as computers, smartphones, and televisions. They are also used in solar cells to convert sunlight into electricity, and in transistors for amplification and switching in electronic circuits. Additionally, semiconductors are used in sensors, optoelectronic devices, and quantum computing.

5) How do impurities affect the electrical conductivity of a semiconductor?

Impurities can greatly affect the electrical conductivity of a semiconductor. When impurities are added to a semiconductor material, they can either donate or accept electrons, creating more free electrons or holes in the material. This can increase or decrease the conductivity of the semiconductor, depending on the type of impurity and its concentration. Doping, which is the controlled introduction of impurities, is commonly used in the production of semiconductors to alter their electrical properties for specific applications.

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