Acceptor Ground State Research Articles

Degenerate impurity states in hopping conduction

Abstract A review of studies on nearest-neighbour hopping (NNH) between impurities, whose ground state (GS) is degenerate or split by the application of a uniaxial stress X or a magnetic field B is presented. The case of acceptors in Ge and Si, whose GS components have different symmetry properties, is discussed in detail. A solution (of the percolation problem involving all the possible transitions between the components of the acceptor GS is provided. For Ge it was preceded by a construction of the acceptor ground state wavefunctions, possessing both a correct symmetry and a correct asymptote behaviour, indispensable for evaluating probabilities of phonon-assisted NNH. For Si the energy diagrams of the accepter GS for various configurations of X and B were obtained and subsequently used in a model calculation. In both Ge and Si the calculation accounted qualitatively for the data.

Hopping conduction through the 2s states of copper acceptors in uniaxially stressed germanium

We have studied hopping conduction in uniaxially stressed Cu-doped Ge. The electronic ground state of neutral Cu acceptors, normally accommodating three 1s holes, undergoes a transformation to a 1s 22s 1 configuration with the application of uniaxial stress greater than 4 kbar. Upon undergoing this transformation, the copper acceptors form a system of lithium-like impurities in which hopping transitions of carriers take place through 2s rather than 1s states. The significant overlap between the more extended 2s wavefunctions located on different sites results in a decrease of the resistivity in the hopping regime by eight orders of magnitude. Good agreement was obtained between the experimental results and our calculations.

Spin–orbit coupling, mass anisotropy, time-reversal symmetry, and spontaneous symmetry breaking in the spectroscopy of shallow centers in elemental semiconductors

The electronic states of shallow donors and acceptors, explored under high resolution with Fourier Transform infrared and Raman spectroscopy, underscore the intimate connection between the localized states of these impurities and the electronic band structure of the host as contemplated in the effective mass theory. Spin–orbit interaction, mass anisotropy of the conduction band minimum (donors) and of the valence band maximum (acceptors), the site symmetry of the impurity and the possible spontaneous departure from it when the electronic ground state is degenerate are the features highlighted in our discussion of the excitation spectra of donors in silicon and boron acceptors in diamond. As in atomic spectroscopy, the removal of degeneracy under external perturbation and the polarization and field dependence of the spectral components provide a wealth of insightful characterizations. We demonstrate them with the Zeeman effect of the Raman transition between the spin–orbit split counterparts of the 1s ground state of boron acceptors in diamond; g-factors and the extreme mass anisotropy of the hole emerge from these studies. They also provide beautiful examples of time-reversal symmetry, conservation laws and selection rules connecting the Stokes to the anti-Stokes Raman scattering.

Resonant acceptor states inGe/Ge1-xSix MQWheterostructures

A new nonvariational theoretical approach allowing us tocalculate both the localized and the continuum states of chargecarriers in quantum well heterostructures in the presence ofthe Coulomb potential has been developed. The method has beenused to calculate the energy spectra of shallow acceptors instrained Ge/GeSi multiple-quantum-well heterostructures.Optical transitions from the acceptor ground states to theresonant states have been revealed in the measured far-infraredphotoconductivity spectra of the heterostructures.

Extreme reduction of the spin-orbit splitting of the deep acceptor ground state of Zn(-)(S) in Si

Electric-dipole spin resonance of the deep acceptor Zn(-)(S) in Si reveals close gamma(8) and gamma(7) ground states with zero-field separation of only 0.31 meV as compared to the 43 meV of the two valence bands. With Lande's formula for the g factors of a 2T2 state split by spin-orbit interaction into gamma(8) and gamma(7) this nearness can be interpreted as strong quenching of the orbital moment. The observed dependence on the Zn isotopic mass indicates a dynamic contribution of the acceptor atom to the electronic state as is expected for a Jahn-Teller effect.

