Haynes Rule Research Articles

Electronic Structure of Biexcitons in Metal Halide Perovskite Nanoplatelets.

A theoretical description of biexcitons in metal halide perovskite nanoplatelets is presented. The description is based on a variational effective mass model, including polaronic effects by means of a Haken potential. The strong quantum and dielectric confinements are shown to squeeze the biexciton under the polaronic radius, which greatly enhances Coulomb attractions and (to a lesser extent) repulsions. This explains the need for effective dielectric constants approaching the high-frequency limit in previous simulations, and the binding energies exceeding 40 meV observed in single-monolayer nanoplatelets. Biexcitons are formed by a pair of weakly interacting excitons, with a roughly rectangular geometry. This translates into a constant ratio between biexciton and exciton binding energies (2D Haynes rule) well below the ideal value of ΔBX/ΔX = 0.228 proposed for squared biexcitons. The ratio is independent of the number of monolayers in the platelet, but it does depend on the lateral and dielectric confinement.

Origin of blue luminescence in Mg-doped GaN

In this work, dual acceptor-bound exciton peaks are observed by low-temperature photoluminescence. The peaks correspond to the dual Mg-related acceptor levels in GaN based on the Haynes rule. By calibrating the energy-level structure, a mechanism for the origin of blue luminescence (BL) in Mg-doped GaN is proposed. The BL band is separated by thermal treatment at different temperatures, confirming the rationality of the dual-factor origin of the BL band. As the annealing temperature increases, the PL spectrum and the p-type conductivity of Mg-doped GaN also change. The experimental results indicate that there is not necessarily a relationship between the BL band and p-type conductivity in GaN grown by metalorganic chemical vapor deposition.

Shallow donor complexes formed by pairing of double-donor magnesium with group-III acceptors in silicon

Magnesium in silicon primarily occupies an interstitial site, where it acts as a moderately deep double donor. It has recently been shown that interstitial magnesium can pair with the substitutional acceptor boron to form a shallow single-donor center. In this work, we demonstrate analogous complexing with the other group-III acceptors Ga, In, and Al. We observe the odd-parity excited states of each shallow donor complex in absorption spectra, from which the ionization energies are obtained. These complexes can localize excitons, and we observe the donor bound exciton transitions of all four centers in photoluminescence spectra. The Mg-acceptor complexes are found to obey Haynes rule, which predicts a linear relationship between donor ionization energy and donor bound exciton localization energy.

High-resolution photoluminescence spectroscopy of Sn-doped ZnO single crystals

Group IV donors in ZnO are poorly understood, despite evidence that they are effective n-type dopants. Here we present high-resolution photoluminescence (PL) spectroscopy studies of unintentionally doped and Sn-doped ZnO single crystals grown by the chemical vapor transport method. Doped samples showed greatly increased emission from the I10 bound exciton transition that was recently proven to be related to the incorporation of Sn impurities based on radio-isotope studies. The PL linewidths are exceptionally sharp for these samples, enabling a clear identification of several donor species. Temperature-dependent PL measurements of the I10 line emission energy and intensity dependence reveal a behavior that is similar to other shallow donors in ZnO. Ionized donor bound-exciton and two-electron satellite transitions of the I10 transition are unambiguously identified and yield a donor binding energy of 71meV. In contrast to recent reports of Ge-related donors in ZnO, the spectroscopic binding energy for the Sn-related donor bound exciton follows a linear relationship with donor binding energy (Haynes rule) similar to recently observed carbon related donors, and confirming the shallow nature of this defect center, which was recently attributed to a SnZn double donor compensated by an unknown single acceptor.

