Franck-Condon Shift Research Articles

Photoluminescence from CdGa and HgGa acceptors in GaN

Photoluminescence from GaN implanted with Cd or Hg ions was studied and compared with first-principles calculations. In Cd-implanted GaN, the blue band (BLCd) with a maximum at 2.7 eV is attributed to the CdGa acceptor with an ionization energy of 0.55 eV. In Hg-implanted GaN, the green band (GLHg) with a maximum at 2.44 eV is attributed to the HgGa acceptor with an ionization energy of 0.77 eV. The shapes of the BLCd and GLHg bands are asymmetric, with a similar Franck–Condon shift of about 0.28 eV. The electron- and hole-capture coefficients for the CdGa and HgGa acceptors are found. The experimentally found parameters agree reasonably well with first-principles calculations using HSE hybrid functional satisfying the generalized Koopmans' theorem.

Charge state transition levels of Ni in β-Ga2O3 crystals from experiment and theory: An attractive candidate for compensation doping

Nickel-doped β-Ga2O3 crystals were investigated by optical absorption and photoconductivity, revealing Ni-related deep levels. The photoconductivity spectra were fitted using the phenomenological Kopylov and Pikhtin model to identify the energy of the zero-phonon transition (thermal ionization), Franck–Condon shift, and effective phonon energy. The resulting values are compared with the predicted ones by first-principle calculations based on the density functional theory (DFT). An acceptor level (0/−) of 1.9 eV and a donor level (+/0) of 1.1 eV above the valence band minimum are consistently determined for NiGa, which preferentially incorporates on the octahedrally coordinated Ga site. Temperature-dependent resistivity measurements yield a thermal activation energy of ∼2.0 eV that agrees well with the determined Ni acceptor level. Conclusively, Ni is an eminently suitable candidate for compensation doping for producing semi-insulating β-Ga2O3 substrates due to the position of the acceptor level (below and close to the mid-bandgap).

P-type nitrogen-doped β-Ga2O3: the role of stable shallow acceptor NO-VGa complexes.

In-depth understanding of the acceptor states and origins of p-type conductivity is essential and critical to overcome the great challenge for the p-type doping of ultrawide-bandgap oxide semiconductors. In this study we find that stable NO-VGa complexes can be formed with ε(0/-) transition levels significantly smaller than those of the isolated NO and VGa defects using N2 as the dopant source. Due to the defect-induced crystal-field splitting of the p orbitals of Ga, O and N atoms, and the Coulomb binding between NO(II) and VGa(I), an a' doublet state at 1.43 eV and an a'' singlet state at 0.22 eV above the valence band maximum (VBM) are formed for the β-Ga2O3:NO(II)-VGa(I) complexes with an activated hole concentration of 8.5 × 1017 cm-3 at the VBM, indicating the formation of a shallow acceptor level and the feasibility to obtain p-type conductivity in β-Ga2O3 even when using N2 as the dopant source. Considering the transition from NO(II)-V0Ga(I) + e to NO(II)-V-Ga(I), an emission peak at 385 nm with a Franck-Condon shift of 1.08 eV is predicted. These findings are of general scientific significance as well as technological application significance for p-type doping of ultrawide-bandgap oxide semiconductors.

Cobalt as a promising dopant for producing semi-insulating β-Ga2O3 crystals: Charge state transition levels from experiment and theory

Optical absorption and photoconductivity measurements of Co-doped β-Ga2O3 crystals reveal the photon energies of optically excited charge transfer between the Co related deep levels and the conduction or valence band. The corresponding photoionization cross sections are fitted by a phenomenological model considering electron–phonon coupling. The obtained fitting parameters: thermal ionization (zero-phonon transition) energy, Franck–Condon shift, and effective phonon energy are compared with corresponding values predicted by first principle calculations based on density functional theory. A (+/0) donor level ∼0.85 eV above the valence band maximum and a (0/−) acceptor level ∼2.1 eV below the conduction band minimum are consistently derived. Temperature-dependent electrical resistivity measurement at elevated temperatures (up to 1000 K) yields a thermal activation energy of 2.1 ± 0.1 eV, consistent with the position of the Co acceptor level. Furthermore, the results show that Co doping is promising for producing semi-insulating β-Ga2O3 crystals.

