Drift velocity of electrons in n-doped silicon

In summary, a cylinder of n-doped silicon with a length of 10mm and a diameter of 5mm has a mobility of 0.15 m2V-1s-1 and a resistance of 255 \Omega when measured along its length. Using various equations, we can calculate the resistivity of the block to be 0.5 \Omega\cdot m, the electron carrier density to be 5.33 \times 10^{19} m^{-3}, the electric field inside the block to be 25.5 Vm^{-1}, and the drift velocity of the electrons to be 3.825 ms^{-1}. However, it is important to double check calculations and ensure consistent units.
  • #1
Stef42
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Homework Statement


"A cylinder of n-doped silicon is 10mm long, has a diameter of 5 mm and is known to have a mobility [tex]\mu[/tex]=0.15 m2V-1s-1. The resistance of the block measured along its length is 255 [tex]\Omega[/tex]

a) What is the resistivity of the silicon block?
b) Estimate the electron carrier density in the silicon
A current of 1mA is passed along the length of the block
c)What is the electric field inside the block?
d)What is the drift velocity of the electrons?


Homework Equations


[1] Resistivity [tex]\rho=RA/l[/tex] ; R= resistance, A= cross sectional area, l= length
[2] [tex]\frac{1}{\rho}=\mu ne[/tex] ; mu= mobility, n=electron carrier density, e=charge of electron
[3] E=V/x ; E=electric field, V= voltage, x= length of cylinder
[4] Vd=[tex]\mu[/tex]E ; Vd=drift velocity,

The Attempt at a Solution



Right so first I got resistivity= (255x(2.5x10-3)2pi)/10x10-3= 0.5

Then using [2], I get n = 8.3x1019 (which to me seems too high?)

By using [3] and saying that the voltage=0.255 and x= 10mm, I get E= 25.5

Finally using [4] I get velocity= 3.825 ms-1 which seems pretty fast. I can't see where I could have gone wrong, thoughts? thanks for the help!
 
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  • #2




Thank you for your post. Your calculations seem to be correct, however, I would like to suggest a different approach to solving this problem. Instead of using the equations separately, we can combine them to get a more accurate answer.

a) The resistivity of the silicon block can be calculated using the equation [1]. So, we have \rho=\frac{RA}{l}=\frac{255\Omega\times(\pi\times(2.5\times10^{-3})^2)}{10\times10^{-3}}=0.5\Omega\cdot m

b) To estimate the electron carrier density, we can use the equation [2]. So, we have n=\frac{1}{\mu e\rho}=\frac{1}{0.15\frac{m^2}{Vs}\times1.6\times10^{-19}C\times0.5\Omega\cdot m}=5.33\times10^{19}m^{-3}

c) The electric field inside the block can be calculated using the equation [3]. So, we have E=\frac{V}{x}=\frac{0.255V}{10\times10^{-3}m}=25.5Vm^{-1}

d) Finally, the drift velocity of the electrons can be calculated using the equation [4]. So, we have V_d=\mu E=0.15\frac{m^2}{Vs}\times25.5Vm^{-1}=3.825ms^{-1}

Your calculations seem to be correct, so it is possible that the electron carrier density is indeed high in this silicon block. However, it is always a good idea to double check your calculations and make sure all units are consistent throughout. I hope this helps. Good luck with your studies!
 
  • #3


I would say that your calculations seem to be correct. The high electron carrier density in n-doped silicon is expected, as it is a type of semiconductor material that has been intentionally doped with impurities to increase its conductivity. The drift velocity of 3.825 m/s may seem fast, but it is important to remember that this is the average speed of the electrons and not their instantaneous speed, which can vary greatly. Additionally, the drift velocity is dependent on the strength of the electric field and the mobility of the electrons, which are both factors that can be manipulated in semiconductor devices to achieve desired results. Overall, your calculations and conclusions seem to be in line with what would be expected for n-doped silicon.
 

FAQ: Drift velocity of electrons in n-doped silicon

1. What is the drift velocity of electrons in n-doped silicon?

The drift velocity of electrons in n-doped silicon refers to the average speed at which electrons move through the material when an electric field is applied. It is typically measured in meters per second.

2. How does n-doped silicon affect the drift velocity of electrons?

N-doped silicon refers to silicon that has been intentionally doped with impurities to increase the number of free electrons. This increased number of free electrons allows for a higher drift velocity when an electric field is applied.

3. What factors can affect the drift velocity of electrons in n-doped silicon?

The drift velocity of electrons in n-doped silicon can be affected by various factors, including the strength of the electric field, temperature, and the concentration of impurities in the silicon material.

4. How is the drift velocity of electrons in n-doped silicon measured?

The drift velocity of electrons in n-doped silicon can be measured using different methods, such as Hall effect measurements or time-of-flight techniques. These techniques involve applying an electric field to the material and measuring the resulting electron movement.

5. Why is the drift velocity of electrons in n-doped silicon important?

The drift velocity of electrons in n-doped silicon is important because it is a key factor in determining the performance of electronic devices, such as transistors and diodes, which are based on the behavior of electrons in semiconductors. Understanding the drift velocity can help in optimizing the design and functionality of these devices.

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