Critical Concentration Nc Research Articles

Metal-insulator transition in films of doped semiconductor nanocrystals.

To fully deploy the potential of semiconductor nanocrystal films as low-cost electronic materials, a better understanding of the amount of dopants required to make their conductivity metallic is needed. In bulk semiconductors, the critical concentration of electrons at the metal-insulator transition is described by the Mott criterion. Here, we theoretically derive the critical concentration nc for films of heavily doped nanocrystals devoid of ligands at their surface and in direct contact with each other. In the accompanying experiments, we investigate the conduction mechanism in films of phosphorus-doped, ligand-free silicon nanocrystals. At the largest electron concentration achieved in our samples, which is half the predicted nc, we find that the localization length of hopping electrons is close to three times the nanocrystals diameter, indicating that the film approaches the metal-insulator transition.

Influence of the shape of inclusions on the percolation thresholds in 2D models of composites

The influence of the shape of inclusions on the conductivity of composites, including critical concentration Nc (percolation threshold), is considered using 2D models as an example. A relationship between constant NI, which characterizes effective conductivity σe for low concentrations N of inclusions and percolation threshold Nc is established.

Hall coefficient and Hall mobility in the variable range hopping conduction regime in n-type CuInSe2

The electrical conductivity ρ and Hall coefficient RH are measured on a n-type CuInSe2 sample that has dopant concentration n below critical concentration nc of the metal-insulator transition. Mott type variable range hopping conduction of between 4 and 20 K is observed at several fixed magnetic fields B up to 1.5 T. The effect of the magnetic field on Hall coefficient and Hall mobility μH is also studied. It is found that temperature dependence of μH is in agreement with the Hall effect theory for hopping conduction.

Variable-range hopping conductivity in thin film of the ladder compound [Ca1+δCu2O3

Low-temperature charge transport in [Ca1+δCu2O3]4 films with δ=0 and 0.08 is investigated at T=1.4–290 K in magnetic fields of B=0–30 T. Between Tv≈20 and 40 K, depending on δ, and Tv′≈2–3 K three-dimensional (3D) Mott variable-range hopping (VRH) conductivity is observed. Deviations from 3D Mott VRH conductivity below Tv′ can be attributed to the onset of the Shklovskii–Efros VRH regime, accompanied by violation of the 3D hopping condition, Rh≪d (where Rh is the mean hopping length and d is the thickness of the film). The density of the localized states (DOS) at the Fermi level, g3(μ)≈4.4×1020 eV−1 cm−3, the values of the localization radius, α≈46 and 34 Å, the concentration of sites involved in hopping charge transfer, N≈9.9×1018 and 9.0×1018 cm−3, the width of the band of localized electron states, 2W≈22 and 20 meV, and the width of the Coulomb gap in the DOS spectrum, 2Δ≈1 and 1.6 meV are obtained for films with δ=0 and 0.08, respectively. These values characterize the films as being near the 3D metal–insulator transition given by the critical concentration NC≈1.3×1019 cm−3.

Scaling behavior of the Hall coefficient of Si:P at the metal-insulator transition

Measurements of the Hall coefficient RH(T, B) of Si:P with P concentration N between 3.54 and 7.0·1018 cm−3 are reported for the temperature range 0.04 K ≤ T ≤ 4K and in magnetic fields up to 7 T. Even far above the metal-insulator transition (MIT), a sign change of the temperature coefficient similar to the behavior of the conductivity σ(T) in moderate fields is not observed in RH(T). Field and temperature dependence of RH both increase as the MIT (at the critical concentration Nc = 3.52 · 1018 cm−3) is approached. A careful extrapolation to T → 0 and B → 0 indicates that RH−1 scales to zero as RH−1 ∼| N − NcμH with μH = (0.44 ± 0.04) in agreement with previous results.

Metal-insulator transition in a two-layer electron-hole system

This paper discusses a quantum-mechanical metal-insulator transition that occurs in an anisotropic electron-hole system with the electrons and holes separated and confined to a double quantum well. The critical concentration nc of carriers in the system above which the excitonic (insulating) phase becomes an electron-hole (metallic) phase is investigated, along with its dependence on the distance between wells D.

