Carrier Degeneracy Research Articles

Synergy of grain size and texture effect for high-performance Mg3Sb2-based thermoelectric materials

High-performance n-type Mg3Sb2-based thermoelectric materials have attracted much attention due to the six-fold degenerate carrier pockets in the conduction band. This study uncovers the electrical and thermal transport behaviors in different directions with respect to the spark plasma sintering (SPS) pressure that is rarely investigated. Results indicate that the grain size in the ⊥P direction (perpendicular to the SPS pressure direction) is slightly larger than that in the ∥P direction. In addition, a moderate texture is observed, reflecting a preferential orientation of the (001)-plane in the ⊥P direction. The synergy of both grain size and the texture leads to an improved electrical conductivity for Mg3.24Sb1.5Bi0.49Te0.01 compounds with lamellar crystal structures. Consequently, the highest thermoelectric figure of merit ZTpeak ∼1.71 and ZTavg ∼1.12 (almost the best ZT values ever reported for Te-doped Mg3Sb2-based materials) are achieved in the ⊥P direction compared to the ∥P direction.

On the Einstein relation between mobility and diffusion cofficint in an active Nanostructured Materials

It is commonly known that the speed at which contemporary switching semiconductors work much depends on the carrier degeneracy of the band. Furthermore, the relation of the diffusivity to mobility ratio of the carriers in semiconductors (referred to as DMR) is very helpful because it is more accurate than any of the individual relations for diffusivity to mobility ratio, which is thought to be the two most frequently used parameters in carrier transport in semiconductors. With n-InSb and Hg1-xCdxTe as examples of numerical calculations, we will examine DMR under strong magnetic quantization of III-V in line with the three- and two-band models of Kane, respectively, along with parabolic energy bands.

Origin of the injection-dependent emission blueshift and linewidth broadening of III-nitride light-emitting diodes

III-nitride light-emitting diodes (LEDs) exhibit an injection-dependent emission blueshift and linewidth broadening that is severely detrimental to their color purity. By using first-principles multi-scale modeling that accurately captures the competition between polarization-charge screening, phase-space filling, and many-body plasma renormalization, we explain the current-dependent spectral characteristics of polar III-nitride LEDs fabricated with state-of-the-art quantum wells. Our analysis uncovers a fundamental connection between carrier dynamics and the injection-dependent spectral characteristics of light-emitting materials. For example, polar III-nitride LEDs offer poor control over their injection-dependent color purity due to their poor hole transport and slow carrier-recombination dynamics, which forces them to operate at or near degenerate carrier densities. Designs that accelerate carrier recombination and transport and reduce the carrier density required to operate LEDs at a given current density lessen their injection-dependent wavelength shift and linewidth broadening.

Electrical properties of zinc nitride and zinc tin nitride semiconductor thin films toward photovoltaic applications

Abstract Zn3N2 (ZN) and ZnSnN2 (ZTN) are a promising class of nitride semiconductors for photovoltaic and light-emitting-diode applications due to their particular electrical and optical properties, elemental abundance and non-toxicity. So far, most of the experimental results show the degenerate carrier concentration. However, we find that low-temperature growth of these films in a chamber with ultra-high background vacuum can attain a non-degenerate electrical conductivity. This work provides the recent progress of the electrical properties of ZN and ZTN semiconductor thin films. The origins for the high carrier concentrations in ZN and ZTN have been discussed, demonstrating that non-intentional oxygen and hydrogen-related defects play significant roles in such high carrier concentrations. The strategies to suppress the carrier concentrations have also been addressed, such as ultra-high vacuum conditions and low temperature growth.

Cellular automaton approach for carrier degeneracy effects on the electron mobility of high electron mobility transistors

GaN-based high electron mobility transistors (HEMTs) are expected to have high performance in base station applications. Recently, it was reported that the combination of the Poisson–Schrödinger method and cellular automaton method is effective for predicting the mobility of channel two-dimensional electron gas of GaN HEMTs. In the operation condition of HEMT, the surface electron density of the channel is on the order of 1013 cm−2, and the effect of degeneracy cannot be ignored in calculating the mobility. Since the electron distribution function is always stably obtained by the cellular automaton method, the degeneracy effect can be considered stably. In this paper, through the comparison of different degeneracy evaluation methods, the anisotropy of the electron distribution function under the electric field acceleration is clarified to affect the HEMT mobility prediction significantly.

