Radial Dopant Segregation Research Articles

Highly Responsive Plasmon Modulation in Dopant-Segregated Nanocrystals.

Electron transfer to and from metal oxide nanocrystals (NCs) modulates their infrared localized surface plasmon resonance (LSPR), revealing fundamental aspects of their photophysics and enabling dynamic optical applications. We synthesized and chemically reduced dopant-segregated Sn-doped In2O3 NCs, investigating the influence of radial dopant segregation on LSPR modulation and near-field enhancement (NFE). We found that core-doped NCs show large LSPR shifts and NFE change during chemical titration, enabling broadband modulation in LSPR energy of over 1000 cm-1 and of peak extinction over 300%. Simulations reveal that the evolution of the LSPR spectra during chemical reduction results from raising the surface Fermi level and increasing the donor defect density in the shell region. These results establish dopant segregation as a useful strategy to engineer the dynamic optical modulation in plasmonic semiconductor NC heterostructures going beyond what is possible with conventional plasmonic metals.

Effect of magnetic field on radial dopant segregation in crystal growth by traveling heater method

A three dimensional time dependent computational model is developed to simulate the melt flow, heat transfer and the dopant transport during the growth of Si 1− x Ge x semiconductor crystals by traveling heater method. The effect of static magnetic fields of different orientations on the radial and axial segregation of dopant is analyzed. It is observed that the flow oscillations are damped and flow becomes steady for both horizontal and vertical applied magnetic fields as the Hartmann number increases. It is found that there is an optimum value of Hartmann number beyond which little improvement in uniformity of concentration can be obtained at the growth interface.

Effect of Magnetic Field on Radial Dopant Segregation in Crystal Growth

A three-dimensional time-dependent computational model is developed to simulate the melt flow and the dopant transport during the growth of Si1−x Ge x semiconductor crystals. The effect of static magnetic fields of different orientations on radial segregation of dopant is analyzed. It is observed that the flow oscillations are damped and flow becomes steady for both horizontal and vertical applied magnetic fields as the Hartman number increases. It is found that there is an optimum value of Hartman number for each Rayleigh number beyond which little or no improvement in uniformity of concentration can be obtained at the growth interface.

Radial segregation in VGF-RMF grown germanium

In this paper experimental results of the radial dopant segregation in Ge:Ga single crystals grown by the vertical gradient freeze technique with a rotating magnetic field are presented. The segregation is analysed on the basis of the carrier concentration measured by means of Hall effect and Fourier transform infrared (FTIR) spectroscopy. In growth without the field the carrier concentration increases towards the axis, whereas much more uniform radial concentration profiles are found in crystals grown under the influence of the rotating field indicating a pronounced impact of the melt flow on the dopant segregation. Apparently, the accumulation of the Ga solute near the centre of the melt during growth under natural buoyancy is reduced by the electromagnetically induced flow. This phenomenon is discussed with respect to analytical and numerical results published recently.

Influence of rotational vibrations on heat and mass transfer during vertical bridgman growth F germanium crystals

The effect of high-frequency vibrations with small amplitude on the directional solidification of binary alloys is studied numerically. The calculations are made in the framework of a quasi-static approach for gallium doped germanium. The finite volume method is used. It is shown that in terrestrial conditions the influence of rotational vibrations on the radial dopant segregation is rather weak: quite high intensity of vibrations is needed to achieve a significant decrease in the dopant segregation. Under reduced gravity conditions, the effect of vibrations is considerable: the radial dopant segregation becomes uniform even at low-intensity vibrations.

Thermocapillary Convection of Liquid Bridge under Axisymmetric Magnetic Fields

Three-dimensional numerical simulation of thermocapillary flow in liquid bridge model is performed. The effects of the magnetic field, including both axial uniform magnetic field and axisymmetric non-uniform magnetic field generated by circle coil, on the thermocapillary flow of semiconductor melt are investigated. For a three-dimensional thermocapillary flow, the axial magnetic field and the axisymmetric nonuniform magnetic field suppress convection effectively, and the three-dimensional thermocapillary flow tends to become an axisymmetric one. Under axial magnetic field, the convection in central core region becomes very weak, and in the meantime, the energetic thermocapillary flow is squeezed toward free surface. While the axisymmetric non-uniform magnetic field generated by single coil is applied on the melt of liquid bridge, the convection structure is similar with that under axial magnetic field. By applying the axisymmetric CUSP magnetic field generated by two coils, convection structure depends on the symmetric plane position of two coils (SPPTC), the surface tension flow penetrates the whole liquid bridge and no stagnant core in the inner part of the melt is observed when SPPTC locates at z � ¼ 0:5, which is thought as a more favorable convection structure to alleviate radial dopant segregation in floating zone crystal growth. [doi:10.2320/matertrans.MB200830]

