AIIMS 2005 Physics Carrier Mobility MCQ Question

In the context of semiconductors, carrier mobility is a crucial concept that describes how quickly charge carriers (electrons and holes) can move through a material when an electric field is applied. The mobilities of electrons and holes are denoted as $\mu_e$ and $\mu_h$, respectively.

Correct Answer: A) $\mu_e > \mu_h$

Explanation:

1. Understanding Carrier Mobility:

   • Electron Mobility ($\mu_e$): This measures how fast an electron can move in response to an electric field. Electrons in a semiconductor are typically more mobile than holes due to their smaller effective mass and the nature of the conduction band.
   • Hole Mobility ($\mu_h$): Holes are the absence of electrons and behave like positive charge carriers. They are created when electrons jump from the valence band to the conduction band. Holes generally have a higher effective mass compared to electrons, leading to lower mobility.

2. Why $\mu_e > \mu_h$ is True:

   • In most common semiconductors like silicon (Si) and germanium (Ge), the effective mass of electrons ($m^*_e$) is less than the effective mass of holes ($m^*_h$). Due to the relationship between mobility and effective mass, given by the equation:

   $\mu = \frac{q \tau}{m^*}$

   where $q$ is the charge of the carrier, $\tau$ is the average time between collisions (scattering time), and $m^*$ is the effective mass of the charge carrier. Since $m^*_e < m^*_h$, it follows that:

   $\mu_e = \frac{q \tau}{m^*_e} > \mu_h = \frac{q \tau}{m^*_h}$

   This indicates that electrons have greater mobility than holes in semiconductors.

Clarification of Other Options:

• B) $\mu_e < \mu_h$: This option is incorrect because it contradicts the established understanding of mobility in semiconductors. As explained, electrons typically have higher mobility than holes.

• C) $\mu_e = \mu_h$: This option is also incorrect. The mobilities of electrons and holes are generally not equal in semiconductors, and the difference in effective mass leads to a notable difference in their mobilities.

• D) $\mu_e < 0 ; \mu_h > 0$: This option is misleading. While it is true that the charge of an electron is negative, mobility itself is a scalar quantity that is defined as positive. Therefore, it does not make sense to have negative mobility for electrons in this context. Both mobilities should be positive values, reflecting the speed of the charge carriers in response to the applied electric field.

Summary:

Thus, the correct conclusion is that in semiconducting materials, the mobility of electrons is greater than that of holes, leading us to the correct answer:

A) $\mu_e > \mu_h$.