Atomically thin In2O3 field-effect transistors with 1017 current on/off ratio

Recent advances have enabled the demonstration of record high-performance atomically thin n-type indium oxide (In2O3) field-effect transistors with low thermal budget suitable for back-end-of-line logic or memory applications. By using ultra-thin layers of In2O3, its degenerate carrier density is suppressed so that it can be modulated by conventional dielectric gating. These devices have high on-currents due to its high mobility and low contact resistance; meanwhile they can have exceptionally low off-currents due to its wide bandgap. For both low-power logic and memory, the off-state performance should be understood in more detail, although they are constrained by the limits of traditional measurement techniques. In this Letter, we systematically probe the off-current of ultra-thin In2O3 transistors by adopting a wide channel geometry with temperature-dependent electrical measurements and demonstrate the potential for record high current on/off ratios of 1017 on In2O3 transistors.

Auger recombination in narrow gap HgCdTe/CdHgTe quantum well heterostructures

We present detailed theoretical analysis of nonradiative Auger recombination in narrow-gap mercury-cadmium-telluride quantum wells (HgCdTe QWs). We suggest a microscopic model to calculate Auger recombination rates in the QWs with different Cd fraction as functions of non-equilibrium carrier density with account to the complex band dispersions and wavefunctions, degenerate carrier statistics, and screening effects. Our model is validated by the comparison of measured photoconductivity kinetics with the simulated curves. Furthermore, we use the developed calculation technique to evaluate different designs of HgCdTe/CdHgTe QWs for the far-IR emitters. In particular, we consider a series of QWs with the fixed bandgap of 40 meV (lasing wavelength about 30 μm) and find out that lasing may be favored in the QWs with moderate (6%–9%) cadmium content and not in the pure binary HgTe QWs, which is in contrast to intuitive expectations within threshold energy concept for Auger recombination. Though cadmium-free QWs do provide the highest possible Auger threshold energies, Cd-containing QWs feature much more efficient screening of Coulomb potential (and so Auger interaction) by free charge carriers. The latter effect contributes decisively into the suppression of Auger processes at low temperatures and high carrier concentrations.

Prediction of enhanced thermoelectric performance in two-dimensional black phosphorus nanosheets

Because of the unique layered structure, black phosphorus (BP) provides a possibility of relatively independent control in electrical and thermal conductivity for thermoelectrical applications. It is therefore of great interest to realize high-performance BP-based thermoelectrics as flexible non-toxic and ultralight devices in spite of the low energy conversion efficiency and structural instability of the bulk BP. In this work, we systematically study the thermoelectric properties for the two-dimensional BP from mono-layer up to quad-layer by first-principles calculations and Boltzmann transport theory. It can be concluded from the calculations that the thermoelectric performance of BP nanosheets can be effectively optimized by tuning the layer thickness. We reveal that the maximum ZT values at 300 and 500 K can reach up to 0.45 and 0.90 in p-type bi-layer BP along armchair direction, respectively, around 5 times higher than that of the bulk at room temperature. The high performance in bi-layer BP is mainly attributed to its highly anisotropic and degenerate carrier pockets. Accordingly, we further propose that the formation of BP/h-BN heterostructure can enhance ZT up to 1.2 at 500 K, which facilitates the real application of thin BP for flexible and eco-friendly thermoelectrics.

Electric-double-layer p\u2013i\u2013n junctions in WSe2

While p–n homojunctions in two-dimensional transition metal dichalcogenide materials have been widely reported, few show an ideality factor that is constant over more than a decade in current. In this paper, electric double layer p–i–n junctions in WSe2 are shown with substantially constant ideality factors (2–3) over more than 3 orders of magnitude in current. These lateral junctions use the solid polymer, polyethylene oxide: cesium perchlorate (PEO:CsClO4), to induce degenerate electron and hole carrier densities at the device contacts to form the junction. These high carrier densities aid in reducing the contact resistance and enable the exponential current dependence on voltage to be measured at higher currents than prior reports. Transport measurements of these WSe2p–i–n homojunctions in combination with COMSOL multiphysics simulations are used to quantify the ion distributions, the semiconductor charge distributions, and the simulated band diagram of these junctions, to allow applications to be more clearly considered.

High Thermoelectric Performance in PbSe–NaSbSe2 Alloys from Valence Band Convergence and Low Thermal Conductivity

AbstractPbSe is an attractive thermoelectric material due to its favorable electronic structure, high melting point, and lower cost compared to PbTe. Herein, the hitherto unexplored alloys of PbSe with NaSbSe2 (NaPbmSbSem+2) are described and the most promising p‐type PbSe‐based thermoelectrics are found among them. Surprisingly, it is observed that below 500 K, NaPbmSbSem+2 exhibits unorthodox semiconducting‐like electrical conductivity, despite possessing degenerate carrier densities of ≈1020 cm−3. It is shown that the peculiar behavior derives from carrier scattering by the grain boundaries. It is further demonstrated that the high solubility of NaSbSe2 in PbSe augments both the thermoelectric properties while maintaining a rock salt structure. Namely, density functional theory calculations and photoemission spectroscopy demonstrate that introduction of NaSbSe2 lowers the energy separation between the L‐ and Σ‐valence bands and enhances the power factors under 700 K. The crystallographic disorder of Na+, Pb2+, and Sb3+ moreover provides exceptionally strong point defect phonon scattering yielding low lattice thermal conductivities of 1–0.55 W m‐1 K‐1 between 400 and 873 K without nanostructures. As a consequence, NaPb10SbSe12 achieves maximum ZT ≈1.4 near 900 K when optimally doped. More importantly, NaPb10SbSe12 maintains high ZT across a broad temperature range, giving an estimated record ZTavg of ≈0.64 between 400 and 873 K, a significant improvement over existing p‐type PbSe thermoelectrics.