Influence of local magnetization on acceptor-bound complex state in Hg1−xMnxTe single crystals

We performed temperature-dependent magnetic measurements and infrared photoluminescence (PL) measurements in various geometries on a series of p-type Hg1–xMnxTe single crystals (0.20≤x≤0.26). Evolution of PL features was observed, and zero-field spin splitting was identified for the acceptor-bound magnetic polaron (A0BMP). The results show direct evidence for local spontaneous magnetization of the A0BMP. Comparison with the Ditel–Spałek model indicates that besides the fluctuation and collective regimes, the A0BMP exhibits a new regime at low temperatures owing to the formation of the spin-glass state in Hg1−xMnxTe. The dissociation energy of the exciton bound to the A0BMP ((A0,X)BMP) varied rapidly with temperature, and the ratio of the dissociation energy of the (A0,X)BMP to the binding energy of the A0BMP was larger than the classical value of the A0X and no longer a constant, which breaks the Haynes rule. The free exciton localization process helps enhance the local magnetization of the (A0,X)BMP by transferring energy from the carrier system to the Mn-spin system, and it may lead to a photoinduced configuration of non-interacting ferromagnetic domains or the photoinduced magnetization effect.

Size dependence of the polarizability and Haynes rule for an exciton bound to an ionized donor in a single spherical quantum dot

We study the effect of an external electric field on an exciton bound to an ionized donor (D+, X) confined in a spherical quantum dot using a perturbative-variational method where the wave function and energy are developed in series of powers of the electric field strength. After testing this new approach in the determination of the band gap for some semiconductor materials, we generalize it to the case of (D+, X) in the presence of the electric field and for several materials ZnO, PbSe, and InAs, with significant values of the mass ratio. Three interesting results can be deduced: First, we show that the present method allows to determine the ground state energy in the presence of a weak electric field in a simple way (E = E0 − αf2) using the energy without electric field E0 and the polarizability α. The second point is that our theoretical predictions show that the polarizability of (D+, X) varies proportionally to R3.5 and follows an ordering αD0<αX<α(D+,X). The last point to highlight is that the Haynes rule remains valid even in the presence of a weak electric field.

Decrease in the binding energy of donors in heavily doped GaN:Si layers

The properties of Si-doped GaN layers grown by molecular-beam epitaxy from ammonia are studied by photoluminescence spectroscopy. It is shown that the low-temperature photoluminescence is due to the recombination of excitons bound to donors at Si-atom concentrations below 1019 cm−3. At a Si-atom concentration of 1.6 × 1019 cm−3, the band of free excitons is dominant in the photoluminescence spectrum; in more heavily doped layers, the interband recombination band is dominant. A reduction in the binding energy of exciton-donor complexes with increasing doping level is observed. With the use of Haynes rule, whereby the binding energy of the complex in GaN is 0.2 of the donor ionization energy ED, it is shown that ED decreases with increasing Si concentration. This effect is described by the dependence {ie1134-1}, where EDotp is the ionization energy of an individual Si atom in GaN. The coefficient that describes a decrease in the depth of the impurity-band edge with increasing Si concentration is found to be α = 8.4 × 10−6 meV cm−1.

Photoluminescence studies of ZnO films fabricated by using a combination of a hydrothermal method and plasma-assisted molecular beam epitaxy regrowth

ZnO films were deposited on Si (100) substrates by using a two-step growth process. In the first step, ZnO nanorods were grown by using the hydrothermal method at 140 °C for 5 min. In the second step, a ZnO amorphous layer was deposited on the ZnO nanorods by spin-coating. After completion of the growth process, the films were annealed at 800 °C for 10 min, and a ZnO active layer was deposited on top of the amorphous layer by using plasma-assisted molecular beam epitaxy. Further, temperature-dependent photoluminescence (PL) measurement were conducted to study the optical properties of the prepared films. In the low-temperature PL spectra, emission peaks in the near-band-edge region were observed at 3.370, 3.362, 3.347, 3.329, 3.317, 3.288, 3.263, 3.219, 3.191, and 3.116 eV; these peaks were attributed to free excitons, neutral donor bound excitons, neutral acceptor donor excitons, two electron satellites, and donor acceptor pairs, respectively. These peaks were red-shifted, and their intensity decreased with increasing temperature. The binding energy of the donor was calculated as 43.1 meV by using the Haynes rule. Further, the value α and β, factors in the equation for the energy of localized excitons of donors and acceptors were obtained as 0.73 meV and 750 K, respectively, by fitting the free exciton (FX) peak according to Varshni’s equation. The full width at half-maximum of PL for the films was about 95.1 meV at room temperature; moreover, the following values were obtained for the films by using theoretical equations: the background impurity broadening, Γ0 = 62 meV, the parameter describing exciton-LO phonon interaction, Γ LO = 80 meV, LO phonon energy, ħω LO = 72 meV, and, the coupling strength of an exciton-acoustic phonon interaction, γ ph = 0.087 meV/K Furthermore, the activation energy was about 60.1 meV.

