Semiconductor

Step 1: Understanding the Concept:
This question asks which type of current is absent in a uniformly doped semiconductor under thermal equilibrium conditions (i.e., no external fields or gradients).
Step 2: Detailed Explanation:
There are two primary mechanisms for current flow in a semiconductor:


Drift Current: This current is caused by the motion of charge carriers (electrons and holes) under the influence of an applied electric field. In the absence of an electric field, there is no net drift, so the drift current is zero.
Diffusion Current: This current arises from the net motion of charge carriers from a region of high concentration to a region of low concentration. It is driven by a concentration gradient ( or ).

The problem states the semiconductor is uniformly doped. This means that the concentration of dopant atoms (and therefore the concentration of majority carriers) is the same everywhere throughout the material. In a state of thermal equilibrium, this results in a constant carrier concentration throughout the crystal.
Since there is no concentration gradient ( and ), there is no driving force for diffusion. Therefore, in a uniformly doped semiconductor at equilibrium, the diffusion current is zero.
Options A and D are types of electrical current in a general sense but not fundamental transport mechanisms within the semiconductor material itself.
Step 3: Final Answer:
Diffusion current requires a carrier concentration gradient, which is absent in a uniformly doped semiconductor at equilibrium.

Step 1: Understanding the Concept:
The effective density of states ( ) in the conduction band is a parameter that simplifies the calculation of the total number of free electrons. It represents the density of available states if they were all located at the conduction band edge energy, .
Step 2: Key Formula or Approach:
The formula for the effective density of states in the conduction band is derived by integrating the density of states function multiplied by the probability of occupation over all energies in the band. The result is:

where is the effective mass of the electron, is the Boltzmann constant, T is the absolute temperature, and h is the Planck constant.
Step 3: Detailed Explanation:
From the formula, we can see that all terms except for the temperature T are constants for a given semiconductor material. Therefore, the effective density of states has a direct dependence on temperature:

Similarly, the effective density of states in the valence band, , also has a dependence.
Step 4: Final Answer:
The effective density of states of electrons ( ) varies with temperature as .