A quasi-ballistic drain current, charge and capacitance model with positional carrier scattering dependency valid for symmetric DG MOSFETs in nanoscale regime

This paper presents a physically valid quasi-ballistic drain current model applicable for nanoscale symmetric Double Gate (SDG) MOSFETs. The proposed drain current model includes both diffusive and ballistic transport phenomena. The model considers the important positional carrier scattering dependency effect near the source region described in terms of transmission and reflection co-efficients related to the scattering theory. The significance of carrier transport near the bottleneck source region is illustrated where the carriers diffuse into the channel at a relatively lower velocity before accelerating ballistically. The results obtained demonstrate carrier scattering dependency at the critical layer defined near the low field source region on the drain current characteristics. The proposed model partly evolves from Natori’s ballistic bulk MOSFET model that is modified accordingly to be valid for a symmetric Double Gate MOSFET in the nanoscale regime. Carrier degeneracy and Fermi–Dirac statistics are included in the work so as to justify the complete physicality of the model. The model is further extended and is shown to be continuous in terms of terminal charges and capacitances in all regions of operation. A comparative analysis is also done between the proposed quasi-ballistic model and a hypothetical complete ballistic device.

Experimental Analysis of Quasi-Ballistic Transport in Advanced Si ${n}$ FinFETs Using New Extraction Method

For the first time, the drain-bias dependence of mean free path, predicted by previous Monte Carlo simulations, is experimentally confirmed in Si ${n}$ FinFETs by using an improved formulation, considering the additional scatterings attributed to source/drain as well as the carrier degeneracy. This letter indicates that, for optimized Si ${n}$ FinFETs, the carrier velocity and drive current still increase monotonically with decreasing channel length. However, the degradation in mean free path leads to the saturation in ballistic ratio (~60%), resulting in quasi-ballistic transport for devices even with sub-20-nm channel length.

Atomic Layer Deposition of Transparent and Conducting p-Type Cu(I) Incorporated ZnS Thin Films: Unravelling the Role of Compositional Heterogeneity on Optical and Carrier Transport Properties

Optically transparent and highly conducting p-type Cu(I) incorporated ZnS (Cu:ZnS) films are deposited by stacking individual layers of CuS and ZnS using atomic layer deposition. The deposition chemistry and growth mechanism are studied by in situ quartz crystal microbalance. Compositional disorder in atomic scale is observed with increasing Cu incorporation in the films that results in systematic decrease in the optical transmittance in the visible spectrum. Again the conductivity also emphatically depends on the volume fraction of phase-segregated conducting covellite phase. An illustrious correlation prevailing the interplay between the optical transparency and the charge transport mechanism is established. The hole transport mechanism that indicates insulator-to-metal transition with increasing Cu incorporation in the composite is explained in terms of an inhomogeneously disordered system. Under optimized conditions, the material having moderately high optical transmission with degenerate carrier conc...

Radiative and Auger recombination processes in indium nitride

InN and In-rich InGaN alloys emit in the infrared range desirable for telecommunication applications. However, the droop problem reduces their efficiency at high power. Nonradiative Auger recombination is a strong contributor to this efficiency loss. Here, we investigate radiative and Auger recombination in InN and In-rich InGaN with first-principles calculations. We find that the direct eeh process dominates Auger recombination in these materials. In the degenerate carrier regime, the Auger and radiative rates are suppressed by different mechanisms: the radiative rate is affected by phase-space filling while Auger recombination is primarily reduced by free-carrier screening. The suppression of the radiative rate onsets at lower carrier densities than that of the Auger rate, which reduces the internal quantum efficiency of InN devices. Droop in InN can be mitigated by increasing the bandgap through alloying with GaN. We demonstrate that the peak efficiency of In0.93Ga0.07N alloys (which emit at 1550 nm) is 33% higher than that of InN and occurs at higher carrier densities.