Arsenic-bound excitons in diamond

A set of new excitonic recombinations is observed in arsenic-implanted diamond. It is composed of two groups of emissions at 5.355/5.361 eV and at 5.215/5.220/5.227 eV. They are respectively attributed to the no-phonon and transverse-optical phonon-assisted recombinations of excitons bound to neutral arsenic donors. From the Haynes rule, an ionization energy of 0.41 eV is deduced for arsenic in diamond, which shows that arsenic is a shallower donor than phosphorus (0.6 eV), in agreement with theory.

Studies on temperature- and excitation-power-dependent photoluminescence of ZnO thin film grown by plasma-assisted molecular beam epitaxy

The temperature- and excitation-power-dependence of near-edge emission in a ZnO thin film were studied. The near-band-edge emission peaks at 3.370, 3.355, 3.338, 3.305, 3.254, 3.184, 3.112, and 3.042 eV were attributed to the emission of free excitons (FX); neutral-donor-bound excitons (D0X); neutral-acceptor or deep donor excitons; two-electron satellites (TES); donor–acceptor pairs (DAP); and the first-order longitudinal optical (1LO) phonon replica of DAP (DAP-1LO), DAP-2LO, and DAP-3LO, respectively. According to Haynes's rule, the factors a and b are 0.3 and 5 meV, respectively (Eloc = 0.3ED + 5 meV). The temperature dependence of the FX transition energy was analyzed using both Varshni's formula and Cody's formula for the variation in the band gap with temperature. Varshni's formula yielded a good fit for FX emission. The dependence of the photoluminescence intensity I on the excitation power L can be described by a power law, i.e., I ∼ Lα, where α is an exponent. Our results show that α is 0.86 for D0X and 0.63 for DAP.

Calibration of the photoluminescence technique for measuring concentrations of shallow dopants in Ge

A systematic study of the photoluminescence (PL) from excitons bound to shallow donors or acceptors in Al-, As-, B-, Ga-, In-, P-, and Sb-doped Ge is presented. The results of the PL measurements are correlated with those from photothermal ionization spectroscopy and Hall effect measurements. The dissociation energy of the excitons is shown to satisfy Haynes rule. A calibration is presented, which allows a determination of the donor and acceptor concentrations from their respective bound exciton intensities related to the free exciton intensity.

Optical signature of Mg-doped GaN: Transfer processes

Mg doping of high quality, metal organic chemical vapor deposition grown GaN films results in distinct traces in their photoluminescence and photoluminescence excitation spectra. We analyze GaN:Mg grown on sapphire substrates and identify two Mg related acceptor states, one additional acceptor state and three donor states that are involved in the donor-acceptor pair band transitions situated at 3.26--3.29 eV in GaN:Mg. The presented determination of the donor-acceptor pair band excitation channels by photoluminescence excitation spectroscopy in conjunction with temperature-dependent photoluminescence measurements results in a direct determination of the donor and acceptor binding, localization, and activation energies, which is put into a broader context based on Haynes's rule. Furthermore, we analyze the biexponential decay dynamics of the photoluminescence signal of the acceptor and donor bound excitons. As all observed lifetimes scale with the localization energy of the donor and acceptor related bound excitons, defect and complex bound excitons can be excluded as their origin. Detailed analysis of the exciton transfer processes in the close energetic vicinity of the GaN band edge reveals excitation via free and bound excitonic channels but also via an excited state as resolved for the deepest localized Mg related acceptor bound exciton. For the two Mg acceptor states, we determine binding energies of 164 $\ifmmode\pm\else\textpm\fi{}$ 5 and 195 $\ifmmode\pm\else\textpm\fi{}$ 5 meV, which is in good agreement with recent density functional theory results. This observation confirms and quantifies the general dual nature of acceptor states in GaN based on the presented analysis of the photoluminescence and photoluminescence excitation spectra.

