The formulae for parameters of a negative electron affinity semiconductor(NEAS)with large mean escape depth of secondary electrons A(NEASLD)are deduced.The methods for obtaining parameters such asλ,B,E_(pom)and the m...The formulae for parameters of a negative electron affinity semiconductor(NEAS)with large mean escape depth of secondary electrons A(NEASLD)are deduced.The methods for obtaining parameters such asλ,B,E_(pom)and the maximumδandδat 100.0 keV≥E_(po)≥1.0 keV of a NEASLD with the deduced formulae are presented(B is the probability that an internal secondary electron escapes into the vacuum upon reaching the emission surface of the emitter,δis the secondary electron yield,E_(po)is the incident energy of primary electrons and E_(pom)is the E_(po)corresponding to the maximumδ).The parameters obtained here are analyzed,and it can be concluded that several parameters of NEASLDs obtained by the methods presented here agree with those obtained by other authors.The relation between the secondary electron emission and photoemission from a NEAS with large mean escape depth of excited electrons is investigated,and it is concluded that the presented method of obtaining A is more accurate than that of obtaining the corresponding parameter for a NEAS with largeλ_(ph)(λ_(ph)being the mean escape depth of photoelectrons),and that the presented method of calculating B at E_(po)>10.0 keV is more widely applicable for obtaining the corresponding parameters for a NEAS with largeλ_(ph).展开更多
An “Eigenstate Adjustment Autonomy” Model, permeated by the Nanosystem’s Fermi Level Pinning along with its rigid Conduction Band Discontinuity, compatible with pertinent Experimental Measurements, is being employe...An “Eigenstate Adjustment Autonomy” Model, permeated by the Nanosystem’s Fermi Level Pinning along with its rigid Conduction Band Discontinuity, compatible with pertinent Experimental Measurements, is being employed for studying how the Functional Eigenstate of the Two-Dimensional Electron Gas (2DEG) dwelling within the Quantum Well of a typical Semiconductor Nanoheterointerface evolves versus (cryptographically) selectable consecutive Cumulative Photon Dose values. Thus, it is ultimately discussed that the experimentally observed (after a Critical Cumulative Photon Dose) Phenomenon of 2DEG Negative Differential Mobility allows for the Nanosystem to exhibit an Effective Qubit Specific Functionality potentially conducive to (Telecommunication) Quantum Information Registering.展开更多
The structural, electronic, and elastic properties of ZnSe1-xSx for the zinc blende structures have been studied by using the density functional theory. The calculations were performed using the plane wave pseudopoten...The structural, electronic, and elastic properties of ZnSe1-xSx for the zinc blende structures have been studied by using the density functional theory. The calculations were performed using the plane wave pseudopotential method, as implemented in Quantum ESPRESSO. The exchange-correlation potential is treated with the local density approximation pz-LDA for these properties. Moreover, LDA+U approximation is employed to treat the "d" orbital electrons properly. A comparative study of the band gap calculated within both LDA and LDA+U schemes is presented. The analysis of results show considerable improvement in the calculation of band gap. The inclusion of compositional disorder increases the values of all elastic constants. In this study, it is found that elastic constants C11, C12, and C44 are mainly influenced by the compositional disorder. The obtained results are in good agreement with literature.展开更多
The processes and characteristics of secondary electron emission in insulators and semiconductors were studied, and the formulae for the maximum yield(δ_m) at W_(pOm)≤ 800 eV and the secondary electron yield from in...The processes and characteristics of secondary electron emission in insulators and semiconductors were studied, and the formulae for the maximum yield(δ_m) at W_(pOm)≤ 800 eV and the secondary electron yield from insulators and semiconductors δ at the primary incident energy of 2 keV≤ W_(pO) < 10 keV(δ_(2-10)) and10 keV ≤ W_(pO)≤100 keV(δ_(10-100)) were deduced. The calculation results were compared with their corresponding experimental data. It is concluded that the deduced formulae can be used to calculate δ_(2-100)at W_(pOm)≤ 800 eV.展开更多
