Restoration of the host band-gap by hydrogenation: dilute, amalgamation, and alloy limits

We describe first the effects of hydrogen irradiation on the optical properties of GaAs1−yNy/GaAs epilayers in the very dilute nitrogen limit (y<0.01%). Figure shows the effect of hydrogen irradiation on the sample. Hydrogenation at various H doses, dH, leads to a progressive and finally complete quenching of the Nrelated lines as well as of the broad underlying band. The dH=5×1015 ions/cm2 spectrum closely reproduces that of pure GaAs, where only two bands are observed, namely, the longitudinal optical (LO) phonon replicas of the C-related free-to-bound transition at 1.4934 eV. This H-induced passivation has never been reported before for any isoelectronic impurity, except for a weak reduction in the luminescence intensity of a few N-related lines in GaP:N. Note that a 100% passivation of impurity luminescence bands is hardly attainable even in the common case of H passivation of shallow impurities in GaAs or Si.

We now move to the so-called amalgamation limit, corresponding to the existence of both localized and extended (or Bloch-like) states in the material electronic structure. Figure illustrates such a case for GaAs1−yNy with y=0.1%. The bottom curve shows the PL spectrum of the H-free sample. H irradiation leads first to a passivation of the N cluster states and then to an apparent reopening of the GaAs1−yNy band-gap toward that of the GaAs reference (top curve). As a matter of fact, both the (e,C) and the E− recombination bands converge to those of the GaAs reference. The energy separation between these two transitions decreases with increasing N concentration, most likely dueto the increase of the tensile strain with increasing x. Indeed, for increasing N concentration, the top of thevalence band acquires a more pronounced light-hole character and, in turn, the binding energy of the acceptor impurity decreases. Similar results have been observed in the full alloy limit as shown in the following section.

                                                  ROSSANA C HERNANDEZ C
                                      ELECTRONICA DEL ESTADO SOLIDO
                   http://www.sciencedirect.com/science/book/9780080445021

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EFFECTS OF NITROGEN AND HYDROGEN ON THE ELECTRONIC PROPERTIES OF InXGA1−XAs1−YNY

Figure shows the low-temperature (T=10 K) photoluminescence spectra of a representative series of as-grown samples whose N concentration varies over about two orders of magnitude. At the very early stage of N incorporation in GaAs (N concentration less than 0.01%, bottommost spec-trum in Figure ), the low-temperature PL spectra are characterized by a number of sharp lines (line width ≈0.5 meV) between 1.40 and 1.48 eV, which are due to the recombination of excitons localized on N complexes. These lines are attributed to carrier recombination from electronic levels due to N pairs and/or clusters  and are superimposed on a broad band also related to N doping. The luminescence intensity associated with these transitions varies from line to line and increases with y (not shown here). An exact assignment of each line to a given N complex is made rather

difficult by the strong dependence of the material optical properties on the growth conditions, as extensively reported in the literature.

Free-electron to neutral-carbon acceptor (e,C) and free-exciton (E−) recombinations of GaAs are observed at 1.493 eV and 1.515 eV, respectively. As the nitrogen concentration is increased further (y=0.043 and 0.1%), the energy of the excitonic recombination from the material's band gap, E−, as well as the (e,C) recombination band start redshifting very rapidly, coexisting with and taking in the levels associated with the N complexes, whose energies do not change with N concentration. This highlights the strongly localized character of the N isoelectronic traps, contrary to that of shallow impurities, whose wavefinctions overlap at smaller concentrations (1016–1018 cm−3). Eventually, at higher N concentrations (alloy limit, y>0.1%), the GaAs1−yNy band-gap keeps redshifting along with the C-related states. The dramatic variation of the GaAs host band-gap with y is accompanied by other major effects on the electronic and optical properties of GaAs1−yNy. Indeed, with increasing N concentration, the electron effective mass increases , a sizable Stokes shift between emission and absorption is observed , the band-gap dependence on temperature and hydrostatic pressure decreases, and N resonant states move to higher energy. In the following discussion, we show that most of the above-mentioned changes can be fully and reversibly counteracted by irradiation with atomic hydrogen.