New Results on the Bound Exciton Luminescence in Germanium

Photoluminescence from excitons bound to shallow donors or acceptors was studied in Al-, As-, B-, Ga- and P-doped Ge. Excitons bound to Al and B acceptors were identified for the first time. The dissociation energy of the excitons satisfies Haynes rule and changes with a factor of 0.1 linearly with the ionization energy of the dopants.

Photoluminescence of ZnO:Sb nanobelts fabricated by thermal evaporation method

Uniform ZnO nanobelts (NBs) were synthesized by a facile thermal evaporation method. Recombination mechanism of acceptor-related emissions in Sb doped ZnO NBs was investigated by temperature-dependent photoluminescence (PL) spectra. UV near-band-edge (NBE) emissions were dominant by acceptor-bound exciton (A 0X) at 3.358 eV and free electron-to-acceptor (FA) at 3.322 eV transitions at 81 K. Studies on A 0X intensity showed a quenching channel, the thermal dissociations of A 0X to a free exciton and electron hole pair with the temperature increase. The active energy of A 0X was estimated to be 19 meV using thermal quenching formula. The acceptor ionization energy was calculated to be 190 meV using Haynes rule. These results were very similar to those of antimony or phosphorus doped ZnO films.

Growth ambient dependent electrical properties of lithium and nitrogen dual-doped ZnO films prepared by radio-frequency magnetron sputtering

Lithium (Li) and nitrogen (N) dual-doped ZnO films with wurtzite structure were prepared by radio-frequency magnetron sputtering ZnO target with Li 3N in growth ambient of pure Ar and the mixture of Ar and O 2, respectively, and then post annealing techniques. The film showed week p-type conductivity as the ambient was pure Ar, but stable p-type conductivity with a hole concentration of 3.46 × 10 17 cm − 3 , Hall mobility of 5.27 cm 2/Vs and resistivity of 3.43 Ω cm when the ambient is the mixture of Ar and O 2 with the molar ratio of 60:1. The stable p-type conductivity is due to substitution of Li for Zn (Li Zn) and formation of complex of interstitial Li (Li i) and substitutional N at O site, the former forms a Li Zn acceptor, and the latter depresses compensation of Li i donor for Li Zn acceptor. The level of the Li Zn acceptor is estimated to be 131.6 meV by using temperature-dependent photoluminescence spectrum measurement and Haynes rule. Mechanism about the effect of the ambient on the conductivity is discussed in the present work.

Photoluminescence and acceptor level state of p-type nitrogen-doped MgZnO films

A wurtzite nitrogen-doped MgZnO (MgZnO:N) film was grown by plasma-assisted molecular-beam epitaxy (PAMBE) on c-plane sapphire using radical NO as oxygen source and nitrogen dopant. The as-grown film shows n-type conduction at room temperature, but transforms into p-type conduction after annealed. Photoluminescence (PL) spectrum measured at 80 K is dominated by neutral donor-bound exciton emission (D0X) located at 3.522 eV for the n-type MgZnO:N film, but by neutral acceptor-bound exciton emission (A0X) located at 3.515 eV for the p-type MgZnO:N film. By fitting exciton emission intensity of temperature-dependent PL spectra, the binding energies of the D0X and A0X were estimated to be 32 and 43 meV, respectively. Based on the energy shift of exciton emission, the band gap of the MgZnO:N film is estimated to be 3.613 eV, which is 179 meV larger than that of ZnO. Using the Haynes rule, the acceptor energy level of the MgZnO:N film was evaluated to be about 176 meV above the valence band.

