Liquidus-zone Method Research Articles

Numerical investigation of growth interface shape and compositional distributions in SiGe crystals grown by the TLZ method in the International Space Station

The second and third microgravity experiments on SiGe crystal growth by the traveling liquidus-zone (TLZ) method were carried out aboard the Japanese Experiment Module (JEM) “Kibo” in the International Space Station (ISS) in July 2013 and February 2014. In this study, we numerically investigated the details of transport phenomena and solidification in these two experiments. We found that the deformation of the melt/SiGe crystal interface shape increased with time, and that the growth rate near the crystal edge was much larger than that near the central axis. Comparing the numerical and experimental results of the concentration distribution of Ge, the numerical concentration distributions are reasonably coincident with the experimental ones in both the axial and radial directions. In addition, both numerical and experimental results show that the radial distributions of the Ge concentration remain relatively uniform throughout the entire crystal, although the mean values depend on the growth length.

Growth of homogeneous mixed A1-xBx bulk crystals: Analytical prediction, phase-field modeling and experiment comparison

An analytical model is proposed to predict the growth behavior of homogeneous mixed A1-xBx bulk crystals by the traveling liquidus-zone (TLZ) method. The solidification and melting rates at the cold and hot solid/liquid (S/L) interfaces are determined by the solute conservation equations, coupled with the non-linear concentration distribution in the liquid zone. A novel time-dependent critical translation rate is derived, which can completely suppress the composition segregation in the grown crystal with an arbitrary liquid zone width. The proposed model is validated by the thin interface phase-field model for the TLZ-grown Si0.5Ge0.5 crystal, regarding the growth kinetics and concentration distributions in the crystal and liquid phase. A good agreement between the analytical predictions and phase-field simulations is achieved. The growth kinetics and composition profiles in the grown crystals predicted by the present analytical model agree well with the experimental measurements reported in the literature. It is found that after an initial transient, the non-linear liquid concentration distribution reaches the quasi-stationary condition. The average crystal growth rate increases with increasing temperature gradient. The proposed critical translation rate can precisely match the time-dependent solidification rate at the cold S/L interface, leading to a completely homogeneous TLZ-grown Si0.5Ge0.5 bulk crystal for an arbitrary initial liquid zone width. It is demonstrated that the present analytical model with the non-linear liquid concentration distribution is applicable to predict the growth behavior of homogeneous mixed crystals with a wide region of temperature gradient, translation rate and initial liquid zone width.

Effects of temperature gradient in the growth of Si0.5Ge0.5 crystals by the traveling liquidus-zone method on board the International Space Station

Si0.5Ge0.5 crystals were grown at two different temperature gradients on board the International Space Station (ISS) using the traveling liquidus-zone (TLZ) method and effects of temperature gradient on crystal quality were investigated. Although average axial Ge concentration profile was not affected by the temperature gradient, crystal quality was affected greatly. Single crystal length was shortened and constitutional supercooling (CS) is shown to occur more easily at higher temperature gradient. The calculated degree of CS based on the solute concentration profile in the melt and phase diagram data is about 4 times larger when the temperature gradient is twice, which supports the experimental results. Instability at high temperature gradient is unique to the TLZ method and is not common to other crystal growth methods such as the directional solidification method and Czochralski method.

Hole Hall mobility of SiGe alloys grown by the traveling liquidus-zone method

The hole Hall mobility of Si1−xGex single crystal alloys grown by the traveling liquidus-zone method has been investigated. Raman analysis of the alloys with various Ge contents show excellent compositional uniformity and high crystal quality without strain. Secondary ion mass spectrometry indicates that the B concentration is homogeneous throughout the depth of the alloys. The hole Hall mobility in alloys with a low carrier concentration of ∼1 × 1015 cm−3 shows a higher mobility compared with previous results, indicating a reduction in alloy scattering effects. These results suggest that scattering processes in alloy semiconductors should be reconsidered both experimentally and theoretically.

