Box 2.

Box 2.

Quantum Wells, Superlattices, and Related Nanostructures

Quantum Wells.

When a thin layer of a semiconductor, with thickness smaller than the extension of the envelope wavefunction of electrons and holes, is sandwiched between two layers of a different semiconductor with larger energy bandgap, the particles are confined in the low energy layer and their energy levels are significantly modified by this so-called quantum confinement. Such layers are called quantum wells. Complex structures consisting of many such layers with extremely high quality now can be fabricated by epitaxial growth techniques (molecular beam epitaxy and metal organic chemical vapor deposition). In a quantum well structure the electron and hole envelope wavefunction is confined in the direction perpendicular to the layers, and they are plane waves in the parallel direction. This produces a series of confined electron and hole levels in the quantum well, and hence the series of absorption edges seen in Fig. 1 Right. The excitons in these structures are compressed, and, as mentioned in Box 1, they look more like pancakes. The distortion of the envelope wavefunctions changes many properties of quantum well structures as compared with the bulk materials. In particular the oscillator strength is significantly enhanced and the exciton resonances remain visible up to room temperature, two characteristics that are exploited in many opto-electronic devices.

a-DQWS.

A slightly more complex, but extremely interesting, structure consists of two such quantum wells of different thickness separated by a thin barrier. A sketch of the conduction band energy and electron envelope wavefunction in an a-DQWS is shown in Fig. 2 Upper for three values of an electric field applied perpendicular to the layers. As the lowest energy level in the NW is tuned through the lowest energy level in the WW by varying the electric field, the energy levels show a typical anticrossing behavior. The magnitude of that splitting is determined by the tunneling probability between the two wells and is controlled primarily by the height and the width of the potential barrier separating the two wells. The interband absorption spectrum from the ground state of the hole in the WW to these electronic levels is schematically illustrated in Fig. 2 Upper. It exhibits two equally strong absorption peaks at resonance, but becomes asymmetric away from resonance.

Superlattices.

Another very interesting semiconductor nanostructure, a semiconductor superlattice, consists of a large number (2N + 1) of (identical) quantum wells separated by thin or low barriers as sketched in Fig. 2 Lower. The tunneling of an electron between the quantum wells spreads the ground electronic state of the superlattice into a miniband of width 4Δ_o, with the energy dispersion ɛ_k = E_o − 2Δ_ocos(kd), where d is the periodicity of the superlattice, kd = j π/2(N + 1) and j = 1,2 . . 2N + 1. The miniband is characterized by a new smaller effective mass in the direction perpendicular to the planes of the quantum wells. A superlattice offers the possibility of manipulating a number of properties of semiconductors. In particular, applying an electric field perpendicular to the interface planes can lead to an equally spaced Wannier-Stark ladder, an ideal system for observing the elusive Bloch oscillations as discussed in the text.

Quantum Wells, Superlattices, and Related Nanostructures

Quantum Wells.

When a thin layer of a semiconductor, with thickness smaller than the extension of the envelope wavefunction of electrons and holes, is sandwiched between two layers of a different semiconductor with larger energy bandgap, the particles are confined in the low energy layer and their energy levels are significantly modified by this so-called quantum confinement. Such layers are called quantum wells. Complex structures consisting of many such layers with extremely high quality now can be fabricated by epitaxial growth techniques (molecular beam epitaxy and metal organic chemical vapor deposition). In a quantum well structure the electron and hole envelope wavefunction is confined in the direction perpendicular to the layers, and they are plane waves in the parallel direction. This produces a series of confined electron and hole levels in the quantum well, and hence the series of absorption edges seen in Fig. 1 Right. The excitons in these structures are compressed, and, as mentioned in Box 1, they look more like pancakes. The distortion of the envelope wavefunctions changes many properties of quantum well structures as compared with the bulk materials. In particular the oscillator strength is significantly enhanced and the exciton resonances remain visible up to room temperature, two characteristics that are exploited in many opto-electronic devices.

a-DQWS.

A slightly more complex, but extremely interesting, structure consists of two such quantum wells of different thickness separated by a thin barrier. A sketch of the conduction band energy and electron envelope wavefunction in an a-DQWS is shown in Fig. 2 Upper for three values of an electric field applied perpendicular to the layers. As the lowest energy level in the NW is tuned through the lowest energy level in the WW by varying the electric field, the energy levels show a typical anticrossing behavior. The magnitude of that splitting is determined by the tunneling probability between the two wells and is controlled primarily by the height and the width of the potential barrier separating the two wells. The interband absorption spectrum from the ground state of the hole in the WW to these electronic levels is schematically illustrated in Fig. 2 Upper. It exhibits two equally strong absorption peaks at resonance, but becomes asymmetric away from resonance.

Superlattices.

Another very interesting semiconductor nanostructure, a semiconductor superlattice, consists of a large number (2N + 1) of (identical) quantum wells separated by thin or low barriers as sketched in Fig. 2 Lower. The tunneling of an electron between the quantum wells spreads the ground electronic state of the superlattice into a miniband of width 4Δ_o, with the energy dispersion ɛ_k = E_o − 2Δ_ocos(kd), where d is the periodicity of the superlattice, kd = j π/2(N + 1) and j = 1,2 . . 2N + 1. The miniband is characterized by a new smaller effective mass in the direction perpendicular to the planes of the quantum wells. A superlattice offers the possibility of manipulating a number of properties of semiconductors. In particular, applying an electric field perpendicular to the interface planes can lead to an equally spaced Wannier-Stark ladder, an ideal system for observing the elusive Bloch oscillations as discussed in the text.