Nonradiative Multiphonon Research Articles

In-Depth Understanding of Nitridation-Induced Endurance Enhancement in FeFETs: Defect Properties and Dynamics Characterized by Nonradiative Multi-Phonon Model

In-Depth Understanding of Nitridation-Induced Endurance Enhancement in FeFETs: Defect Properties and Dynamics Characterized by Nonradiative Multi-Phonon Model

Comphy v3.0—A compact-physics framework for modeling charge trapping related reliability phenomena in MOS devices

Charge trapping plays an important role for the reliability of electronic devices and manifests itself in various phenomena like bias temperature instability (BTI), random telegraph noise (RTN), hysteresis or trap-assisted tunneling (TAT). In this work we present Comphy v3.0, an open source physical framework for modeling these effects in a unified fashion using nonradiative multiphonon theory on a one-dimensional device geometry. Here we give an overview about the underlying theory, discuss newly introduced features compared to the original Comphy framework and also review recent advances in reliability physics enabled by these new features. The usefulness of Comphy v3.0 for the reliability community is highlighted by several practical examples including automatic extraction of defect distributions, modeling of TAT in high-κ capacitors and BTI/RTN modeling at cryogenic temperatures.

Optical cooling at the optimal SPR angle of a glass–ITO–CdSe/ZnS(QDs) interface

In practice, cooling effects must dominate over heating associated with nonradiative decay and multiphonon emission to attain optical cooling in semiconductors. Although quantum confinement nanostructures (e.g., quantum dots [QDs]) have been used to reduce the self-absorption of anti-Stokes luminescence, their low quantum efficiency precludes high light extraction, thus reducing net cooling generation. Superficial plasmon resonance (SPR) generated in some metal–dielectric interfaces provides an efficient way to tune and enhance the optical properties and photoluminescence (PL) of QDs. In this work, the optimal SPR angle (θSPR) was used to enhance the PL of CdSe/ZnS core–shell QDs, and hence their cooling properties, in a glass–indium tin oxide–QD interface. Three excitation wavelengths (λexc = 405, 532, and 640 nm) were used to evaluate the cooling properties. The best results were obtained when λexc = 640 nm. A PL increment and temperature decrement (Δt) of 2-fold and 4 °C, respectively, were obtained at θSPR in 50 min due to the generation of anti-Stokes PL by the QDs and the enlargement of such generated PL because of the presence of the SPR effect at the interface.

Charge Trapping and Emission Properties in CAAC-IGZO Transistor: A First-Principles Calculations.

The c-axis aligned crystalline indium-gallium-zinc-oxide field-effect transistor (CAAC-IGZO FET), exhibiting an extremely low off-state leakage current (~10-22 A/μm), has promised to be an ideal candidate for Dynamic Random Access Memory (DRAM) applications. However, the instabilities leaded by the drift of the threshold voltage in various stress seriously affect the device application. To better develop high performance CAAC-IGZO FET for DRAM applications, it's essential to uncover the deep physical process of charge transport mechanism in CAAC-IGZO FET. In this work, by combining the first-principles calculations and nonradiative multiphonon theory, the charge trapping and emission properties in CAAC-IGZO FET have been systematically investigated. It is found that under positive bias stress, hydrogen interstitial in Al2O3 gate dielectric is probable effective electron trap center, which has the transition level (ε (+1/-1) = 0.52 eV) above Fermi level. But it has a high capture barrier about 1.4 eV and low capture rate. Under negative bias stress, oxygen vacancy in Al2O3 gate dielectric and CAAC-IGZO active layer are probable effective electron emission centers whose transition level ε (+2/0) distributed at -0.73~-0.98 eV and 0.69 eV below Fermi level. They have a relatively low emission barrier of about 0.5 eV and 0.25 eV and high emission rate. To overcome the instability in CAAC-IGZO FET, some approaches can be taken to control the hydrogen concentration in Al2O3 dielectric layer and the concentration of the oxygen vacancy. This work can help to understand the mechanisms of instability of CAAC-IGZO transistor caused by the charge capture/emission process.

