Einstein relation in n-i-p-i and microstructures of nonlinear optical, optoelectronic and related materials: Simplified theory, relative comparison and suggestions for an experimental determination

We investigate the Einstein relation for the diffusivity-mobility ratio (DMR) for n-i-p-i and the microstructures of nonlinear optical compounds on the basis of a newly formulated electron dispersion law. The corresponding results for III-V, ternary and quaternary materials form a special case of our generalized analysis. The respective DMRs for II-VI, IV-VI and stressed materials have been studied. It has been found that taking CdGeAs₂, Cd₃As₂, InAs, InSb, Hg_1−xCd_xTe, In_1−xGa_xAs_yP_1−y lattices matched to InP, CdS, PbTe, PbSnTe and Pb_1−xSn_xSe and stressed InSb as examples that the DMR increases with increasing electron concentration in various manners with different numerical magnitudes which reflect the different signatures of the n-i-p-i systems and the corresponding microstructures. We have suggested an experimental method of determining the DMR in this case and the present simplified analysis is in agreement with the suggested relationship. In addition, our results find three applications in the field of quantum effect devices.     

Simple theoretical analysis of the Fowler-Nordheim field emission from microstructures and quantum wires of optoelectronic materials

We present a simplified theoretical formulation of the Fowler-Nordheim field emission (FNFE) under magnetic quantization and also in quantum wires of optoelectronic materials on the basis of a newly formulated electron dispersion law in the presence of strong electric field within the framework of k.p formalism taking InAs, InSb, GaAs, Hg_1−xCd_xTe and In_1−xGa_x As_yP_1−y lattice matched to InP as examples. The FNFE exhibits oscillations with inverse quantizing magnetic field and electron concentration due to SdH effect and increases with increasing electric field. For quantum wires the FNFE increases with increasing film thickness due to the existence van-Hove singularity and the magnitude of the quantum jumps are not of same height indicating the signature of the band structure of the material concerned. The appearance of the humps of the respective curves is due to the redistribution of the electrons among the quantized energy levels when the quantum numbers corresponding to the highest occupied level changes from one fixed value to the others. Although the field current varies in various manners with all the variables in all the limiting cases as evident from all the curves, the rates of variations are totally band-structure dependent. Under certain limiting conditions, all the results as derived in this paper get transformed in to well known Fowler-Nordheim formula.     

The existence of giant magnetocaloric effect and laminar structure in Fe73.5−xCrxSi13.5B9Nb3Cu1

Amorphous soft magnetic ribbons Fe_73.5−xCr_xSi_13.5B₉Nb₃Cu₁ (x=1–5) have been fabricated by rapid quenching on a single copper wheel. The differential scanning calorimetry (DSC) patterns showed that the crystallization temperature of α-Fe(Si) phase is ranging from 542 to 569 °C, a little higher than that of pure Finemet (x=0). With the same annealing regime, the crystallization volume fraction as well as the particle size of α-Fe(Si) crystallites decreased with increasing Cr amount substituted for Fe in studied samples. Especially, the interesting fact is that the laminar structure of heat-treated ribbons on the surface contacted to copper wheel in the fabricating process has been firstly discovered and explained to be related to the existence of Cr in studied samples. The hysteresis loop measurement indicated that there is the pinning of displacement of domain walls. The giant magnetocaloric effect (GMCE) has been found in amorphous state of the samples. After annealing, the soft magnetic properties of investigated nanocomposite materials are desirably improved.     

