Effective-mass States Research Articles

Electrical characterization of AlAs layers and GaAs-AlAs superlattices

We characterize by electrical techniques uniformly Si-doped AlAs layers and short-period GaAs-AlAs superlattices grown in the same conditions by molecular-beam epitaxy. Deep level transient spectroscopy shows that both the layers and the superlattices contain the DX center. The AlAs layers contain, in addition, a distribution of electron traps emitting in the temperature range 50–200 K. Using electron irradiation to introduce defects as probes we verified that the band structures of the superlattices we deduce are consistent with theoretical calculations using a widely accepted value of the band offset (67%). Finally, we observe that the DX center remains present, with the same ionization energy, when the energy position of the first Γ miniband varies while the first L miniband remains practically at the energetical position of the L band in the AlAs barriers. From this result we conclude that the DX center is linked to the L band and thus must be ascribed to an L effective-mass state.

Metastable state of the EL2 defect in GaAs.

We present an analysis of the pressure and alloy dependence of the EL2 ground and excited states. The results can be quantitatively interpreted if the EL2 metastable state is attributed to the ${A}_{1}$(1s) effective-mass state associated with the L conduction-band minimum. The apparently contradictory results on the EL2 point symmetry obtained from optical absorption and optically detected electron-nuclear double-resonance studies find a simple explanation within this model.

Electron trapping by metastable effective-mass states of DX donors in indirect-band-gap AlxGa1-xAs:Te.

Electron trapping by metastable effective-mass states of Te donors bound to the X minimum of the conduction band is reported. Their identification is based upon the analysis of a photoinduced metastable infrared absorption and thermally activated persistent photoconductivity in indirect-band-gap ${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As. Analysis of Hall-effect measurements within a two-level donor model supports the hypothesis of a bistable character of DX-type donors.

Donors in semiconductors and metastability.

We observed that excited or ground effective-mass states of deep or shallow donor defects linked to the different conduction bands of the semiconductor can exhibit long lifetimes characteristics of their depth from the corresponding band. This way the metastable behaviors of the so-called DX center and EL2 defects in GaAs and related alloys can be understood without the need to introduce distorted atomic configurations of these defects.

DX center in Ga1-xAlxAs alloys.

From the electron-emission and -capture variations with the alloy composition, we deduce that the DX center in ${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Al}}_{\mathrm{x}}$As alloys is linked to the L conduction band. This is verified by the study of the DX center in GaAs-${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Al}}_{\mathrm{x}}$As superlattices, where it is observed that the DX center does exist only in GaAs-AlAs superlattices such that the L miniband which replaces the L band of the AlAs barrier is at the same energy as the bottom of this L band, although the X conduction band has been replaced by a \ensuremath{\Gamma} miniband. This property can only find an explanation in the effective-mass approximation and cannot be justified in large--lattice-relaxation models. Within this model the DX level is the effective-mass state of the doping impurity associated with the L band which undergoes a shallow-deep instability due to intervalley mixing. This description implies a small, if any, electron-phonon interaction. From our electron-paramagnetic-resonance studies we conclude that the large threshold for optical ionization involves a transition to a higher state than the bottom of the conduction band and must probably be attributed to an internal transition. The barrier for electron capture is explained as originating from a change of the local force constants of the defect with its charge state. The variation of the capture barrier height with alloy composition is quantitatively accounted for by electron emission from the bottom of the conduction band into the L band, followed by a multiphonon-emission process over a constant barrier.

Observation by ESR of electrons localized at intrinsic shallow traps in silver halide systems

AbstractElectrons shallowly trapped at intrinsic sites in single‐crystal and polycrystalline samples of AgBr, AgCl, and mixed iodohalides are observed by ESR. The results are consistent with a model in which the electron is localised by a silver ion in an effective mass state. The observed ESR linewidths are explained in terms of exchange narrowing. The effect of iodide on the free or nearly‐free electron g‐value is determined. Addition of iodide to AgCl or AgBr resulted in alloy line broadening. The amount of shallow trapping depended in part on dislocation density. In polycrystalline samples of AgBr, cyclotron resonance of the free electron polaron is observed simultaneously with the ESR signals from localized electrons. From the linewidth of the cyclotron resonance signal, the mobility of the free electron polaron in some polycrystalline samples is determined to be the same as that measured previously in very pure single crystals of AgBr.

Suppression of D X centers in GaAlAs-GaAs heterostructures

Using deep level transient spectroscopy we have studied the DX center in a series of periodic GaAs/GaAlAs uniformly Si doped structures. The presence of the DX center is only detected when the structures do not exhibit superlattice behavior. This is understood by the fact that either the DX associated level is resonant in the first conduction miniband (or above it) or that it does not exist because the original band structure of GaAlAs is destroyed by electron delocalization. Examination of the variation of the concentration of DX centers in periodic planar doped GaAlAs structures shows that this disappearance is due to a band structure effect, thus demonstrating that the DX center originates from a shallow-deep instability of the L-band effective mass state of the Si impurity due to intervalley mixing.

Optically Detected Magnetic Resonance of Group IV and Group VI Donors in Al0.6Ga0.4As/GaAs Heterostructures

AbstractThe influence of chemically different donor species on the nature of shallow donor states in Al0.6Ga0.4As/GaAs heterostructures has been investigated by optically detected magnetic resonance (ODMR). Previous theoretical work by Morgan predicts a triplet state for group IV donors and a singlet state for group VI donors. ODMR experiments were performed on as-grown and implanted Si-, Se-, and S-doped epitaxial layers of Al0.6Ga0.4As grown on (001) GaAs substrates. The effective-mass states are modified by the heter-oepitaxial strain in these layers. The Si donors are characterized as quasi-independent valley states. The Se and S donors have valley-orbit splitting energies (i.e. chemical shifts) of 19-20 meV . The results indicate that Si, Se, and S donors are on the lattice sites in the metastable state of DX.

The Metastability of the EL2 and DX Defects in GaAs and 3-5 Alloys

AbstractThe metastability of the EL2 and DX defects in GaAs and Ga1-x AlxAs alloys is discussed in the context of recent hydrostatic pressure and photo-EPR results. A unified model is presented based on the metastable trapping of carriers in excited effective-mass (EM) states derived from secondary conduction band (CB) minima. The metastability is attributed to small lattice relaxation effects.

Electric Field Enhancement of Electron Emission from DX Centers and Consequences

AbstractWe present data which show that electron emission from the DX center is sensitive to the Poole-Frenkel effect. We demonstrate that this result implies that the DX center is an L effective-mass state of the donor impurity accompanied by a small lattice relaxation. We show that all the observations so far obtained on this center are in agreement with this model.

The Role of EL2 for the Mobility-Lifetime Product of Photoexcited Electrons in GaAs

abstractThe mobility lifetime products for photo-electrons in semi-insulating GaAs, which fit successfully the results of photorefractive studies undertaken in the presence of electric fields are three orders of magnitude smaller than those inferred from transport measurements or from the photorefractive effect with no applied electrical field. Consideration of enhanced recombination via EL2 effective-mass states linked to the L-conduction band minimum allows us to fit the dependence of the photorefractive beam coupling gain coefficient on the grating period for both AC fields and moving gratings. A cascade-capture process, which is three orders of magnitude faster than recombination by multiphonon emission from the Γ band to EL2, leads to greatly reduced mobility-lifetime products for field strengths greater than 1 kV/cm. Our results establish the dominant influence of the EL2 defect properties on the recombination processes essential for modelling and optimizing the photorefractive effect in semi-insulating GaAs.

Theory of the exciton molecule bound to an isoelectronic impurity in GaP.

We present a theoretical calculation of the fine structure of an exciton molecule bound to a nitrogen center in GaP. The conduction-band structure is properly taken into account (except for the camel's back effect) by using a combination of Wannier states and effective-mass states for the center electron. The valence-band warping is included by using s-like and d-like effective-mass states for the holes. Solving the one-exciton problem, we obtain a splitting of 0.78 meV of the J=2 and 1 levels due to the electron-hole exchange Coulomb interaction. Including the electron-hole exchange Coulomb interaction and the j-j coupling between holes in the exciton molecule gives a splitting of 0.20 meV for the lowest-lying states with total angular momenta J=0 and J=2. The results are in good agreement with experiment.

Effective-mass states for prolate and oblate ellipsoid bands

The authors report a new and accurate numerical calculation of the excited states of shallow defects in semiconductors, associated with simple ellipsoid energy bands. They use the reduced-matrix-element technique to eliminate the angular part of the effective-mass equation, and the resulting set of radial differential equations is solved variationally. They present the calculated energy levels as a function of the anisotropy parameter gamma =m*perpendicular to /m*/sub ///, covering both the cases of prolate and oblate ellipsoid bands. The former case (0 1) applies, for example, to the problem of shallow acceptors in cubic semiconductors in the limit of very high uniaxial stress applied to the sample parallel to a (001) or a (111) direction. It is of considerable theoretical interest, and is treated here for the first time in a systematic way. Where a comparison with experiment is possible, they find a very close agreement in this case too.

0.79 eV (C line) defect in irradiated oxygen-rich silicon: excited state structure, internal strain and luminescence decay time

Highly excited states of the 0.79 eV luminescent defect observed in photoluminescence excitation (PLE) measurements are interpreted as effective-mass (EMT) states of a pseudo-donor with Ei=38.3 meV. The interpretation implies that the 1s ground state of the donor electron is fivefold split in the C1h symmetric strain field of the defect. Modelling of the internal deformation around the defect by a compressive uniaxial field of 80 MPa along (001) allows the authors to explain the ground state splitting quantitatively and gives rise to a re-interpretation of published uniaxial stress data. Transient decay data suggest that the lowest excited defect state is a split singlet-triplet bound exciton, the 0.79 eV line being emitted by the higher-energy singlet.

