https://file.aiquickdraw.com/mathbot/file/17279871684769a7lh12i.jpg

The problem in the image asks to calculate the charge carrier concentration \( n \) in a semiconductor, given the electrical conductivity \( \sigma \), electron mobility \( \mu_e \), and hole mobility \( \mu_h \). The relevant formula for conductivity in semiconductors is:

\[
\sigma = q \cdot n \cdot (\mu_e + \mu_h)
\]

Where:
- \( \sigma \) is the conductivity,
- \( q \) is the elementary charge (\( q = 1.6 \times 10^{-19} \, \text{C} \)),
- \( n \) is the charge carrier concentration (what we are solving for),
- \( \mu_e \) is the electron mobility,
- \( \mu_h \) is the hole mobility.

We are given:
- \( \sigma = 4.3 \times 10^{-6} \, \text{S/m} \),
- \( \mu_e = 9.0 \, \frac{\text{m}^2}{\text{V} \cdot \text{s}} \),
- \( \mu_h = 0.9 \, \frac{\text{m}^2}{\text{V} \cdot \text{s}} \).

### Step 1: Rearrange the formula to solve for \( n \)

\[
n = \frac{\sigma}{q \cdot (\mu_e + \mu_h)}
\]

### Step 2: Substitute the known values

\[
n = \frac{4.3 \times 10^{-6}}{(1.6 \times 10^{-19}) \cdot (9.0 + 0.9)}
\]

### Step 3: Calculate

First, calculate the sum of mobilities:

\[
\mu_e + \mu_h = 9.0 + 0.9 = 9.9
\]

Now, calculate the denominator:

\[
q \cdot (\mu_e + \mu_h) = 1.6 \times 10^{-19} \cdot 9.9 = 1.584 \times 10^{-18}
\]

Now calculate \( n \):

\[
n = \frac{4.3 \times 10^{-6}}{1.584 \times 10^{-18}} = 2.715 \times 10^{12} \, \text{m}^{-3}
\]

So, the charge carrier concentration is:

\[
n = 2.72 \times 10^{12} \, \text{m}^{-3}
\]

Would you like more details or have any questions?

Here are five related questions for further study:
1. How does temperature affect electron and hole mobilities in semiconductors?
2. What is the relationship between conductivity and charge carrier concentration in different types of semiconductors?
3. How would the carrier concentration change if the mobility of holes were significantly higher?
4. Can this equation be applied to intrinsic semiconductors, and how does it differ for extrinsic semiconductors?
5. How does the concept of mobility vary between different types of materials like metals and semiconductors?

**Tip:** When dealing with semiconductor problems, keep in mind that both the mobility of electrons and holes contribute to conductivity, and their sum is key to calculating charge carrier concentration.

Laske puolijohteen varauksensiirtokonsentraatio, kun tiedetään johtavuus σ = 4.3 * 10^(-6) S/m, elektronien liikkuvuus μe = 9.0 m^2/(Vs) ja aukkojen liikkuvuus μh = 0.9 m^2/(Vs).

Learn how to calculate the charge carrier concentration in a semiconductor using given conductivity (4.3 * 10^(-6) S/m), electron mobility (μe = 9.0 m^2/(Vs)), and hole mobility (μh = 0.9 m^2/(Vs)). Detailed step-by-step solution included, suitable for university-level physics or engineering students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation