Inhomogeneous Doping Research Articles

Electrostatics of an inhomogeneous quantum hall liquid

The distribution of electron density in the quantum Hall liquid is considered in the presence of macroscopic density gradient caused by side electrodes or inhomogeneous doping. In this case different Landau levels are occupied in different regions of a sample. These regions are separated by incompressible liquid. It is shown that the applicability of the approach by Chklovskii et al. is substantially restricted if the density gradient is not very large and disorder is important. Due to the fluctuations of the remote donor's density the liquid in the transition region can not be considered as completely incompressible. In the typical situation, when the gap between Landau levels is not much larger than the energy of disorder, the transition region is a wide band where electron density, averaged over the fluctuations, is independent of magnetic field. The band is a random mixture of regions occupied by electrons of upper level, by holes of lower level and by incompressible liquid. The width of this band is calculated and an analytical expression for the fraction of incompressible liquid in different parts of this band is given.

Composite materials for photovoltaics: A realistic aim?

Layer-type microcrystalline powders of WS 2, MoS 2, WSe 2 and MoSe 2, which were tested for photoeffects with contact free microwave conductivity measurements, were incorporated into a nanostructured TiO 2 matrix in an attempt to obtain macroscopic photocurrents. Even though only 10% of the microcrystals were found to be active in contact with an iodide/iodine solution, photocurrents of the order of 100 μA/cm 2 to 1 mA/cm 2 were measured. The photoelectrochemical behavior of microcrystals was studied with space resolved photocurrent and photovoltage measurement techniques and it was attempted to understand the mechanism of current generation via the TiO 2/microcrystal/electrolyte interaction. Critical and still unresolved problems are recognized to be the control and optimization of photoeffects in microcrystals and the adjustment of doping levels of the two material faces. Only small photopotentials could be observed up to now, probably due to an insufficient and inhomogeneous doping of microcrystals. More research will be needed to determine whether this strategy could lead to realistic photovoltaic systems.

Measurement of temperature fluctuations and microscopic growth rates in a silicon floating zone under microgravity

A silicon crystal growth experiment has been accomplished using the floating-zone technique under microgravity on a sounding rocket (TEXUS 36). Measurements of temperature fluctuations in the silicon melt zone due to time-dependent thermocapillary convection (Marangoni convection) and an observation of the microscopic growth rate were simultaneously performed during the experiment. Temperature fluctuations of about 0.5–0.7°C with a frequency range <0.5 Hz were detectable. The microscopic growth rate fluctuates considerably around the average growth rate of 1 mm/min: Growth rates up to 3–4 mm/min, close to zero mm/min, as well as negative values (backmelting) were observed. Dopant striations are clearly visible in the Sb-doped crystal. They were characterized by spreading resistance measurements and differential interference contrast microscopy. The frequencies of temperature fluctuations, microscopic growth rates, and the dopant inhomogeneities correspond quite well, with main frequencies between 0.1 and 0.3 Hz. 3D numerical simulations were performed to predict the optimum position of the temperature sensor, and the characteristic temperature amplitudes and frequencies. At a position 3.4 mm above the interface and 1.4 mm inside the melt, equivalent to the sensor tip position in the experiment, temperature fluctuations up to 1.8°C and frequencies ⩽0.25 Hz were found in the simulations.

Doping profile effects on modulation-doped single nonabrupt GaAs/AlxGa1 − xAs quantum wells

We study inhomogeneous doping effects on the confinement properties of modulation-doped single nonabrupt GaAs/AlxGa1−xAs quantum wells. We describe the inhomogeneous doping using error function profiles, and we solve self-consistently the coupled Schrödinger (with a position dependent kinetic energy operator) and Poisson equations to obtain the electron energy levels. When the nonabrupt interfaces (spacer layer) are 10Å(100Å) wide and the presence of Si-dopant density in a 100 Å GaAs well region is only 10% of the Si-dopant density in the Al0.3Ga0.7As barriers, the lowest intersubband transition energy increases 37 meV in comparison with that calculated within the homogeneous doping-abrupt interface picture.

