Understanding Semiconductor Behavior Under Heat

The question describes a scenario where heating one end of a semiconductor bar generates a voltage across it. Specifically, it states that the heated end is positive. This phenomenon is related to the thermoelectric effect, often referred to as the Seebeck effect in solid-state physics.

The Seebeck Effect and Charge Carriers

When a temperature gradient ($ \Delta T $) is applied across a material, charge carriers (electrons or holes) tend to diffuse from the hotter region to the colder region due to their increased thermal energy. This movement of charge creates a potential difference (voltage) across the material.

The sign of the voltage developed depends on the type of majority charge carrier:

• N-type Semiconductor: The majority charge carriers are electrons ($ e^- $). When heated, electrons gain kinetic energy and diffuse from the hot end towards the cold end. As negative charges move away from the hot end, they leave behind the fixed positive donor ions. This accumulation of positive charge at the hot end makes it relatively positive compared to the cold end. The electrons gather at the cold end, making it negative.
• P-type Semiconductor: The majority charge carriers are holes ($ h^+ $). When heated, holes diffuse from the hot end towards the cold end. As positive charges move away from the hot end, they leave behind the fixed negative acceptor ions. This accumulation of negative charge at the hot end makes it relatively negative compared to the cold end. The holes gather at the cold end, making it positive.
• Intrinsic Semiconductor: These contain both electrons and holes. While a voltage can be developed, the specific outcome (positive or negative hot end) depends on the relative concentrations and mobilities of electrons and holes. Typically, for materials like Silicon (Si) and Germanium (Ge), electron mobility is higher than hole mobility ($ \mu_e > \mu_h $), leading to a behavior more akin to N-type semiconductors under a temperature gradient.

Analyzing the Condition: Heated End is Positive

The question explicitly states that the heated end of the semiconductor bar becomes positive. Based on the analysis above:

• In an N-type semiconductor, the diffusion of electrons from the hot end results in the hot end becoming positive.
• In a P-type semiconductor, the diffusion of holes from the hot end results in the hot end becoming negative.

Therefore, the observation that the heated end is positive directly indicates that the semiconductor material primarily relies on the movement of electrons to establish this voltage difference. This is characteristic of an N-type semiconductor.