The electronic and optical properties of zincblende ZnX(X=S, Se, Te) and ZnX:Co are studied from density functional theory (DFT) based first principles calculations. The local crystal structure changes around the...The electronic and optical properties of zincblende ZnX(X=S, Se, Te) and ZnX:Co are studied from density functional theory (DFT) based first principles calculations. The local crystal structure changes around the Co atoms in the lattice are studied after Co atoms are doped. It is shown that the Co-doped materials have smaller lattice constant (about 0.6%-0.9%). This is mainly due to the shortened Co-X bond length. The (partial) density of states (DOS) is calculated and differences between the pure and doped materials are studied. Results show that for the Co-doped materials, the valence bands are moving upward due to the existence of Co 3d electron states while the conductance bands are moving downward due to the reduced lattice constants. This results in the narrowed band gap of the doped materials. The complex dielectric indices and the absorption coefficients are calculated to examine the influences of the Co atoms on the optical properties. Results show that for the Co-doped materials, the absorption peaks in the high wavelength region are not as sharp and distinct as the undoped materials, and the absorption ranges are extended to even higher wavelength region.展开更多
Simple models are proposed for the calculation of refractive index n and electronic polarizability α of AⅠBⅢC2Ⅵ and AⅡBⅣC2Ⅴ compounds of groups of chalcopyrite semiconductors from their energy gap data. The val...Simple models are proposed for the calculation of refractive index n and electronic polarizability α of AⅠBⅢC2Ⅵ and AⅡBⅣC2Ⅴ compounds of groups of chalcopyrite semiconductors from their energy gap data. The values family and 12 compounds of AⅡBⅣC2Ⅴ family are calculated for the work. The proposed models are applicable for the whole range of energy gap materials. The calculated values are compared with the available experimental and reported values. A fairly good agreement between them is obtained.展开更多
Lattice constants and electronic structures of diluted magnetic semiconductors ( In, Mn ) As were investigated using the first principles LMTO-ASA band calculation by assuming supercell structures. Three concentrati...Lattice constants and electronic structures of diluted magnetic semiconductors ( In, Mn ) As were investigated using the first principles LMTO-ASA band calculation by assuming supercell structures. Three concentrations of the 3 d impurities were studied ( x = 1/2, 1/4, 1/8). The effect of varying Mn coucentrations on the lattice constants and the electronic structures are shown.展开更多
This paper reviews our recent development of the use of the large-scale pseudopotential method to calculate the electronic structure of semiconductor nanocrystals,such as quantum dots and wires,which often contain ten...This paper reviews our recent development of the use of the large-scale pseudopotential method to calculate the electronic structure of semiconductor nanocrystals,such as quantum dots and wires,which often contain tens of thousands of atoms.The calculated size-dependent exciton energies and absorption spectra of quantum dots and wires are in good agreement with experiments.We show that the electronic structure of a nanocrystal can be tuned not only by its size,but also by its shape.Finally,we show that defect properties in quantum dots can be significantly different from those in bulk semiconductors.展开更多
This paper studies the drain current collapse of A1GaN/GaN metal insulator-semiconductor high electron-mobility transistors (MIS-HEMTs) with NbA10 dielectric by applying dual-pulsed stress to the gate and drain of t...This paper studies the drain current collapse of A1GaN/GaN metal insulator-semiconductor high electron-mobility transistors (MIS-HEMTs) with NbA10 dielectric by applying dual-pulsed stress to the gate and drain of the device. For NbA10 MIS-HEMT, smaller current collapse is found thorough study of the gate-drain conductance dispersion especially when the gate static voltage is -8 V. Through a it is found that the growth of NbA10 can reduce the trap density of the AlGaN surface. Therefore, fewer traps can be filled by gate electrons, and hence the depletion effect in the channel is suppressed effectively. It is proved that the NbAIO gate dielectric can not only decrease gate leakage current but also passivate the A1GaN surface effectively, and weaken the current collapse effect accordingly.展开更多
We report on the performance of La203/InA1N/GaN metal-oxide-semiconductor high electron mobility transistors (MOSHEMTs) and InA1N/GaN high electron mobility transistors (HEMTs). The MOSHEMT presents a maximum drai...We report on the performance of La203/InA1N/GaN metal-oxide-semiconductor high electron mobility transistors (MOSHEMTs) and InA1N/GaN high electron mobility transistors (HEMTs). The MOSHEMT presents a maximum drain current of 961 mA/mm at Vgs = 4 V and a maximum transconductance of 130 mS/mm compared with 710 mA/mm at Vgs = 1 V and 131 mS/mm for the HEMT device, while the gate leakage current in the reverse direction could be reduced by four orders of magnitude. Compared with the HEMT device of a similar geometry, MOSHEMT presents a large gate voltage swing and negligible current collapse.展开更多
