Donor Impurities In Silicon Research Articles

Spin preservation during THz orbital pumping of shallow donors in silicon

We investigate the spin relaxation under conditions of optical excitation between the Rydberg orbital states of phosphorus donor impurities in silicon. Here we show that the spin relaxation is less than a few percent, even after multiple excitation/relaxation cycles. The observed high level of spin preservation may be useful for readout cycling or in quantum information schemes where coupling of neighbor qubits is via orbital excitation.

Addressable electron spin resonance using donors and donor molecules in silicon.

Phosphorus donor impurities in silicon are a promising candidate for solid-state quantum computing due to their exceptionally long coherence times and high fidelities. However, individual addressability of exchange coupled donors with separations ~15 nm is challenging. We show that by using atomic precision lithography, we can place a single P donor next to a 2P molecule 16 ± 1 nm apart and use their distinctive hyperfine coupling strengths to address qubits at vastly different resonance frequencies. In particular, the single donor yields two hyperfine peaks separated by 97 ± 2.5 MHz, in contrast to the donor molecule that exhibits three peaks separated by 262 ± 10 MHz. Atomistic tight-binding simulations confirm the large hyperfine interaction strength in the 2P molecule with an interdonor separation of ~0.7 nm, consistent with lithographic scanning tunneling microscopy images of the 2P site during device fabrication. We discuss the viability of using donor molecules for built-in addressability of electron spin qubits in silicon.

Silicon as a model ion trap: Time domain measurements of donor Rydberg states

One of the great successes of quantum physics is the description of the long-lived Rydberg states of atoms and ions. The Bohr model is equally applicable to donor impurity atoms in semiconductor physics, where the conduction band corresponds to the vacuum, and the loosely bound electron orbiting a singly charged core has a hydrogen-like spectrum according to the usual Bohr–Sommerfeld formula, shifted to the far-infrared because of the small effective mass and high dielectric constant. Manipulation of Rydberg states in free atoms and ions by single and multiphoton processes has been tremendously productive since the development of pulsed visible laser spectroscopy. The analogous manipulations have not been conducted for donor impurities in silicon. Here, we use the FELIX pulsed free electron laser to perform time-domain measurements of the Rydberg state dynamics in phosphorus- and arsenic-doped silicon and we have obtained lifetimes consistent with frequency domain linewidths for isotopically purified silicon. This implies that the dominant decoherence mechanism for excited Rydberg states is lifetime broadening, just as for atoms in ion traps. The experiments are important because they represent a step toward coherent control and manipulation of atomic-like quantum levels in the most common semiconductor and complement magnetic resonance experiments in the literature, which show extraordinarily long spin lattice relaxation times—key to many well known schemes for quantum computing qubits—for the same impurities. Our results, taken together with the magnetic resonance data and progress in precise placement of single impurities, suggest that doped silicon, the basis for modern microelectronics, is also a model ion trap.

Electric-field control and adiabatic evolution of shallow donor impurities in silicon

We present a tight-binding study of donor impurities in Si, demonstrating the adequacy of this approach for this problem by comparison with effective mass theory and experimental results. We consider the response of the system to an applied electric field: donors near a barrier material and in the presence of an uniform electric field may undergo two different ionization regimes according to the distance of the impurity to the Si/barrier interface. We show that for impurities ~ 5 nm below the barrier, adiabatic ionization is possible within switching times of the order of one picosecond, while for impurities ~ 10 nm or more below the barrier, no adiabatic ionization may be carried out by an external uniform electric field. Our results are discussed in connection with proposed Si:P quantum computer architectures.

Infrared absorption spectrum of singly ionized magnesium donors in silicon

The infrared absorption spectrum of singly ionized magnesium donor impurities in silicon has been measured. Due to better sample preparation and higher resolution of the instrument, the absorption spectrum obtained is much better than previous reports. Some new lines have been observed and identified. Besides the 2p± line, the 3p± line has also been observed for the first time to be a doublet indicating that the excited state np± splits into two states due to chemical splitting.

Hyperfine interactions in muonium-impurity complexes in silicon

The properties of paramagnetic complexes formed by muonium located near acceptor and donor impurities in silicon are calculated using the quantum chemical methods. The calculated data are compared to the experimentally observed characteristics of “normal” and “anomalous” muonium centers.

Infrared absorption spectrum of neutral magnesium donors in silicon

The infrared absorption spectrum of neutral magnesium donor impurities in silicon has been investigated under the high resolution of a Fourier-transform infrared spectrometer. The absorption spectrum measured at liquid helium temperature are observed to be clearly better than those reported earlier in the literature. Several new lines corresponding to excitation from ground state to higher excited states have been observed and identified.

Elastic scattering of electrons by neutral donor impurities in silicon.

We consider the elastic scattering of low-energy electrons by neutral donor impurities in silicon, taking account of the actual anisotropic many-valley conduction band. Necessary modifications of the standard formulas of elastic-scattering theory that result from band anisotropy are derived. S matrices are determined by the solution of a set of coupled differential equations in which the static Coulomb potential and approximate representations of exchange and polarization interactions appear. The scattering is strongly anisotropic and spin dependent, even at very low energies.

