@article{wang_ma_bliss_isler_becla_2007, title={Combining static and rotating magnetic fields during modified vertical bridgman crystal growth}, volume={21}, ISSN={["1533-6808"]}, DOI={10.2514/1.28772}, abstractNote={Static magnetic fields have been widely used to control the heat and mass transfer during crystal growth, whereas rotating magnetic fields are attracting a growing attention for crystal-growth technologies from the melt A combination of static and rotating magnetic fields can be used to control the transport phenomena during semiconductor crystal growth. This paper treats the flow of molten gallium-antimonide and the dopant transport during the vertical Bridgman process using submerged heater growth in this combination of externally applied fields. This paper investigates the effects of these fields on the transport in the melt and on the dopant distributions in the crystal.}, number={4}, journal={JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER}, author={Wang, X. and Ma, N. and Bliss, D. F. and Isler, G. W. and Becla, P.}, year={2007}, pages={736–743} }
 @article{yang_ma_bliss_bryant_2007, title={Melt motion during liquid-encapsulated Czochralski crystal growth in steady and rotating magnetic fields}, volume={28}, ISSN={["0142-727X"]}, DOI={10.1016/j.ijheatfluidflow.2006.08.001}, abstractNote={During the liquid-encapsulated Czochralski (LEC) process, a single compound semiconductor crystal such as gallium-antimonide is grown by the solidification of an initially molten semiconductor (melt) contained in a crucible. The motion of the electrically-conducting molten semiconductor can be controlled with externally-applied magnetic fields. A steady magnetic field provides an electromagnetic stabilization of the melt motion during the LEC process. With a steady axial magnetic field alone, the melt motion produces a radially-inward flow below the crystal–melt interface. Recently, an extremely promising flow phenomenon has been revealed in which a rotating magnetic field induces a radially-inward flow below the crystal–melt interface that may significantly improve the compositional homogeneity in the crystal. This paper presents a model for the melt motion during the LEC process with steady and rotating magnetic fields.}, number={4}, journal={INTERNATIONAL JOURNAL OF HEAT AND FLUID FLOW}, author={Yang, Mei and Ma, Nancy and Bliss, David F. and Bryant, George G.}, year={2007}, month={Aug}, pages={768–776} }
 @article{wang_ma_2007, title={Semiconductor crystal growth by the vertical Bridgman process with transverse rotating magnetic fields}, volume={129}, ISSN={["1528-8943"]}, DOI={10.1115/1.2352790}, abstractNote={During the vertical Bridgman process, a single semiconductor crystal is grown by the solidification of an initially molten semiconductor contained in an ampoule. The motion of the electrically conducting molten semiconductor can be controlled with an externally applied magnetic field. This paper treats the flow of a molten semiconductor and the dopant transport during the vertical Bridgman process with a periodic transverse or rotating magnetic field. The frequency of the externally applied magnetic field is sufficiently low that this field penetrates throughout the molten semiconductor. Dopant distributions in the crystal are presented.}, number={2}, journal={JOURNAL OF HEAT TRANSFER-TRANSACTIONS OF THE ASME}, author={Wang, X. and Ma, N.}, year={2007}, month={Feb}, pages={241–243} }
 @article{wang_ma_2006, title={Bridgman-Stockbarger growth of binary alloyed semiconductor crystals with steady magnetic fields}, volume={20}, ISSN={["1533-6808"]}, DOI={10.2514/1.15584}, abstractNote={Single crystals of alloyed compound semiconductor crystals such as gallium‐aluminum‐antimonide are needed for optoelectronic devices. These crystals are solidified from a solution of molten gallium‐antimonide and aluminum‐antimonide in a Bridgman‐Stockbarger furnace. During the growth of alloyed semiconductor crystals, the solute’s concentration is not small so that the density differences in the melt are very large. These compositional variations drive compositionally driven buoyant convection, or solutal convection, in addition to thermally driven buoyant convection. These buoyant convections drive convective species transport, which produce nonuniformities in the concentration in both the melt and the crystal. A numerical model is presented for the unsteady transport for the growth of alloyed semiconductor crystals during the vertical Bridgman‐Stockbarger process with a steady axial magnetic field. Predictions of alloy concentration in the crystal and in the melt at several different stages during crystal growth are presented.}, number={2}, journal={JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER}, author={Wang, X and Ma, N}, year={2006}, pages={313–319} }
