Question

A 2.5μm thick layer of n-type GaAs has a resistivity, rho, of 0.45ohmcm and a mobility, μ, of 7000 cm² /Vs. It has a width of 0.45 mm and a length of 1.0 mm.

a) Calculate the resistance of this semiconductor material for current flow along its length.

Answer 1

The resistance of the n-type GaAs semiconductor material with the given dimensions and properties is calculated to be 40,000 ohms using the formula R = ρ(L/A).

Step-by-step explanation:

The question asks us to calculate the resistance of n-type GaAs semiconductor material for current flow along its length. To find the resistance, you would typically use the formula R = ρ(L/A), where ρ is the resistivity, L is the length, and A is the cross-sectional area.

Given:

• Resistivity (ρ): 0.45 ohm·cm
• Length (L): 1.0 mm = 0.1 cm
• Width (w): 0.45 mm = 0.045 cm
• Thickness (t): 2.5 μm = 0.00025 cm

The cross-sectional area (A) is width times thickness (w*t), so A = 0.045 cm * 0.00025 cm = 1.125e-5 cm².

Then, applying the formula:

R = ρ(L/A) = 0.45 ohm·cm (0.1 cm / 1.125e-5 cm²) = 0.45 ohm·cm / 1.125e-5 cm² = 40,000 ohms

Note: It is crucial to keep units consistent when doing calculations. In this scenario, we converted all lengths to centimeters to match the units of resistivity.