The study of electrical and magnetic properties of LiPF 6 doped polyaniline

The results of temperature dependent dc conductivity, EPR magnetic susceptibility, and X-ray photoelectron spectroscopy experiments (XPS) are reported for polyaniline (PAN) doped with lithium hexafluorophosphate (LiPF 6), PAN-LiPF 6. DC conductivity ( σ dc) and its temperature dependence of PAN-LiPF 6 samples vary with the average molecular weight (Mw) of polyaniline used and the composition of doping solution. The EPR linewidth and Pauli susceptibility ( χ P) depend on the Mw of PAN used. The σ dc and the χ P of the intermediate Mw PAN-LiPF 6 samples are higher than those of the low Mw PAN samples, indicating more highly conducting state of the intermediate Mw PAN samples. Based on the results of XPS and EPR experiments, some portions of quinoid rings in emeraldine base form of PAN are transformed into benzenoid rings through LiPF 6 doping process, indicating the formation of polarons. However, the existence of some portions of quinoid rings in PAN-LiPF 6 samples after doping suggests an inhomogeneous doping or a pseudo doping.

Doped CuO 2 Planes in High T c Cuprates: 2D Or Not 2D ?

The key problem in physics of underdoped cuprates is whether the doping is inhomogeneous and holes are expelled into the 1D domains (“stripes”). Direct comparison of the resistivity vs T curves of the recently discovered 1D spin-ladder cuprates and underdoped cuprates below the pseudogap temperature T* shows a remarkable similarity which implies that the main scattering mechanism is the same for these two classes of cuprates and therefore in the pseudogap regime the transport in underdoped cuprates is essentially 1D. All the resistivity curves in underdoped cuprates can then be fitted by the model of the 1D quantum transport with the inelastic length in charge stripes being fully controlled by the magnetic spin correlation length in even-chain spin-ladders formed in the Cu-O plane as a result of inhomogeneous doping. Knight shift data are also successfully interpreted by taking the same spin-gap value as the one found from resistivity data.

Bistability and hysteresis of solitons in inhomogeneously doped fibers with saturating nonlinearity

Inhomogeneous doping of a silica glass fiber is proposed to have bistable soliton propagation. The properties of the solitons in one of the possible models are studied and interpreted.Received 5 June 1997DOI:https://doi.org/10.1103/PhysRevE.58.5021©1998 American Physical Society

Fabrication of sub-μm bipolar transistor structures by scanning probe microscopy

We show how sub-μm sized transistor structures (down to 50 nm cross section) can be fabricated by thermally assisted electromigration of mobile dopants inside the semiconductor CuInSe2. Small device structures are fabricated by application of an electric field to the sample via the contact, defined by a conducting atomic force microscope tip. The structures are characterized by nm scale scanning spreading resistance and scanning capacitance measurements to reveal the inhomogeneous doping profiles created by the electric field.

Optimization of arbitrarily doped MINP + solar cell performance

A comprehensive model of four layered MINP + (metal-tunnel insulator - NP + semiconductor) structure incorporating an inhomogeneous impurity doping profile is numerically simulated. The influence of built-in electric field in the device on its performance is investigated. The drift fields are the result of the nonuniformaly doped semiconductor. The dependence of the minority carrier lifetime and mobility on the doping density are taken into account. Solution curves for the complete set of transport, continuity and Poisson equations for the device as solar cell are obtained. Significant device parameters are identified and model calculations are carried out over a range covering most physically realizable values for these parameters. The I-V characteristics are calculated as a function of insulator thickness, metal workfunction, substrate doping density and semiconductor thickness with present semiconductor fabrication technology.

Dopant inhomogeneities due to convection in microgravity: Spatial effects

Spatial structure of thermal convection, onset of the secondary flows and concentration inhomogeneities induced by thermal convection in a parellelipiped are investigated on the basis of three dimensional unsteady Navier-Stokes equations for Boussinesq approach using direct numerical simulation as well as stability analysis.