Evidence for effective-mass states of a gold-related doubly charged donor in silicon

Luminescence lines of a gold-doped silicon sample fit a scheme of electron transitions from effective-mass levels into the ground state of a doubly charged donor. The donor's existence also is supported by photoconductivity measurements. It has not been observed in goldless samples.

Theory of core excitons

The observation of core excitons with binding energies much larger than those of the valence excitons in the same material has posed a long-standing theoretical problem1. Here we review our proposed solution to this problem2 and show that Frenkel excitons and Wannier excitons can coexist naturally in a single material. A primary-edge core exciton is created by exciting a core electron to an orbital with energy in the forbidden gap below the lowest conduction band edge. Such an exciton may be either a Frenkel exciton or a Wannier exciton, depending on the strength of the static core-hole potential in the central-cell. Frenkel resonances may occur above the primary gap even when the primary-gap excitons are extended effective-mass Wannier states. We have predicted the major chemical trends in the binding energies of core Frenkel excitons in zincblende semiconductors, including the dependences on: (i) the host, (ii) the site to which the core hole is attached, (iii) the angular momentum or irreducible representation of the electron orbital, and (iv) the atom or impurity excited in the core transition. Furthermore, we have exhibited how a surface or interface alters these results3,4 and how the presence of a ‘spectator’ impurity adjacent to the core-excited atom5 affects the Frenkel exciton binding energy.

Radiative recombination of donor-acceptor pairs in polar semiconductors

A variational treatment of effective-mass electronic states is made for donor-acceptor (D-A) pairs, including the effects of electron-phonon interaction within the static approximation. The effective Hamiltonian is based on the Fr\"ohlich continuum model. Expressions for the energy levels are obtained analytically and in terms of integrals involving trigonometric functions. The variational parameters for the orbital radii and for the $p$-state admixtures are determined, all as a function of D-A distance $R$. Both pairs with equal and those with unequal radii are investigated. The electron-phonon interaction is found to decrease at small $R$, and the departure from spherical symmetry increases at small $R$. The theory is applied to the zero-phonon spectra of D-A pairs in GaP and in ZnSe, using a procedure for obtaining the static dielectric constant ${\ensuremath{\epsilon}}_{0}$ from distant-pair spectra and then focusing attention on the deviations from the ideal $\frac{1}{R}$ law for nearer-pair spectra. Comparisons are made with previous theoretical work.

Trapped exciton states in lead halides

The absorption spectra of thin films of PbCl 2 containing 4 mol.% of NaCl, and PbI 2 containing 4 mol.% of KI measured at room temperature are presented. The study indicates the presence of effective mass states associated with substitutional sodium (or potassium) impurities. The character of these states as intermediate excitons in lead halides are discussed.

Valley-orbit interaction and effective-mass theory for indirect gap semiconductors

It is shown that in the absence of core repulsion and intervalley kinetic energy, the intervalley coulomb scattering leads to instability of the effective-mass donor state in silicon. In this material, overlap of Bloch functions from different valleys is essential to reduce the intervalley scattering below a threshold for instability.

Radiation-Produced Absorption Bands in Silicon: Piezospectroscopic Study of a Group-V Atom-Defect Complex

A series of sharp new infrared-absorption bands produced by high-energy-electron irradiation in phosphorus- and arsenic-doped float-zone-refined silicon is reported. In P-doped silicon, the dominant band is at 1150 ${\mathrm{cm}}^{\ensuremath{-}1}$, with associated weaker bands at 1310, 970, 1000, 1025, 1040, and 1450 ${\mathrm{cm}}^{\ensuremath{-}1}$. In As-doped silicon, the corresponding bands are at 1260 ${\mathrm{cm}}^{\ensuremath{-}1}$ and 1480, 1080, 1110, 1135, 1160, and 1650 ${\mathrm{cm}}^{\ensuremath{-}1}$. The spectra recover in both materials at \ensuremath{\sim}140\ifmmode^\circ\else\textdegree\fi{}C. Uniaxial-stress studies of these bands in oriented single crystals with polarized light are described. The results cannot be fit to the usual "piezospectrospic" classification of Kaplyanskii and Runciman. A model is presented which identifies the spectra as electronic transitions from the orbital singlet ground state of a single anistropic donor defect to a manifold of bound large-orbit effective-mass excited states. Extension of the Kaplyanskii classification to include the accidental degeneracy inherent in the effective-mass excited states in silicon explains the stress results. The symmetry of the defect is deduced to be monoclinic II. It is deduced that one or more group-V atoms are involved in the defect, but a microscopic identification of the defect is not possible.