Question

At what temperature does an intrinsic semiconductor have number of electrons = number of holes?

• A. 0K
• B. 0°C
• C. at high temperatures
• D. none

Answer 1

Answer: (D)

d

Answer 2

An intrinsic semiconductor is a pure semiconductor material. In such a material, charge carriers (electrons and holes) are generated in pairs due to thermal excitation. When an electron gains enough thermal energy to break a covalent bond and move into the conduction band, it leaves behind a vacancy called a hole in the valence band. This process ensures that for every free electron created, one hole is also created.

Therefore, in an intrinsic semiconductor, the number of free electrons ($n_e$) is always equal to the number of holes ($n_h$). This equality holds true at:

1. 0 K (Absolute Zero): At this temperature, there is ideally no thermal energy, so no electron-hole pairs are generated. Thus, $n_e = 0$ and $n_h = 0$. In this case, $n_e = n_h$ is satisfied.
2. Temperatures above 0 K (e.g., 0°C, room temperature, high temperatures): As the temperature increases, more thermal energy is available, leading to the generation of more electron-hole pairs. However, for every electron promoted to the conduction band, a hole is created in the valence band. Consequently, the number of electrons always remains equal to the number of holes ($n_e = n_h > 0$).

Since the condition $n_e = n_h$ is a fundamental characteristic of an intrinsic semiconductor that holds true at all temperatures (where it behaves as an intrinsic semiconductor), none of the options (0K, 0°C, or high temperatures) is the exclusive temperature at which this occurs. It occurs at all of them. Hence, the most appropriate answer is "none".