Influence of light waves on the thermoelectric power under large magnetic field in III‐V,ternary and quaternary materials

We study theoretically the influence of light waves on the thermoelectric power under large magnetic field (TPM) for III‐V, ternary and quaternary materials, whose unperturbed energy‐band structures, are defined by the three‐band model of Kane. The solution of the Boltzmann transport equation on the basis of this newly formulated electron dispersion law will introduce new physical ideas and experimental findings in the presence of external photoexcitation. It has been found by taking n‐InAs, n‐InSb, n‐Hg_1‐xCd_xTe and n‐In_1‐xGa_xAs_yP_1‐y lattice matched to InP as examples that the TPM decreases with increase in electron concentration, and increases with increase in intensity and wavelength, respectively in various manners. The strong dependence of the TPM on both light intensity and wavelength reflects the direct signature of light waves that is in direct contrast as compared with the corresponding bulk specimens of the said materials in the absence of external photoexcitation. The rate of change is totally band‐structure dependent and is significantly influenced by the presence of the different energy‐band constants. The well‐known result for the TPM for nondegenerate wide‐gap materials in the absence of light waves has been obtained as a special case of the present analysis under certain limiting conditions and this compatibility is the indirect test of our generalized formalism. Besides, we have also suggested the experimental methods of determining the Einstein relation for the diffusivity:mobility ratio, the Debye screening length and the electronic contribution to the elastic constants for materials having arbitrary dispersion laws.     

On the two-dimensional thermoelectric power in quantum wells of non-parabolic materials under magnetic quantization

We present a simplified theoretical formulation of the thermoelectric power (TP) under magnetic quantization in quantum wells (QWs) of nonlinear optical materials on the basis of a newly formulated magneto-dispersion law. We consider the anisotropies in the effective electron masses and the spin–orbit constants within the framework of k.p formalism by incorporating the influence of the crystal field splitting. The corresponding results for III–V materials form a special case of our generalized analysis under certain limiting conditions. The TP in QWs of Bismuth, II–VI, IV–VI and stressed materials has been studied by formulating appropriate electron magneto-dispersion laws. We also address the fact that the TP exhibits composite oscillations with a varying quantizing magnetic field in QWs of n- Cd₃As₂, n- CdGeAs₂, n-InSb, p-CdS, stressed InSb, PbTe and Bismuth. This reflects the combined signatures of magnetic and spatial quantizations of the carriers in such structures. The TP also decreases with increasing electron statistics and under the condition of non-degeneracy, all the results as derived in this paper get transformed into the well-known classical equation of TP and thus confirming the compatibility test. We have also suggested an experimental method of determining the elastic constants in such systems with arbitrary carrier energy spectra from the known value of the TP.     

Structural, electrical, optical and magnetic properties of Co0.2AlxZn0.8−xO films

Co_0.2Al_xZn_0.8−xO films prepared with different molar ratio of aluminum nitrate to zinc acetate were deposited on substrates by the sol-gel technique. X-ray diffraction, photoluminescence and ferromagnetism measurements were used to characterize the Co_0.2Al_xZn_0.8−xO diluted magnetic semiconductors. The authors found that the intensity of the acceptor-related photoluminescence increased with increasing aluminum concentration and an increase in the number of the acceptor-like defects (zinc vacancies especially) in the Co_0.2Al_xZn_0.8−xO film might lead to the enhancement of the magnetic properties. This implies that controls of the aluminum concentration and the number of the acceptor-like defects are important factors to produce strong ferromagnetism Co_0.2Al_xZn_0.8−xO films prepared by the sol-gel method.     

Thermoelectric power in superlattices of nonparabolic semiconductors with graded interfaces under magnetic quantization

Summary We study the thermoelectric power of the electrons under magnetic quantization in III–V, II–VI, PbTe/PbSnTe and strained layer superlattices with graded interfaces and compare the same with the corresponding bulk specimens of the constituent materials by formulating the respective expressions incorporating the broadening. It is found, by taking GaAs/Ga_1−x Al _x As, CdS/CdTe, PbTe/PbSnTe and InAs/GaSb superlattices with graded interfaces as examples, that the thermoelectric power exhibits oscillatory dependence with the inverse quantizing magnetic field due to Shubnikov-de Hass effect and increases with decreasing electron concentration in an oscillatory manner in all the aforementioned cases. The thermopower in graded superlattices is greater than that of constituent bulk materials together with the fact that the oscillations in superlattices show up much more significantly as compared to the respective constituent materials. In addition, the well-known expressions for bulk specimens of wide-gap semiconductors have also been obtained as special cases from our generalized expressions under certain limiting conditions.     