Possible terahertz laser structures based on population inversion induced by resonant states in semiconductors

We theoretically examine the possible InGaAs/GaAs and SiGe/Si QW structures that may fulfill the criterion to achieve a terahertz (THz) laser device according to the new mechanism of unipolar-type population inversion discussed in the recent letter (Phys. Rev. Lett. 83 (1999) 644. Our calculations are based on well-developed effective-mass theory that accounts for valence-band mixing as well as the mismatch of band parameters and dielectric constants between well and barrier materials. The advantage of the model is that the ground and excited states of acceptors confined in strained quantum well structures can be calculated. Therefore, by calculating the splitting of the acceptor ground states in strained In x Ga 1− x As/GaAs and Si 1− x Ge x /Si quantum well structures versus well widths and alloy concentrations, our results provide a guiding to design the structures that may be suitable for realizing THz stimulated emissions in a range between 2.5 and 7.5 THz, which corresponds to an energy range between 10 and 30 meV.

Jahn–Teller splitting and Zeeman effect of acceptors in diamond

Employing the high resolution of a 5+4 tandem Fabry–Pérot interferometer, we discovered that Δ′, the Raman active electronic transition between the spin–orbit split 1s(p3/2):Γ8 and 1s(p1/2):Γ7 acceptor ground states, is a doublet for a boron impurity in diamond with a clearly resolved spacing of 0.81±0.15cm−1. The direct observation of a Stokes/anti-Stokes pair with 0.80±0.04 cm−1 shift provides a striking confirmation that the lower 1s(p3/2):Γ8 ground state has experienced a splitting due to a static Jahn–Teller distortion. The Zeeman effect of Δ′ has been investigated with a magnetic field along several crystallographic directions. Theory of the Zeeman effect, formulated in terms of the symmetry of the substitutional acceptor and the Luttinger parameters of the valence band, allows quantitative predictions of the relative intensities of the Zeeman components in full agreement with experiments. The observation of transitions within the Γ8 Zeeman multiplet, i.e., the Raman-electron-paramagnetic-resonances, is yet another novel feature to emerge from the present study. The investigation has also yielded g-factors characterizing the Zeeman multiplets.

An acceptor in a quantum dot

Energy levels and oscillator strengths for transitions between the lowest states of an acceptor in a semiconductor quantum dot with a finite potential barrier have been computed in the effective-mass approximation, with the valence-band degeneracy in cubic semiconductors taken into account in the spherical approximation. Variational envelope functions have to satisfy the appropriate boundary conditions to ensure the hermiticity of the Hamiltonian matrix. In typical cubic semiconductors the acceptor optical transition energies and oscillator strengths are found to have enhanced values, larger by one order of magnitude than those in the bulk, in the dots of radius approximating in value to the diameter of the acceptor ground-state envelope.

Stress dependence of infrared absorption frequencies and oscillator strengths of acceptors confined in GaAs/AlGaAs quantum wells

Infrared absorption of acceptors confined in a GaAs/AlGaAs quantum well (QW) has been calculated in the presence of an external stress. The absorption frequency and oscillator strength of the dominating infrared transitions of acceptors confined in the QW are examined. The effects of the confined QW potential and the applied stress on the acceptor binding energies are investigated. A simple relation between the acceptor ground state splitting and the first heavy hole-light hole subband splitting is obtained for a GaAs/AlGaAs QW.

Theoretical Calculations of Shallow Acceptor States in Strained Quantum Well Structures

Acceptors confined in strained InxGa1—xAs/Al0.3Ga0.7As quantum well (QW) structures are theoretically investigated. The impurity states are calculated using a four-band effective-mass theory, in which the valence-band mixing as well as the mismatch of the band parameters and the dielectric constants between well and barrier materials have been taken into account. The binding energies of acceptors and the oscillator strengths of the active infrared electronic transitions between the acceptor ground states and the different excited p-like states are calculated with different indium fractions x and different well widths. The results show clearly, that a built-in strain strongly influences the transition energies and the relative oscillator strengths. Due to the splitting of the acceptor ground states, the absorption spectra of the acceptors also show a strong temperature dependence. The calculated spectra of the acceptor electronic transitions are ready to be compared with the infrared absorption measurements.

Nonlinear Zeeman Splitting of the Si:Be?s Acceptor Ground State: Influence of the p1/2 Split-Off Valence Band?

Electric-dipole spin resonance (EDSR) spectra at 24, 34, and 60 GHz of Si:Be show six absorption lines with characteristics similar to those previously observed for the Γ+8 ground state of group-III single acceptors. From the dependence on Fermi level position we attribute these absorptions to the singly ionized substitutional double acceptor Be−s. The observed strong nonlinearity of the Zeeman splitting can be approximately described by a Hamiltonian containing terms up to second order in the magnetic field. A much better description is achieved by including the interaction with the Γ+7 state derived from the split-off valence band, if one assumes that it lies only about 0.6 meV above the ground state.