Vibronic fingerprint of singlet fission in hexacene

Singlet fission has the great potential to overcome the Shockley–Queisser thermodynamic limit and thus promotes solar power conversion efficiency. However, the current limited understandings of detailed singlet fission mechanisms hinder a further improved design of versatile singlet fission materials. In the present study, we combined ultrafast transient infrared spectroscopy with ab initio calculations to elucidate the roles played by the vibrational normal modes in the process of singlet fission for hexacene. Our transient infrared experiments revealed three groups of vibrational modes that are prominent in vibronic coupling upon photoexcitation. Through our computational study, those normal modes with notable Franck-Condon shifts have been classified as ring-twisting modes near 1300.0 cm−1, ring-stretching modes near 1600.0 cm−1, and ring-scissoring modes near 1700.0 cm−1. Experimentally, a ring-stretching mode near 1620.0 cm−1 exhibits a significant blue-shift of 4.0 cm−1 during singlet fission, which reaction rate turns out to be 0.59 ± 0.07 ps. More interestingly, the blue-shifted mode was also identified by our functional mode singlet fission theory as the primary driving mode for singlet fission, suggesting the importance of vibronic coupling when a correlated triplet pair of hexacene is directly converted from its first excited state singlet exciton. Our findings indicate that the ultrafast transient infrared spectroscopy, in conjunction with the nonadiabatic transition theory, is a powerful tool to probe the vibronic fingerprint of singlet fission.

Donor–acceptor pair emission via defects with strong electron–phonon coupling in heavily doped AlxGa1−xN:Si layers with Al content x > 0.5

We report the results of time-resolved and temperature-dependent stationary photoluminescence investigations of the defects responsible for emission in the visible spectral range in heavily silicon-doped AlxGa1–xN layers grown by molecular beam epitaxy on sapphire substrates. The emission band was attributed to donor–acceptor transitions. The transitions were described using the one-dimensional configuration coordinate model taking into account the high-doping regime. An increase in Al content from 0.56 to 1 leads to an increase in the acceptor ionization energy from 1.4 to 1.87 eV. The value of the Franck–Condon shift is about 1 eV at x = 0.56–0.74 and decreases to 0.8 eV at x > 0.74. The changes in the donor–acceptor transition energy parameters with increasing silicon concentration are discussed.

Electron paramagnetic resonance tagged high-resolution excitation spectroscopy of NV-centers in 4H -SiC

We show that electron paramagnetic resonance (EPR) tagged high resolution photoexcitation spectroscopy is a powerful method for the correlation of zero phonon photoluminescence spectra with atomic point defects. Applied to the case of NV centers in $4H$-SiC it allows to associate the photoluminescence zero phonon lines (ZPL) at 1243, 1223, 1180, and 1176 nm with the (hk, kk, hh, kh) configurations of the ${\mathrm{NV}}^{\ensuremath{-}}$centers in this material. These results lead to a revision of a previous tentative assignment. Contrary to theoretical predictions, we find that the NV centers in $4H$-SiC show a negligible Franck-Condon shift as their ZPL absorption lines are resonant with the ZPL emission lines. The high subnanometer energy resolution of this technique allows us further to resolve additional fine-structure of the ZPL lines of the axial NV centers which show a doublet structure with a splitting of 0.8 nm. Our results confirm that NV centers in $4H$-SiC provide strong competitors for sensing and qubit application due to the shift of their optical transitions into the technology compatible near-infrared region and the superior material properties of SiC. Given that single center spin readout will be realized, they are suitable for scalable nanophotonic devices compatible with optical communication network.

Origins of the Stokes Shift in PbS Quantum Dots: Impact of Polydispersity, Ligands, and Defects.

