If in a material one dimension is reduced to the Nano range while the other two dimensions remain large, the structure so obtained is known as

Correct — option (2), Quantum well.

Nanostructures of this family are named by how many of their dimensions are shrunk to the nanoscale. When a dimension is small enough, the electrons are confined in that direction and can move freely only in the others.

The stem reduces one dimension and leaves two large. In a quantum well, charge carriers are confined in one direction and move freely in the other two, within a plane.

The Wikipedia article on potential wells sets out the family: a quantum dot confines in three dimensions, a quantum wire in two, and a quantum well in only one. So the structure is a Quantum well.

The idea to remember: count the nano-sized dimensions: one gives a quantum well, two a quantum wire, three a quantum dot.

Why the others are wrong

• (1)
  Quantum step — The structures named by the number of confined dimensions are the quantum well, quantum wire and quantum dot. "Quantum step" is not one of the three.

  For one small dimension and two large ones, the name in that set is the quantum well.

• (3)
  Quantum dot — A quantum dot is confined in all three dimensions: a semiconductor particle only a few nanometres across. Its electrons have discrete energy levels, which is why quantum dots are sometimes called artificial atoms.

  Their light depends on size: larger dots of 5–6 nm emit orange or red, smaller ones of 2–3 nm blue or green.

• (4)
  Quantum wire — A quantum wire is confined in two dimensions: its diameter is nanoscale while its length stays large, so electrons move freely only along it.

  Such wires are also called nanowires. One effect of the confinement is that their electrical conductance comes in steps, multiples of 2e²/h.

Quantum confinement is what makes nanoscale structures different from bulk material. When the size of a region in some direction becomes comparable to the de Broglie wavelength of the electrons, their energy in that direction takes only discrete values.

Counting confined directions gives three structures. A quantum well confines one, a quantum wire two and a quantum dot three; they are also called two-, one- and zero-dimensional structures, after the directions in which carriers stay free.

The same counting describes nanomaterials generally: a nanotextured surface has one nanoscale dimension, a nanotube two, a spherical nanoparticle three.

Key facts

• One dimension at the nanoscale, two large: quantum well; carriers move freely in a plane.
• Two dimensions at the nanoscale, one large: quantum wire (nanowire); carriers move freely along its length.
• All three dimensions at the nanoscale: quantum dot; carriers are confined in every direction.
• Quantum wells, wires and dots are also called two-, one- and zero-dimensional structures.
• For quantum effects to show clearly at room temperature in a semiconductor quantum well, the well width is typically under 30 nm.

Common traps

• Counting the wrong thing: a quantum well confines one dimension but is called two-dimensional, because the name counts the free directions.
• Well versus wire: a thin layer (one small dimension) is a well, a thin rod (two small dimensions) is a wire.
• Dot as the extreme case: only when all three dimensions are nanoscale is the structure a quantum dot.

UnlockIAS will link similar questions from RAS Pre 2021 and 2018 here once those papers are published on this site.

• practice — not a real PYQ

  A nanostructure in which two dimensions are reduced to the nanometre range while the third remains large is known as

  • (a)Quantum well
  • (b)Quantum wire
  • (c)Quantum dot
  • (d)Bulk crystal
  Answer(2) — Two confined dimensions and one free direction make a quantum wire. Option (1) has one confined dimension, option (3) all three, and option (4) none.
• practice — not a real PYQ

  A quantum dot is described as a zero-dimensional structure because

  • (a)it has no mass
  • (b)its charge carriers are confined in all three dimensions
  • (c)it is smaller than a single atom
  • (d)its electrons move freely only along one axis
  Answer(2) — Zero-dimensional means no direction is left free, since all three are confined. Option (1) is false; option (3) is false, as quantum dots are a few nanometres across; option (4) describes a quantum wire.