Spin quantum computation in silicon nanostructures

Proposed silicon-based quantum-computer architectures have attracted attention because of their promise for scalability and their potential for synergetically utilizing the available resources associated with the existing Si technology infrastructure. Electronic and nuclear spins of shallow donors (e.g. phosphorus) in Si are ideal candidates for qubits in such proposals because of their long spin coherence times due to their limited interactions with their environments. For these spin qubits, shallow donor exchange gates are frequently invoked to perform two-qubit operations. We discuss in this review a particularly important spin decoherence channel, and bandstructure effects on the exchange gate control. Specifically, we review our work on donor electron spin spectral diffusion due to background nuclear spin flip-flops, and how isotopic purification of silicon can significantly enhance the electron spin dephasing time. We then review our calculation of donor electron exchange coupling in the presence of degenerate silicon conduction band valleys. We show that valley interference leads to orders of magnitude variations in electron exchange coupling when donor configurations are changed on an atomic scale. These studies illustrate the substantial potential that donor electron/nuclear spins in silicon have as candidates for qubits and simultaneously the considerable challenges they pose. In particular, our work on spin decoherence through spectral diffusion points to the possible importance of isotopic purification in the fabrication of scalable solid state quantum computer architectures. We also provide a critical comparison between the two main proposed spin-based solid state quantum computer architectures, namely, shallow donor bound states in Si and localized quantum dot states in GaAs.     

Observation of shallow residual donors in high purity epitaxial GaAs by means of photoluminescence spectroscopy

We report the first observation of three different residual donors in undoped high purity vapor phase epitaxial GaAs using the high resolution photoluminescence spectroscopy technique at temperatures ～ 2 K. The binding energies of these shallow donors were determined from the excited state transitions of excitons bound to neutral donors and they are found to be in very good agreement with corresponding values obtained from high-resolution far infrared Fourier transform spectroscopy, using the modulated photoconductivity technique.     

Central cell effects on the polarizabilities of shallow donors in silicon

With the Topp and Hopfield form for the ionic pseudopotentials, the screened impurity pseudopotentials of the shallow donors P, As and Sb in silicon are obtained in closed form in the linearized Thomas-Fermi model. The results are compared with the screening using a k-dependent dielectric function. Using these impurity pseudopotentials in the multivalley effective mass equation, the binding energies of these donors in Si are estimated variationally. Adopting the Hasse variational method, the polarizabilities of the P, As and Sb donors in Si are computed and are found to be in excellent agreement with the polarizability values of isolated P and Sb in Si, deduced from recent piezocapacitance measurements.     

Local field corrections to binding energies of substitutional and interstitial donors in Si and Ge

Intervalley Umklapp matrix elements, with inclusion of local field screening effects, are computed for substitutional and interstitial point-charge impurity potentials in Si and Ge. The shallow character of substitutional donors is not affected in Ge and is even reinforced in Si, where a 20% reduction of the binding energy is obtained as a consequence of the local field effect. In both semiconductors the local field corrections strongly reinforce the non-effective-mass, deep-level character of interstitial point-charge donors.     

Mutual passivation of donors and isovalent nitrogen in GaAs

We study the mutual passivation of shallow donor and isovalent N in GaAs. We find that all the donor impurities, SiGa, GeGa, SAs, and SeAs, bind to N in GaAs:N, which has a large N-induced band-gap reduction relative to GaAs. For a group-IV impurity such as Si, the formation of the nearest-neighbor SiGa-NAs defect complex creates a deep donor level below the conduction band minimum (CBM). The coupling between this defect level with the CBM pushes the CBM upwards, thus restoring the GaAs band gap; the lowering of the defect level relative to the isolated SiGa shallow donor level is responsible for the increased electrical resistivity. Therefore, Si and N mutually passivate each other's electrical and optical activities in GaAs. For a group-VI shallow donor such as S, the binding between SAs and NAsdoes not form a direct bond; therefore, no mutual passivation exists in the GaAs:(S+N) system.     

Compensation-induced optical transitions within the ground state of shallow donors in Ge and Si

An approximate formula for integral intensity of the compensation-induced parity-forbidden optical transition within the ground state of shallow donors in Ge and Si is derived in the limit of small compensations. The lineshapes for absorptions in Ge(Sb), Ge(P), Ge(As) and Si(As) are also calculated.     