Three-dimensional modelling of radial segregation due to weak convection

A comprehensive three-dimensional, time-dependent model of heat, momentum and solute transfer during solidification is carried out to illustrate the influence of weak convection, caused by surface tension forces, on radial dopant segregation occurring in crystal growth under micro-gravity conditions. 3D adaptive finite element method is used in order to simulate the motion and deformation of the solidification interface. The geometry studied is a Bridgman configuration with a partly coated surface. The small slots in the coating gives a free surface in a controlled way, and is varied in order to alter the Marangoni flow. In this study, A comparison is made between the numerical results and the experimental results. A good agreement has been observed for the effective distribution coefficient k eff and for the radial segregation Δ c′. The radial dopant segregation is affected by weak convection.

Three-dimensional analysis of flow and segregation control by slow rotation for Bridgman crystal growth in microgravity

Although the buoyancy convection in the melt during crystal growth is greatly reduced in microgravity, the residual gravity, or the so-called g-jitter effect, can lead to three-dimensional (3D) unsteady flow and severe radial dopant segregation. Using a centrifuge to rotate the system about the growth axis could be an effective way to suppress the 3D flow and improve dopant uniformity. Through fully time-dependent 3D simulation of Bridgman growth of gallium-doped germanium crystals, we investigate the feasibility of using a centrifuge at low rotation rate to improve the dopant uniformity in the grown crystal. In this numerical model, in addition to the heat flow and the moving interface, both radial and axial segregations are also computed simultaneously for a growth period. The effect of slightly eccentric rotation is also considered and they can be an issue in practical implementation.

Simulation of radial dopant segregation in vertical Bridgman growth of GaSe, a semiconductor with anisotropic solid-phase thermal conductivity

For a range of growth conditions of practical interest, we simulate liquid- and solid-phase dopant distributions and radial segregation for several dopants (In, Sn, Cu, Se, Zn, and Cd) in vertical Bridgman growth of the nonlinear optical material gallium monoselenide. Besides these dopants, which have been used to modify the properties of Bridgman-grown GaSe and have segregation coefficients in the range 0.01⩽ k ̃ ⩽0.3 , we also consider a hypothetical dopant with k ̃ =0.8 . The computational model accounts for the anisotropic solid-phase thermal conductivity characteristic of nonlinear optical materials, interface deformation, convection in the melt, and conduction in the ampoule wall. The results show a strong dependence of radial segregation on growth rate over the range 0.25 μm s −1⩽ U⩽3 μm s −1, and a much weaker dependence on the maximum ampoule-wall temperature gradient over the range 15° C cm −1⩽ dT b (0)/ dz⩽60° C cm −1 . Overall radial segregation depends weakly on whether the melting temperature is “centered” between the high and low temperatures, and is insensitive to both the 23°C difference in the measured values of the melting temperature, and the large difference between the two measurements of the enthalpy of fusion. The overall radial segregation depends approximately linearly on the product of 1− k ̃ and the growth rate U over the entire range of segregation coefficients and growth rates considered. Radial segregation computed using an isotropic conductivity (one-third the trace of the conductivity tensor) gives results qualitatively different than predictions using the anisotropic conductivity. We also show how localized ampoule-wall heating in the “adiabatic” zone of a three-zone Bridgman furnace can dramatically alter radial segregation by creating one or more additional, weak, toroidal vortices just above the interface.

Radial segregation due to weak convection in a floating zone

The influence of weak convection, caused by surface tension forces, on radial dopant segregation occurring in crystals grown under microgravity conditions is studied numerically. The geometry considered corresponds to a floating-zone configuration with partially coated melt surfaces consisting of small evenly distributed spots of free surfaces. In order to distinguish dopant distribution due to weak convection clearly from distribution due to diffusion the spots only cover one quarter of the periphery. Thus, surface tension-driven convection is allowed only over one quarter of the floating-zone configuration resulting in an asymmetric dopant distribution. The percentage of free surfaces present is varied in order to alter the Marangoni flow rates. The maximum dopant concentration due to radial segregation is plotted as a function of a certain convection level. The results of the present numerical study are supposed to be used to design corresponding space experiments launched at the end of the year 2000.

