Semiconductor physics and light-matter interaction
PHYS-433
Recorded version of Lecture 3
PHYS-433 Lecture 3
06.10.2021, 14:43
In this lecture, we go beyond the nearly-free electron model by providing some insights related to the k.p method, which is a more quantitative method to derive the band structure of semiconductors. By making use of Newton's law, we recall that the effective mass of free carriers are inversely proportional to the curvature of the k-space energy dispersion. The case of direct and indirect bandgap semiconductors is addressed, which allows highlighting the isotropic or anisotropic nature of a dispersion curve near a band extremum. The anisotropic case leads to the definition of transverse and longitudinal masses for free carriers. Finally, the complexity of the valence band extremum is also addressed. Within this framework, it is thus shown that three subbands are expected with the topmost bands, the heavy and light hole subbands being degenerate at the Gamma point for diamond and zincblende semiconductors. Using the Luttinger Hamiltonian, the order of magnitude related to each effective mass can be obtained for those bands.
PHYS-433 Lecture 3
06.10.2021, 14:43
In this lecture, we go beyond the nearly-free electron model by providing some insights related to the k.p method, which is a more quantitative method to derive the band structure of semiconductors. By making use of Newton's law, we recall that the effective mass of free carriers are inversely proportional to the curvature of the k-space energy dispersion. The case of direct and indirect bandgap semiconductors is addressed, which allows highlighting the isotropic or anisotropic nature of a dispersion curve near a band extremum. The anisotropic case leads to the definition of transverse and longitudinal masses for free carriers. Finally, the complexity of the valence band extremum is also addressed. Within this framework, it is thus shown that three subbands are expected with the topmost bands, the heavy and light hole subbands being degenerate at the Gamma point for diamond and zincblende semiconductors. Using the Luttinger Hamiltonian, the order of magnitude related to each effective mass can be obtained for those bands.
PHYS-433 Lecture 3
06.10.2021, 14:43
In this lecture, we go beyond the nearly-free electron model by providing some insights related to the k.p method, which is a more quantitative method to derive the band structure of semiconductors. By making use of Newton's law, we recall that the effective mass of free carriers are inversely proportional to the curvature of the k-space energy dispersion. The case of direct and indirect bandgap semiconductors is addressed, which allows highlighting the isotropic or anisotropic nature of a dispersion curve near a band extremum. The anisotropic case leads to the definition of transverse and longitudinal masses for free carriers. Finally, the complexity of the valence band extremum is also addressed. Within this framework, it is thus shown that three subbands are expected with the topmost bands, the heavy and light hole subbands being degenerate at the Gamma point for diamond and zincblende semiconductors. Using the Luttinger Hamiltonian, the order of magnitude related to each effective mass can be obtained for those bands.
PHYS-433 Lecture 3
06.10.2021, 14:43
In this lecture, we go beyond the nearly-free electron model by providing some insights related to the k.p method, which is a more quantitative method to derive the band structure of semiconductors. By making use of Newton's law, we recall that the effective mass of free carriers are inversely proportional to the curvature of the k-space energy dispersion. The case of direct and indirect bandgap semiconductors is addressed, which allows highlighting the isotropic or anisotropic nature of a dispersion curve near a band extremum. The anisotropic case leads to the definition of transverse and longitudinal masses for free carriers. Finally, the complexity of the valence band extremum is also addressed. Within this framework, it is thus shown that three subbands are expected with the topmost bands, the heavy and light hole subbands being degenerate at the Gamma point for diamond and zincblende semiconductors. Using the Luttinger Hamiltonian, the order of magnitude related to each effective mass can be obtained for those bands.
PHYS-433 Lecture 3
06.10.2021, 14:43
In this lecture, we go beyond the nearly-free electron model by providing some insights related to the k.p method, which is a more quantitative method to derive the band structure of semiconductors. By making use of Newton's law, we recall that the effective mass of free carriers are inversely proportional to the curvature of the k-space energy dispersion. The case of direct and indirect bandgap semiconductors is addressed, which allows highlighting the isotropic or anisotropic nature of a dispersion curve near a band extremum. The anisotropic case leads to the definition of transverse and longitudinal masses for free carriers. Finally, the complexity of the valence band extremum is also addressed. Within this framework, it is thus shown that three subbands are expected with the topmost bands, the heavy and light hole subbands being degenerate at the Gamma point for diamond and zincblende semiconductors. Using the Luttinger Hamiltonian, the order of magnitude related to each effective mass can be obtained for those bands.
PHYS-433 Lecture 3
06.10.2021, 14:43
In this lecture, we go beyond the nearly-free electron model by providing some insights related to the k.p method, which is a more quantitative method to derive the band structure of semiconductors. By making use of Newton's law, we recall that the effective mass of free carriers are inversely proportional to the curvature of the k-space energy dispersion. The case of direct and indirect bandgap semiconductors is addressed, which allows highlighting the isotropic or anisotropic nature of a dispersion curve near a band extremum. The anisotropic case leads to the definition of transverse and longitudinal masses for free carriers. Finally, the complexity of the valence band extremum is also addressed. Within this framework, it is thus shown that three subbands are expected with the topmost bands, the heavy and light hole subbands being degenerate at the Gamma point for diamond and zincblende semiconductors. Using the Luttinger Hamiltonian, the order of magnitude related to each effective mass can be obtained for those bands.