Quantum wells are artificially engineered semiconductor structures that confine electrons and holes in a narrow region along one direction, creating a potential well. They are typically composed of layers of different semiconductor materials with varying energy bandgaps.
Electrons and holes are fundamental charge carriers in semiconductors. In a quantum well, the confinement of electrons and holes occurs in the direction perpendicular to the layers of the well. The electrons and holes are confined within a region called the well, which has a lower energy compared to the surrounding layers. This confinement leads to unique quantum mechanical effects.
Electrons in a quantum well:
Energy levels: The energy levels of electrons in a quantum well become quantized due to the confinement along one direction. Only certain energy levels are allowed for electrons within the well, forming a discrete energy spectrum. These energy levels are often referred to as subbands.
Wave functions: The wave functions of electrons in a quantum well are spatially localized within the well. The wave function describes the probability distribution of finding an electron at a specific position. In a quantum well, the wave functions are typically spread out across the width of the well but are localized within that region.
Density of states: The density of states, which represents the number of available energy states per unit energy, is modified in a quantum well. The discrete energy levels in the well result in a quantized density of states, meaning there are only certain allowed energy states for electrons.
Holes in a quantum well:
Holes are essentially vacancies in the valence band, representing the absence of an electron. In a quantum well, holes behave similarly to electrons with some important differences:
Energy levels: Like electrons, the energy levels of holes become quantized in a quantum well. However, the energy levels for holes are typically opposite in nature to those of electrons. This means that the energy levels for holes are higher as the energy decreases.
Wave functions: The wave functions of holes in a quantum well are also spatially localized within the well but are opposite in nature to the wave functions of electrons. The wave functions for holes describe the probability distribution of finding a hole at a specific position within the well.
Density of states: Similar to electrons, the density of states for holes in a quantum well is also quantized due to the confinement. The allowed energy states for holes are discrete, leading to a modified density of states.
In summary, a quantum well provides a means of confining electrons and holes in a narrow region, leading to quantized energy levels and modified density of states. These characteristics are utilized in various applications, such as quantum well lasers, quantum well infrared photodetectors, and other electronic and optoelectronic devices.