Effective Mass Calculation of the Shallow Acceptor Ground State g-Factor for A3B5 Semiconductors

Effective mass calculation of the acceptor ground state g-factor is presented for two limiting cases: infinite and zero spin–orbit coupling. Simple analytical expressions for the g-values are obtained within the framework of the zero-radius potential model. These results are in good agreement with experimental data for GaAs. Analytical expressions for the tensor g-factor are presented for strained wide-bandgap semiconductors with weak spin–orbit interaction (such as GaN). These results can be used for qualitative analysis of ODMR and ESR experimental data.

Electronic Raman and infrared spectra of acceptors in isotopically controlled diamonds

The Lyman spectrum of substitutional boron acceptors in diamonds with natural composition and that in a ${}^{13}\mathrm{C}$ diamond exhibit remarkably similar features, but shifted to higher energies in the latter by 0.4--1.5 meV. Additional lines appear when the spectra are recorded as a function of temperature, indicating the thermal population of a level ${\ensuremath{\Delta}}^{\ensuremath{'}}\ensuremath{\sim}2\mathrm{meV}$ above the ground state; this can be interpreted as the spin-orbit splitting of the $1s$ acceptor ground state into ${1s(p}_{3/2})$ and ${1s(p}_{1/2}),$ the latter located ${\ensuremath{\Delta}}^{\ensuremath{'}}$ above the former. The Raman-allowed ${1s(p}_{3/2})\ensuremath{\rightarrow}{1s(p}_{1/2})$ electronic transition is directly observed at 2.07(1) and 2.01(1) meV in the Raman spectrum of natural and ${}^{13}\mathrm{C}$ diamond, respectively. Polarization features of the ${\ensuremath{\Delta}}^{\ensuremath{'}}$ Raman line reveal that it is predominantly ${\ensuremath{\Gamma}}_{5}$ in character, as predicted by a theoretical calculation formulated in terms of the known values of Luttinger parameters. The theoretical expression for the Raman cross section for ${\ensuremath{\Delta}}^{\ensuremath{'}}$ enables the acceptor concentration to be deduced from an intercomparison of the intensity of the ${\ensuremath{\Delta}}^{\ensuremath{'}}$ line and that of the zone-center optical phonon. The presence of boron acceptors produces a quasicontinuous absorption spectrum in the range of the optical phonon branch, flanked by a sharp feature at the zone-center optical phonon frequency; their appearance can be attributed to the partial breakdown of the translational symmetry and the activation of otherwise inactive vibrations.

Theoretical study of shallow acceptor states under the influence of both a confinement potential and a deformation potential

Energy levels of the ground and the excited shallow acceptor states have been calculated for center-doped strain-free ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ quantum wells (QW's) in the presence of an external pressure and in strained ${\mathrm{In}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{y}{\mathrm{Ga}}_{1\ensuremath{-}y}\mathrm{As}$ QW's. The impurity states are calculated using a four-band effective-mass theory, in which the valence-band mixing as well as the mismatch of the band parameters and the dielectric constants between well and barrier materials have been taken into account. The acceptor binding energies and the internal electronic transitions are calculated. The results show that an applied external pressure in ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ QW's or built-in strain in ${\mathrm{In}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{y}{\mathrm{Ga}}_{1\ensuremath{-}y}\mathrm{As}$ QW's strongly influences the acceptor states. The oscillator strengths between the acceptor ground states and the different excited $p$-like states are also calculated for the ${\mathrm{In}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}$ system with three different indium fractions $x.$ The results show clearly that a built-in strain strongly influences the transition energies and the relative oscillator strengths.

Cathodoluminescence investigation of isotope effects in diamond

We report high-resolution cathodoluminescence (CL) measurements near the indirect gap of isotopically modified diamonds. From the energies of intrinsic phonon-assisted peaks, as well as the no-phonon recombination of boron-bound excitons, we determine the contribution of isotope disorder to the frequencies of various phonons with nonzero wave vector. The results confirm calculations of the phonon self-energy based on ab-initio lattice dynamics. For some modes we predict an asymmetric variation of the disorder-induced shift with the 13C concentration which is observed in second-order Raman spectra. The no-phonon emission from boron-bound excitons (D 0 and D 0 ′ lines) exhibits a fine structure which arises from a splitting of the neutral boron acceptor ground state (2 meV) and the initial bound excitons (3.3 meV). When varying the 13C content all components shift with a slope of (14.6 ± 0.5) meV/amu.