Understanding the origins of the excessive Stokes shift in the lead chalcogenides family of colloidal quantum dots (CQDs) is of great importance at both the fundamental and applied levels; however, our current understanding is far from satisfactory. Here, utilizing a combination of ab initio computations and UV-vis and photoluminescence measurements, we investigated the contributions to the Stokes shift from polydispersity, ligands, and defects in PbS CQDs. The key results are as follows: (1) The size and energetic disorder of a polydisperse CQD film increase the Stokes shift by 20 to 50 meV compared to that of an isolated CQD; (2) Franck-Condon (FC) shifts increase as the electronegativities of the ligands increase, but the variations are small (<15 meV). (3) Unlike the aforementioned two minor factors, the presence of certain intrinsic defects such as VCl+ (in Cl-passivated CQDs) can cause substantial electron density localization of the band edge states and consequent large FC shifts (100s of meV). This effect arising from defects can explain the excessive Stokes shifts in PbS CQDs and improve our understanding of the optical properties of PbS CQDs.

A first-principles study of carbon-related energy levels in GaN. I. Complexes formed by substitutional/interstitial carbons and gallium/nitrogen vacancies

Various forms of carbon based complexes in GaN are studied with first-principles calculations employing Heyd-Scuseria-Ernzerhof hybrid functionals within the framework of the density functional theory. We consider carbon complexes made of the combinations of single impurities, i.e., CN−CGa, CI−CN, and CI−CGa, where CN, CGa, and CI denote C substituting nitrogen, C substituting gallium, and interstitial C, respectively, and of neighboring gallium/nitrogen vacancies (VGa/VN), i.e., CN−VGa and CGa−VN. Formation energies are computed for all these configurations with different charge states after full geometry optimizations. From our calculated formation energies, thermodynamic transition levels are evaluated, which are related to the thermal activation energies observed in experimental techniques such as deep level transient spectroscopy. Furthermore, the lattice relaxation energies (Franck-Condon shift) are computed to obtain optical activation energies, which are observed in experimental techniques such as deep level optical spectroscopy. We compare our calculated values of activation energies with the energies of experimentally observed C-related trap levels and identify the physical origins of these traps, which were unknown before.

Photocapacitance spectroscopy of InAlN nearly lattice-matched to GaN

We study the deep levels in InAlN nearly lattice-matched to GaN by photocapacitance spectroscopy. This technique allows the study of very deep levels having too slow thermal emission rates to be detected by other deep level spectroscopy techniques. We will identify a broad band of deep levels centered 1.7 eV below the InAlN conduction band edge. The deep level band is characterized by a negligible Franck-Condon shift and by a broadening parameter ΔE = 0.38 eV. Furthermore, we will show evidences for a second class of deep levels with optical ionization energy &amp;gt;2 eV, which will be attributed to previously reported oxygen-related DX centers.

Characteristic Energies and Shifts in Optical Spectra of Colloidal IV−VI Semiconductor Nanocrystals

We investigate structural, electronic, and optical properties of colloidal IV-VI semiconductor quantum dots (QDs) using an ab initio pseudopotential method and a repeated supercell approximation. In particular, rhombo-cuboctahedral quantum dots consisting of PbSe, PbTe, and SnTe with a pseudohydrogen passivation shell are investigated for different QD sizes. The obtained dependence of the confinement energy on the QD size questions the use of three-dimensional spherical potential well models for small QD structures. The predicted band gaps are almost in agreement with measured values. The calculated Franck-Condon shifts vary significantly with the QD size. Only for PbSe they may explain the Stokes shift between optical absorption and emission. For the tellurides, spectral properties such as the oscillator strength are more important.

Deep level investigation of p-type GaN using a simple photocurrent technique

The deep level spectrum of p-type GaN was investigated using time-resolved photocurrent spectroscopy. The spectral dependence of the optical cross section for hole photoemission from a deep level was determined from the initial value of the photocurrent transient. Unlike other implementations of photocurrent, the present method does not require multiple excitation sources or determination of the optical emission rate. A deep level was observed at Ev+1.84 eV, where Ev is the valence band maximum, with a Franck-Condon shift of 0.25 eV. A bias-dependent component of the photocurrent, possibly due to metal-semiconductor interface states, complicated the steady-state response but did not affect the measured spectrum for the Ev+1.84 eV deep level. This photocurrent method is expected to be readily extended to materials with very deep dopants, such as p-type AlGaN, for which many other deep level spectroscopy techniques are unsuited.