Single- Versus Multi-Step Trap Assisted Tunneling Currents—Part II: The Role of Polarons

Using the framework developed in the first part of this work, we demonstrate the capabilities of the extended two-state nonradiative multi-phonon (NMP) model by reproducing leakage current characteristics of two selected technologies. First, we identify the temperature-activated leakage mechanism in SiC / SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> stacks using a tens of nanometer thick thermally grown oxide as trap-assisted tunneling (TAT) through defects. Interestingly, this effect can be reproduced with the same parameters in a SiC / SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> stack with deposited oxide. Our simulations demonstrate that these charge transition centers are distributed within only a few nanometers from the SiC / SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> interface. The low thermal activation of the leakage current is linked to the low relaxation energies of the involved traps compared with those typically involved in bias temperature instability (BTI) and Random Telegraph Noise (RTN). Second, a similar mechanism can explain TAT characteristics and transient charge trapping currents in Metal–Insulator–Metal (MIM) capacitors with a ZrO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> insulating layer. By comparison of our model parameters to theoretical density functional theory (DFT) calculations, we identify self-trapped electrons (polarons) as a likely cause for these effects, as they have the required low relaxation energies.

Single- Versus Multi-Step Trap Assisted Tunneling Currents—Part I: Theory

Leakage currents through dielectrics in modern logic, memory, and power devices, and back-end interlevel layers can severely increase the time-zero power dissipation and shorten the lifetime of the material structure. Depending on thickness, material properties, and fabrication quality, different conduction mechanisms through the insulating layer, such as band-to-band and trap-assisted tunneling (TAT) are observed. These leakage currents can be distinguished by their dependence on electric field strength, temperature, and their transient characteristics. The identification of the underlying mechanisms is of utmost importance for the selection of suitable dielectrics and optimization of device processing. In this work, we present a nonradiative multiphonon model which extends our compact physics (Comphy) reliability framework to also account for TAT. The model is based on a single physical defect parameter set from which charge transfer kinetics between charge carrier reservoirs and oxide defects (single-TAT) as well as between the defects (multi-TAT) can be derived. We thereby demonstrate that the thermal barrier for inelastic defect–defect carrier tunneling is approximately twice as large in comparison to reservoir-defect interaction and further show in which parameter regime multi-TAT plays a role. Our results show that multi-TAT currents are a less important contribution to the overall tunnel current than previously assumed.

On the accuracy of the formula used to extract trap density in MOSFETs from 1/f noise

Noise spectroscopy is a powerful non-destructive technique to characterize the quality of gate dielectrics in MOSFETs. Trap densities are routinely extracted by fitting the 1/f part of the drain current noise spectrum with a widely known analytical expression containing several approximations within. This paper compares this 1/f noise analytical expression with microscopic simulations, evaluates its accuracy under different scenarios, and highlights when the main assumptions fall short. It is found that the expression agrees well with non-radiative multi-phonon (NMP) models at room temperature for devices featuring a thick dielectric. However, the formula fails to correctly predict the noise of nowadays aggressively scaled devices, because it neglects trapping/de-trapping with the gate electrode and the electrostatic charge scaling of the traps due to their distance from the channel.

Rationalizing the structural changes and spectra of manganese and their temperature dependence in a series of garnets with first-principles calculations

Detailed first-principles calculations have been carried out to study the stabilization, excitation and luminescence mechanisms of the ion ${\mathrm{Mn}}^{3+}$ in a series of ${A}_{3}{B}_{2}{B}_{3}^{\ensuremath{'}}{\mathrm{O}}_{12}$ garnet hosts. The formation energy shows that ${\mathrm{Mn}}^{3+}$ is dominant and is situated at the octahedral $B$ site. The excited states, excitation, and emission energies of ${\mathrm{Mn}}^{3+}$ have then been calculated. The calculated energy levels of ${\mathrm{Mn}}^{3+}$ confirm that the red emission is due to the ${}^{5}{\mathrm{T}}_{2}\phantom{\rule{4pt}{0ex}}\ensuremath{\rightarrow}{\phantom{\rule{4pt}{0ex}}}^{5}{\mathrm{E}}^{\ensuremath{'}}$ transition and the near-infrared (NIR) emission arises from the ${}^{1}{\mathrm{T}}_{2}\phantom{\rule{4pt}{0ex}}\ensuremath{\rightarrow}{\phantom{\rule{4pt}{0ex}}}^{3}{\mathrm{T}}_{1}$ transition. The populations of the ${}^{5}{\mathrm{T}}_{2}$ and ${}^{1}{\mathrm{T}}_{2}$ excited states and the corresponding radiative rates lead to the temperature dependence of the red to NIR emission. Furthermore, the adiabatic potential energy surfaces along the ${A}_{1g}$ and ${E}_{g}$ moeity modes of [${\mathrm{MnO}}_{6}$] have been calculated and fitted well in the harmonic approximation. The high activation energy for ${\mathrm{Mn}}^{3+}$ indicates a low nonradiative multiphonon relaxation rate of ${}^{5}{\mathrm{T}}_{2}$ to ${}^{3}{\mathrm{T}}_{1}$. Hence, the ionization process was considered, and we show that it is responsible for the luminescence quenching of ${\mathrm{Mn}}^{3+}$, so that the luminescence has rarely been reported experimentally. This work illustrates a well-designed approach based on the density-functional theory framework to predict the optical transition properties of the transition metal ion ${\mathrm{Mn}}^{3+}$ by calculating the structural distortions due to the Jahn-Teller effect, the optical transitions, quenching processes and the influence of pressure.