                                        ROSSANA HERNANDEZ
                              ELECTRONICA DEL ESTADO SOLIDO
             http://www.sciencedirect.com/science/book/9780080445021

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EXPERIMENTAL: HYDROGENATION AND CHARACTERIZATION TECHNIQUES

The samples considered in this review were grown by different techniques. One set of samples was grown by solid-source molecular-beam epitaxy (MBE) and consists of GaAs1−yNy/GaAs and InxGa1−xAs1−yNy/GaAs single quantum wells (QWs) having In concentration x=25 to 42%, N concentration y=0.7 to 5.2%, and QW thickness L=6.0 to 8.2 nm. MBE-grown GaAs1−y Ny/GaAs epilayers were also considered (layer thickness t=310 nm, with y <0.01 and y=0.81 and 1.3%). Another set of samples consists of four 0.5-μm-thick GaAs1−yNy/GaAs epilayers (y=0.043, 0.1, 0.21, and 0.5%) grown by metalorganic vapor-phase epitaxy [28,29]. Finally, GaP1−yNy epilayers were grown by gas-source MBE on GaP. In this case, nitrogen concentrations are y=0.05, 0.12, 0.6, 0.81, and 1.3%. The GaP1−yNy epilayer thickness is 250 nm for all samples, except for the y=1.3% epilayer, which is 750-nm thick. In all cases, the composition and layer thickness of the samples have been derived by X-ray diffraction measurements. Hydrogenation was obtained by ion-beam irradiation from a Kaufman source with the samples held at 300°C . The ion energy was about 100 eV, and the current density was a few tens of μA/cm2. Several hydrogen doses (dH=1014 to 1020 ions/cm2) were used.

Posthydrogenation thermal annealing was performed at 1.0×10−6 torr at temperatures, Ta, ranging between 220°C and 550°C and for various durations, ta, ranging between 1 and 50 h. The electronic properties of the samples were investigated mainly by means of photoluminescence (PL) spectroscopy. For InxGa1−xAs1−yNy and GaAs1−yNy samples, PL was excited by the 515-nm line of an Ar+ laser or by an Nd-vanadate laser (excitation wavelength equal to 532 nm). For GaP1− yNy, the 458-nm line of an Ar+ laser was used, instead. PL was dispersed then by a 1-m single-grating monochromator or a 0.75-m double monochromator and detected by a liquid-nitrogen-cooled Ge detector or (InGa)As linear array, or by a photomultiplier with a GaAs/Cs cathode. 

                                                ROSSANA HERNANDEZ

                                    ELECTRONICA DEL ESTADO SOLIDO

                    http://www.sciencedirect.com/science/book/9780080445021

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Local N-Environment and Fine Structure of the Band Gap

In the following, we will focus on the rearrangement of the local N environment. In many samples grown by MOVPE or MBE, there are indications of changes of the local N environment from a configuration with four Ga nearest neighbors (nn) to configurations with more In nns . This change of the local N environment can be detected by changes of the local vibrational modes of N in (Ga,In)(N,As) in Raman or infraredabsorption spectra . Very convincing evidence for such changes is obtained by Raman spectroscopy close to the E+ resonance with excitation energies of 2.18 eV  and 1.92 eV or by infrared absorption. Recently, these findings were also confirmed by X-ray absorption spectroscopy. It is worth mentioning that under certain growth and annealing conditions, there do not seem to be significant changes of the nn environment of N in (Ga,In)(N,As), i.e., the four-Ga environment dominates even after annealing .

To reach a better understanding of the effect of the nitrogen nn environment on the band structure of Ga1−yInyNxAs1−x, full sp3s* tight-binding supercell calculations have been performed, in which the central group V site was constrained to have a given number m (=0 to 4) of In nns. In atoms were placed at random on the remaining sites to give the desired overall y. The Hamiltonian was written as H1=H0+ΔH, where H0 is the Hamiltonian for (Ga,In)As, and ΔH is the change due to N incorporation. Pairs of supercells H0 and H1 were defined by placing As and N, respec-tively, onto the central group V site. Calculating separately the wavefunctions ψc0 and ψc1 for H0 and H1, one canderive a nitrogen resonant level wavefunction ψN. This allows one to relate the supercell calculations to the simple level repulsion model by VNc=<ψN |H1|ψc0>, EN=<ψN|H1|ψN>, and Ec=<ψc0|H1|ψc0>. Details of the model are given in Refs. [17,25] and Chapter 3 of this volume. These results are corroborated by other

theoretical models.