Transport properties of silicon implanted with bismuth

in Van der Pauw structures delineated in Si chips. The measured resistivities were compared with the ones calculated by a generalized Drude approach at similar temperatures and doping concentration, presenting fairly good agreement. The critical impurity concentration Nc of the metal-nonmetal transition was measured to be around 2310 19 cm 23 . The critical concentration Nc was calculated by comparing the ionization energy of the insulating phase with the total energy of the metallic phase. This value of Nc agreed very well with the one obtained experimentally and the values estimated from other theoretical approaches. @S0163-1829~97!01612-3#

Clustering of asbestos fibres in cell damage: A percolational perspective

In vitro researches on rat cells exposed to several types of thin asbestos fibres show a saturation in cytotoxicity as one increases the fibre concentration n on the cell surface. For given average fibre lengths, the saturation occurs at values that are 2-3 times the critical concentration nc for a percolative arrangement of randomly thrown sticks on a surface. Measurements of the threshold for genotoxic damage give concentrations that are about 0.1nc. One expects that, somewhere between these concentrations, large scale "critical fluctuations" will be observed in the data. These fluctuations are indeed seen in chrysotile treated rat pleural mesothelial cells, exhibiting DNA damage and chromosomal-number aberrations. We hypothesize that at such concentrations that fibre-clustering occurs, the fibres lock together and are hindered from traversing the cell membranes and internalizing. Some damage processes are thereby impeded. The kinetics of internalization is worked out with models involving continuum percolation. Pieces of evidence from in vivo results that support the theory are noted.

Theoretical electronic properties of silicon-containing bismuth

The electrical conductivities of n-doped silicon and, in particular Si:Bi, have been investigated for doping levels greater than the impurity critical concentration Nc for the metal-nonmetal transitions. A general feature of the conductivity for concentration normalized to Nc is presented in the order σ(Bi)≳σ(As)≳σ(P)≳σ(Sb). For Si:Bi, the value of Nc is calculated for different criteria. The mobility of electrons presents a lower value compared to Si:P. The results for Si:P and Si:As are compared to the experimental data available in the literature.

A mean-field-type approximation for the (t-J) model

The equations for a mean-field-type approximation in the (t-J) model are formulated in terms of a diagrammatic technique with Hubbard X-operators. With their help, equations for the order parameters are derived in ferromagnetic and antiferromagnetic phases of a metal. In both cases, two coupled order parameters exist: a magnetization m and a gap Delta in the electron spectrum. They reflect a dual behaviour of a strongly correlated system: it is simultaneously an itinerant and a localized magnet. Formulae for Curie temperature TC and Neel temperature TN are derived, from which the different nature of ferromagnetic and antiferromagnetic ordering is explicitly seen. For a simple cubic lattice the electron concentration n dependences of TC and TN are numerically calculated. It is shown that TN rapidly falls with deviation from half-filling, when n=1. Magnetic correlation length lc varies at low temperature as approximately (1-n)- 12 /. Such behaviour corresponds to that observed in experiments in copper oxide high-Tc superconductors. The magnetic phase diagram is constructed on the (t/U, n) plane. The equations for the coupled order parameters are solved for T=0 and the dependences of the order parameters m and Delta on n are presented in a wide interval of electron concentrations. They indicate the growing degree of itinerancy with deviation from half-filling. It is shown that the critical concentration nc for a crossover from itinerant magnetism to magnetism with localized magnetic moments should be a peculiar point where perturbation theory breaks down.

Theory of Strongly Correlated Systems in the Limit of Large On-Site Coulomb Repulsion

A strongly correlated electronic system is studied within the framework of the t—J model with the help of diagram technique for the Hubbard X-operators. The summing of some series of diagrams is suggested, corresponding to the following three types of approximations: the generalized random phase approximation, the mean field approximation, and the low density approximation. In generalized random phase approximation the dynamic magnetic susceptibility of paramagnetic phase is calculated, and boundaries of stability of this phase are found on the plane of Hamiltonian parameters and electron concentration n. It is shown that at some critical concentration nc the system undergoes a crossover from the itinerant magnetism (n n c ). Simultaneously, the system transfers from the Fermi-liquid behaviour to the regime of strong electron correlations with nonquasiparticle states. In mean field approximation equations for the order parameters were derived and phase transitions temperatures in a ferromagnetic and antiferromagnetic phases were obtained. In low density approximation a state of the saturated ferromagnetism was investigated and a critical concentration n $ was calculated when the nonsaturated ferromagnetism follows the saturated ferromagnetism. PACS numbers: 75.10.Lp, 75.30.Cr

