John P. Wallace

Eddy current measurement of crystal axial thermal profiles during Czochralski silicon crystal growth

Abstract The axial thermal profiles of silicon crystals during the Czochralski crystal growth process were measured experimentally by using an eddy current technology. The intrinsic conductivity changes in the crystal resulting from cooling were measured in terms of the eddy current amplitude and phase responses, and the axial thermal profiles of the growing crystal were subsequently derived from the results. The experimental setup consisted of a resistance-heated Czochralski puller with a 203 mm (8 inch) hot-zone, a multifrequency encircling eddy current sensor and a commercially available eddy current system interfaced with an IBM PC. The silicon crystals, 70 mm in diameter and up to 406 mm (16 inches) in length, were grown from 5 kg melts. The eddy current sensor was initially positioned 100 mm above the melt, and then the measurements were made as it was lowered to 25 mm above the melt at a constant speed of 25 mm/min. The experimental results indicate that the axial thermal profile in the region is nearly linear and quite transient during the initial phase of body growth. As the crystal gets longer, the increasing heat loss by radiation from the crystal surface causes the overall profile to shift downward. When the crystal reaches 200–250 mm in length, a steady state condition is achieved, and the overall axial thermal profile stays nearly invariant for the remainder of the growth. The steady state axial thermal gradient in the region is estimated to be about 4–6°C/mm.

Eddy current monitoring system and data reduction protocol for Czochralski silicon crystal growth

Abstract A computer controlled eddy current system for the in situ monitoring of Czochralski silicon crystal growth is introduced. A scheme to reduce eddy current sensor data to temperature values and thermal profiles in the growing crystal is presented. The principle of eddy current testing involves the behavior of electromagnetic radiation penetrating the silicon crystal and its subsequent reflection. This behavior is outlined by Maxwells equations, and it is the solution of the electromagnetic field boundary-value problem that relates voltage measurements from the eddy current probe to the changing electrical conductivity of the crystal. Due to a strong temperature dependence of the electrical conductivity in solid silicon, it is then possible to determine thermal profiles within the growing crystal.

Internal heat transfer in Czochralski grown silicon crystals

Silicon crystals grown by the CZ process have recently been studied with eddy current techniques to determine thermal profiles within the growing crystal. A key question concerning heat transfer in this semiconductor system during CZ growth is whether optical semitransparency in the infrared is important in affecting the high‐temperature thermal distribution within the crystal. From normal Fourier’s law calculations, well behaved profiles with rather flat radial isotherms are predicted in CZ growth. Eddy current data, though, show abrupt temperature changes near the crystal outer surface, indicating sharp radial thermal gradients. It is proposed that these sharp gradients are due in part to the onset of optical semitransparency in the crystal in the infrared. It is expected that such a transparency phenomenon will occur below a transition temperature. Any sharp gradients can be responsible for creep damage during growth.

Eddy current study of solidification in lead and lead 20 pct tin

The use of eddy currents to nondestructively evaluate metallic solidification is modelled in one dimension. Calculated responses of the reflected signals show characteristics that can be identified with different solidification morphologies, the extent of freezing, and temperature changes. Experimental verification of the calculated results is done with lead and a lead-20 tin alloy. Morphological details of the solidification for both lead and lead-20 tin alloy are extracted from the eddy current responses in real time. Features such as uniform freezing front motion in pure lead and phase formation in the alloy are detected. Finally, compensation for the thermal gradients in the copper mold and the phase shift in the balancing network allow for good agreement between the eddy current response and the calculated response for freezing.

Effects of growth conditions on thermal profiles during Czochralski silicon crystal growth