Macro-segregation, dynamics of interface and stresses in high pressure LEC grown crystals

High dislocation density and strong dopant inhomogeneities have been found in high pressure liquid-encapsulated Czochralski (HPLEC) grown crystals. The origin and underlying mechanisms of these defects are attributed to the complex nature of transport phenomena in the HPLEC system. Our integrated computer model (MASTRAPP) can simulate this process by calculating the flow and heat transfer in both the melt and the gas, and thermal-elastic stress in the crystal. In this work, this model has been further extended to investigate the development of thermal stress in the growing crystal and the redistribution of dopant in the melt. The results for InP growth show complex gas flow and heat transfer pattern in the system. Two large stress spots are predicted by the model, one at the edge of the crystal just above the encapsulant layer and the other in the top corner of the crystal. Although the stress always remains largest at the first location, its value decreases as the crystal grows, due to the enhanced cooling of the crystal. A curved crystal/melt interface is also found to introduce high thermal stresses in its vicinity, which may be dangerous because of a high temperature at the interface and thus a low strength of the crystal. The model also predicts both radial and longitudinal dopant segregation in the growing crystal, and shows that the dopant redistribution in the melt is caused by the complex flow pattern in the melt. This is the first time, that a strong radial dopant segregation has been predicted based on a comprehensive flow model for a HPLEC growth.

Effect of finite metallization and inhomogeneous dopings on slow-wave-mode propagation

A finite-element simulation has been implemented to evaluate the slow-wave-mode propagation characteristics in metal-insulator-semiconductor (MIS) waveguiding structures. Particular emphasis has been placed on coplanar waveguides compatible with silicon integrated circuits (ICs), with an objective of evaluating the effect of inhomogeneous doping on propagation characteristics. The simulator has been successfully benchmarked against a number of cases presented in the literature, including MIS coplanar waveguides. The effect of inhomogeneous doping and finite metallization in maintaining a large slowing factor while reducing the attenuation constant and increasing transmission-line Q is presented, and constraints on slow-wave-mode passive components are discussed.

A new analytical method of solving 2D Poisson's equation in MOS devices applied to threshold voltage and subthreshold modeling

In this paper we present a new theoretical approach in MOS modeling to derive analytical, physics-based model equations for the geometry and voltage dependence of threshold voltage and for the subthreshold behavior of short-channel MOSFETs. Our approach uses conformal mapping techniques to analytically solve the two-dimensional Poisson equation, whereby inhomogeneous substrate doping is taken into account. The presented model consists of analytical equations in closed form and uses only physically meaningful parameters. Therefore, the results are not only useful in circuit simulators but also in calculations of scaling behavior, where planned processes can be investigated. Comparison with numerical device simulation results and measurements confirm the high accuracy of the presented model.

Contactless measurement of dopant distribution using etch roughnesses

The analysis of striae patterns is commonly restricted to their lateral frequency distribution. Using surface mappings made by shearing interference microscopy (SIM), however, the effects of dopant inhomogeneities on etch roughnesses can be quantitatively detected. The SIM technique allows nanoscale measurements in the vertical direction. Thus, the determination of the height of striations up from ∼ 0.5 nm is possible. The lateral pixel resolution reaches 0.14 μm. Contrarily, wide image fields (maximum 2.2 × 2.2 mm2) permit the recording of macrosegregations. The application on the axial segregation in Si floating-zone crystals (FZ) grown under 1g and μg conditions shows a good correlation of spreading resistance (SR) and roughness profiles.

Phase separation kinetics in La2CuO4+? and inhomogeneous hole doping in the antiferromagnetic regime (0 &lt;x &lt; 0.02) of La2?x Sr x CuO4

The diffusion of the excess oxygen during phase separation in La2CuO4+δ was studied using thermal history-dependent normal state magnetic susceptibilityϰ(T, t) measurements versus temperatureT and timet as a probe. A large thermal hysteresis ofϰ(T) was observed for La2CuO4.044 between data obtained after quenching to 5 K and then warming, and data obtained while or after slowly cooling from 300 K. A model for the excess oxygen diffusion is presented, from which theϰ(T, t) data yield aT-independent activation energy of 0.24(3) eV for the diffusion coefficient of the excess oxygen from 150 to 220 K. In related work, we have used139La NQR andμSR measurements to probe the antiferromagnetic (AF) region (x<0.02) of the La2−xSr x CuO4 system below the Neel temperatureTN(x), from which we extract the Cu+2 staggered magnetizationM†(x, T). M†(x, T=0), extrapolated from above 30 K, was successfully modeled with spin-wave theory, assuming that the doped holes are mobile and are situated in walls in the CuO2 plane which uncouple undoped AF domains; these domains are coupled to those in adjacent CuO2 planes. This agreement supports the previous hypothesis that microsegregation of the (mobile) doped holes into domain walls occurs above ∼30 K, consistent with the phenomenology of Emery and Kivelson. Below ∼30 K, an anomalous increase inM†(x, T) is observed, such thatM†(x, T=0) is nearly independent ofx. We interpret this effect as arising from localization of the doped holes below ∼30 K.