Effects of nonparabolicity of energy band on thermopower, in-plane effective mass and Fermi energy are inves- tigated in size-quantized semiconductor films in a strong while non-quantized magnetic field. We obtain the...Effects of nonparabolicity of energy band on thermopower, in-plane effective mass and Fermi energy are inves- tigated in size-quantized semiconductor films in a strong while non-quantized magnetic field. We obtain the expressions of these quantities as functions of thickness, concentration and nonparabolicity parameter. The influence of nonparabolicity is studied for degenerate and non-degenerate electron gases, and it is shown that nonparabolicity changes the character of thickness and the concentration dependence of thermopower, in-plane effective mass and Fermi energy. Moreover, the magnitudes of these quantities significantly increase with respect to the nonparabolicity parameter in the case of strong nonparabolicity in nano-films. The concentration depen- dence is also studied, and it is shown that thermopower increases when the concentration decreases. These results are in agreement with the experimental data.展开更多
Power-electronic devices are widely used in various applications, such as voltage and frequency control for transmitting and converting electric power. As these devices are becoming increasingly important, there is a ...Power-electronic devices are widely used in various applications, such as voltage and frequency control for transmitting and converting electric power. As these devices are becoming increasingly important, there is a need to reduce their losses and improve their performance to reduce electric power consumption. Current power semiconductor devices, such as inverters, are made of silicon (Si), but the performance of these Si power devices is reaching its limit due to physical properties and energy bandgap. To address this issue, recent developments in wide bandgap (WBG) semiconductor materials, such as silicon carbide (SiC) and gallium nitride (GaN), offer the potential for a new generation of power semiconductor devices that can perform significantly better than silicon-based devices. In this research, a green synthesized copper-zinc-tin-sulfide (CZTS) nanoparticle is proposed as a new WBG semiconductor material that could be used for optical and electronic devices. Its synthesis, consisting of the production methods and materials used, is discussed. The characterization is also discussed, and further research is recommended in the later sections to enable the continual advancement of this technology.展开更多
Influence of spin–orbit coupling on spin-polarized electronic transport in magnetic semiconductor nanowires with nanosized sharp domain walls is investigated theoretically.It is shown that the Rashba spin–orbit coup...Influence of spin–orbit coupling on spin-polarized electronic transport in magnetic semiconductor nanowires with nanosized sharp domain walls is investigated theoretically.It is shown that the Rashba spin–orbit coupling can enhance significantly the spin-flip scattering of charge carriers from a nanosized sharp domain wall whose extension is much smaller than the carrier's Fermi wavelength.When there are more than one domain wall presented in a magnetic semiconductor nanowire,not only the spin-flip scattering of charge carriers from the domain walls but the quantum interference of charge carriers in the intermediate domain regions between neighboring domain walls may play important roles on spin-polarized electronic transport,and in such cases the influences of the Rashba spin–orbit coupling will depend sensitively both on the domain walls' width and the domain walls' separation.展开更多
We report here the structural, surface morphology, mechanical, and current voltage characteristics of Zn1-xMxO ceramic samples with various x and M (0.00≤〈 x ≤ 0.20, M = Ni, Cu). It is found that the considered d...We report here the structural, surface morphology, mechanical, and current voltage characteristics of Zn1-xMxO ceramic samples with various x and M (0.00≤〈 x ≤ 0.20, M = Ni, Cu). It is found that the considered dopants do not influence the well-known peaks related to the wurtzite structure of ZnO ceramics, while the shapes and the sizes of grains are clearly affected. The average crystalline diameters deduced from the SEM micrographs are between 2.06 μm and 4.8 μm for all samples. The oxygen element ratio is increased by both dopants. Interestingly, the potential barrier can be formed by adding Cu up to 0.20, while it is completely deformed by 0.025 Ni addition. The breakdown field can be enhanced up to 4138 V/cm by 0.025 Cu addition, followed by a decrease with further increase of Cu up to 0.20. On the other hand, a gradual decrease in Vickers microhardness is reported for both dopants, and the values in the Ni samples are higher compared to those in the Cu samples. The electricul conductivity is generally improved by Ni, while the addition of Cu improves it only in the over doped region (≥ 0.10). These results are discussed in terms of the differences of valency and ferromagnetic ordering.展开更多