 @article{wang_ma_bliss_iseler_becla_2006, title={Comparing modified vertical gradient freezing with rotating magnetic fields or with steady magnetic and electric fields}, volume={287}, ISSN={["1873-5002"]}, DOI={10.1016/j.jcrysgro.2005.11.036}, abstractNote={This investigation treats the flow of molten gallium-antimonide and the dopant transport during the vertical gradient freezing process using submerged heater growth. A rotating magnetic field or a combination of steady magnetic and steady electric fields is used to control the melt motion. This paper compares the effects of these externally applied fields on the transport in the melt and on the dopant segregation in the crystal. Crystal growth in a combination of steady magnetic and electric fields produces a crystal with more radial and axial dopant homogeneity than growth in a rotating magnetic field.}, number={2}, journal={JOURNAL OF CRYSTAL GROWTH}, author={Wang, X and Ma, N and Bliss, DF and Iseler, GW and Becla, P}, year={2006}, month={Jan}, pages={270–274} }
 @article{ma_walker_2006, title={Electromagnetic stirring in crystal growth processes}, volume={2}, number={2}, journal={Fluid Dynamics & Materials Processing : FDMP}, author={Ma, N. and Walker, J. S.}, year={2006}, pages={119–125} }
 @article{wang_ma_bliss_iseler_becla_2006, title={Parametric study of modified vertical bridgman growth in a rotating magnetic field}, volume={20}, ISSN={["1533-6808"]}, DOI={10.2514/1.19572}, abstractNote={Using the vertical Bridgman process, a single semiconductor crystal is grown by the solidification of an initially molten semiconductor (melt) contained in a crucible. In addition to the main Bridgman heater, a submerged heater is added that separates the melt into two zones, i.e., an upper melt and a lower melt that is continuously replenished with fluid from the upper melt to offset the rejection of species along the crystal-melt interface. As crystal growth progresses, the crucible is slowly lowered to maintain a constant lower melt depth. An externally applied rotating magnetic field produced by a synchronous motor stator is used to control the transport of the electrically conducting molten semiconductor. This paper treats the flow of a molten semiconductor and the dopant transport during the vertical Bridgman process with a submerged heater and with a transverse rotating magnetic field. This paper also investigates the effects of the crystal radius, the melt depth, the strength of the magnetic field, and the number of poles in the inductor on the dopant distributions in the crystal.}, number={3}, journal={JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER}, author={Wang, X. and Ma, N. and Bliss, D. F. and Iseler, G. W. and Becla, P.}, year={2006}, pages={384–388} }
 @article{wang_ma_bliss_iseler_2006, title={Solute segregation during modified vertical gradient freezing of alloyed compound semiconductor crystals with magnetic and electric fields}, volume={49}, ISSN={["1879-2189"]}, DOI={10.1016/j.ijheatmasstransfer.2006.03.008}, abstractNote={Single crystals of gallium–aluminum–antimonide are solidified from a solution of molten gallium–antimonide and aluminum–antimonide. Electromagnetic stirring can be induced in the melt by applying a weak electric field together with a weak axial magnetic field. This paper presents a numerical model which uses a Chebyshev spectral collocation method with a second-order implicit time integration scheme with Gauss–Lobatto collocation points. This investigation models the unsteady motion and solute transport during vertical gradient freezing by submerged heater growth with electromagnetic stirring. The radial homogeneity in the crystal improves as the solute’s concentration increases.}, number={19-20}, journal={INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER}, author={Wang, X. and Ma, N. and Bliss, D. F. and Iseler, G. W.}, year={2006}, month={Sep}, pages={3429–3438} }
 @article{ma_walker_2006, title={Strong-field electromagnetic stirring in the vertical gradient freeze process with a submerged heater}, volume={291}, ISSN={["1873-5002"]}, DOI={10.1016/j.jcrysgro.2006.02.041}, abstractNote={This paper treats a steady, axisymmetric melt motion due to electromagnetic (EM) stirring during vertical gradient freeze crystal growth with a submerged heater. There is a radial electric current through the melt from a graphite electrode around the crystal and melt to another graphite electrode at the center of the heater. There is a strong axial magnetic field produced by an external solenoid. Solutions are presented for the azimuthal and meridional velocities in the subregions of the melt. The melt motion depends on the electric currents through the crystal, even though the electrical conductivity of the crystal is much less than that of the melt.}, number={1}, journal={JOURNAL OF CRYSTAL GROWTH}, author={Ma, Nancy and Walker, John S.}, year={2006}, month={May}, pages={249–257} }