Compositional uniformity of a Si0.5Ge0.5 crystal grown on board the International Space Station

A Si0.5Ge0.5 crystal was grown on board the International Space Station (ISS) using the traveling liquidus-zone method. Average Ge concentration was 49±2at% for the growth length of 14.5mm. Radial compositional uniformity was excellent especially between the growth length of 3 and 9mm; concentration fluctuation was less than 1at%. In this experiment, cartridge surface temperatures were monitored and heater temperatures were adjusted based on the monitored temperatures for improving compositional uniformity of a grown crystal. A step temperature change by 1°C was imposed for adjusting heater temperatures. This procedure made it possible to observe growth interface shape; striations due to heater temperature change were observed by a backscattered electron image. Growth rates were precisely determined by the relation between interval of heater temperature change and the distance between striations. Based on the measured growth rates, two-dimensional growth model for the traveling liquidus-zone method was discussed.

SiGe crystal growth aboard the international space station

A silicon germanium mixed crystal Si1−xGex (x~0.5) 10mm in diameter and 9.2mm in length was grown by the traveling liquidus-zone (TLZ) method in microgravity by suppressing convection in a melt. Ge concentration of 49.8±2.5 at% has been established for the whole of the grown crystal. Compared with the former space experiment, concentration variation in the axial direction increased from ±1.5 at% to ±2.5 at% although average Ge concentration reached to nearly 50 at%. Excellent radial Ge compositional uniformity 52±0.5 at% was established in the region of 7–9mm growth length, where axial compositional uniformity was also excellent. The single crystalline region is about 5mm in length. The interface shape change from convex to concave is implied from both experimental results and numerical analysis. The possible cause of increase in concentration variation and interface shape change and its relation to the two-dimensional growth model are discussed.

Numerical simulations of SiGe crystal growth by the traveling liquidus-zone method in a microgravity environment

Recently, a Si1−xGex (approximately x=0.5) crystal has been grown by the traveling liquidus-zone (TLZ) method under microgravity condition in the International Space Station (ISS). In this work, a mathematical model of the TLZ crystal growth has been developed to investigate details of the transport and solidification phenomena occurred during the TLZ growth of SiGe crystals performed in the ISS. Using this model, the experimental Ge concentration distributions in the grown SiGe crystal is explained, and the emissivity variation of the metal cartridge surface due to oxidation during the crystal growth is revealed to strongly affect the Ge concentration distribution in the grown crystal. In addition, a strategy for growing SiGe crystals, which are more homogeneous than those obtained in the current experiment, is proposed on the basis of the numerical results.

Growth of a Si0.50Ge0.50 crystal by the traveling liquidus-zone (TLZ) method in microgravity

An alloy semiconductor Si1−xGex (x~0.5) crystal was grown by the TLZ method in microgravity. Ge concentration was 48.5±1.5at% for the whole region of 10mm diameter and 17.2mm long crystal. Compositional uniformity was established but the average concentration was a little deviated from the expected 50at%. For further improving compositional uniformity and for obtaining Si0.5Ge0.5 crystals in microgravity, growth conditions were refined based on the measured axial compositional profile. In determining new growth conditions, difference in temperature gradient in a melt, difference in freezing interface curvature, and difference in melt back length of a seed between microgravity and terrestrial growth were taken into consideration.

Characterization of crystalline structures of SiGe substrate formed by traveling liquidus-zone method for devices with Ge/SiGe structures

Bulk and surface crystalline structures of the SiGe (001) substrate formed by the traveling liquidus-zone (TLZ) method were characterized. In addition, a possibility of the SiGe substrate as a seed for the strained-Ge/SiGe structures in optoelectronic and electronic devices has been investigated through surveying cleaning methods of the SiGe surface. It was found that the TLZ method can provide the high quality SiGe substrate with the threading dislocation density of the range from 4×105 to 6×107cm−2. The high quality SiGe substrate treated with the appropriate chemical and thermal cleaning makes it possible to grow the epitaxial Ge layer with large strain of 1.3%. Consequently, we clarified that the high quality SiGe substrate fabricated by the TLZ method has a high potential as the seed for the strained-Ge layer in the devices.

Increase of Si0.5Ge0.5 Bulk Single Crystal Size as Substrates for Strained Ge Epitaxial Layers

Compositionally uniform 2 and 10 mm diameter Si0.5Ge0.5 bulk crystals have been grown by the traveling liquidus-zone (TLZ) method. The TLZ method requires diffusion controlled mass transport in a melt and crystal size was limited for suppressing convection in a melt. For substrate use, however, larger diameter crystals are required. Increase of crystal diameter was challenged in spite of the concern that compositional homogeneity of grown crystals might be degraded due to faster convective flow in a larger diameter melt. As a result, however, increase of crystal diameter was possible up to 30 mm although single crystal length was limited to 5 mm. Si0.55Ge0.45 and Si0.6Ge0.4 bulk crystals with 30 mm diameter showed excellent compositional homogeneity and high crystallinity without mosaicity.

