91Ó°ÊÓ

To determine the conductivity type of a material, we use the Hall voltage, which is a direct indicator of the type of charge carriers present. In the Hall effect, the sign of the Hall voltage, denoted as \( V_H \), tells us whether the material is n-type or p-type. A negative Hall voltage indicates that electrons are the majority charge carriers, pointing to an n-type conductivity. Conversely, a positive Hall voltage would suggest that the majority carriers are holes, indicating a p-type material. In our exercise, \( V_H \) is \(-4.5 \, \text{mV}\), signifying an n-type gallium arsenide sample.

Carrier concentration refers to the number of charge carriers, either electrons or holes, in a unit volume of a semiconductor. It is a vital parameter for determining a material's conductivity. In an n-type material, this concentration is predominantly the number of electrons, whereas, in a p-type, it would be mainly the number of holes.
To find the carrier concentration \( n \), we use the Hall effect equation:

• \( V_H = \frac{I \times B}{n \times e \times t} \)

Here, \( I \) is the current, \( B \) is the magnetic field, \( e \) is the charge of an electron (approximately \( 1.6 \times 10^{-19} \, \text{C} \)), and \( t \) is the thickness. Rearranging this formula allows us to solve for \( n \), thus providing an estimate of the electron concentration in the sample. In our given example, the calculations reveal \( n \approx 6.94 \times 10^{15} \, \text{m}^{-3} \).

Carrier mobility is a measure of how quickly charge carriers (electrons or holes) can move through a semiconductor material when an electric field is applied. The unit of mobility is \( \text{cm}^2/\text{V}\cdot\text{s} \). It quantifies the ability of carriers to conduct current, which directly influences a material's conductivity.

• The formula for calculating mobility \( \mu \) is given by \( \mu = \frac{\sigma}{n \times e} \).
• \( \sigma \) here represents the electrical conductivity.

In our example, the conductivity \( \sigma \) was previously determined to be \( 1.136 \, \text{S/m} \). With \( n \) being \( 6.94 \times 10^{15} \, \text{m}^{-3} \), and \( e \) is \( 1.6 \times 10^{-19} \, \text{C} \), we find that \( \mu \approx 1028 \, \text{cm}^2/\text{V}\cdot\text{s} \), signifying relatively high mobility.

Resistivity is a fundamental property of a material that measures how strongly it opposes the flow of electric current. Unlike resistance, which changes with the dimensions of a material, resistivity is an intrinsic property.
It is essentially the opposite of conductivity, and is calculated as the reciprocal of it:

• \( \rho = \frac{1}{\sigma} \)

Where \( \sigma \) represents the conductivity of the material. In our practical scenario, we previously found \( \sigma \) to be \( 1.136 \, \text{S/m} \). Calculating resistivity gives us \( \rho \approx 0.88 \, \Omega\cdot\text{m} \). This result suggests a moderately resistive material, which is typical for semiconductors like gallium arsenide.