Si DX centers in GaAs at large hydrostatic pressures

A number of experimental and theoretical studies indicate that DX centers in GaAs, its alloys and other III–V semiconductors have negative U properties. Using far infrared localized vibrational mode (LVM) spectroscopy of Si donors in GaAs under large hydrostatic pressure in a diamond anvil cell we have discovered an LVM of the Si DX center. From the ratio of the LVM absorption lines of Si_Ga and Si_DX and the compensation in our GaAs samples, we show unambiguously that two electrons are trapped when the ionized shallow Si donors transform into negatively charged DX centers, in full agreement with the negative U model.Dedicated to H.-J. Queisser on the occasion of his 60th birthday     

Probing of the shallow donor and acceptor wave functions in silicon carbide and silicon through an EPR study of crystals with a modified isotopic composition

The spatial distributions of the unpaired-electron wave functions of shallow N donors in SiC crystals and of shallow P and As donors in silicon crystals were determined by studying crystals with a modified content of the ²⁹Si and ¹³C isotopes having a nonzero nuclear magnetic moment. As follows from the present EPR and available ENDOR data, the distribution of donor electrons in SiC depends substantially on the polytype and position in the lattice; indeed, in 4H-SiC, the unpaired electrons occupy primarily the Si s and p orbitals, whereas in 6H-SiC these electrons reside primarily in the s orbitals of C. The electron distributions for the N donor in the hexagonal position, which has a shallow level close to that obtained for this material in the effective-mass approximation, and for the donor occupying the quasi-cubic position differ substantially. The EPR spectrum of N in quasi-cubic positions was observed to have a hyperfine structure originating from a comparatively strong coupling with the first two coordination shells of Si and C, which were unambiguously identified. The effective-mass approximation breaks down close to the N donor occupying the quasi-cubic position, and the donor structure and the donor electron distribution become less symmetric. In silicon, reduction of the ²⁹Si content brought about a substantial narrowing of the EPR line of the shallow P and As donors and an increase in the EPR signal intensity, as well as a noticeable increase in the spin-lattice relaxation time T₁. This offers the possibility of selectively studying these spectra by optically exciting a region of the crystal in order to shorten T₁ and thereby precluding EPR signal saturation only in the illuminated part of the material. This method may be used to advantage in developing materials for quantum computers based on donors in silicon and SiC.     

EPR and ENDOR Studies of Shallow Donors in SiC

Recent progress in the investigation of the electronic structure of the shallow nitrogen (N) and phosphorus (P) donors in 3C–, 4H– and 6H–SiC is reviewed with focus on the applications of magnetic resonance including electron paramagnetic resonance (EPR) and other pulsed methods such as electron spin echo, pulsed electron nuclear double resonance (ENDOR), electron spin-echo envelope modulation and two-dimensional EPR. EPR and ENDOR studies of the ²⁹Si and ¹³C hyperfine interactions of the shallow N donors and their spin localization in the lattice are discussed. The use of high-frequency EPR in combination with other pulsed magnetic resonance techniques for identification of low-temperature P-related centers in P-doped 3C–, 4H– and 6H–SiC and for determination of the valley–orbit splitting of the shallow N and P donors are presented and discussed.     

Photothermal ionization spectroscopy for shallow impurities in ultra-pure silicon

We report the comprehensive results obtained in our group and last few years for the shallow impurities in ultrapure silicon by use of photothermal ionization spectroscopy. The new results reported here include the discovery and investigation of new shallow impurity centers in Si, the detection for the compensation of different types of impurities, the accurate determination for the spin-orbit splitting . of valence band for Si, and the phonon duplicates and Fano resonance for the transitions of shallow impurities in Si. In addition it is also shown experimentally that the sensitivity of the photothermal ionization spectroscopy as used for detecting the concentration of shallow donors in Si can reach as high as 10⁸ cm^–3, much higher than that reported in the literatures up to date, and line width for the sharpest spectral lines in the spectrum is about 0.08 cm^–1, that is, 10 eV.     