The carrier contribution to the elastic constants in III-V, ternary and quaternary materials in the presence of light waves: Simplified theory, relative comparison and a suggestion for experimental determination

In this paper, we have studied the electronic contribution to the elastic constants for III-V, ternary and quaternary materials in the presence of light waves on the basis of newly formulated electron statistics. It has been found taking n-InAs, n-InSb, n-Hg_1−xCd_xTe and n-In_1−xGa_xAs_yP_1−y lattice matched to InP, as examples that the elastic constants increase with increasing electron concentration, intensity and wavelength in various manners. The strong dependence of the elastic constants on both the light intensity and wavelength reflects the direct signature of the light waves which is in contrast as compared with the corresponding bulk specimens in the absence of photo-excitation. The well-known results for degenerate wide gap materials in the absence of light waves have been obtained as a special case under certain limiting conditions and this compatibility is the indirect test of our generalized formalism. In this context, we have suggested the experimental method of determining the carrier contribution to the elastic constants for materials having arbitrary carrier energy spectra and our results find six important applications in the regime of photon-assisted transport in modern optoelectronic devices.     

On the Einstein Relation in Ternary Semiconductors in the Presence of Crossed Electric and Magnetic Fields

We investigate theoretically the Einstein relation for the diffusivity-mobility ratio of the electrons in ternary semiconductors at low temperatures in the presence of crossed electric and quantizing magnetic fields on the basis of threeband Kane model. It is found, taking n-Hg_1-xCd_xTe as an example, that DMR shows an oscillatory magnetic field dependence. Besides, the DMR increase both with increasing electron concentration and decreasing alloy composition respectively.     

Assessment of electronic properties of InNxSb1−x for long-wavelength infrared detector applications

This work assesses theoretically the potential of dilute nitride alloys of InN_xSb_1−x for long-wavelength IR applications. A 10-band k.p approximation modified to account for conduction/valence band coupling is implemented to extract the bandgap as a function of the nitrogen concentration in the alloy and the temperature. The calculations show the possibility to obtain a band closure at ∼2% of nitrogen for InSbN at 300 K. The absorption coefficient, and its temperature dependence, is then determined using an Elliot-like formalism, predicting stronger absorption properties associated with the enhancement of conduction band effective masses. This enhancement yields over an order of magnitude increase in the non-radiative Auger recombination lifetimes suggesting the potential of InNSb for significantly enhancing detectivity limits and operation temperatures of long-wavelength IR detectors.     

Influence of quantization of band states on the effective electron mass in quaternary alloys

Summary An attempt is made to study the effective electron mass in quaternary alloys, taking a In_1−x Ga _x As _y P_1−y lattice matched to InP, by using the three-band Kane model under different physical conditions,e.g. bulk specimens, magnetic quantization, cross-field configuration, quantum well, electric-field-aided quantum well, magnetic-field-aided quantum well, quantum well under cross fields, quantum well wires, electric-field-aided quantum well wires, magnetic-field-aided quantum well wires and quantum well wires under cross fields by formulating the respective expressions. We have plotted the effective Fermi level mass with various physical variables under different conditions. In the presence of a quantizing magnetic field the effective mass depends on the spin splitting of Landau levels due to the spin-orbit splitting parameter of the valence bands. Under cross-field configuration and the various quantum confined low-dimensional systems, the effective masses depend on the respective quantum numbers in addition to the Fermi energies even for parabolic models because of the inherent features of such systems. In addition, the corresponding results for relatively wide-gap materials have also been obtained from our generalized formulations under certain limiting conditions.     