 @article{yang_ma_2005, title={A computational study of natural convection in a liquid-encapsulated molten semiconductor with a horizontal magnetic field}, volume={26}, number={5}, journal={International Journal of Heat and Fluid Flow}, author={Yang, M. and Ma, N.}, year={2005}, pages={810–816} }
 @article{wang_ma_bliss_iseler_2005, title={A numerical investigation of dopant segregation by modified vertical gradient freezing with moderate magnetic and weak electric fields}, volume={43}, number={12-Nov}, journal={International Journal of Engineering Science}, author={Wang, X. and Ma, N. and Bliss, D. F. and Iseler, G. W.}, year={2005}, pages={908–924} }
 @article{yang_ma_2005, title={Free convection in a liquid-encapsulated molten semiconductor in a vertical magnetic field}, volume={48}, ISSN={["1879-2189"]}, DOI={10.1016/j.ijheatmasstransfer.2005.04.019}, abstractNote={This paper treats the free convection in a layer of boron oxide, called a liquid encapsulant, which lies above a layer of a molten compound semiconductor (melt) between cold and hot vertical walls in a rectangular container with a steady vertical magnetic field. The magnetic field provides an electromagnetic (EM) damping of the molten semiconductor which is an excellent electrical conductor but has no direct effect on the motion of the liquid encapsulant. The competition between the two free convections determines the direction of the velocity of the interface.}, number={19-20}, journal={INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER}, author={Yang, M and Ma, N}, year={2005}, month={Sep}, pages={4010–4018} }
 @article{lapointe_ma_mueller_2005, title={Growth of binary alloyed semiconductor crystals by the vertical Bridgman-Stockbarger process with a strong magnetic field}, volume={127}, ISSN={["1528-901X"]}, DOI={10.1115/1.1899169}, abstractNote={This paper presents a model for the unsteady species transport for the growth of alloyed semiconductor crystals during the vertical Bridgman-Stockbarger process with a steady axial magnetic field. During growth of alloyed semiconductors such as germanium-silicon (GeSi) and mercury-cadmium-telluride (HgCdTe), the solute’s concentration is not small, so that density differences in the melt are very large. These compositional variations drive compositionally driven buoyant convection, or solutal convection, in addition to thermally driven buoyant convection. These buoyant convections drive convective transport, which produces nonuniformities in the concentration in both the melt and the crystal. This transient model predicts the distribution of species in the entire crystal grown in a steady axial magnetic field. The present study presents results of concentration in the crystal and in the melt at several different stages during crystal growth.}, number={3}, journal={JOURNAL OF FLUIDS ENGINEERING-TRANSACTIONS OF THE ASME}, author={LaPointe, SJ and Ma, N and Mueller, DW}, year={2005}, month={May}, pages={523–528} }
 @article{yang_ma_d. f._morton_2005, title={Liquid-encapsulated Czochralski growth of doped gallium-antimonide semiconductor crystals using a strong steady magnetic field}, volume={41}, number={1}, journal={Magnetohydrodynamics}, author={Yang, M. and Ma, N. Bliss and D. F. and Morton, J. L.}, year={2005}, pages={73–86} }
 @article{wang_ma_2005, title={Numerical model for Bridgman-Stockbarger crystal growth with a magnetic field}, volume={19}, ISSN={["1533-6808"]}, DOI={10.2514/1.13307}, abstractNote={This paper presents a model for the unsteady species transport for the growth of doped semiconductor crystals during the vertical Bridgman‐Stockbarger process with a steady axial magnetic field. This dilute species transport depends on the convective and diffusive species transport of the dopant. This convective species transport is driven by buoyant convection in the melt, which produces compositional nonuniformities in both the melt and the crystal. This transient model predicts the distribution of species in the entire crystal grown in a steady axial magnetic field. The present study presents results of concentration in the crystal and in the melt at several different stages during crystal growth. I. Introduction D URING crystal growth without a magnetic field or with a weak magnetic field, turbulent or oscillatory melt motions can produce undesirable spatial oscillations of the concentration, or microsegregation, in the crystal. 