Direct Observation of the Hubbard Gap in a Semiconductor

The transformation of the ground state of Cu acceptors in uniaxially stressed Ge from the $(1s{)}^{3}$ to the $(1s{)}^{2}(2s{)}^{1}$ configuration results in a unique system in which a highly delocalized hole wave function corresponds to a relatively deep electronic state. This leads to electronic conduction via an isolated impurity band within the Ge band gap. By changing the Cu concentration we observe an evolution of the Hubbard gap for the $2s$ state from the full gap of $3.7\mathrm{meV}$ at $3\ifmmode\times\else\texttimes\fi{}{10}^{14}\phantom{\rule{0ex}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ to zero gap at $1.6\ifmmode\times\else\texttimes\fi{}{10}^{16}\phantom{\rule{0ex}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$, in good agreement with our calculations.

Theory of acceptor-ground-state description and hot photoluminescence in cubic semiconductors

An approach to the theory of the acceptor ground state in cubic semiconductors is presented. The model has been developed within the framework of the four-band effective Luttinger Hamiltonian and is applicable for both Coulomb and non-Coulomb acceptors. The system of integral equations for the ground-state wave functions has been derived and its solution has been numerically computed. We present the general form of the acceptor-ground-state wave function. The wave functions for a set of acceptor dopants in GaAs are calculated with an accuracy of 2%. The obtained wave functions have been used for qualitative and quantitative analysis of the hot photoluminescence (HPL) spectra and linear polarization in GaAs crystals. Analytical expressions for the line shape and anisotropy of the linear polarization degree have been derived. The dependencies of the HPL characteristics on the excitation energy as well as on the acceptor binding energy have been analyzed. The HPL theory presented allows us to describe the wide spectrum of available experimental data.

The nitrogen acceptor energy in ZnTe measured by Hall effect and optical spectroscopy

The binding energy of the nitrogen acceptor in zinc telluride is measured. The zinc telluride samples were grown by molecular beam epitaxy using a plasma source for nitrogen doping. The acceptor ionization energy at infinite dilution limit is deduced from Hall effect analysis to be 53.2±1.5 meV. This value agrees with that of the acceptor ground state energy obtained from photoluminescence spectra, 53.6±0.7 meV. The acceptor energy in strain-free material may be slightly higher due to some residual tensile strain in the samples.

Strain-dependent Zeeman effect of the nitrogen acceptor bound exciton in ZnSe-epilayers

We report on high resolution magneto-optical studies of the exciton bound to the neutral nitrogen acceptor in freestanding strain-free and strained ZnSe epilayers. The Zeeman results for absorption and photoluminescence are discussed in terms of the j-j coupling scheme in cubic symmetry including Zeeman and strain terms. It is shown that the bound-exciton state from the two hole J = 0 state is below the bound-exciton states from the J = 2 two-hole state. A diamagnetic shift of 5.6 μeV/T2 is found. The g-value of the acceptor ground state is 0.7. The g-value of the bound-exciton state from the J = 0 two-hole state is 1.35 representing the electron g-value. The g-value of the bound exciton from the J = 2 two-hole state is 0.9.

Dependence of the hole lifetime on uniaxial stress in Ga-doped Ge.

The effect of uniaxial stress on the hole lifetime in gallium-doped germanium single crystals has been studied by photo-Hall-effect measurements. We demonstrate that the stress dependence of the hole lifetime offers a critical test for competing models of the capture of holes by acceptors. We find that below 5 K the hole lifetime increases by over one order of magnitude upon the application of 4 kbar in a 〈100〉 direction. Our results show the hole lifetime to be proportional to the acoustic-phonon-scattering component of the hole mobility, in very good agreement with the cascade capture theory for Coulomb-attractive centers and in clear contradiction to the recently proposed model in which holes are directly captured into the acceptor ground state [Phys. Rev. Lett. 69, 2839 (1992)].