Uniaxial Stress Effect on the Electron Affinity of theD−State in Germanium

Abstract

and doctoral dissertation, University of Stuttgart, 1971 (unpub-Though many experimental results 1 " 6 associated with the impurity states in semiconductors have been ascribed to their (or A + ) states, conclusive evidence of the existence of theD~ (A + ) state has not been reported. In the submillimeter photoconductivity measurements on Ge, 6 the experimental electron affinity of the shallow trapping state, which has been supposed to be the D~ state, was about 3 times larger than the theoretical value 7 estimated by a simple analogy to H". 8 Moreover the spectral shape of the photoconductivity does not agree with the theoretical one. Even if the existence of the D" state in Ge (or Si) is assumed, the complete analogy of it with H" would not hold, because the conduction band in Ge (Si) has many-valley structure with anisotropic energy surfaces.In this Comment we wish to report a stress experiment on the long-wavelength (submillimeter plus millimeter) photoconductivity in Ge, performed in order to reduce the many-valley structure to the single-valley one. ment, we have confirmed that the mentioned discrepancy between experiment and the theory comes mainly from the effect of the many-valley structure in Ge, and we believe our results to be the first conclusive evidence for the existence of theD" states in semiconductors.The present photoconductivity measurements are performed on Sb-doped germanium crystals under uniaxial compressive stress along the [ill] crystal direction by the use of a lamellar grating spectrometer and extending the wavelength range from submillimeter to millimeter. By applying a [ill] stress, the four conductionband valleys in germanium become inequivalent in energy; that is, the energy of the valley with the principal axis of the energy ellipsoid parallel to the [111] stress direction is lowered, while the other three valleys are equally elevated in energy. Thus, under sufficient stress, the electrons in the four valleys are accumulated into the lowest [111] valley and the crystal behaves as a semiconductor with a single conduction-band val-Long-wavelength (submillimeter plus millimeter) photoconductivity measurements in doped germanium have been performed under uniaxial compressive stress along the Ull] crystal direction,, The electron affinity estimated from newly observed spectra is smaller than that in a previous measurement without stress and is consistent with the theoretical prediction for the D" state. The larger electron affinity of the D" state without stress is ascribed to a many-valley effect.913

Trion ground state, excited states, and absorption spectrum using electron-exciton basis

“…(3,4) through Eq. (6). The interest of this derivation is to evidence that the relevant function is not by no means ψ…”

Observation of two distinct negative trions in tungsten disulfide monolayers

“…Similarly, a positive trion is prototyped by a helium cation where one electron is bound to two protons [1]. In semiconductors, and particularly two-dimensional transition metal dichalcogenide monolayers (2D-TMDs), trions arise from charging bound electron-hole pairs (excitons) [2][3][4][5][6][7][8][9]. After their predicted existence in bulk semiconductors in the late 1950s [4], the journey for observing them took almost two decades [9].…”

“…In semiconductors, and particularly two-dimensional transition metal dichalcogenide monolayers (2D-TMDs), trions arise from charging bound electron-hole pairs (excitons) [2][3][4][5][6][7][8][9]. After their predicted existence in bulk semiconductors in the late 1950s [4], the journey for observing them took almost two decades [9]. With the development of confined nanostructures in the 1990s, both positive and negative trions with binding energies on the order of few meV were observed in semiconductor quantum wells [2,3].…”

Way to observe the implausible “trion-polariton”

“…Semiconductor trions [8][9][10][11][12][13][14] are made of two conduction-electrons and one valence-hole, or one conduction-electron and two valence-holes. We will here focus on the former case, denoted as X − .…”

“…Many objections lead us to first reject the idea: (i) the trion coupling to photon is intrinsically weak because the emitted photon can have a momentum different from its initial value, even when the trion lifetime is long; (ii) the photon-trion coupling is vanishingly small because it scales as the inverse of the sample volume; (iii) an increase of the number of electrons available for pairing broadens the photon-trion resonance due to the fermionic nature of trions and electrons; (iv) it also reduces the trion binding by Coulomb screening and by Pauli blocking the electronic states relevant to the formation of bound trion. Despite all these objections, we will show that there exists a narrow window in which "trion-polariton" can be formed.Semiconductor trions [8][9][10][11][12][13][14] are made of two conduction-electrons and one valence-hole, or one conduction-electron and two valence-holes. We will here focus on the former case, denoted as X − .…”