Comparative analysis of thermocapillary convection in one- and two-layer systems. Problem of oscillatory convection

The numerical investigation of thermocapillary convection and heat and mass transfer under fluid crystallization had been carried out for one-layer fluid column and for two-layer systems of rectangular form with crystallization of one of layers. The dependence of dopant distribution inhomogeneity in melt on phase boundary had been obtained for Pr = 0.023 and 1 and Ma = 10 0–10 5. The effect of constant magnetic field on micro- and macrosegregation of dopant in growing crystals is studied under action of thermocapillary convection and vibration. A primary attention is given the oscillatory regime of thermocapillary convection and its effects on dopant distribution. By way of illustration as it should be solved the transition problem to oscillatory regime it was shown that oscillatory regime of thermal buoyancy convection is associated with the Kelvin-Helmholz 's instability.

Scanning tunnelling microscopy of diamond irradiated with high energy ions

The surfaces of boron-doped synthetic diamonds have been investigated by scanning tunnelling microscopy before and after irradiation at room temperature with Kr ions of an energy of about 1 MeV a.m.u. −1 and a dose of about 10 12 ions cm −2. The structures observed after irradiation showed diameters ranging from 3 to 20 nm and are attributed to single-ion tracks and multiple hits of ions at the same position on the surface. The distribution of the surface roughening by ion impact was found to be inhomogeneous on a submicron scale. This is proposed to be due to an inhomogeneous boron doping during the process of crystal growth.

Dopant migration in conducting polymers

Dopant migration in conducting polymers due to an applied potential difference over the sample has been investigated by computer simulations. Dopant ions migrate as a result of three influences: the electrical field due to the applied potential difference, the redox-potential gradient in the conducting polymer due to an uneven dopant distribution and the dopant concentration gradient. It has been found that an applied potential difference can cause strongly inhomogeneous dopant distributions and considerable changes in the sample conductance as a function of time. The simulation results are supported by experimental evidence.

The inversion layer of subhalf-micrometer n- and p-channel MOSFET's in the temperature range 208-403 K

Minority carrier mobility has been extracted from I-V measurements on N- and PMOS-transistors entirely processed by means of X-ray lithography with effective channel lengths down to 0.35 mu m. The measurements have been performed within the temperature range 208-403 K (-65 degrees C to +130 degrees C). The accuracy of the mobility determination has been investigated, especially with regard to the determination of the effective channel length and the series resistance. The results indicate a significant mobility reduction for short-channel NMOS devices at temperatures below 300 K. A slight increase of the threshold-voltage is observed in the short-channel region. Both effects can be required by an inhomogeneous lateral doping profile within the channel due to standard submicron technology; this has been confirmed by two-dimensional device simulation. >

Photoluminescence mapping of AlGaAs/GaAs HBT layer sequences

Photoluminescence mapping of 2 inch and 3 inch wafers with AlGaAs/GaAs heterojunction bipolar transistor (HBT) layer sequences is reported. Photoluminescence spectra taken at 77 K on these layers reveal four well distinct emission lines from cap, emitter, collector and base, respectively. The mapping of line intensities and spectral positions allows the analysis of doping, composition and thickness homogeneities influenced by epitaxy or device processing. The characteristics of the luminescence light emitted from GaAs: C base layers and the DC current gain of HBT structures after processing exhibit the same lateral distribution over the wafer. The analysis of the spectra showed that the intensity variations can partially be explained by an inhomogeneous base doping. Luminescence mapping of the HBT base related luminescence line was also performed on partially and fully processed wafers. This measurement allowed a comparison of luminescence data with high frequency device results. We found that the ratio between maximum oscillation frequency f max and transit frequency f T of the HBTs clearly reflect the variation of the base hole concentration.