1 Turbulent or oscillatory melt motions lead to fluctuations in the heat transfer across the growth interface from the melt to the crystal. Because the local rate of crystallization depends on the balance between the local heat fluxes in the melt and the crystal, fluctuations in the heat flux from the melt create fluctuations in the local growth rate, which create microsegregation. A moderate magnetic field can be used to create a body force that provides an electromagnetic (EM) damping of the melt motion can to eliminate oscillations in the melt motion and thus in the concentration of the crystal. Unfortunately, the elimination of mixing and a moderate or strong EM damping of the residual melt motion can lead to a large variation of the crystal’s composition in the direction perpendicular to the growth direction (radial macrosegregation). On the other hand, if the magnetic field strength is so strong that the melt motion is reduced sufficiently so that it has no effect on the composition in the crystal, then this diffusion-controlled species transport can produce a radially and axially uniform composition in the crystal grown. 2 To achieve diffusion-controlled species trans�}, number={3}, journal={JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER}, author={Wang, XH and Ma, N}, year={2005}, pages={406–412} }
 @article{wang_ma_bliss_iseler_2005, title={Semiconductor crystal growth by modified vertical gradient freezing with electromagnetic stirring}, volume={19}, ISSN={["1533-6808"]}, DOI={10.2514/1.10279}, abstractNote={This paper presents a numerical model for the unsteady transport of a dopant during the VGF process by submerge d heater growth with a steady axial magnetic field and a steady radial electric current. Electromagnetic (EM) stirring can be induced in the gallium antimonide melt just above the crystal growth interface by applying a small radial electric current in the melt together with an axial magnetic field. The application of EM stirring provides a significant convective dopant transport in the melt so that the crystal solidifies with relatively good radial homogeneity. Dopant distributions in the crystal and in th e melt at several different stages during growth are presented.}, number={1}, journal={JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER}, author={Wang, XH and Ma, N and Bliss, DF and Iseler, GW}, year={2005}, pages={95–100} }
 @inproceedings{wang_ma_bliss_iseler_2005, title={Semiconductor crystal growth by modified vertical gradient freezing with electromagnetic stirring}, volume={2005-0916}, number={2005 Jan.}, booktitle={AIAA 43rd Aerospace Sciences Meeting and Exhibit, Reno, NV, Jan. 2005}, author={Wang, X.-H. and Ma, N. and Bliss, D. F. and Iseler, G. W.}, year={2005} }
 @article{holmes_wang_ma_bliss_iseler_2005, title={Vertical gradient freezing using submerged heater growth with rotation and with weak magnetic and electric fields}, volume={26}, number={5}, journal={International Journal of Heat and Fluid Flow}, author={Holmes, A. M. and Wang, X. and Ma, N. and Bliss, D. F. and Iseler, G. W.}, year={2005}, pages={792–800} }
 @article{ma_walker_witkowski_2004, title={Combined effects of rotating magnetic field and rotating system on the thermocapillary instability in the floating zone crystal growth process}, volume={126}, ISSN={["1528-8943"]}, DOI={10.1115/1.1666883}, abstractNote={This paper presents a linear stability analysis for the thermocapillary convection in a liquid bridge bounded by two planar liquid-solid interfaces at the same temperature and by a cylindrical free surface with an axisymmetric heat input. The two solid boundaries are rotated at the same angular velocity in one azimuthal direction, and a rotating magnetic field is applied in the opposite azimuthal direction. The critical values of the Reynolds number for the thermocapillary convection and the critical-mode frequencies are presented as functions of the magnetic Taylor number for the rotating magnetic field and of the Reynolds number for the angular velocity of the solid boundaries.}, number={2}, journal={JOURNAL OF HEAT TRANSFER-TRANSACTIONS OF THE ASME}, author={Ma, N and Walker, JS and Witkowski, LM}, year={2004}, month={Apr}, pages={230–235} }
