Final answer:
The resistance between two opposite sides of a 1.0 µm silicon cube with a given resistivity of 2.5 Ω-cm is calculated to be 0.25 Ω after converting the given dimensions to appropriate units.
Step-by-step explanation:
To calculate the resistance of a silicon cube with each side measuring 1.0 µm, we apply the formula for resistance, R = ρL/A, where ρ is resistivity, L is the length of the material, and A is the cross-sectional area. Given the resistivity of silicon as 2.5 Ω-cm, we first need to convert it to Ω-m by multiplying by 100 to account for the centimeter to meter conversion. Therefore, the resistivity is 2.5 Ω-cm × 100 = 250 Ω-m.
Next, we convert the length of the cube side to meters: 1.0 µm = 1.0 x 10-6 m. The area A is the square of the side, which gives A = (1.0 x 10-6 m)2 = 1.0 x 10-12 m2. Plugging the values into R = ρL/A, we find the resistance between opposite sides of the cube to be R = 250 Ω-m × (1.0 x 10-6 m) / (1.0 x 10-12 m2) = 0.25 Ω.