The effect of In composition on two-dimensional electron gas in wurtzite AlGaN/InGaN heterostructures is theoretically investigated. The sheet carrier density is shown to increase nearly linearly with In mole fraction...The effect of In composition on two-dimensional electron gas in wurtzite AlGaN/InGaN heterostructures is theoretically investigated. The sheet carrier density is shown to increase nearly linearly with In mole fraction x, due to the increase in the polarization charge at the AlGaN/InGaN interface. The electron sheet density is enhanced with the doping in the AlGaN layer. The sheet carrier density is as high as 3.7×1013 cm^-2 at the donor density of 10×1018 cm^-3 for the HEMT structure with x=0.3. The contribution of additional donor density on the electron sheet density is nearly independent of the In mole fraction.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.11873013)。
文摘The formulae for parameters of a negative electron affinity semiconductor(NEAS)with large mean escape depth of secondary electrons A(NEASLD)are deduced.The methods for obtaining parameters such asλ,B,E_(pom)and the maximumδandδat 100.0 keV≥E_(po)≥1.0 keV of a NEASLD with the deduced formulae are presented(B is the probability that an internal secondary electron escapes into the vacuum upon reaching the emission surface of the emitter,δis the secondary electron yield,E_(po)is the incident energy of primary electrons and E_(pom)is the E_(po)corresponding to the maximumδ).The parameters obtained here are analyzed,and it can be concluded that several parameters of NEASLDs obtained by the methods presented here agree with those obtained by other authors.The relation between the secondary electron emission and photoemission from a NEAS with large mean escape depth of excited electrons is investigated,and it is concluded that the presented method of obtaining A is more accurate than that of obtaining the corresponding parameter for a NEAS with largeλ_(ph)(λ_(ph)being the mean escape depth of photoelectrons),and that the presented method of calculating B at E_(po)>10.0 keV is more widely applicable for obtaining the corresponding parameters for a NEAS with largeλ_(ph).
文摘An “Eigenstate Adjustment Autonomy” Model, permeated by the Nanosystem’s Fermi Level Pinning along with its rigid Conduction Band Discontinuity, compatible with pertinent Experimental Measurements, is being employed for studying how the Functional Eigenstate of the Two-Dimensional Electron Gas (2DEG) dwelling within the Quantum Well of a typical Semiconductor Nanoheterointerface evolves versus (cryptographically) selectable consecutive Cumulative Photon Dose values. Thus, it is ultimately discussed that the experimentally observed (after a Critical Cumulative Photon Dose) Phenomenon of 2DEG Negative Differential Mobility allows for the Nanosystem to exhibit an Effective Qubit Specific Functionality potentially conducive to (Telecommunication) Quantum Information Registering.
文摘The structural, electronic, and elastic properties of ZnSe1-xSx for the zinc blende structures have been studied by using the density functional theory. The calculations were performed using the plane wave pseudopotential method, as implemented in Quantum ESPRESSO. The exchange-correlation potential is treated with the local density approximation pz-LDA for these properties. Moreover, LDA+U approximation is employed to treat the "d" orbital electrons properly. A comparative study of the band gap calculated within both LDA and LDA+U schemes is presented. The analysis of results show considerable improvement in the calculation of band gap. The inclusion of compositional disorder increases the values of all elastic constants. In this study, it is found that elastic constants C11, C12, and C44 are mainly influenced by the compositional disorder. The obtained results are in good agreement with literature.
基金supported by the National Natural Science Foundation of China(No.11473049)
文摘The processes and characteristics of secondary electron emission in insulators and semiconductors were studied, and the formulae for the maximum yield(δ_m) at W_(pOm)≤ 800 eV and the secondary electron yield from insulators and semiconductors δ at the primary incident energy of 2 keV≤ W_(pO) < 10 keV(δ_(2-10)) and10 keV ≤ W_(pO)≤100 keV(δ_(10-100)) were deduced. The calculation results were compared with their corresponding experimental data. It is concluded that the deduced formulae can be used to calculate δ_(2-100)at W_(pOm)≤ 800 eV.