For each y, the EN for the five nn configurations are equally spaced with the value for four-Ga nns being always about 220 meV lower than that of four-In nns. Such strong dependence of the energy of isolated, strongly localized impurities on the nn environment is common. Calculations, where the atomic arrangement in the second group III shell and higher shells was altered, only shift EN by ±20 meV. This agrees with experiments on Ga(As,P):N, where a broadening of 30 meV of the localized N state is observed due to disorder on the group V sublattice. The derived matrix element VNc linking the N resonant state and the conduction band edge varies between about 2.00 eV·x1/2 for four- Ga nns to about 1.35 eV·x1/2 for four-In nns, i.e., the strength of the perturbation of the crystal decreases with increasing number of In nns. The large differences of the five nn environments of N are also reflected in the derived conduction-band-edge energies E−. For each y at x=1%, the E− values for the five nn configurations are evenly spread over an energy range of about 80 meV below the corresponding unperturbed Ec of (Ga,In)As, with that for fourGa nns being lowest in energy.

                                                 ROSSANA HERNANDEZ

                                       ELECTRONICA DEL ESTADO SOLIDO

                    http://www.sciencedirect.com/science/book/9780080445021

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TEN-BAND k·p MODEL FOR DILUTE NITRIDE ALLOYS

The k·p and envelope-function methods are widely applied to study III–V semiconductor heterostructures. The strong interaction between the N resonant states and the conduction band edge means that the conventional eight-band k·p method cannot be applied to GaInNAs and related hetero-structures. We must include the interaction between the N resonant states and the conduction band edge to describe the variation of the (zonecenter) conduction-band-edge energy with N. This leads to a modified ten-band k·p Hamiltonian for GaInNAs, with the modified Hamiltonian giving a good description of the conduction-band dispersion over an energy range at least on the order of 200 meV, sufficient for most analyses.

We illustrate this by comparing the band structure of a Ga32As32 and a Ga32N1As31 supercell in Figure a, where the dotted lines show the sp3s* band structure plotted with the spin-orbit interaction Eso set to zero. The GaAs eight-band k·p Hamiltonian reduces to a two-band Hamiltonian for the conduction and light-hole valence bands along the [0,0,1] direction when Eso=0, as illustrated by the thick solid lines, which show the dispersion of these two bands calculated using ψc0 and the light-hole zone-center wavefunction, ψlh0, as the k·p basis states. The k·p matrix elements were found by explicitly evaluating <ψi0|H(kz)|ψj0> using the tight-binding Hamiltonian . We must add the nitrogen resonant state ψN0 to the k·p Hamiltonian for Ga32NAs31. The conduction and light-hole band dispersion are then

found by diagonalizing a 3×3 k·p model. The most general form of this 3×3 Hamiltonian includes k-dependent diagonal and off-diagonal matrix elements linking the ψN0, ψc0. 

The thick solid lines in Figure b show the band structure of Ga32NAs31 calculated, where we evaluate the matrix elements directly using the tightbinding Hamiltonian. This Hamiltonian gives an excellent fit to the conduction-band dispersion within about 200 meV of the band edge. However, it is notable that the N impurity band in Figure b does not correspond to a specific higher-lying conduction b and in the supercell. This is to be expected from our analysis of resonant states in the previous section.

ROSSANA HERNANDEZ

ELECTRONICA DEL ESTADO SOLIDO

http://www.sciencedirect.com/science/book/9780080445021

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NITROGEN RESONANT STATES IN DISORDERED GaNxAs1−x STRUCTURES

Overall, clearly demonstrate that the conduction band edge in GaNxAs1−x is being perturbed and pushed downward due to its interaction with a higherlying localized resonant state, centered on the nitrogen atoms. Why, then, has this state not been identified in previous calculations? To answer this question, and to investigate the role of disorder, we extend the tight-binding and two-level model to disordered GaNxAs1−x supercells.

We first consider a set of 1000 atom supercells containing up to 15 randomly distributed N atoms. In these supercells we fit the number, but not the distribution, of NN pairs to the number given statistically, so that each cell contains n isolated N sites and p N-N pairs. For each configuration, we used the GULP molecular relaxation package [48] to calculate the equilibrium positions of all the atoms, using a parameterized valence-force-field model, while using Végard's law to vary the unit cell basis vectors as a(x)=x aGaN+(1−x) aGaAs. The calculated relaxed bond lengths are in good agreement with those obtained by other authors [46] who used an ab initio pseudopotential approach.

In a disordered supercell, we can again try to describe the GaNxAs1−x conduction band edge by a Linear Combination of Isolated Nitrogen Resonant States (LCINS) interacting with the unperturbed conduction band edge, ψc0. 