Efficient Modeling of Charge Trapping at Cryogenic Temperatures—Part I: Theory

Charge trapping is arguably the most important detrimental mechanism distorting the ideal characteristics of MOS transistors, and nonradiative multiphonon (NMP) models have been demonstrated to provide a very accurate description. For the calculation of the NMP rates at room temperature or above, simple semiclassical approximations have been successfully used to describe this intricate mechanism. However, for the computation of charge transition rates at cryogenic temperatures, it is necessary to use the full quantum mechanical description based on Fermi’s golden rule. Since this is computationally expensive and often not feasible, we discuss an efficient method based on the Wentzel–Kramers–Brillouin (WKB) approximation in combination with the saddle point method and benchmark this approximation against the full model. We show that the approximation delivers excellent results and can, hence, be used to model charge trapping behavior at cryogenic temperatures.

Energy Resonance Transfer between Quantum Defects in Metal Halide Perovskites.

Quantum defects have been shown to play an essential role in nonradiative recombination in metal halide perovskites (MHPs). Nonetheless, the processes of charge transfer assisted by defects are still ambiguous. Herein, we theoretically study the nonradiative multiphonon processes among different types of quantum defects in MHPs using Markvart's model for the induced mechanisms of electron-electron and electron-phonon interactions. We find that the charge carrier can transfer between the neighboring levels of the same type of shallow defects by multiphonon processes, but it will be distinctly suppressed with an increase in the defect depth. For the nonradiation multiphonon transitions between donor- and acceptor-like defects, the processes are very fast and not sensitive to the defect depth, which provides a possible explanation for the phenomenon of blinking of photoluminescence spectra. We also discuss the temperature dependence of these multiphonon processes and find that their variational trends depend on the comparison of the Huang-Rhys factor with the emitted phonon number. These theoretical results not only fill some of the gaps in defect-assisted nonradiative processes in the perovskite materials but also provide deeper physical insights into producing higher-performance perovskite-based devices.

Physical Modeling of Charge Trapping in 4H-SiC DMOSFET Technologies

Silicon carbide (SiC) MOSFETs still exhibit higher drifts of the threshold voltage than comparable silicon devices due to charge trapping, especially regarding small time scales. Understanding this behavior and the consequences in application relevant conditions is therefore of high research interest. Since charge trapping at different defects close to the SiC/ SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> interface and in the bulk oxide is strong bias and temperature-dependent, the phenomenon is referred to as bias temperature instability (BTI). It has been shown that drifts caused by BTI vary both in transient shape and magnitude for commercially available devices. These differences arise from defect densities and properties in the respective technologies. A physical model together with defect parameters that explain the charge transfer reactions at the defects is essential to understand all peculiarities of the transient degradation. In this work, we use a novel method to semiautomatically extract defect parameters within a two-state nonradiative multiphonon model framework. Our work reveals properties of defects responsible for shifts of the threshold voltage for both short-term ac and long-term dc stress conditions which are accurately reproduced for three different DMOS technologies. Our calibrated simulation framework is further used to extrapolate device degradation at operation relevant ac bias conditions to typical device lifetimes.

TCAD modeling of bias temperature instabilities in SiC MOSFETs

TCAD simulations of SiC power MOSFETs have been performed to study the dependence of positive-bias temperature instability (PBTI) on temperature and electric field. The model used to describe the kinetics of the transition rates between neutral and charged traps is the extended Non-Radiative Multi Phonon (eNMP). Connections between oxide defect configurations at the interface with SiC substrate have been made. Validation against experiments is shown.

Applicability of Shockley–Read–Hall Theory for Interface States

The Shockley-Read-Hall (SRH) model has been successfully used for decades to describe the dynamics of interface states. Interestingly, the SRH model neglects structural relaxation at the defect site, which has a dramatic effect on the dynamics of oxide defects. One may, therefore, wonder why this omission has not led to serious and obvious discrepancies with experimental data. Using ab initio approaches to investigate Si dangling bonds, known as P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> centers, within a realistic Si/a-SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> environment together with the more complete nonradiative multiphonon (NMP) theory, we explore why the SRH model provides an excellent approximation for interface traps but not for bulk oxide defects. We will also show that the commonly used Arrhenius correction of the capture cross section can be used to introduce a modified SRH model, which provides a reasonable approximation to the results obtained from a full NMP approach. However, it is shown that this Arrhenius correction may lead to incorrect relaxation energy estimations, especially for bulk oxide defects.