수직 Bridgman 법에 의한 CdTe 단결정 성장과 특성

High quality CdTe single crystal for the solar cell fabrication was grown by vertical Bridgman method. The etch pits patterns of (111) surfaces of CdTe etched by Nakagawa solution was observed the (111)A compesed of Cd atoms with typical triangle etch pits of pyramid mode. From the photoluminescence measurement on (111)A, we observed free exciton (<TEX>$E_{x}$</TEX>) existing only high quality crystal and neutal acceptor bound exciton (<TEX>$A^{0}$</TEX>,X) having very strong peak intensity. Then, the full width at half maximum and binding energy of neutral acceptor bound exciton were 7 meV and 5.9 meV, respectively. By Haynes rule, an activation enery of impurity was 59 meV. Therefore, the origins on impurity level acting as a neutral acceptor were associated Ag or Cu elements.

Photoluminescence investigations on a native donor in ZnO

ABSTRACTThe shallow donor impurities in ZnO with binding energies between 46 and 56 meV have been studied in great detail in the recent years. They give rise to neutral donor bound exciton recombinations with the A- and B-valence bands, show rotator states and two-electron-satellite transitions. These properties allowed to establish the excited state splittings of the donors as well as confirming Hayne's rule in ZnO. So far they all seem to be of extrinsic origin, hydrogen, aluminum, gallium and indium in order of increasing binding energy. For many years it was common sense that intrinsic defects would dominate the n-type conductivity of ZnO. Interstitial zinc as well as oxygen vacancies should be double donors, and in order to contribute to the n-type-conduction they should have shallow levels, and low formation energies to be abundant. In PL-measurements at T∼100 K on various ZnO samples, single crystals as well as thin films, a luminescence around 3.31 eV was detected. Due to its line shape and temperature behaviour it is identified as bound-to-free recombination. If we assume that the 3.31 eV band with its level at EC ∼ 130 meV is the ++/+ level of the zinc interstitial we calculate for the binding energy of the +/0 level ∼ 130 meV, i.e. around 33 meV. Undoped Zn-rich epitaxial films grown by CVD show a dominant I3 recombination at 3.367 eV which according to Haynes rule is consistent with a shallow donor level at 33 meV. Moreover, they have free n-type carrier densities of 2×1019 cm−3 and as revealed by SIMS the common donor impurities (Al, Ga, In) cannot account for the high carrier densities.

On the validity of Haynes rule for the binding of excitonic complexes in low dimensions

Using a two-dimensional geometrical model and fractional dimension approach, it is found analytically that the ratio of the binding energy of a biexciton to that of an exciton is 0.228 in quantum wells and it is independent of the quantum-well width. This agrees very well with the results in GaAs and ZnSe quantum wells, and CuCl crystals and large quantum dots. It is suggested that, while Haynes rule may be valid for bulk, much higher ratios may be expected in lower dimensions.

Shallow donors in epitaxial GaN

Photoluminescence (PL) of GaN is commonly dominated by the annihilation of excitons bound to a 34.5 meV deep donor appearing at 3.472 eV (for strain free GaN at 4 K). With PL we were able to resolve two additional donor bound exciton transitions. The excitons have localization energies of 3.7 ± 0.3 and 11.3 ± 05 meV, respectively. Using Haynes rule the respective donors lie 56.5 and 18.5 meV below the conduction band. The applicability of Haynes rule could nicely be confirmed by IR absorption where the 1s-2p transition of the 34.5 and 58 meV donor are observed. The issue of residual donors in GaN will be discussed in this context.