Si0.5Ge0.5 bulk single crystals with uniform composition

Compositionally uniform 10mm diameter Si0.5Ge0.5 bulk crystals were grown by the traveling liquidus-zone (TLZ) method which we developed for the alloy crystal growth. Axial compositional variation was less than 0.5at% for the length of 12mm and radial one was less than 0.3at% and showed excellent compositional uniformity. The average full width at half maximum of X-ray rocking curves for 004 diffraction measured across a disk is less than 36arcsec (0.01°) at a distance of 3.5mm away from the seed/crystal interface. This shows high crystallinity and promise of TLZ-grown crystals as substrates for CMOS devices using n-channels of strained Si thin films and p-channels of strained Ge thin films.

Growth of Si0.5Ge0.5 Single Crystals by the Traveling Liquidus-zone Method and their Structural Characterization

We have succeeded in growing compositionally homogeneous Si0.5Ge0.5 crystals with a newly developed growth method named the travelling liquidus-zone (TLZ) method. In this method, a narrow liquidus-zone saturated by a solute is formed at relatively low temperature gradients, 5 – 15°C/cm. Since the solubility depends on temperature, solute concentration gradient is established at the freezing interface. The concentration gradient causes diffusion of the solute towards a low concentration side. At the freezing interface, crystal growth proceeds due to the decrease in solute. As a result, solute concentration increases at the opposite side of the zone by transported solute and part of the remaining feed is dissolved. Thus, the zone travels under the temperature gradient spontaneously. Here, we report on 30mm diameter homogeneous Si0.5Ge0.5 crystal growth by the TLZ method. Compositional homogeneity of grown crystals was excellent but the length of single crystal was limited to about 2mm and origins of polycrystallization were discussed.

Homogeneous SiGe crystal growth in microgravity by the travelling liquidus-zone method

Homogeneous SiGe crystal growth experiments will be performed on board the ISS "Kibo" using a gradient heating furnace (GHF). A new crystal growth method invented for growing homogeneous mixed crystals named "travelling liquidus-zone (TLZ) method" is evaluated by the growth of Si0.5Ge0.5 crystals in space. We have already succeeded in growing homogeneous 2mm diameter Si0.5Ge0.5 crystals on the ground but large diameter homogeneous crystals are difficult to be grown due to convection in a melt. In microgravity, larger diameter crystals can be grown with suppressing convection. Radial concentration profiles as well as axial profiles in microgravity grown crystals will be measured and will be compared with our two-dimensional TLZ growth model equation and compositional variation is analyzed. Results are beneficial for growing large diameter mixed crystals by the TLZ method on the ground. Here, we report on the principle of the TLZ method for homogeneous crystal growth, results of preparatory experiments on the ground and plan for microgravity experiments.

Numerical analysis of two-dimensional model of the traveling liquidus-zone method

Abstract In order to investigate more suitable sample configurations for obtaining radially larger and more homogeneous compound semiconductor crystals, a two-dimensional model of the traveling liquidus-zone method is introduced. From numerical results of the model, it is found that inhomogeneity increases with the thermal conductivity of a crucible wall. This is mainly attributed to the heat flow slanted towards the crucible wall near an interface. The numerical results show, however, that the low thermal conductivity of the crucible does not sufficiently reduce the inhomogeneity, which is caused by the slanted heat flow. We also investigate the influence of a seed crystal. It is found that a seed crystal with large thermal conductivity is far more effective to improve the homogeneity.