Measurements of optical cross sections of the carbon vacancy in 4H-SiC by time-dependent photoelectron paramagnetic resonance

Time-dependent photoinduced electron paramagnetic resonance measurements have been made on high purity semi-insulating 4H-SiC to develop a more complete understanding of the optical transitions of the positively charged carbon vacancy VC+. The single defect model originally proposed is given validity by demonstrating that the time dependence of the photoinduced changes in VC+ may be fitted by a first order kinetic process. In addition, the photon energy dependence of the optical cross sections for capture and emission of electrons from VC+ is extracted by incorporating both processes into one expression for charge transfer. The data are interpreted by considering the role of the electronic density of states as well as participation of phonons. Analysis assuming only phonon participation yields thermal and optical energies of 1.6 and 2.15 eV, respectively, for charge transitions between VC+ and one of the band edges. Charge transfer between VC+ and the opposite band edge is associated with a thermal and an optical energy of 1.9 and 2.45 eV, respectively. An upper limit for the Franck–Condon shift of 0.55 eV is extracted from the difference between the thermal and optical energies.

Structural and electronic properties of PbSe nanocrystals from first principles

This work reports density-functional calculations of the structural and electronic properties of PbSe nanocrystals ranging in radius from 8.4 to 14.8 {angstrom}. We considered nearly spherical, rocksalt-structure nanocrystals with 1:1 Pb:Se stoichiometry and no molecular species adsorbed at the surface. We found that: (1) The Pb-Se bond lengths and bond angles are significantly distorted compared to those in bulk PbSe, in an {approx} 8-{angstrom}-thick shell near the surface of the nanocrystal. (2) Even in the absence of surface passivants, there are no surface states in the band gap of the nanocrystals. (3) The nanocrystal band gap undergoes a significant redshift (Franck-Condon shift) when an electron is promoted from the valence band to the conduction band. For nanocrystals of radius R=8.4 {angstrom}, the calculated Franck-Condon shift is {approx}0.18 eV. (4) The calculated electronic density of states shows a significant asymmetry between valence and conduction states, suggesting that the postulated 'mirror symmetry' between valence band and conduction band does not exist.

Novel deep centers for high-performance optical materials

Materials exhibiting strong optical emission also exhibit strong absorption at the same wavelengths because both emission and absorption are governed by the same optical dipole and density-of-states. Laser action requires a carrier injection large enough for emission to exceed absorption at laser wavelengths. Thus, strong self-absorption at luminescent wavelengths raises the operating current of LEDs, lasers, and optical amplifiers. Here we demonstrate that, contrary to conventional expectations, materials designed with novel deep centers achieve surprisingly large optical emission while, simultaneously, the inverse process of optical absorption remains very small. A striking consequence is that materials designed with our novel deep centers achieve transparency at a carrier injection which is four-orders-of-magnitude lower than in all technologically important semiconductors. Simultaneously, and surprisingly, our novel deep centers in GaAs achieve an optical gain, Einstein B coefficient, and radiative efficiency significantly larger than in direct-band-gap materials at 1.3–1.5 μm. We engineered this dramatic reduction of the injection to achieve transparency while retaining strong optical emission in our novel material by making use of a Franck–Condon shift of absorption away from luminescent wavelengths.

The nature of the green luminescence band in zinc selenide crystals

This paper analyzes the features of the behavior of the green luminescence band of diffusion layers of ZnSe:Te, in which it is dominant. As a result of a detailed study of the emission, transmission, and reflection, it is established that deep-lying levels at 0.2 eV participate in its formation. It correlates with the ionization energy of acceptor centers of singly charged zinc vacancies, whose concentration in the objects of interest can reach 1021 cm−3. The experimental data are used as a basis for calculating the Franck-Condon shift, which equals 0.08 eV for the indicated centers.