Optical properties of excitons bound to neutral SiGa-donors in GaP and the degeneracy of the SiGa-donor ground state

Low temperature near band-edge absorption and luminescence spectra of Si-doped n-type GaP are reported. Electrical and optical evidence is presented that these spectra are due to the creation and decay of excitons bound to neutral Si donors on Ga sites. Several zero-phonon transitions, each with strong replications by momentum conserving phonons, were observed in both absorption and luminescence. From these measurements it is concluded that the ground state of the Si_Ga donor is split into two sublevels 0.6 meV apart. Crystals containing a sufficiently low concentration of S to be suitable for a reliable analysis of temperature-dependent Hall-effect measurements were selected by combining 300°K Hall-effect data with low temperature S-exciton absorption data. The electrical measurements support the identification of Si as the main shallow donor. Moreover, it is concluded from these measurements that the degeneracy of the ground state of a Ga-site donor is 3 times that of a P-site donor, in agreement with theoretical expectations.     

Phonons heat transport at an atomic well boundary in ultrathin solid films

The effect of the central-cell corrections on the shallow donor states in Si spherical quantum dot is studied within the effective mass approximation. Finite step-like spatial confining potential, Coulomb and image charge potentials arising from the dielectric mismatch at the interface of the media are taken into account. We found that it is possible to tune the impurity energies by varying the dot radius and dielectric constant of the barrier material. In the strong confinement regime, due to the enhanced weight of the donor wave functions on the impurity atoms, large values of the chemical shifts for typical donors in Si compared to the ones in bulk are obtained. The calculated size-dependence of the effective Bohr radius in donor doped nanocrystals is in reasonable accord with electron spin resonance measurements on Si quantum dots embedded in insulating glass matrices. We conclude that both the dielectric mismatch and central-cell corrections must be considered in the study of these systems in order to obtain satisfactory agreement with experimental data.     

Dopability, intrinsic conductivity, and nonstoichiometry of transparent conducting oxides

Existing defect models for In(2)O(3) and ZnO are inconclusive about the origin of conductivity, nonstoichiometry, and coloration. We apply systematic corrections to first-principles calculated formation energies Delta H, and validate our theoretical defect model against measured defect and carrier densities. We find that (i) intrinsic acceptors ("electron killers") have a high Delta H explaining high n-dopability, (ii) intrinsic donors ("electron producers") have either a high Delta H or deep levels, and do not cause equilibrium-stable conductivity, (iii) the O vacancy V(O) has a low Delta H leading to O deficiency, and (iv) V(O) has a metastable shallow state, explaining the paradoxical coexistence of coloration and conductivity.     

Rotational spectrum and structure of Si3

The rotational spectrum of a pure silicon cluster, the Si3 trimer, has been observed for the first time. From the rotational constants of the normal and the 29Si and 30Si isotopic species, a precise geometrical structure has been derived: the trimer is an isosceles triangle with a bond to the apex Si of length 2.177(1) A and an apex angle of 78.10(3) degrees. The substantial inertial defect and fairly large centrifugal distortion suggest that the molecule possesses a shallow bending potential. Si3 is a good candidate for astronomical detection because radio lines of comparably massive silicon molecules (e.g., SiC2, SiC4, and SiS) are readily observed in at least one astronomical source. The rotational spectra of Si6, Si9, and even larger polar silicon clusters may be detectable with the present technique, as well as similar germanium clusters.     

Confined electron and shallow donor states in graded GaAs/Al Ga As spherical quantum dots

A theoretical study is performed on the confined electron and shallow donor states properties in graded GaAs/Al_xGa_1-xAs spherical quantum dots. The two lowest energy levels of a confined electron are obtained taking into account the dependence of the electron effective mass on the spatial profile of the Al molar fraction. The ground state of a single Si shallow donor, which may be located at an arbitrary position in the structure, is calculated through a variational approach. Depending on the dot interface width and localization, we find that the energy levels of the electron and donor states for the system under study can be blue or red shifted appreciably in comparison to those calculated within the sharp interface picture. We show that it is necessary to have accurate information concerning the interface of semiconductor dots whose samples are used in the experiments, in order to achieve a better understanding of their optical properties. Received 31 May 1999     