H=Ho+  Vn+ Vn-n

where H0 is the Ga500As500 Hamiltonian, ΔVN is the sum of defect potentials associated with the n isolated N atoms, and ΔVNN is the sum of defect Hamiltonians associated with the p N-N pairs. In extension of the approach for ordered structures, we now determine the GaNxAs1−x conduction band edge E− and the N-related conduction-band levels by constructing and solving a (n+2p+1)×(n+2p+1). Hamiltonian matrix involving the GaAs conduction-band-edge wavefunction, and the n+2p N-related states. 

                                             ROSSANA HERNANDEZ

                                     ELECTRONICA DEL ESTADO SOLIDO

http://www.elsevier.com/wps/find/bookdescription.cws_home/703091/description#description

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NITROGEN RESONANT STATES IN ORDERED GaNxAs1−x STRUCTURES

The BAC model explains the extreme band-gap bowing observed in InyGa1− yNxAs1−x in terms of an interaction between two levels, one at energy Ec associated with the extended onduction band edge (CBE) states of the InGaAs matrix, and the other at energy EN associated with the localized N impurity states, with the two states linked by a matrix element VNc describing the interaction between them [23]. The CBE energy of Ga(In)NxAs1−x, E−, is then given by the lower eigenvalue of the determinant

FIGURE 3.1

which showed the measured variation in E− and E+ as a function of N composition x in GaNxAs1−x. However, initial pseudopotential calculations found no direct evidence for the upper state, although they do confirm its effect on the conduction band edge, and it has more recently been identified for relatively low N compositions (x<~1%) . To investigate the resonant state, and its behavior, we have developed an accurate sp3s* tight-binding (TB) Hamiltonian to describe the electronic structure of GaInNxAs1−x . This Hamiltonian fully accounts for the observed experimental data, and also gives results in good agreement with pseudopotential calculations. Figure 3.1 shows, for instance, the variation of the band-gap energy across the full alloy range in free-standing GaNxAs1−x, calculated using the sp3s* Hamiltonian: the observed variation matches well that obtained in the literature . 

To investigate the resonant state and its behavior, we calculated the electronic structure of ordered GaNxAs1−x supercells . By comparing the calculated CBE states ψc1 and ψc0 in large supercells (Ga864N1As863 and Ga864As864, respectively), we canderive the nitrogen resonant state ψN0 associated with an isolated N atom. In the BAC model, ψc1 is a linear combination of ψc0 and ψN0. 

ROSSANA HERNANDEZ

ELECTRONICA DEL ESTADO SOLIDO

http://www.elsevier.com/wps/find/bookdescription.cws_home/703091/description#description

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Modulation Spectroscopy and Optical Excitation of Band-to- Band Transitions in Quantum-Well Structures

In QW structures, the electron and hole confinement energies as well as their subband structures are sensitive functions of the electron and hole masses. These physical properties are commonly retrieved from band-to-band optical transitions between the CB and the VB by using photoluminescence excitation (PLE), photovoltaic measurements, ora variant of modulation spectroscopy. In the latter, instead of measuring optical reflectance (or transmittance), the spectral response modified by a repetitive perturbation (e.g., light, an electric field, a heat pulse, or stress) is evaluated. This gives rise to derivativelike spectral features in the photon energy region corresponding to inter-band transitions or critical points of the band structures.

To determine me* from this experimental approach, solid knowledge on some other parameters that are also important for interband transitions is required. For example, values of conduction- and valence-band offsets at the heterointerfaces, the hole effective mass, strain field, and exact QW width should be separately obtained or self-consistently fitted or assumed. Depending on the choices of these parameters, a large uncertainty can arise in some cases. 

ROSSANA HERNANDEZ

ELECTRONICA DEL ESTADO SOLIDO

http://www.elsevier.com/wps/find/bookdescription.cws_home/703091/description#description

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FW: THEORY OF BAND ANTICROSSING

The electronic structure of highly mismatched alloys (e.g., GaNxAs1−x) can be described by considering the interaction between the localized states and extended states within the many-impurity Anderson model]. The total Hamiltonian of the system is the sum of  three terms.

The first term is the Hamiltonian of the electrons in the band states with energy dispersion The second term corresponds to the electron localized on the jth impurity site with energy The third term describes the change in the single electron energy due to the dynamic mixing between the band states and the localized states. Following Anderson's scheme, the hybridization strength is characterized by the parameter Vkj defined by Anderson.