基金Project supported by the National Natural Science Foundation of China (Grant No 10564002) and the 0pen Foundations of Key Laboratory for 0pto-electronics of Jiangxi Province, China (Grant Nos 2004003 and 2004008), the Natural Science Foundation of Jiangxi Province, China (Grant No 0512017) and the Youth Science Program of Jiangxi Normal University, China(Grant No 1075).
文摘The electronic and optical properties of zincblende ZnX(X=S, Se, Te) and ZnX:Co are studied from density functional theory (DFT) based first principles calculations. The local crystal structure changes around the Co atoms in the lattice are studied after Co atoms are doped. It is shown that the Co-doped materials have smaller lattice constant (about 0.6%-0.9%). This is mainly due to the shortened Co-X bond length. The (partial) density of states (DOS) is calculated and differences between the pure and doped materials are studied. Results show that for the Co-doped materials, the valence bands are moving upward due to the existence of Co 3d electron states while the conductance bands are moving downward due to the reduced lattice constants. This results in the narrowed band gap of the doped materials. The complex dielectric indices and the absorption coefficients are calculated to examine the influences of the Co atoms on the optical properties. Results show that for the Co-doped materials, the absorption peaks in the high wavelength region are not as sharp and distinct as the undoped materials, and the absorption ranges are extended to even higher wavelength region.
文摘Simple models are proposed for the calculation of refractive index n and electronic polarizability α of AⅠBⅢC2Ⅵ and AⅡBⅣC2Ⅴ compounds of groups of chalcopyrite semiconductors from their energy gap data. The values family and 12 compounds of AⅡBⅣC2Ⅴ family are calculated for the work. The proposed models are applicable for the whole range of energy gap materials. The calculated values are compared with the available experimental and reported values. A fairly good agreement between them is obtained.
基金Funded by the National Natural Science Foundation of China(No.60476047) ,the Key Teacher Foundation of the EducationalBureau of Henan Province ,and the Natural Science Foundation ofthe Educational Bureau of Henan Province , China ( No:2003140027 ,2004140004)
文摘Lattice constants and electronic structures of diluted magnetic semiconductors ( In, Mn ) As were investigated using the first principles LMTO-ASA band calculation by assuming supercell structures. Three concentrations of the 3 d impurities were studied ( x = 1/2, 1/4, 1/8). The effect of varying Mn coucentrations on the lattice constants and the electronic structures are shown.
文摘This paper reviews our recent development of the use of the large-scale pseudopotential method to calculate the electronic structure of semiconductor nanocrystals,such as quantum dots and wires,which often contain tens of thousands of atoms.The calculated size-dependent exciton energies and absorption spectra of quantum dots and wires are in good agreement with experiments.We show that the electronic structure of a nanocrystal can be tuned not only by its size,but also by its shape.Finally,we show that defect properties in quantum dots can be significantly different from those in bulk semiconductors.
基金Project supported by the State Key Program and Major Program of the National Natural Science Foundation of China (Grant Nos. 60736033 and 60890191)the Fundamental Research Funds for the Central Universities (Grant Nos. JY10000925002 and JY10000904009)
文摘This paper studies the drain current collapse of A1GaN/GaN metal insulator-semiconductor high electron-mobility transistors (MIS-HEMTs) with NbA10 dielectric by applying dual-pulsed stress to the gate and drain of the device. For NbA10 MIS-HEMT, smaller current collapse is found thorough study of the gate-drain conductance dispersion especially when the gate static voltage is -8 V. Through a it is found that the growth of NbA10 can reduce the trap density of the AlGaN surface. Therefore, fewer traps can be filled by gate electrons, and hence the depletion effect in the channel is suppressed effectively. It is proved that the NbAIO gate dielectric can not only decrease gate leakage current but also passivate the A1GaN surface effectively, and weaken the current collapse effect accordingly.
基金Project supported by the Basic Science Research Fund for the Central Universities (Grant No. K50511250009).
文摘We report on the performance of La203/InA1N/GaN metal-oxide-semiconductor high electron mobility transistors (MOSHEMTs) and InA1N/GaN high electron mobility transistors (HEMTs). The MOSHEMT presents a maximum drain current of 961 mA/mm at Vgs = 4 V and a maximum transconductance of 130 mS/mm compared with 710 mA/mm at Vgs = 1 V and 131 mS/mm for the HEMT device, while the gate leakage current in the reverse direction could be reduced by four orders of magnitude. Compared with the HEMT device of a similar geometry, MOSHEMT presents a large gate voltage swing and negligible current collapse.