Abstract An eddy current testing method was used to continuously monitor crystal growth process and investigate the effects of growth conditions on thermal profiles during Czochralski silicon crystal growth. The experimental concept was to monitor the intrinsic electrical conductivities of the growing crystal and deduce temperature values from them. In terms of the experiments, the effects of changes in growth parameters, which include the crystal and crucible rotation rates, crucible position, and pull rate, and hot-zone geometries were investigated. The results show that the crystal thermal profile could shift significantly as a function of crystal length if the closed-loop control fails to maintain a constant thermal condition. As a direct evidence to the effects of the melt flow on heat transfer processes, a thermal gradient minimum was observed when the crystal/crucible rotation combination was 20/-10 rpm cw. The thermal gradients in the crystal near the growth interface were reduced most by decreasing the pull rate or by reducing the radiant heat loss to the environment; a nearly constant axial thermal gradient was achieved when either the pull rate was decreased by half, the height of the exposed crucible wall was doubled, or a radiation shield was placed around the crystal. Under these conditions, the average axial thermal gradient along the surface of the crystal was about 4–5°C/mm. When compared to theoretical results found in literature, the axial profiles correlated well with the results of the models which included radiant interactions. However, the radial gradients estimated from three-frequency data were much higher than what were predicted by known theoretical models. This discrepancy seems to indicate that optical phenomenon within the crystal is significant and should be included in theoretical modeling.

Eddy current responses of an encircling sensor in a Czochralski silicon crystal puller

Abstract For a situation involving a finite length crystal in a circular coil atop the melt, as in a Czochralski puller, two types of spatially dependent effects are expected as the coil makes a vertical scan towards the melt surface. One is the exponential response to the highly conductive silicon melt. The other is a rise in temperature of the sensor if the sensor cooling system is inadequate. Here, a physical model of the Czochralski crystal growth condition was constructed, and appropriate simulation experiments were conducted to measure the strength of these extraneous signals. A low resistivity (3 mΩ cm) silicon crystal doped with 3.6×10 19 atoms/cm 3 of boron was used to simulate the hot intrinsic silicon crystal, and a type 309 stainless steel plate which has an electrical resistivity of 0.078 mΩ cm at room temperature was used to simulate the silicon melt. The simulation results were then used to filter out the extraneous signals from eddy current data collected during actual Czochralski crystal growth experiments and derive crystal axial thermal profiles using a one-dimensional solution. When the same simulation data were analyzed two-dimensionally, the results correlated well with the responses predicted by a numerical model.

Eddy current response to metallic solidification in one dimension

The eddy current response to solidification is modelled in one dimension. The calculated responses show characteristics that can be identified with different solidification morphologies and the extent of solidification. Similarly, the calculated response to cooling the melt and mold either prior to or after freezing have a characteristic behavior which is different from that of the solidification process. The results indicate that for the case of lead and most metals with similar electrical conductivity discontinuities between liquid and solid metal actual eddy current responses to cooling and solidification can be measured.

Multifrequency eddy current diagnostics of axial and radial thermal profiles during silicon crystal growth

Abstract Two-dimensional thermal profiles of growing Czochralski silicon crystals have been determined in situ using an eddy current probe. An analysis of multifrequency eddy current data was accomplished by modelling the interactions of the induced electromagnetic fields with the growing crystal and silicon melt. A two-dimensional numerical solution of the governing electromagnetic wave equation derived from Maxwells relations was employed to translate multifrequency data into axial and radial crystal thermal profiles. Experiments were conducted in a resistance-heating type CZ puller with a 203 mm (8 inch) hot-zone and 6.5 kg charge capacity. The silicon crystals grown were 80 mm in diameter and monitored with an encircling eddy current coil. It was found that crystal thermal profiles are greatly influenced by the radiant interaction with the environment and crucible position within the hot-zone. Some of the eddy current data were correlated with heat transfer model calculations as well as experimental measurements found in the literature. Heat transfer model predictions were consistent with our crystal surface temperature measurements. However, the radial gradients near the crystal surface were larger than those predicted by the same heat transfer models. This finding is significant since any sharp gradients can be responsible for creep damage during growth.

Positron Probing of Microstructures and Substructures in Metals and Alloys

Publisher Summary A recent model with supporting experimental observations has extended and generalized the positron-defect interaction process to show that the positron lifetimes in metals may also be influenced by nonthermal positrons. It has also been proposed that multiple scattering interactions of the positron with such extended defects as dislocations can also be a mechanism for prolonged positron lifetimes in metals. This proposal supports the potential of positrons as nondestructive probes to characterize extended defects in metals and alloys, through experimentally distinguishable annihilation signatures. This chapter presents and discusses the results of the experimental evaluation of this possibility through the positron annihilation studies in metals and alloys with well-characterized microstructures and extended defect substructures and damage introduced by heat treatments and by various deformation processes such as creep, fatigue, tension and compression, and fracture.