Final answer:
The maximum current density in silicon given the maximum drift velocity of 10⁷ cm/s and charge density of 0.4 C/cm³ is 6.4 × 10⁴ A/cm².
Step-by-step explanation:
To determine the maximum current density in silicon with a given maximum drift velocity and charge density, you can use the relationship I = nq A vd, where I is the current, n is the charge density, q is the elementary charge, A is the cross-sectional area, and vd is the drift velocity. The maximum drift velocity of electrons in silicon is given as 10⁷ cm/s, and the charge density is 0.4 C/cm³. To find the current density (J), which has units of current per unit area, you use the formula J = nq vd.
To find the maximum current density, we need to find the number density of the charge carriers (n) and the cross-sectional area (A). The formula for calculating the number density of charge carriers is n = q / V, where V is the volume of the silicon. The volume is given as V = 1 cm^3. Therefore, n = 0.4 C / 1 cm^3.
Next, we need to find the cross-sectional area (A) of the silicon. The cross-sectional area can be calculated using the formula A = L x W, where L is the length of the silicon and W is the width. The length and width are not given. Therefore, we cannot determine the maximum current density in the silicon without knowing the length and width of the silicon.
Plugging in the values, where q (the charge of an electron) is 1.60 × 10⁻¹⁹ C, we get:
J = (0.4 C/cm³)(1.60 × 10⁻¹⁹ C)(10⁷ cm/s)
J = 6.4 × 10⁴ A/cm²
Thus, the maximum current density is 6.4 × 10⁴ A/cm².