Extensive assessment of the charge-trapping kinetics in InGaAs MOS gate-stacks for the demonstration of improved BTI reliability

Gate-stack reliability has been a major roadblock in the realization of InGaAs-channel based logic technology. Excessive charge trapping in the gate-oxide causes time-dependent drift in transistor threshold voltage (Vth). The extent to which Vth drifts under certain stress conditions depends on (i) the defect ground-state energy distributions in the oxide bandgap, and (ii) the specific activation energy distributions for charge capture/emission process. In this work, semi-empirical modelling of ground-state defect energy distributions is revisited to determine the Total Operating Voltage Range of InGaAs-based MOSFETs for a DC-BTI lifetime of 10 years under DC operating conditions. Non-radiative Multiphonon (NMP) theory is subsequently used to describe the microscopic physics of charge (de-)trapping kinetics in terms of activation energy barriers for charge capture (EAc) and emission (EAe) into/from gate-stack defects. These activation energy barriers are visualized using Capture/Emission Time (CET) maps, which are efficient and powerful tools to predict the BTI degradation under different AC operating conditions as well. We demonstrate that the enhanced BTI reliability of a gate-stack with a novel ASM interfacial layer (ASM-IL), as compared to the bilayer gate-stack of Al2O3/HfO2, results from the favorable reconfiguration of the defect energy distribution in the oxide bandgap, as well as their activation energies for capture and emission process.

Anharmonic multi-phonon nonradiative transition: An ab initio calculation approach

Nonradiative carrier recombinations at deep centers in semiconductors are of great importance for both fundamental physics and device engineering. In this article, we provide a revised analysis of Huang’s original nonradiative multi-phonon (NMP) theory with ab initio calculations. First, we confirmed at the first-principles level that Huang’s concise formula gives the same results as the matrix-based formula, and that Huang’s high-temperature formula provides an analytical expression for the coupling constant in Marcus theory. Secondly, we correct for anharmonic effects by taking into account local phonon-mode variations for different charge states of a defect. The corrected capture rates for defects in GaN and SiC agree well with experiments.

Improved PBTI Reliability in Junction-Less FET Fabricated at Low Thermal Budget for 3-D Sequential Integration

Junction-less FETs are used as top-tier devices in a 3-D sequential integration. Due to the low thermal budget allowed in the 3-D integration, conventional inversion mode FETs show extremely poor BTI reliability. In contrast, a junction-less FET shows improved BTI reliability, which is attributed to the reduced oxide electric field of operation. We observe that the reliability of junction-less FETs can be further improved by increasing the channel doping and/or the channel thickness. Correspondingly, a tradeoff exists between performance (subthreshold slope, carrier mobility), reliability, and variability. This tradeoff is verified in both planar/FinFET structures and can serve as a device optimization matrix. Furthermore, we use the non-radiative multi-phonon (NMP) theory, as implemented in the imec/T.U. Vienna BTI simulation framework “Comphy,” to investigate the degradation kinetics and show that the stress/recovery traces measured in inversion mode and junction-less nFETs can be reproduced with the same set of oxide defect parameters. This observation confirms that the reliability improvement in junction-less devices is inherent to their specific operation mode and not related to the different fabrication flows compared to standard inversion mode devices. Based on the calibrated Comphy model, we perform BTI lifetime projections, exposing for junction-less devices a substantial deviation from the commonly used power-law voltage acceleration.

Reliability studies on biaxially tensile strained-Si channel p-MOSFETs

An integrated technology computer aided simulation framework is used for the first time to predict the reliability (degradation) of substrate-induced strained-Si channel heterojunction field effect transistors on relaxed Silicon-Germanium buffer layer with ultra-thin SiO2 and high-k gate stacks. State-of-the-art four-state nonradiative multiphonon model is used for the degradation studies. Single defects and trap studies have been taken up on devices subjected to negative voltage stressing at an elevated temperature. Threshold voltage shift (due to charge capture and emission processes) in virtually fabricated devices has been studied in detail. For the first time, non radiative multiphonon model is used to explain the degradation mechanisms (oxide defects dominating the partial recovery of threshold voltage after stressing) in strained-Si channel heterojunction field effect transistors. It is shown that degradation in strained-Si channel device on relaxed-SiGe buffer is more compared to its Si-channel counterpart.