文摘Effects of nonparabolicity of energy band on thermopower, in-plane effective mass and Fermi energy are inves- tigated in size-quantized semiconductor films in a strong while non-quantized magnetic field. We obtain the expressions of these quantities as functions of thickness, concentration and nonparabolicity parameter. The influence of nonparabolicity is studied for degenerate and non-degenerate electron gases, and it is shown that nonparabolicity changes the character of thickness and the concentration dependence of thermopower, in-plane effective mass and Fermi energy. Moreover, the magnitudes of these quantities significantly increase with respect to the nonparabolicity parameter in the case of strong nonparabolicity in nano-films. The concentration depen- dence is also studied, and it is shown that thermopower increases when the concentration decreases. These results are in agreement with the experimental data.
文摘Power-electronic devices are widely used in various applications, such as voltage and frequency control for transmitting and converting electric power. As these devices are becoming increasingly important, there is a need to reduce their losses and improve their performance to reduce electric power consumption. Current power semiconductor devices, such as inverters, are made of silicon (Si), but the performance of these Si power devices is reaching its limit due to physical properties and energy bandgap. To address this issue, recent developments in wide bandgap (WBG) semiconductor materials, such as silicon carbide (SiC) and gallium nitride (GaN), offer the potential for a new generation of power semiconductor devices that can perform significantly better than silicon-based devices. In this research, a green synthesized copper-zinc-tin-sulfide (CZTS) nanoparticle is proposed as a new WBG semiconductor material that could be used for optical and electronic devices. Its synthesis, consisting of the production methods and materials used, is discussed. The characterization is also discussed, and further research is recommended in the later sections to enable the continual advancement of this technology.
文摘Influence of spin–orbit coupling on spin-polarized electronic transport in magnetic semiconductor nanowires with nanosized sharp domain walls is investigated theoretically.It is shown that the Rashba spin–orbit coupling can enhance significantly the spin-flip scattering of charge carriers from a nanosized sharp domain wall whose extension is much smaller than the carrier's Fermi wavelength.When there are more than one domain wall presented in a magnetic semiconductor nanowire,not only the spin-flip scattering of charge carriers from the domain walls but the quantum interference of charge carriers in the intermediate domain regions between neighboring domain walls may play important roles on spin-polarized electronic transport,and in such cases the influences of the Rashba spin–orbit coupling will depend sensitively both on the domain walls' width and the domain walls' separation.
文摘We report here the structural, surface morphology, mechanical, and current voltage characteristics of Zn1-xMxO ceramic samples with various x and M (0.00≤〈 x ≤ 0.20, M = Ni, Cu). It is found that the considered dopants do not influence the well-known peaks related to the wurtzite structure of ZnO ceramics, while the shapes and the sizes of grains are clearly affected. The average crystalline diameters deduced from the SEM micrographs are between 2.06 μm and 4.8 μm for all samples. The oxygen element ratio is increased by both dopants. Interestingly, the potential barrier can be formed by adding Cu up to 0.20, while it is completely deformed by 0.025 Ni addition. The breakdown field can be enhanced up to 4138 V/cm by 0.025 Cu addition, followed by a decrease with further increase of Cu up to 0.20. On the other hand, a gradual decrease in Vickers microhardness is reported for both dopants, and the values in the Ni samples are higher compared to those in the Cu samples. The electricul conductivity is generally improved by Ni, while the addition of Cu improves it only in the over doped region (≥ 0.10). These results are discussed in terms of the differences of valency and ferromagnetic ordering.
文摘The effect of In composition on two-dimensional electron gas in wurtzite AlGaN/InGaN heterostructures is theoretically investigated. The sheet carrier density is shown to increase nearly linearly with In mole fraction x, due to the increase in the polarization charge at the AlGaN/InGaN interface. The electron sheet density is enhanced with the doping in the AlGaN layer. The sheet carrier density is as high as 3.7×1013 cm^-2 at the donor density of 10×1018 cm^-3 for the HEMT structure with x=0.3. The contribution of additional donor density on the electron sheet density is nearly independent of the In mole fraction.