 @article{farrell_ma_2004, title={Macrosegregation during alloyed semiconductor crystal growth in strong axial and transverse magnetic fields}, volume={47}, ISSN={["1879-2189"]}, DOI={10.1016/j.ijheatmasstransfer.2004.02.021}, abstractNote={Abstract This paper presents a model for the unsteady species transport during bulk growth of alloyed semiconductor crystals with both axial and transverse magnetic fields. During growth of alloyed semiconductors such as germanium–silicon (GeSi) and mercury–cadmium–telluride (HgCdTe), the solute's concentration is not small so that density differences in the melt are very large. These compositional variations drive compositionally-driven buoyant convection, or solutal convection, in addition to thermally-driven buoyant convection. These buoyant convections drive convective transport which produce non-uniformities in the concentration in both the melt and the crystal. This transient model predicts the distribution of species in the entire crystal grown in a magnetic field. The present study investigates the effects of magnetic field orientation and strength on the segregation in alloyed semiconductor crystals, and presents results of concentration in the crystal and in the melt at several different times during crystal growth.}, number={14-16}, journal={INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER}, author={Farrell, MV and Ma, N}, year={2004}, month={Jul}, pages={3047–3055} }
 @article{wang_ma_2004, title={Strong magnetic field asymptotic model for binary alloyed semiconductor crystal growth}, volume={18}, ISSN={["1533-6808"]}, DOI={10.2514/1.11905}, abstractNote={We present an asymptotic model for the unsteady species transport during bulk growth of alloyed semiconductor crystals with a transverse magnetic field. During growth of alloyed semiconductors such as germanium-silicon (GeSi), the solute's concentration is not small, so that density differences in the melt are very large. These compositional variations drive compositionally driven buoyant convection, or solutal convection, in addition to thermally driven buoyant convection. These buoyant convections drive convective transport, which produces nonuniformities in the concentration in both the melt and the crystal. This transient model predicts the melt motion and the distribution of species for a crystal grown in a strong transverse magnetic field}, number={4}, journal={JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER}, author={Wang, X and Ma, N}, year={2004}, pages={476–480} }
 @inproceedings{dust_ma_2003, title={Macrosegregation during directional solidification of alloyed semiconductor crystals with a transverse magnetic field}, booktitle={AIAA Aerospace Sciences Meeting and Exhibit (41st: Reno, NV, 2003).  (AIAA paper; no. 2003-1310)}, author={Dust, J. C. and Ma, N.}, year={2003} }
 @article{morton_ma_bliss_bryant_2003, title={Magnetic field effects during liquid-encapsulated Czochralski growth of doped photonic semiconductor crystals}, volume={250}, ISSN={["0022-0248"]}, DOI={10.1016/S0022-0248(02)02261-3}, abstractNote={During the liquid-encapsulated Czochralski (LEC) process, a single compound semiconductor crystal such as indium phosphide or gallium antimonide is grown by the solidification of an initially molten semiconductor contained in a crucible. The motion of the electrically conducting molten semiconductor can be controlled with an externally applied magnetic field. This paper presents a model for the unsteady transport of a dopant during the LEC process with a steady axial magnetic field. The convective species transport during growth produces significant segregation in both the melt and the crystal. Dopant distributions in the crystal and in the melt at several different stages during growth are presented.}, number={1-2}, journal={JOURNAL OF CRYSTAL GROWTH}, author={Morton, JL and Ma, N and Bliss, DF and Bryant, GG}, year={2003}, month={Mar}, pages={174–182} }
 @article{kuniholm_ma_2003, title={Natural convection in a liquid-encapsulated molten semiconductor with a steady magnetic field}, volume={24}, ISSN={["0142-727X"]}, DOI={10.1016/S0142-727X(02)00205-9}, abstractNote={This paper treats the buoyant convection in a layer of boron oxide, called a liquid encapsulant, which lies above a layer of a molten compound semiconductor (melt) between cold and hot vertical walls in a rectangular container with a steady horizontal magnetic field B. The magnetic field provides an electromagnetic damping of the molten semiconductor which is an excellent electrical conductor but has no direct effect on the motion of the liquid encapsulant. The temperature gradient drives counter-clockwise circulations in both the melt and encapsulant. These circulations alone would lead to positive and negative values of the horizontal velocity in the encapsulant and melt, respectively, near the interface. The competition between the two buoyant convections determines the direction of the horizontal velocity of the interface.}, number={1}, journal={INTERNATIONAL JOURNAL OF HEAT AND FLUID FLOW}, author={Kuniholm, JF and Ma, N}, year={2003}, month={Feb}, pages={130–136} }
