Three scattering mechanisms  are present in a particular semiconductor material. If only the first scattering mechanism were present, the mobility would be u1=
2000 cm^2/V-s, , if only the second mechanism were present, the mobility would be u2
=1500 cm^2/V-s ,, and if only the third mechanism were present, the mobility would be u3
=500cm^2/V-s . what is net mobility ?n

(a) 316 cm^2/V-s

(b) 212 cm^2/V-s

(c) 632 cm^2/V-s

(d) None of These

In semiconductor physics, when multiple scattering mechanisms are present, the overall or net mobility (\( \mu_n \)) is given by the reciprocal of the sum of the reciprocals of the individual mobilities. Mathematically, this is expressed as:

\[
\frac{1}{\mu_n} = \frac{1}{\mu_1} + \frac{1}{\mu_2} + \frac{1}{\mu_3}
\]

Given:
- \( \mu_1 = 2000 \) cm\(^2\)/V·s
- \( \mu_2 = 1500 \) cm\(^2\)/V·s
- \( \mu_3 = 500 \) cm\(^2\)/V·s

Let's calculate the net mobility \( \mu_n \):

\[
\frac{1}{\mu_n} = \frac{1}{2000} + \frac{1}{1500} + \frac{1}{500}
\]

Calculating each term:

\[
\frac{1}{2000} = 0.0005
\]

\[
\frac{1}{1500} \approx 0.0006667
\]

\[
\frac{1}{500} = 0.002
\]

Now, sum these values:

\[
\frac{1}{\mu_n} = 0.0005 + 0.0006667 + 0.002 = 0.0031667
\]

Finally, take the reciprocal to find the net mobility:

\[
\mu_n \approx \frac{1}{0.0031667} \approx 316 \text{ cm}^2/\text{V·s}
\]

Thus, the net mobility \( \mu_n \) is approximately **316 cm\(^2\)/V·s**, corresponding to option (a).

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**Do you want any more details or have any questions?**

Here are some related questions:

1. How does scattering affect mobility in semiconductors?
2. What are the common scattering mechanisms in semiconductors?
3. Can the net mobility be higher than the individual mobilities?
4. How does temperature influence the mobility in semiconductors?
5. What is the relation between mobility and conductivity?
6. How is the concept of drift velocity related to mobility?
7. What role does doping play in affecting mobility?
8. How does mobility vary between different types of semiconductors?

**Tip:** Understanding the interplay of different scattering mechanisms is crucial for optimizing the performance of semiconductor devices.

Learn how to calculate the net mobility in a semiconductor material with multiple scattering mechanisms. Understand the impact of different scattering mechanisms on mobility, using specific mobility values. Practice solving semiconductor physics problems.

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