Ab initio study of electronic structures and magnetism in ZnMnTe and CdMnTe diluted magnetic semiconductors

In this work, we aimed to examine the spin-polarized electronic band structures, the local densities of states as well as the magnetism of ZnMnTe- and CdMnTe-diluted magnetic semiconductors (DMSs) in the ferromagnetic phase, and with 25% of Mn. The calculations are performed by the recent ab initio full potential augmented plane waves plus local orbitals (FP−L/APW+lo) method within the spin-polarized density-functional theory and the local spin density approximation. We have determined the exchange splittings produced by the Mn d states: Δ_x(d) and Δ_x(pd), and we found that the effective potential for the minority spin is more attractive than that for the majority spin. Also, we show the nature of the bonding from the charge spin-densities calculations, and we calculate the exchange constants N₀α and N₀β, which mimics a typical magneto-optical experiment. The calculated total magnetic moment is found to be equal to 5μ_B for both DMSs. This value indicates that every Mn impurity adds no hole carriers to the perfect ZnTe and CdTe crystals. Furthermore, we found that p–d hybridization reduces the local magnetic moment of Mn and produces small local magnetic moments on the nonmagnetic Te, Zn and Cd sites.     

Effect of Gd doping on structural, electrical and magnetic properties of BiFeO3 electroceramic

Room temperature multiferroic electroceramics of Gd doped BiFeO₃ monophasic materials have been synthesized adopting a slow step sintering schedule. Incorporation of Gd nucleates the development of orthorhombic grain growth habit without the appearance of any significant impurity phases with respect to original rhombohedral (R3c) phase of un-doped BiFeO₃. It is observed that, the materials showed room temperature enhanced electric polarization as well as ferromagnetism when rare earth ions like Gd doping is critically optimized (x=0.15) in the composition formula of Bi_1+2xGd_2x/2Fe_1−2xO₃. We believe that magnetic moment of Gd⁺³ ions in Gd doped BiFeO₃ tends to align in the same direction with respect to ferromagnetic component associated with the iron sub lattice. The dielectric constant as well as loss factor shows strong dispersion at lower frequencies and the value of leakage current is greatly suppressed with the increase in concentration of x in the above composition. Addition of excess bismuth and Gd (x=0.1 and 0.15) caused structural transformation as well as compensated bismuth loss during high temperature sintering. Doping of Gd in BiFeO₃ also suppresses spiral spin modulation structure, which can change Fe-O-Fe bond angle or spin order resulting in enhanced ferromagnetic property.     

A simplified analysis of the electronic contribution to the elastic constants in ultrathin films of stressed semiconductors under magnetic quantization

An attempt is made to study the electronic contribution to the second- and third-order elastic constants in ultrathin films of strained semiconductors under magnetic quantization in the presence of broadening on the basis of a newly formulated electron dispersion law. It is found, taking stressed n-InSb as an example, that the carrier contribution to the second- and third-order elastic constants oscillates with increasing carrier degeneracy and decreasing film thickness, respectively, in different manners and the stress enhances their numerical values. A relationship between the said contributions and the thermoelectric power has been derived for quantum confined semiconductors having arbitrary dispersion laws and our analysis agrees quite well with the suggested relationship.     

Theoretical Analysis of the Einstein Relation in n-Channel Inversion Layers on A3IIB2V Semiconductors under Magnetic Quantization

We have investigated the Einstein relation in n-channel inversion layers on A₃^IIB₂^V semiconductors at low temperatures on the basis of a newly derived dispersion relation of the carriers under arbitrary magnetic quantization for the general case which occurs from the consideration of the anisotropies of the band parameters within the frame work of k · p formalism. It is found by incorporating both the effects of electron spin and broadening of Landau levels, using n-Cd₃As₂ as an example, that the theoretical formulation is in qualitative agreement with the suggested experimental method of determining the Einstein relation in degenerate semiconductors having arbitrary dispersion law. In addition, the corresponding well-known results for bulk specimens of two band Kane model both in the presence and absence of magnetic quantization, are also obtained from the generalized expressions as special cases.     