 @article{ma_2003, title={Solutal convection during growth of alloyed semiconductor crystals in a magnetic field}, volume={17}, ISSN={["0887-8722"]}, DOI={10.2514/2.6736}, abstractNote={We present a model for the unsteady species transport during bulk growth of alloyed semiconductor crystals with a planar crystal-melt interface and with an externally applied steady axial magnetic field. During growth of alloyed semiconductors such as germanium-silicon (GeSi) and mercury-cadmium-telluride (HgCdTe), the solute's concentration is not small so that density differences in the melt are very large. These compositional variations drive compositionally driven buoyant convection, or solutal convection, in addition to thermally driven buoyant convection. These buoyant convections drive convective transport, which produces nonuniformities in the concentration in both the melt and the crystal. This transient model predicts the distribution of species in the entire crystal}, number={1}, journal={JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER}, author={Ma, N}, year={2003}, pages={77–81} }
 @inproceedings{ma_j. s._witkowski_2003, title={Thermocapillary instability with a rotating magnetic field and system rotation}, booktitle={ASME Proceedings of the International Mechanical Engineering Congress and Exposition, Washington D. C.}, publisher={Washington, DC: ASME}, author={Ma, N. Walker and J. S. and Witkowski, L. M.}, year={2003}, pages={297–303} }
 @article{ma_bliss_iseler_2003, title={Vertical gradient freezing of doped gallium-antimonide semiconductor crystals using submerged heater growth and electromagnetic stirring}, volume={259}, ISSN={["0022-0248"]}, DOI={10.1016/S0022-0248(03)01575-6}, abstractNote={An investigation of the melt growth of uniformly doped gallium–antimonide (GaSb) semiconductor crystals as well as other III–V alloy crystals with uniform composition are underway at the US Air Force Research Laboratory at Hanscom Air Force Base by the vertical gradient freeze (VGF) method utilizing a submerged heater. Stirring can be induced in the GaSb melt just above the crystal growth interface by applying a small radial electric current in the liquid together with an axial magnetic field. The transport of any dopant and/or alloy component by the stirring can promote better melt homogeneity and allow for more rapid growth rates before the onset of constitutional supercooling. This paper presents a numerical model for the unsteady transport of a dopant during the VGF process by submerged heater growth with a steady axial magnetic field and a steady radial electric current. As the strength of the electromagnetic (EM) stirring increases, the convective dopant transport increases, the dopant transport in the melt reaches a steady state at an earlier time during growth, and the top of the crystal which has solidified after a steady state has been achieved exhibits axial dopant homogeneity. For crystal growth with stronger EM stirring, the crystal exhibits less radial segregation and the axially homogeneous section of the crystal is longer. Dopant distributions in the crystal and in the melt at several different stages during growth are presented.}, number={1-2}, journal={JOURNAL OF CRYSTAL GROWTH}, author={Ma, N and Bliss, DF and Iseler, GW}, year={2003}, month={Nov}, pages={26–35} }
 @article{walker_ma_2002, title={Convective mass transport during bulk growth of semiconductor crystals with steady magnetic fields}, volume={12}, number={2002}, journal={Annual Review of Heat Transfer}, author={Walker, J. S. and Ma, N.}, year={2002}, pages={223–263} }