Excited-state absorption and fluorescence dynamics in Er:CaF2

Emission, ground- and excited-state absorption spectra of Er:CaF2 single crystals were registered from the visible to the mid-infrared. These spectra were calibrated in unit of cross section and analyzed to derive purely radiative lifetimes and branching ratios. Fluorescence decays were then recorded to determine effective emission lifetimes and branching ratios including non-radiative multiphonon relaxations. These fluorescence data along with population ratios and emission intensity measurements performed versus pumping rates were finally confronted with a rate equation model to derive energy transfer rates.

Nd3+,Ho3+-Codoped apatite-related NaLa9(GeO4)6O2 phosphors for the near- and middle-infrared region.

The apatite-like NaLa9(GeO4)6O2:Nd3+,Ho3+ phosphor is prepared using the solid-state method. Rietveld refinement of high-resolution time-of-flight neutron powder diffraction measurements indicate that this compound crystallizes in the hexagonal system with space group P63/m, Z = 1 and unit cell parameters a = 9.88903(6) Å, c = 7.25602(5) Å, V = 614.521(7) Å3 at room temperature. The 4f sites are statistically occupied by La, Nd and Na, while 6h sites are occupied by La and Nd. Luminescence in the near- and middle-IR range caused by the transitions in neodymium and holmium ions is excited under 808 nm laser diode radiation. The highest emission intensity in NaLa9-x-yNdxHoy(GeO4)6O2 is attained at trace amounts of holmium, and it decreases sharply when y increases to 0.01. The IR phosphors have a good thermal stability and exhibit a very weak upconversion emission in the red spectral range upon 808 nm excitation. A scheme of excitation and emission pathways involving ground/excited state absorption, energy transfer, cross-relaxation, nonradiative multiphonon relaxation processes in Nd3+ and Ho3+ ions has been proposed. The data analysis indicates that Nd3+ ions serve as sensitizers for Ho3+ ions in these compounds, stimulating intense 2.1 μm and 2.7 μm emissions. These apatite-related germanate phosphors are promising materials for near- and middle-infrared solid-state lighting applications.

White light emission and spectroscopic properties of Dy3+ ions doped bismuth sodiumfluoroborate glasses for photonic applications

Dy3+ ions doped Bismuth sodium fluoroborate glasses (BiNFBxD) have been prepared following the melt quenching technique and characterized through XRD, FTIR, UV-Vis-NIR absorption, luminescence and decay measurements for developing potential WLEDs and yellow lasers. The local symmetry around the Dy3+ ions in the prepared glasses were investigated through optical basicity, covalent character factor, bonding parameter, Judd-Ofelt parameters and Y/B intensity ratio values. The least squares fitting method have been employed to determine the Judd-Ofelt intensity parameters Ωλ to study the nature of bonding and symmetry orientation of the Dy-ligand field environment and to derive the radiative properties for the various emission transitions of the Dy3+ ions. The higher spectroscopic quality factor Ω4/Ω6 values of the prepared glasses indicate its suitability for the fabrication of laser devices and the values were compared with the reported literature. While exciting the Dy3+ doped title glasses at 452 nm (6H15/2 → 4I15/2), the emission bands 4F9/2 → 6H15/2 (blue), 4F9/2 → 6H13/2 (yellow) and 4F9/2 → 6H11/2 (red) were observed at 482 nm, 575 nm and 679 nm, respectively. The radiative properties like stimulated emission cross-section (σPE), transition probability (A), effective wavelength (λeff), branching ratio (βR) and experimental lifetimes (τm) for all the emission bands of the Dy3+doped title glasses have been computed. From the luminescence spectra the Y/B ratio values, CIE chromaticity color coordinates and Color Correlated Temperature (CCT) for different concentrations of Dy3+ ions were calculated. The CIE chromaticity co-ordinate values of the present glasses suggest their suitability for the development of visible luminescent photonic devices and white light applications. The decay curves pertaining to the 4F9/2 level have been measured for the title glasses and the fall in lifetime values with the increase in Dy3+ ions concentration could be attributed to the cross-relaxation takes place among the Dy3+ ions and the non-radiative multiphonon relaxation process takes place through the phonon modes of the glass host. The non-exponential behavior of the decay curves have been analyzed through Inokuti-Hirayama model to identify the nature of the energy transfer process takes place among the Dy3+ ions and the dipole-dipole interaction(s) is responsible for the dominant energy transfer process.