(A): A heavily doped semiconductor can exhibit positive temperature coefficient of resistance.(R): The carrier mobility decreases with an increase of temperature.a)Both A and R are true and R is a correct explanation of Ab)Both A and R are true but R is not a correct explanation of Ac)A is true but R is falsed)R is false but R is trueCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

Introduction:
In this question, we are given two statements (A and R) related to the behavior of heavily doped semiconductors and the carrier mobility with respect to temperature. We need to determine whether both statements are true and if R is a correct explanation of A.

Statement A: A heavily doped semiconductor can exhibit a positive temperature coefficient of resistance.
When a semiconductor is heavily doped, it means that there is a high concentration of impurities (either donors or acceptors) introduced into the crystal lattice. These impurities create extra charge carriers (either electrons or holes) in the material, resulting in a higher conductivity compared to an intrinsic semiconductor.

When the temperature increases, the thermal energy provided to the charge carriers also increases. This leads to an increase in carrier scattering mechanisms such as lattice vibrations, impurity scattering, and phonon scattering. As a result, the mobility of the charge carriers decreases, leading to an increase in resistance.

Therefore, statement A is true. A heavily doped semiconductor can exhibit a positive temperature coefficient of resistance.

Statement R: The carrier mobility decreases with an increase in temperature.
The carrier mobility is a measure of how easily charge carriers can move through a semiconductor material under the influence of an electric field. It is influenced by various factors such as lattice structure, impurities, and temperature.

At higher temperatures, the lattice vibrations and thermal energy increase, leading to more scattering events for the charge carriers. These scattering events hinder the motion of the charge carriers, resulting in a decrease in carrier mobility.

Therefore, statement R is true. The carrier mobility decreases with an increase in temperature.

Explanation:
Both statements A and R are true, and statement R provides a correct explanation for statement A. The increase in resistance observed in heavily doped semiconductors with an increase in temperature is directly linked to the decrease in carrier mobility. The increase in resistance is a consequence of the reduced ability of charge carriers to move freely through the material due to increased scattering events.

Hence, the correct answer is option 'A': Both A and R are true, and R is a correct explanation of A.

Answer

Statement (A), "A heavily doped semiconductor can exhibit a positive temperature coefficient of resistance," is true. In heavily doped semiconductors, the increase in temperature can result in an increase in the number of charge carriers, leading to an increase in conductivity and a decrease in resistance. This behavior is commonly observed in heavily doped semiconductors.

Statement (R), "The carrier mobility decreases with an increase in temperature," is also true. In semiconductors, the mobility of charge carriers, such as electrons or holes, decreases as the temperature increases. This decrease in mobility is due to increased scattering and collisions between charge carriers and lattice vibrations, reducing their ability to move through the material.

Statement (B) provides a correct explanation for statement (A). The increase in the number of charge carriers in heavily doped semiconductors due to temperature leads to a decrease in resistance, which is consistent with the positive temperature coefficient of resistance observed in those materials.

Therefore, both statement (A) and statement (R) are true, and statement (B) is a correct explanation of statement (A). Thus, the correct answer is a).

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