Final answer:
The question pertains to calculating the current density in a semiconductor given the donor impurity concentration and involves finding the electric field to express J(x). Specific values for J at certain points require knowledge of the electric field, and the induced electric field needs to be determined from the properties and conditions of the semiconductor.
Step-by-step explanation:
Calculating the current density J(x) for a semiconductor with a given donor impurity concentration involves considering the mobility of the charge carriers (electrons) and the electric field induced in the material. The question also asks to calculate J at specific values of x, and to determine the induced electric field inside the semiconductor.
Finding the Current Density J(x)
The current density J(x) is the product of charge, carrier concentration, mobility, and electric field (J = nqμmE). Since the impurity concentration is given, n(x) = 5 x 10'% exp (-x/L), we must find the electric field E in order to express J(x).
Calculating J at Specific Points
To calculate J(0), J(0.5L), and J(L), we need explicit values for the electric field at these points, which would typically be provided by additional information or equations relating to the semiconductor's properties and the external conditions (e.g., applied voltage).
Determining the Induced Electric Field
The induced electric field in the semiconductor can be related to the potential difference and physical dimensions of the specimen or can be derived from the relationship between the charge carrier density and electric field across the semiconductor.