 @article{farrell_ma_2002, title={Coupling of buoyant convections in boron oxide and a molten semiconductor in a vertical magnetic field}, volume={124}, DOI={10.1115/1.1473141}, abstractNote={This paper treats the buoyant convection in a layer of boron oxide, called a liquid encapsulant, which lies above a layer of a molten compound semiconductor (melt) between cold and hot vertical walls in a rectangular container with a steady vertical magnetic field B. The magnetic field provides an electromagnetic (EM) damping of the molten semiconductor which is an excellent electrical conductor but has no direct effect on the motion of the liquid encapsulant. The temperature gradient drives counter clockwise circulations in both the melt and encapsulant. These circulations alone would lead to positive and negative values of the horizontal velocity in the encapsulant and melt, respectively, near the interface. The competition between the two buoyant convections determines the direction of the horizontal velocity of the interface. For B=5 T, there is significant EM damping of the melt motion and the encapsulant drives a positive interfacial velocity and a small clockwise circulation in the melt. For a much weaker field B=0.1 T, the maximum velocity in the melt is hundreds of times larger than that of the encapsulant, thus causing nearly all the encapsulant to circulate in the clockwise direction.}, number={4}, journal={Journal of Heat Transfer}, author={Farrell, M. V. and Ma, N.}, year={2002}, pages={643–649} }
 @article{morton_ma_bliss_bryant_2002, title={Dopant segregation during liquid-encapsulated Czochralski crystal growth in a steady axial magnetic field}, volume={242}, ISSN={["1873-5002"]}, DOI={10.1016/S0022-0248(02)01425-2}, abstractNote={During the magnetically stabilized liquid-encapsulated Czochralski (MLEC) process, a single compound semiconductor crystal such as indium-phosphide (InP) or gallium-antimonide (GaSb) is grown by the solidification of an initially molten semiconductor (melt) contained in a crucible. The motion of the electrically conducting molten semiconductor can be controlled with an externally applied magnetic field. This paper presents a model for the unsteady transport of a dopant during the MLEC process with a steady axial magnetic field. The convective species transport during growth is driven by the melt motion, which produces segregation, i.e. non-uniformities in the dopant concentration, in both the melt and the crystal. This convective transport is significant even for a magnetic field strength of 2 T. Except for the last-solidified part of the crystal, the crystal's axial dopant homogeneity, i.e. uniformity in the dopant concentration, improves as the magnetic field strength is decreased. Dopant distributions in the crystal and in the melt at several different stages during growth are presented for several magnetic field strengths.}, number={3-4}, journal={JOURNAL OF CRYSTAL GROWTH}, author={Morton, JL and Ma, N and Bliss, DF and Bryant, GG}, year={2002}, month={Jul}, pages={471–485} }
 @inproceedings{ma_2002, title={Models of mass transport during microgravity crystal growth of alloyed semiconductor crystals in a magnetic field}, booktitle={NASA Microgravity Materials Science Conference proceedings, NASA/CP-2003-212339}, publisher={Huntsville, Ala.: NASA}, author={Ma, N.}, year={2002}, pages={380–382} }
 @inproceedings{ma_2002, title={Solutal convection during melt growth of alloyed semiconductor crystals in a steady magnetic field}, booktitle={AIAA Aerospace Sciences Meeting and Exhibit (40th: Reno, NV, 2002).  (AIAA paper; no. 2002-1113)}, author={Ma, N.}, year={2002} }
 @article{morton_ma_bliss_bryant_2001, title={Diffusion-controlled dopant transport during magnetically-stabilized liquid-encapsulated Czochralski growth of compound semiconductor crystals}, volume={123}, ISSN={["1528-901X"]}, DOI={10.1115/1.1411968}, abstractNote={During the magnetically-stabilized liquid-encapsulated Czochralski (MLEC) process, a single compound semiconductor crystal is grown by the solidification of an initially molten semiconductor (melt) contained in a crucible. The melt is doped with an element in order to vary the electrical and/or optical properties of the crystal. During growth, the so-called melt-depletion flow caused by the opposing relative velocities of the encapsulant-melt interface and the crystal-melt interface can be controlled with an externally applied magnetic field. The convective dopant transport during growth driven by this melt motion produces nonuniformities of the dopant concentration in both the melt and the crystal. This paper presents a model for the unsteady transport of a dopant during the MLEC process with an axial magnetic field. Dopant distributions in the crystal and in the melt at several different stages during growth are presented.}, number={4}, journal={JOURNAL OF FLUIDS ENGINEERING-TRANSACTIONS OF THE ASME}, author={Morton, JL and Ma, N and Bliss, DF and Bryant, GG}, year={2001}, month={Dec}, pages={893–898} }
 @article{hockenhull_ma_2000, title={Dopant transport during semiconductor crystal growth in space with a steady magnetic field}, volume={36}, number={3}, journal={Magnetohydrodynamics}, author={Hockenhull, T. E. and Ma, N.}, year={2000}, pages={289–296} }