A Core Compact Model for IGZO TFTs Considering Degeneration Mechanism

A core scheme including dc and capacitance models of amorphous indium gallium zinc oxide thin-film transistors is presented based on terms of surface potential. Due to the intrinsic physical fact, carrier degeneracy is taken into account. A simpler symmetric quadrature version of charge-sheet model is adopted, which offers a new approach to deduce the expressions of current and terminal charges. Through the extensive comparisons between model results and numerical iterations or experimental data, the validity of the proposed models is strongly supported. The simplicity of algorithm and clear physical conception make the model suitable for circuit simulators.

Excitation-dependent carrier lifetime and diffusion length in bulk CdTe determined by time-resolved optical pump-probe techniques

We applied time-resolved pump-probe spectroscopy based on free carrier absorption and light diffraction on a transient grating for direct measurements of the carrier lifetime and diffusion coefficient D in high-resistivity single crystal CdTe (codoped with In and Er). The bulk carrier lifetime τ decreased from 670 ± 50 ns to 60 ± 10 ns with increase of excess carrier density N from 1016 to 5 × 1018 cm−3 due to the excitation-dependent radiative recombination rate. In this N range, the carrier diffusion length dropped from 14 μm to 6 μm due to lifetime decrease. Modeling of in-depth (axial) and in-plane (lateral) carrier diffusion provided the value of surface recombination velocity S = 6 × 105 cm/s for the untreated surface. At even higher excitations, in the 1019–3 × 1020 cm−3 density range, D increase from 5 to 20 cm2/s due to carrier degeneracy was observed.

Experimental and computational phase boundary mapping of Co4Sn6Te6.

Binary Co4Sb12 skutterudite (also known as CoSb3) has been extensively studied; however, its mixed-anion counterparts remain largely unexplored in terms of their phase stability and thermoelectric properties. In the search for complex anionic analogs of the binary skutterudite, we begin by investigating the Co4Sb12-Co4Sn6Te6 pseudo-binary phase diagram. We observe no quaternary skutterudite phases and as such, focus our investigations on the ternary Co4Sn6Te6 via experimental phase boundary mapping, transport measurements, and first-principles calculations. Phase boundary mapping using traditional bulk syntheses reveals that the Co4Sn6Te6 exhibits electronic properties ranging from a degenerate p-type behavior to an intrinsic behavior. Under Sn-rich conditions, Hall measurements indicate degenerate p-type carrier concentrations and high hole mobility. The acceptor defect SnTe, and donor defects TeSn and Coi are the predominant defects and rationally correspond to regions of high Sn, Te, and Co, respectively. Consideration of the defect energetics indicates that p-type extrinsic doping is plausible; however, SnTe is likely a killer defect that limits n-type dopability. We find that the hole carrier concentration in Co4Sn6Te6 can be further optimized by extrinsic p-type doping under Sn-rich growth conditions.

Two Regimes of Carrier Diffusion in Vapor-Deposited Lead-Halide Perovskites

Metal halide perovskites are attractive materials for the realization of cheap and effective solar cells, thin film transistors, and light emitters. Carrier diffusion at high excitations, however, is poorly addressed in perovskites, even though it governs the diffusion length and determines the efficiency of photonic devices. To fully understand the dependence of diffusion length on carrier density, we performed direct and independent measurements of the carrier diffusion coefficient and recombination rate in several methylammonium lead-halide perovskite layers by applying the light-induced transient grating technique. We demonstrate the existence of two distinct carrier diffusion regimes within the density range of 1018–1020 cm–3. In the perovskite films of high compositional quality, diffusion is governed by a bandlike transport of free carriers. The diffusivity is high (0.28–0.7 cm2/s) in these samples, even at low carrier density, and further increases with excitation due to carrier degeneracy. The op...

Effect of degenerate carriers on Si band gap narrowing

Various mechanisms causing band gap narrowing in strongly heated silicon are considered. In the high-temperature region, it becomes necessary to use Fermi–Dirac quantum statistics to describe carriers, since the silicon chemical potential appears in the valence band and in the conduction band at high carrier concentrations. It is shown that carrier degeneracy under conditions of sufficiently strong heating of intrinsic semiconductor causes strong band gap narrowing. The obtained values of band gap narrowing are compared to experimental results.

Degeneracy and bandgap narrowing in the semiconductor electron-hole product

It is shown that previously proposed expressions for the semiconductor electron-hole product, which purport to separate the influence of carrier degeneracy and bandgap narrowing, fail to properly delineate these effects. A reformulation of the expression in which the two effects are successfully separated is proposed, valid when the majority carrier concentration is independent of bandgap narrowing, as occurs in the common case of low injection and quasi-neutrality. It is shown that under other conditions, the two effects may not be treated in isolation but that only their combined effect or the marginal effect of one or the other on the total electron-hole product may be assessed. Convenient expressions are provided for the latter case. The revised expression provides both conceptual and computational advantages for semiconductor device modelling.