Solid State Devices - Energy Band Diagram, Mobility, Diffusivity

[CE0711]

Homework Statement

http://img121.imageshack.us/img121/2910/ssphysucks.th.jpg

Stuck on 1d

Homework Equations

Na - Nd = p₀

p₀ = n_ie^(E_F-E_i)/kT
kT here is 0.0259 eV

n₀ = (n_i)²/p₀

N_v = p₀e^(E_F-E_V)/kT
N_c = n₀e^(E_C-E_F)/kT

The Attempt at a Solution

I have found:
p₀ = 3.6x10¹⁶
n_i = 2x10⁶
n₀ = 1.11x10^-4
E_i-E_F = 0.6116
E_i = 0.715
E_F = 0.0979

a)
N_v = p₀e^(E_F-E_V)/kT = 1.58x10¹⁸
N_c = n₀e^(E_C-E_F)/kT = 2.40x10¹⁸

b) (I got this down, but no scanner.)

c)
p₀/N_V = 0.0222

d)
My problem here is I don't know how to calculate mobility at all I know that
qt/m^* = u_n
But I do not know where to get q or t, and I am assuming I can use my index for GaAs for m^*

 

[KataKoniK]

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Thank you for sharing your progress on this problem. It seems like you have made good progress so far, but are stuck on calculating the mobility. Let me try to help you with that.

First, let's define the terms in the equation you mentioned: qt/m* = un
- q is the elementary charge, with a value of 1.6x10^-19 C
- t is the time, which we can assume to be the relaxation time, with a typical value of 10^-14 s
- m* is the effective mass, which you can indeed use your index for GaAs for (typically around 0.067 times the mass of an electron)

Now, using the values you have already calculated, we can plug them into the equation to find the mobility:
un = (1.6x10^-19 C)(10^-14 s)/(0.067m0)(1.58x10^18) = 1.44 m^2/Vs

I hope this helps you with your problem! Keep up the good work. If you have any other questions, please feel free to post them in this forum.

 

[Mene]

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The energy band diagram shown in the image is a representation of the energy levels of a solid state device. It shows the conduction band, valence band, and the Fermi level, which is the energy level at which the electrons have a 50% probability of being occupied. The difference between the Fermi level and the valence band is known as the electron affinity, which is an important parameter in determining the properties of the device.

Mobility and diffusivity are important parameters in solid state devices as they determine the movement and transport of charge carriers within the device. Mobility is a measure of how easily charge carriers can move through the material, while diffusivity is a measure of how easily they can spread out or diffuse.

In order to calculate mobility, you will need the charge of the carrier (q) and the temperature (T). These values can be obtained from the given information in the problem. The charge of the carrier can be either positive or negative, depending on whether it is an electron or a hole. In this case, it seems that the carrier is a hole, so the charge would be positive. The temperature can be obtained from the given value of kT, which is 0.0259 eV.

The mobility can then be calculated using the equation you provided: qt/m* = un. The value of m* can be obtained from the index of GaAs, as you mentioned. Once you have calculated the mobility, you can then use it to calculate the diffusivity using the equation D = kT/m*. This will give you a measure of how easily the charge carriers can diffuse within the material.

In conclusion, the energy band diagram, mobility, and diffusivity are important parameters in understanding the behavior of solid state devices. By using the given equations and values, you can calculate these parameters and analyze the characteristics of the device.