Comment on "Interstitial hydrogen and neutralization of shallow-donor impurities in single-crystal silicon"

It has been well established that shallow acceptor impurities in single-crystal silicon can be neutralized by exposure to monoatomic hydrogen. On the other hand, several studies have concluded that shallow donor impurities in silicon cannot be passivated. Contrary to these previous conclusions, Johnson, Herring, and Chadi1 have recently reported neutralization of phosphorus by hydrogenation. Here we show that a detailed analysis of the electrical measurements in Ref. 1 indicates that P neutralization is not necessarily implied. The results can also be explained as a combined effect of generation of H-associated acceptors in the $n^+$ layer and neutralization of substrate boron in the p region. The former reduces the effective free-electron concentration and also the effective mobility as discussed by Johnson, Herring, and Chadi. The effect of the latter is to increase the effective mobility. Since this latter effect was not taken into account in Ref. 1, donor neutralization was considered as the only possibility.

Multivalley spin splitting of1sstates for sulfur, selenium, and tellurium donors in silicon

Spin-valley splitting of the $1s$ ((${T}_{2}$)) states of the ionized chalcogen donors ${\mathrm{S}}^{+}$, ${\mathrm{Se}}^{+}$, and ${\mathrm{Te}}^{+}$ in silicon is reported. The magnitude of the splitting is shown to be related to the impurity atomic spin-orbit splitting. The data are compared with the corresponding splittings of ${\mathrm{Sb}}^{0}$ and ${\mathrm{Bi}}^{0}$ donor impurities in silicon. Predictions of the magnitudes of the hitherto unobserved splittings of the neutral chalcogen donors and other group-V donors are made. In addition, the binding energies of the $1s$ ((${T}_{2}$)) states are compared with recent calculations by Altarelli. The available data on $1s$ states of group-V and -VI donor impurities in silicon are discussed.

Density-functional theory of the metal-insulator transition

The spin-density-functional theory is used to investigate the phase transitions of electrons in a lattice of fixed point charges (a model first studied by Mott). We find a first-order metal-insulator transition at ${r}_{s}=2.84$ and a second-order magnetic transition at ${r}_{s}=2.74$. Results are presented for the magnetization and the spin susceptibility. Extrapolating our results for the case of donor impurities in silicon (neglecting disorder), we estimate that the first-order metal-insulator transition would not be observable above ${T}_{c}\ensuremath{\approx}50$ mK.

Localized states in semiconductors: isocoric impurities in Si and Ge

A formalism is developed within the multi-valley effective mass approximation for the calculation of the groundstate energies for isocoric donor impurities in silicon and germanium taking into account the ellipsoidal shape of their energy surfaces. For the impurity potential a general screened Coulomb form is considered and its parameters are determined from the k dependent dielectric functions of Si and Ge. Variational trial wavefunctions, belonging to an irreducible representation of the tetrahedral point group Td of the Hamiltonian, are used. The groundstate energies as expressed in terms of the effective masses, the potential parameters and the location k0 of the conduction band minima, are then determined by minimization. The results for Si are in good agreement with experiments; however for Ge the predicted E(A1)-E(T2) splitting is rather too small, -0.5 to -0.7 meV compared with the observed value of -4.23 meV.

A note on the many-valley effective mass theory

The equations which are currently used to calculate intervalley mixing for shallow impurity states in semiconductors are examined critically. It is shown that terms which have been neglected so far can be responsible for effects of the same order of magnitude as the ones considered. Evidence is given for this by means of qualitative and numerical arguments in the case of donor impurities in silicon.

Photoconductivity from shallow negative donor ions in silicon: A new far-infrared detector

Shallow donor impurities in silicon at low temperatures are able to bind two electrons, forming negative donor ions, analogous to atomic H− ions. The second electron has a binding energy of only a few meV. Far-infrared radiation can be used to excite these electrons into the conduction band, giving a photoconductive signal. This mechanism is the basis of a new type of far-infrared detector, with promising applications for heterodyne detection at wavelengths on the order of 300 μm. The nature of the negative donor ion is discussed, in part from the effective mass analogy with H− atomic ions, and also with H−2 molecular ions. The theory of how this detector will perform as a function of such variables as bias voltage, background intensity, signal level, and signal speed has been examined. Response speeds on the order of 1 nsec are expected, for operation at temperatures ?2 K, with bias voltage as high as 100 V/cm. With unfiltered 300-K background radiation, the NEP is estimated to be on the order of 10−11 W/(Hz)1/2 at the response peak. In the heterodyne mode of operation, the theoretical noise level will be only fractionally larger than the noise level of a conventional impurity photoconductor. Unlike GaAs far-infrared detector material which is only available in relatively thin epitaxial layers, silicon detectors can be made thick enough to absorb the radiation effectively, and should have much higher quantum efficiency. The wavelength dependence of the photosignal as a function of temperature indicates that for samples doped on the order of 1016 cm−3, a distribution of binding energies exists for an electron bound to a group of randomly spaced donors. Such a distribution of binding energies may be related to excitonic spectra seen at similar doping densities.