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 axisymmetric magnetic fields on radial dopant segregation of floating-zone silicon growth in a mirror furnace

The effect of axisymmetric magnetic fields on radial dopant segregation of floating-zone silicon growth in a mirror furnace is studied through computer simulation. The mirror furnace is modeled by a point lamp model, and the magnetic fields are generated by wire coils carrying different currents. Heat and mass transfer, fluid flow, melt/solid interfaces, and the free surface are solved globally by a robust finite-volume/Newton's method. Both axial and cusp fields are considered. It is observed that the magnetic fields suppress the convection in the core region effectively, and squeeze the thermocapillary flow toward the free surface. However, due to poor mixing in the core region, large radial segregation is induced by strong magnetic fields, particularly by the cusp field. With a higher heat input, multiple steady states are also observed in weak magnetic fields.

Effect of rotation on radial dopant segregation in microgravity floating-zone crystal growth

Computer simulation was conducted to study the effect of rotation on radial dopant segregation in floating-zone crystal growth under microgravity. Heat transfer, fluid flow and mass transfer in the melt zone were considered simultaneously, with the surface tension gradients along the free surface of the melt and the centrifugal force induced by rotation as the driving forces for fluid flow. The growth front, feed front and free surface were calculated, these interfaces being nonisothermal and having nonuniform dopant concentrations. The most common case where the dopant has a segregation ratio k 0<1 was considered. In the absence of thermocapillary convection, dopant segregation can be easily reversed from toward the crystal surface to toward the crystal axis when the feed rod alone is rotated during crystal growth. As the rotation speed is increased further, dopant segregation is still toward the crystal axis but reduced significantly due to mixing. Dopant segregation, however, is not reversed when the crystal alone is rotated or when the crystal and the feed rod are counterrotated. A nearly uniform dopant distribution can be produced by counterrotation at sufficient speeds. Thermocapillary convection tends to cause dopant segregation toward the crystal axis. In the presence of thermocapillary convection, crystal rotation and counterrotation both cause the location of the maximum dopant concentration to shift radially outward from the crystal axis, whereas feed-rod rotation does not. Again, a nearly uniform dopant distribution can be produced by counterrotation at sufficient speeds. The stronger the thermocapillary convection, the higher these counterrotation speeds become.

Radial dopant segregation in zero-gravity floating-zone crystal growth

A computer model was developed to study radial dopant segregation in floating-zone crystal growth under zero-gravity. Heat transfer, fluid flow and mass transfer in the melt zone were considered simultaneously. The growth front, feed front and free surface were calculated, these interfaces being nonisothermal and having nonuniform dopant concentrations. For a dopant with a segregation ratio k 0<1, the model showed the following trends. A convex growth front causes the dopant to segregate toward the crystal surface whereas a concave one toward the crystal axis, the former being consistent with the experiment of Levenstam et al. The effect of the growth front shape is quickly overshadowed as thermocapillary convection begins to increase in strength. Thermocapillary convection causes the dopant to segregate toward the crystal axis. However, as thermocapillary convection grows stronger, dopant segregation toward the crystal axis first increases and then decreases due to improved mixing. The direction of dopant segregation is reversed when k 0 & 1. Finally, the shape of the growth front can be affected by radial dopant segregation.

Radial segregation induced by natural convection and melt/solid interface shape in vertical bridgman growth

The influence of natural convection in the melt and the shape of the melt/solid interface on radial dopant segregation are analyzed for a prototype vertical Bridgman crystal growth system by finite element methods that solve simultaneously for the velocity field in the melt, the shape of the solidification isotherm, and the temperature distribution in both phases. Results are presented for crystal and melt with thermophysical properties similar to those of gallium-doped germanium in Bridgman configurations with melt below (thermally destabilizing) and above (stabilizing) the crystal. Steady axisymmetric flows are classified according to Rayleigh number and are either nearly equal to the growth velocity, have a weak cellular structures or have large amplitude cells. The flows in the two Bridgman configurations are driven by different temperature gradients and are in opposite directions. Finite element calculations for the transport of a dilute dopant by these flow fields reveal radial segregation levels as large as 60% of the mean concentration. Radial segregation is most severe at an intermediate value of Rayleigh number above which the dopant distribution along the interface levels as the intensity of the flow increases. The complexity of the concentration field coupled with calculations of the effective segregation coefficient show the coarseness of the usual diffusion-layer approximation for describing the dopant distribution adjacent to the crystal. The length of the insulated zone and the ratio of thermal conductivities between melt and crystal are identified as additional critical parameters for setting the degree of radial segregation.