Where a(r−j) and φd(r−j) are the Wannier function belonging to the band and the localized wavefunction of the impurity on the jth site, respectively. HHF(r) is the singleelectron energy described in the Hartree-Fock approximation.

The hybridization term produces a profound effect on the electronic structure of the system. In general, one shall consider finite but dilute concentrations of impurities, 0<x<<1. In this case, the single-site coherent potential approximation (CPA) is adequate for the manyimpurity system. In the CPA treatment, a configurational averaging is performed, neglecting correlations between positions of the impurities. Consequently, the spacetranslational invariance of the average Green's function is partially restored, and k resumes its well-defined properties as a good quantum number. In momentum space, the diagonal Green's function in CPA can be written as

The integration converges rapidly with in a small range that is proportional to x. The calculated perturbed DOS for GaNxAs1−x with several small values of x is shown in Figure 2.3. Note that the anticrossing interaction leads to a dramatic redistribution of the electronic states in the conduction band. The most striking feature of the DOS curves is the clearly seen gap between E+ and E− that evolves with increasing N content. In the Green's function calculation, the k dependence of Vkj is assumed to be weak on the momentum scale we are interested in.

There is experimental evidence indicating that the values of Vk at the L point in GaNxAs1−x and at the X point in GaNxP1−x  are about three to four times smaller than the Vk at the point. This ratio corresponds to a localized wave function decay length (ld) on the order of the lattice constant. This result indicates that the off-zone-center conduction-band minima are affected by the anticrossing interaction only when their energies are close to the localized level. This is consistent with recent measurements of the optical properties of InyGa1−yNxAs1−x alloys, which have shown that alloying with N has only very small effects on the high energy transitions at large k vectors.

ROSSANA HERNANDEZ

ELECTRONICA DEL ESTADO SOLIDO

http://www.elsevier.com/wps/find/bookdescription.cws_home/703091/description#description

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HIGH EFFICIENCY & RADIATION RESISTANT InGaP/GaAs/Ge 3-JUNCTION SOLAR CELLS

The most recent InGaP/GaAs/Ge solar cell design uses a C-doped AlGaAs/ Si-doped InGaP heterostructure tunnel junction with DH AlInP barriers, described previously. A schematic of the device is shown in figure 1 together with light-IV and  quantum efficiency results from a 1cm2 device. Such solar cells have achieved efficiencies of 31.7% (1cm x 1cm) and 31.2% (5cm x 5cm) under 1 sun AM1.5G and were fabricated by Japan Energy Co. [8]. Under AM0, a 29.2% efficient 2x2cm2 device  has been demonstrated; the light-IV.
Other notable cells include:

– InGaP/GaAs/InGaAs mechanical stack that achieved a world record 33.3% efficiency under AM1.5G, following joint work by  Japan Energy Co., Sumitomo Electric Co. and Toyota Tech. Inst.
– AlGaAs/GaAs monolithic tandem cell with a 1 sun AM1.5 efficiency of 27.6% by Hitachi Cable Co.

– GaAs/GaInAsP mechanical stack tandem cell with a 1 sun AM1.5 efficiency of 31.1% by Sumitomo Electric Co.

– InGaP/GaAs/Ge concentrator cell with an efficiency in excess of 36% for concentrations from 100-500 suns; the increase in efficiency under concentration.
Due to the series connection in the multi-junction solar cell, the radiation resistance of the cell as a whole will be dominated by the worst performing layer.

The effect of radiation damage is first a reduction in the minority carrier diffusion length followed by majority carrier removal under heavy irradiation. It is clear that the InGaP is reasonably radiation hard, maintaining a high Isc, while the Ge and GaAs junctions fall quite quickly. However, as the Ge junction is current rich, its effect on the overall multi-junction cell radiation performance is small. It is then the degradation of the GaAs junction that dominates the degradation of the multi-junction cell under irradiation. Various schemes such as thinning the emitter and base layers and field assisted collection can be employed to improve the radiation response of each sub-cell in a multi-junction device. When considering the multi-junction cell as a whole, the standard means for maintaining high efficiency is to design the solar cell such that the GaAs junction is current rich at the beginning of life (BOL) and becomes current matched to the InGaP at the end of life (EOL), as shown in figure 6. Nevertheless, this compromises the BOL efficiency, so it is desirable to replace the GaAs junction with a more radiation resistant material, such as InGaAsP.

ROSSANA HERNANDEZ

ELESCTRONICA DEL ESTADO SOLIDO

19234948

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