Intrinsic semiconductors at room temperature: An intrinsic (undoped) semiconductor has some holes present. What primarily causes the creation of these holes?

Introduction / Context:
In an intrinsic semiconductor such as pure silicon, charge carriers (electrons and holes) exist due to thermal excitation. Understanding the origin of intrinsic carriers is fundamental to band theory, diode operation, and temperature dependence of conductivity.

Given Data / Assumptions:

• Material is intrinsic (undoped).
• Room temperature conditions (thermal energy available).
• We seek the mechanism that creates holes without impurities.

Concept / Approach:
Thermal energy excites some valence electrons across the bandgap into the conduction band. When an electron leaves the valence band, it leaves behind a vacant state—called a hole. In intrinsic material, electrons and holes are generated in pairs, so n = p, and both concentrations rise with temperature according to an exponential dependence on the bandgap.

Step-by-Step Solution:
Start with a fully occupied valence band at absolute zero.At room temperature, thermal energy occasionally promotes electrons to the conduction band.Each promoted electron leaves a hole behind in the valence band.Thus, intrinsic carriers (electrons and holes) arise due to thermal generation-recombination equilibrium.

Verification / Alternative check:
Carrier concentration in intrinsic silicon n_i increases with temperature. No dopants are needed; adding dopants would make the material extrinsic and unbalance n and p.

Why Other Options Are Wrong:
(a) Doping intentionally adds impurities; intrinsic means no dopants. (b) “Valence electrons” exist by definition, but their mere presence does not create holes without excitation. (c) Free electrons are the counterpart carriers created together with holes; they are an effect, not the cause.

Common Pitfalls:
Confusing intrinsic and extrinsic semiconductors; assuming holes are “preexisting” rather than generated with electrons; overlooking the temperature dependence.

Final Answer:
Thermal energy.