Indium-incorporation-induced transformation of optical, photoluminescence and lasing properties of InGaN epilayers

A comparative combined study of photoluminescence (PL), PL kinetics, stimulated emission (SE) and photoreflectance (PR) properties in In_xGa_1−xN epilayers is carried out in the composition range 0≤x≤0.19. In-incorporation up to 4% leads to the sufficient longer radiative recombination decay time due to the decrease in non-radiative recombination channels, which are peculiar to GaN, and band-to-band optical transitions predominate the spontaneous PL spectrum. Further In-incorporation (x>4%) leads to the localization of carriers and/or excitons at band-tails in the In-rich areas. Correlation between the position of dominant low-energy PR oscillation due to the main band gap and SE peak position shows that band-to-band transitions are responsible for lasing and dominate the PL spectrum in all highly pumped In_xGa_1−xN samples.     

Magnetocaloric effects in Ni-Mn-X based Heusler alloys with X=Ga, Sb, In

The Mn-based Heusler alloys encompass a rich collection of useful materials from highly spin-polarized systems to shape memory alloys to magnetocaloric materials. In this work we have summarized our studies of magnetostructural transitions from paramagnetic austenite to ferromagnetic martesite phases at TMC in Ni₂MnGa-based alloys (Ni₂Mn_0.75Cu_0.25-xCo_xGa, Ni₂Mn_0.70Cu_0.30Ga_0.95Ge_0.05, Ni₂Mn_1-xCu_xGa, Ni_2+xMn_1-xGa, and Ni₂Mn_0.75-xCu_xGa), and martensitic transitions from the ferromagnetic austenite to the martesite state in off-stoichiometric Ni-Mn-(In/Sb) Heusler alloys. The phase transition temperatures and respective magnetic entropy changes (ΔS) depend on composition in these systems and have been determined from magnetization measurements in the temperature interval 5-400 K, and in magnetic fields up to 5 T. It is shown that, depending on the composition and doping scheme the “giant” ΔS=40-60 J/(kgK) (for a field change of 5 T) can be observed in the temperature range (300-360 K) for the Ga-based alloys. The interplay between or coupling of the various transitions in Ni₂Mn(Mn,X) systems with X=Sb and In leads to exchange bias effects, giant magnetoresistance, and both inverse and “normal” magnetocaloric effects.     

The energy spectra and wavefunctions of MSQW

On the basis of the quasistationary state approximation, the asymptotic transfer method (ATM) was extended to calculate the energy spectra, envelope functions of carriers and dispersion relations of Ga_1−xAl_xAs multiple sawtooth quantum wells (MSQW) in the presence of an electric field applied along the growth direction and a magnetic field parallel to the MSQW interfaces. It turned out that the energy spectra revealed the Landau-like behavior of carriers under a magnetic field. The envelope functions of carriers displayed obvious fluctuation and the dispersion relations showed a non-parabolic shape.     

A simple analysis of the subband energies in quantum-confined non-parabolic semiconductors in the presence of a parallel magnetic field

Summary We study the subband energies in quantum wells and quantum wires in the presence of a parallel magnetic field in non-parabolic semiconductors, on the basis of a generalized dispersion relation considering all types of anisotropies of the energy-band parameters within the framework ofk·p formalism, by formulating the respective electron energy spectra. It is found, by takingn-Cd₃As₂ as an example, that the subband energies are greater for quantum wires and smaller for quantum wells, respectively. The magnetic field diminishes the above values and the corresponding well-known results for quantum-confined parabolic semiconductors have also been obtained from our generalized expressions under certain limiting conditions.     

Interband absorption and exciton binding energy in an inverse parabolic quantum well under the magnetic field

We have investigated the effects of the magnetic field which is applied perpendicular to the growth direction of the well on the interband absorption and on the binding energy of the excitons in an GaAs/Ga1−xAlxAs inverse parabolic quantum well (IPQW) with different widths as well as different Al concentrations at the well center. The calculations were performed within the effective mass approximation, using a variational method. We observe that IPQW structure turns into parabolic quantum well with the inversion effect of the magnetic field and the effective band gap of the system can be modified by changing Al concentration at the well center, the strength of the magnetic field and well dimensions. This case directly influences the nature of electronic and optical properties in this structure.