Optical cross sections of deep levels in 4H-SiC

We have characterized deep levels in 4H-SiC epilayers grown by cold wall chemical vapor deposition by the deep level transient spectroscopy (DLTS) and the optical-capacitance-transient spectroscopy (O-CTS). Four kinds of DLTS peaks were detected in the epilayers. Three of them are identified as the Z1∕2, EH6∕7, and RD1∕2 centers, while the other one has never been reported previously, and was named the NB center. On the basis of these DLTS data we have estimated the thermal ionization energies. The classical optical ionization energies of these centers, which are given by the sums of thermal ionization energies and Franck-Condon shifts, were estimated via fittings of the measured optical cross sections from O-CTS data by means of a sufficiently general theoretical model. Temperature dependences of nonradiative multiphonon carrier capture cross sections for the Z1∕2 and NB centers were roughly estimated in terms of parametrical dependences on thermal ionization energies and Franck-Condon shifts.

Large Dynamic Stokes Shift of DNA Intercalation Dye Thiazole Orange has Contribution from a High-Frequency Mode

Fluorescence of the cyanine dye Thiazole Orange (TO) is quenched by intramolecular twisting in the excited state. In polypeptide nucleic acids, a vibrational progression in a 1400 cm(-1) mode depends on base pairing, from which follows that the high-frequency displacement is coupled to the twist coordinate. The coupling is intrinsic to TO. This is shown by femtosecond fluorescence upconversion and transient absorption spectroscopy with the dye in methanol solution. Narrow emission from the Franck-Condon state shifts to the red and broadens within 100 fs. The radiative rate does not decrease during this process. Vibrational structure builds up on a 200 fs time scale; it is assigned to asymmetric stretching activity in the methine bridge. Further Stokes shift and decay are observed over 2 ps. Emission from the global S(1) minimum is discovered in an extremely wide band around 12 000 cm(-1). As the structure twists away from the Franck-Condon region, the mode becomes more displaced and overlap with increasingly higher vibrational wave functions of the electronic ground state is achieved. Twisting motion is thus leveraged into a fast-shrinking effective energy gap between the two electronic states, and internal conversion ensues.

Density-functional studies of excited states of silicon nanoclusters

The molecular structures of ${\mathrm{Si}}_{29}{\mathrm{H}}_{24}$, ${\mathrm{Si}}_{29}{\mathrm{H}}_{36}$, and ${\mathrm{Si}}_{35}{\mathrm{H}}_{36}$ clusters in the ground state as well as in the lowest singlet and triplet excited states have been studied at the density-functional theory level using the first-order linear-response-theory approach for the singlet excited state. Structural changes compared to the ground state due to Franck-Condon relaxation of the singlet excited state are small, whereas optimization of the lowest triplet state is found to result in a dissociation of a $\mathrm{Si}\mathrm{Si}$ bond. The electronic excitation spectra up to $5\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ for the ground-state and excited-state structures of the silicon nanoclusters are also reported. The obtained Franck-Condon shift for the first excited state of ${\mathrm{Si}}_{29}{\mathrm{H}}_{36}$ is $0.70\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, yielding a luminescence energy of $3.14\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ which is in good agreement with experimental data. The Franck-Condon shifts for ${\mathrm{Si}}_{29}{\mathrm{H}}_{24}$ and ${\mathrm{Si}}_{35}{\mathrm{H}}_{36}$ are found to be 1.17 and $1.67\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, yielding emission energies of 1.57 and $2.03\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, respectively, which are significantly smaller than the experimental value of about $3\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. Thus, the present study supports the notion that the silicon nanoclusters fabricated through electrochemical etching consist of 29 Si atoms surrounded by 36 hydrogen atoms.

Characterization of deep levels in n‐GaN by combined capacitance transient techniques

AbstractDeep centers in undoped n‐GaN grown by Hydride Vapor Phase Epitaxy were characterized by Deep Level Transient Spectroscopy (DLTS), revealing four known levels with activation energies in the range 0.17–0.94 eV. Deeper levels in the bandgap were observed by photocapacitance (PHCAP) experiments. A correspondence can be established for the dominant DLTS level observed both by thermal and optical experiments, exploiting the temperature as a key parameter in PHCAP measurements. The Franck–Condon shift dF–C for this level was estimated around 0.33 eV, in close agreement with results obtained by Hacke and coworkers in a more elaborate way. The tentative assignment of most levels is discussed on the basis of literature, pointing out unsettled origins for some of them. (© 2005 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)