Multivalley Effective-Mass Approximation for Donor States in Silicon. I. Shallow-Level Group-V Impurities

Following the procedures of the Kohn-Luttinger one-valley effective-mass approximation (EMA), but without neglecting the intervalley overlap terms, a multivalley EMA is developed within the pseudopotential formalism for shallow-level group-V donors in silicon. A phenomenological two-parameter model impurity potential is proposed which behaves like a square well at small $r$ and a screened Coulomb potential at large $r$. The relative smoothness of the model impurity potential compared with the true impurity potential justifies the use of the EMA. Within the EMA, the valley-orbit interaction can be incorporated completely in the energy calculations, instead of treated as a perturbation. The effects of the higher-energy subsidiary valleys and the $1s\ensuremath{-}2s$ coupling etc. can also be estimated quantitatively in this EMA. The energy levels of the group-$\mathrm{V}$ donor impurities in silicon are calculated using the variation method. The two potential parameters are adjusted to fit the observed $1s({A}_{1})\ensuremath{\rightarrow}2{p}_{\ifmmode\pm\else\textpm\fi{}}$ and $1s({T}_{2})\ensuremath{\rightarrow}2{p}_{\ifmmode\pm\else\textpm\fi{}}$ transition energies. It is shown that the proposed potential describes well the central-cell effects. For the $p$ states, it is found that the usual one-valley approximation is adequate. It is also found that in the multivalley approximation the valley-orbit interaction shifts the $1s({A}_{1})$ level downward and the $1s({T}_{2})$ and $1s(E)$ levels upward relative to the one-valley $1s$ level. The effects of the uncertainty in the position of the ${\ensuremath{\Delta}}_{1}$ conduction-band valleys and of the coupling between the $1s$ and $2s$ states on the ground-state energy are shown to be negligible. The contribution from wave-function components of an ${L}_{1}$ valley of the conduction band to the ground-state energy is computed to be less than 1% of that from wave-function components of $\mathrm{a} {\ensuremath{\Delta}}_{1}$ valley. It indicates that the higher-energy subsidiary conduction-band valleys may be neglected. The ground-state-model wave function is used to calculate the photo-ionization cross section and to predict the Fermi contact hyperfine constants. These results are compared with reported experimental and theoretical results.

The Breakdown of Effective Mass Equations Due to Rapidly Varying Potentials

One of the major causes for the breakdown of the effective mass theory of shallow impurity states in semiconductors is the rapid variation of the potential in the impurity core region. A formalism is developed for treating this breakdown and then applied to the ground state of donor impurities in silicon in the following cases: 1) a simple coulomb potential; 2) potentials that account both for the spatial dependence of the dielectric constant and for the difference between the charge distributions of the core of the impurity atom and the silicon atom it replaces for P , As, and Sb impurities. It is shown that the breakdown is negligible for a coulomb potential and for P impurities, but significant for As and Sb impurities.

THE TEMPERATURE DEPENDENCE OF THE ENERGY LEVELS OF SHALLOW DONOR IMPURITIES IN SILICON

A calculation is made of the temperature dependence of the energy levels of shallow donor impurities in silicon. This temperature dependence arises from the electron–phonon interaction and we consider mixing only of the {1s}, {2s), and {2p0} electronic states. A comparison is made with experiment for the case of phosphorus-doped silicon.

An optical study of lithium and lithiumoxygen complexes as donor impurities in silicon

Infrared absorption spectra have been determined for lithium-doped single crystal silicon samples in the energy range 23.0 meV to 45.0 meV. A series of resonant absorptions corresponding to a donor ionization energy of 32.5 meV was found in oxygen-free silicon; it is concluded that this series is due to the monatomic lithium donor. Samples originally containing some oxygen show a series of resonant absorptions corresponding to a donor ionization energy of 39.2 meV. This is attributed to LiO. The complexity of the spectra obtained increases with increasing oxygen content, presumably due to absorption in other lithiumoxygen complexes.

An optical study of lithium and lithium-oxygen complex as donor impurities in silicon

Upper bounds for the ground-state energy of the exciton-phonon system in a magnetic field are calculated variationally using a wavefunction whose symmetry is suited both to low and high magnetic fields. The displacement amplitudes for the exciton-phonon interaction are those known from the free field case. The results compare satisfactorily with experimental data for TlCl and TlBr.

OPTICAL ABSORPTION SPECTRA OF ARSENIC AND PHOSPHORUS IN SILICON

The optical absorption spectra of arsenic and phosphorus donor impurities in silicon have been studied under conditions of improved resolution. Absorption lines due to transitions from the impurity ground state to the excited states 2p0, 2p±, 3p0, 3p±, 4p0, 4 p±, and 5p0, and 5p± have been observed at 4.2° K. The relative intensities of some of these absorption lines are compared with existing experimental and theoretical estimates. The contribution of instrumental broadening to the observed line widths is assessed and natural line widths are estimated. The estimates indicate values for the natural line widths which are much less than those previously reported. For phosphorus impurity, the natural line widths are estimated to be less than 0.08 × 10−3 electron volts full width at half-maximum. The possibility of concentration broadening is discussed in connection with the arsenic data.