Question

In quantum well, electrons are confined in :

• A. All 3 dimensions
• B. 2 dimensions
• C. 1 dimension
• D. 0 dimension

Hint:

A great trick to remember nanostructure naming: The term (2D, 1D, 0D) refers to the number of dimensions the electrons are FREE to move in. A Quantum Well is a 2D material $\rightarrow$ free in 2 dimensions $\rightarrow$ confined in $3 - 2 = 1$ dimension.

Answer 1

The Correct Option is C

Step 1: Concept:
The question asks to identify the number of dimensions in which charge carriers (electrons or holes) are physically confined within a "quantum well" nanostructure.

Step 2: Key Formula or Approach:
Nanomaterials are classified by how many dimensions restrict the free movement of electrons (quantum confinement):
- Bulk (3D): 0 dimensions of confinement. Electrons move freely in $x, y, z$.
- Quantum Well (2D film): Confined in 1 dimension (thickness). Electrons move freely in a 2D plane.
- Quantum Wire (1D wire): Confined in 2 dimensions. Electrons move freely along a 1D line.
- Quantum Dot (0D dot): Confined in all 3 dimensions. Electrons are fully trapped, like in an atom.

Step 3: Step-by-step Explanation:

• A quantum well is typically formed by sandwiching a thin layer of a narrow-bandgap semiconductor between two layers of a wider-bandgap material.

• Because the middle layer is extremely thin (on the order of the de Broglie wavelength of the electrons), the electrons are energetically and physically trapped (confined) in that $z$-direction.

• However, they are completely free to propagate in the $x$ and $y$ plane of the thin film.

• Therefore, confinement happens in exactly 1 dimension, allowing 2 degrees of freedom.

Step 4: Final Answer:
Electrons in a quantum well are confined in 1 dimension. This corresponds to option (C).