Read the following passage and answer the questions.
A student studies a slab of pure silicon. It contains about \(5\times10^{28}\) atoms per cubic metre. The atoms are arranged in a diamond-like structure, and each silicon atom has four valence electrons. Germanium has the same kind of structure. First, the slab is kept in a cold chamber at a temperature very close to 0 K. It is then taken out and allowed to warm up to room temperature (300 K). At this temperature, the intrinsic carrier concentration of silicon is about \(1.5\times10^{16}\ \mathrm{m^{-3}}\). Finally, the student connects a battery and an ammeter in series with the slab. The ammeter shows a small but steady current. The slab is kept at room temperature throughout this test.
Consider the following statements about the silicon slab:
(A) The current read by the ammeter is the sum of the electron current and the hole current.
(B) At room temperature, the rate at which electron-hole pairs are generated is equal to the rate at which they recombine.
(C) Recombination takes place when an electron collides with a hole.
(D) Near 0 K, a few bonds in the slab remain broken, so the slab can carry a small current.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A), (B) and (C) only
Two processes go on together in a pure semiconductor. Thermal energy keeps creating free electrons and holes, while some electrons meet holes and recombine.
(A) The current read by the ammeter is the sum of the electron current and the hole current. — True. Free electrons give the electron current \( I_e \) and holes give the hole current \( I_h \). The ammeter reads their sum.
(B) At room temperature, the rate at which electron-hole pairs are generated is equal to the rate at which they recombine. — True. At a steady temperature the slab is in equilibrium. So the number of carriers stays steady, at about \( 1.5\times10^{16}\ \mathrm{m^{-3}} \) of each kind.
(C) Recombination takes place when an electron collides with a hole. — True. A free electron that meets a hole fills the empty bond, and both carriers are lost.
(D) Near 0 K, a few bonds in the slab remain broken, so the slab can carry a small current. — False. At 0 K all the bonds are intact, and there are no free electrons or holes. The slab then behaves like an insulator and carries no current.
NCERT (2026-27):
Intrinsic Semiconductor – “… The total current, I is thus the sum of the electron current Ie and the hole current Ih:”
\( I=I_e+I_h \)\( \qquad (14.2) \)
Intrinsic Semiconductor – “… At equilibrium, the rate of generation is equal to the rate of recombination of charge carriers. The recombination occurs due to an electron colliding with a hole.”
Intrinsic Semiconductor – “An intrinsic semiconductor will behave like an insulator at T = 0 K …”