Ab initio study of the diffusion mechanisms of gallium in a silicon matrix

We present the results of a study into the diffusion mechanisms of Ga defects in crystalline Si using ab initio techniques. Five stable neutral configurations for single and multi-atom defects are identified by density-functional theory (DFT) calculations within the local density approximation and using a localized basis set as implemented in the SIESTA package. Formation energy (E _F ) calculations on these stable structures show the most likely neutral single-atom defect to be the Ga substitutional, with an E _F of 0.7 eV in good agreement with previous work. Charge state studies show the Ga tetrahedral interstitial defect to be in a + 1 state for most doping conditions. They also indicate the possibility for a gallium substitutional-tetrahedral interstitial complex to act as a deactivating center for the Ga dopants except in n-doped regime, where the complex adopts a − 1 charge state. Migration pathway calculations using SIESTA coupled with the activation relaxation technique (ART nouveau) allow us to determine possible migration paths from the stable configurations found, under various charge states. In general, diffusion barriers decrease as the charge state becomes more negative, suggesting that the presence of Si self-interstitials can enhance diffusion through the kicking out of substitutional Si and by adding negative charge carriers to the system. An overall picture of a possible Ga diffusion and complex formation mechanism is presented based on these results.     

Identification of the carbon antisite-vacancy pair in 4H-SiC

The metastability of vacancies was theoretically predicted for several compound semiconductors alongside their transformation into the antisite-vacancy pair counterpart; however, no experiment to date has unambiguously confirmed the existence of antisite-vacancy pairs. Using electron paramagnetic resonance and first principles calculations we identify the S15 center as the carbon antisite-vacancy pair in the negative charge state (C(Si)V-(C)) in 4H-SiC. We suggest that this defect is a strong carrier-compensating center in n-type or high-purity semi-insulating SiC.     

Nuclear spins of ionized phosphorus donors in silicon

We demonstrate the coherent control and electrical readout of ionized phosphorus donor nuclear spins in (nat)Si. By combining time-programed optical excitation with coherent electron spin manipulation, we selectively ionize the donors depending on their nuclear spin state, exploiting a spin-dependent recombination process at the Si/SiO(2) interface, and find a nuclear spin coherence time of 18 ms for the ionized donors. The presented technique allows for spectroscopy of ionized-donor nuclear spins and enhances the sensitivity of electron nuclear double resonance to a level of 3000 nuclear spins.     

Si–Si bond as a deep trap for electrons and holes in silicon nitride

A two-stage model of the capture of electrons and holes in traps in amorphous silicon nitride Si₃N₄ has been proposed. The electronic structure of a “Si–Si bond” intrinsic defect in Si₃N₄ has been calculated in the tight-binding approximation without fitting parameters. The properties of the Si–Si bond such as a giant cross section for capture of electrons and holes and a giant lifetime of trapped carriers have been explained. It has been shown that the Si–Si bond in the neutral state gives shallow levels near the bottom of the conduction band and the top of the valence band, which have a large cross section for capture. The capture of an electron or a hole on this bond is accompanied by the shift of shallow levels by 1.4–1.5 eV to the band gap owing to the polaron effect and a change in the localization region of valence electrons of atoms of the Si–Si bond. The calculations have been proposed with a new method for parameterizing the matrix elements of the tightbinding Hamiltonian taking into account a change in the localization region of valence electrons of an isolated atom incorporated into a solid.     

Intensities of the line and photoionization spectra of shallow nonhydrogenlike impurities in semiconductors

Numerical nonvariational methods are proposed for the calculation of energies and wave functions of bound states, ground state wave functions with the account of central cell corrections, and the orthonormalized wave functions of the continuous spectrum of nonhydrogenlike shallow impurities in semiconductors. A number of different spectral characteristics is calculated for donor impurities in Ge and Si and for acceptor impurities in Ge and GaAs. The theory of photofield ionization i.e. tunnel ionization of an optically excited impurity atom is presented for shallow donors with the account of the effective mass anisotropy. The possibility of the observation of the line spectrum (due to transitions to shallow Coulomb excited levels) of a deep impurity in the presence of a high magnetic field is shown.