Homogeneous Si0.5Ge0.5 bulk crystal growth as substrates for strained Ge thin films by the traveling liquidus-zone method

Compositionally uniform Si0.5Ge0.5 bulk crystals were grown by the traveling liquidus-zone method which we developed for alloy crystal growth. Grown crystals were characterized as substrates for compressive-strained Ge thin films for high mobility p-channels of complementary metal oxide semiconductor transistors. Compositional uniformity was excellent and crystallinity was also excellent for 10mm diameter crystals. However, crystallinity was degraded for 30mm diameter crystals although compositional uniformity was excellent. Transmission electron microscope (TEM) observation showed high dislocation density at the interface between a Si seed and a grown crystal due to lattice mismatch. However, the dislocation density decreased as crystal growth proceeded. High quality 30mm diameter crystals will be grown when the single crystal length is extended judging from TEM results. In this paper, we report on the growth and characterization of Si0.5Ge0.5 crystals as substrates for strained Ge thin films.

Growth of homogeneous semiconductor mixed crystals by the traveling liquidus-zone method

Compositionally uniform mixed crystals of InxGa1−xAs (0.07<x<0.35) and Si0.5Ge0.5 were grown by the traveling liquidus-zone (TLZ) method. The TLZ method is a kind of zone-melting method but is different from a conventional method in forming a liquidus-zone at a relatively low temperature gradient of about 10°C/cm. In the paper, the principle of the TLZ method, examples of TLZ-grown crystals and merits and demerits of the TLZ method are described. Finally, application of the TLZ-grown In0.13Ga0.87As crystals to substrates and successful fabrication of high performance laser diodes are introduced.

Crystallographic investigation of homogeneous SiGe single crystals grown by the traveling liquidus-zone method

Crystallographic investigation of Si 0.5Ge 0.5 single crystals grown by the traveling liquidus-zone (TLZ) method was carried out using an X-ray diffraction method, a back-reflection Laue camera and X-ray rocking curve measurements. X-ray rocking curve of the Si 0.5Ge 0.5 crystals showed excellent crystallinity: full-width at half-maximum (FWHM) of the (4 4 0) diffraction was 0.009°, which is comparable to that of Si single crystal. Such high-quality Si 0.5Ge 0.5 bulk crystals were obtained for the first time and showed the superiority of the TLZ growth method for growing alloy bulk crystals.

High-Characteristic-Temperature 1.3-$\mu$m-Band Laser on an InGaAs Ternary Substrate Grown by the Traveling Liquidus-Zone Method

We have developed high-performance 1.3-mum-band laser diodes on an InGaAs ternary substrate with a low indium content (In:0.1) grown by a novel bulk crystal growth technique called the traveling liquidus-zone (TLZ) method. This laser has a long-wavelength lasing of 1.28 mum and provides lasing operation up to 195degC by using a highly strained InGaAs quantum well. The characteristic temperatures are 130 K from 25 to 95degC and 95 K from 95 to 155degC. We investigated junction heating by comparing the lasing wavelengths for pulsed and continuous-wave (CW) operation. And, we showed the possibility of realizing a high-performance laser on an InGaAs ternary substrate.

05/01877 Numerical analysis of crystal growth of an InAs-GaAs binary semiconductor by the Travelling Liquidus-Zone method under microgravity conditions: Maekawa, T. et al. International Journal of Heat and Mass Transfer,2004, 47, (21), 4535–4546

05/01877 Numerical analysis of crystal growth of an InAs-GaAs binary semiconductor by the Travelling Liquidus-Zone method under microgravity conditions: Maekawa, T. et al. International Journal of Heat and Mass Transfer,2004, 47, (21), 4535–4546

Homogeneous SiGe crystals grown by using the traveling liquidus-zone method

It is indispensable to estimate a diffusion coefficient in a solution zone in order to grow a homogeneous crystal by using the traveling liquidus-zone (TLZ) method. To estimate the diffusion coefficient of Ge in the SiGe solution zone, result of a two-dimensional numerical simulation is compared with an experimental result. From the comparison, the diffusion coefficient is estimated to be 9.5×10 −5 cm 2/s. By using this coefficient, a sample translation rate for obtaining a homogeneous SiGe crystal is determined. By translating samples with appropriate rates, homogeneous Si 0.5Ge 0.5 crystals are successfully grown. The typical Ge composition is 0.496±0.006 for more than 13 mm long. The experimental result shows the homogeneity of ±1.2% in the mole fraction. This deviation corresponds to the variation of less than ±0.03% in the lattice constant. Since this variation is negligibly small, the homogeneity is excellent. Thus it is found that the TLZ method is the universal growth technique, which is applicable to the crystal growth of not only the III–V compounds but also the IV–IV compounds.