SUPERCONDUCTIVITY IN THE HUBBARD MODEL WITH STRONG COULOMB REPULSION

Within the Hubbard model with strong Coulomb interaction U ≫ t (the t-J model), the possibility is studied for the superconducting state to exist due to charge and spin fluctuations in a system. Within the generalized random phase approximation (GRPA) used earlier by the authors for the calculation of magnetic susceptibility, the effective interaction between electrons in the Cooper channel was calculated. The calculations were performed by the diagram technique for the Hubbard operators. In GRPA, the effective interaction takes into account all diagram sequences with fermion loops and spin Green functions. The effective interaction is expressed via dynamical magnetic and dielectric susceptibilities; therefore it is considerably enhanced near the boundaries of the paramagnetic phase's instability towards the appearance of magnetic order, or of a state with charge density wave. Equations for the strong coupling in a superconductor are derived for the normal Z and anomalous φ parts of the electron Green function, linearized in the order parameter φ. The superconducting transition temperature T c is calculated with various sets of parameters in the (t/U, n) plane, n being the electron concentration. It is shown that in the itinerant magnetism regime (n < nc), where there is no localized magnetic moments in the system, spin fluctuations in the vicinity of antiferromagnetic phase transition lead to electron coupling with d-type symmetry, in analogy to the case of weak Coulomb repulsion. In the localized magnetic moment regime (n > nc), a quasistatistical term appears in the magnetic susceptibility. This terms leads to the pair-breaking mechanism, acting analogously to magnetic impurities. The dynamical part of the susceptibility may result in pairing interaction; however, high values of T c can hardly be expected in this case because of the pair-breaking interaction with localized magnetic moments. In the "Hubbard 1" approximation, the critical concentration nc for band with symmetric density of states equals 2/3. For n > 0.88, CDW instability appears in the system. Near its boundary, charge fluctuations may lead to coupling interaction with trivial symmetry of the order parameter. However, the critical line of the CDW instability lies within the region of ferromagnetic phase, and superconductivity becomes suppressed due to spin splitting of the electron spectrum.

The change in the sound velocity in Sb-doped Ge

The authors have measured the change Delta v in the sound velocity in Sb-doped Ge over a concentration N range 3.1*1016-1.6*1018cm-3 and a temperature range 1.8-40 K. The stress dependence of Delta v has been also measured in a limited concentration range near the critical concentration Nc for the metal-nonmetal transition over a temperature range 2.3-4.2 K. The density of states for N>1017cm-3 has been derived from fitting to Delta v under the assumption that the electron-phonon coupling in the impurity band is identical with that in the conduction band. The stress dependence is qualitatively explained using the density of states obtained. The relaxation time in the sound attenuation near Nc is found to be sensitive to the stress. The metal-nonmetal transition in this system occurs in the impurity band.

Metal-Non-metal Transition in the Double-Donors Si:P, As and Si:P, Sb: A Simple Approach

We report the first calculation for the critical concentration Nc of the MNM transition in double-donors Si:P, As and Si:P, Sb. From an interpretation of the Hubbard model for the transition we found the result for Si:P, As in good agreement with recent experimental finding [Newman and Holcomb, Phys. Rev. Lett. 51, 2144 (1983)]. We also find that the model predicts value of Nc for Si:P, Sb in the following order NcSb < NcP,Sb < NcP < NcP,As < NcAs.

Infrared absorption in phosphorus doped silicon and the D-band

Measurements are reported of the optical absorption in phosphorus doped silicon in the wavelength range 25 mu m to 700 mu m, together with the concentration dependence of refractive index. Sample doping levels varied from Nd=5*1015 Pcm-3, where the donors are virtually isolated, to Nd=2.7*1018 Pcm-3 where they are strongly interacting and just on the insulator side of the metal-insulator transition (critical concentration Nc=3*1018 Pcm-3). Specimens doped to 6*1016 Pcm-3 exhibited two new absorption lines at 294 cm-1 and 250 cm-1, and it is proposed that these lines lead to the formation of an absorption edge which moves towards smaller wavenumber as Nd to Nc. The absorption line at 294 cm-1 is identified as being the lower limit of a D2- band, and its position is in good agreement with Norton's measurement of a band edge using the temperature dependence of a photoexcitation technique.

Critical temperature of two-band superconductors with paramagnetic impurities

The two-band model proposed by Suhl, Matthias, and Walker for pure transition metal superconductors is extended to transition metals with paramagnetic impurities under the assumption that the cutoff parameters Ω ij (i, j = s, d) of the pairing interactions between electrons V ij are different from each other. An equation is derived for the critical temperature T c .In the dilute limit T c (n) can increase with impurity concentration n only for Ω ss ≠ Ω sd , Ω dd ≠ Ω sd . In the one-band limit the results reduce to those of Abrikosov and Gor' kov. The theoretical function T c (n) is used to fit the experimental data for the alloys La 1 − n Ce n and Ce 1 − n Nd n Ru2. The agreement of the theoretical T c (n) curve with the experimental points is good, with the exception of La 1 − n Ce n for values n near the critical concentration n c ,where stronger deviations appear as a consequence of magnetic ordering.