Study of SiGe crystal growth interface processed in microgravity

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Study of SiGe crystal growth interface processed in microgravity Yasutomo Arai, Kyoichi Kinoshita, Takao Tsukada, Masaki Kubo, Keita Abe, Sara Sumioka, Satoshi Baba, and Yuko Inatomi Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.8b00544 • Publication Date (Web): 15 May 2018 Downloaded from http://pubs.acs.org on May 22, 2018

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Crystal Growth & Design

Study of SiGe crystal growth interface processed in microgravity Yasutomo Arai,†,* Kyoichi Kinoshita,‡ Takao Tsukada,§ Masaki Kubo,§ Keita Abe,§ Sara Sumioka, § Satoshi Baba§ and Yuko Inatomi† †

Japan Aerospace Exploration Agency, 2-1-1 Sengen, Tsukuba, Ibaraki 305-8505, Japan

‡

Meiji University, 1-1-1 Higashi-mita, Kawasaki, Kanagawa, Japan

§

Tohoku University, 6-6-07 Aramaki, Aoba-ku, Sendai 980-8579, Japan

A Si1-XGeX(x~0.5) crystal measuring 10 mm in diameter was grown by the traveling liquidus-zone method using the Gradient Heating Furnace aboard the International Space Station. We quantitatively investigated the composition and shape of the crystal-melt interface during growth by analyzing the grown crystal. Several growth interfaces showed a highly uniform Ge composition within ±0.0005 mole fraction. Detailed measurements of the shapes and the Ge concentrations on those interfaces revealed that millimeter-scale Ge concentration gradient fluctuations existed for more than 16 hours in non-steady and unsaturated SiGe melt in front of a crystal-growth interface grown under the microgravity condition.

Yasutomo Arai, e-mail: [email protected], tel. +81-50-3362-7986

ACS Paragon Plus Environment

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Study of SiGe crystal growth interface processed in microgravity Yasutomo Arai,†,* Kyoichi Kinoshita,‡ Takao Tsukada,§ Masaki Kubo, § Keita Abe, § Sara Sumioka, § Satoshi Baba§ and Yuko Inatomi† †

Japan Aerospace Exploration Agency, 2-1-1 Sengen, Tsukuba, Ibaraki 305-8505, Japan

‡

Meiji University, 1-1-1 Higashi-mita, Kawasaki, Kanagawa, Japan

§

Tohoku University, 6-6-07 Aramaki, Aoba-ku, Sendai 980-8579, Japan

SiGe, crystal growth, microgravity

A Si1-XGeX(x~0.5) crystal measuring 10 mm in diameter was grown by the traveling liquiduszone method using the Gradient Heating Furnace aboard the International Space Station. We quantitatively investigated the composition and shape of the crystal-melt interface during growth by analyzing the grown crystal. The growth interface shapes were obtained by tracing the artifact striations that varied from modulating nearby the Si seed to a smooth convex according as the SiGe crystal growth proceeded. We also successfully measured the Ge concentrations on the interface by using an electron probe micro analyzer. Several growth interfaces showed a highly uniform Ge composition within ±0.0005 mole fraction. Detailed measurements of the shapes and the Ge concentrations on those interfaces revealed that millimeter-scale Ge concentration gradient


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fluctuations existed for more than 16 hours in non-steady and unsaturated SiGe melt in front of a crystal-growth interface grown under the microgravity condition.

1. Introduction Silicon-germanium crystals are promising materials for post-silicon high mobility devices1, as well as infrared optical 2 and thermoelectric applications. 3 Many bulk SiGe crystal growth experiments and measurements of physical properties have been conducted on the ground (briefly reviewed in references).4, 5 Recently, SiGe crystals grown by the Bridgman method with magnetic field and accelerated crucible rotation techniques have resulted in producing a partially flat growth interface and suppressing radial segregations.6 The traveling liquidus-zone (TLZ) method is a type of zone method where the SiGe molten zone is sandwiched by the silicon seed and feed. The TLZ method has been very useful in producing high mobility bulk Si1-XGeX crystals of uniform composition.7 In the ground experiments, the TLZ growth method produced no transient growth regions that gradually alter the crystal compositions. Adachi et al.8 proposed a two-dimensional TLZ (2D-TLZ) growth model that describes the growth rate, as well as the interface shape and its composition, but excludes the effect of convection. Four Si0.5Ge0.5 crystal growth experiments were conducted on board the International Space Station (ISS) from FY2011 to FY2014 using the Gradient Heating Furnace (GHF). Kinoshita et al. reported a series of SiGe space experiments. Specifically, clear artifact striations in the third SiGe growth experiment,9 nucleation in the melt by constitutional supercooling,10 and a high growth rate in the initial growth region 11 were reported. Briefly, the growth interface in the third experiment was slightly convex toward a melt near the seed, and thus the opposite shape relative


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to terrestrial-grown crystals. In addition, space-grown SiGe crystals show a highly homogeneous Ge concentration (0.485±0.015 mole fraction) along the center axis. Abe et al. reported the numerical simulations of heat transfer in the GHF and the Ge concentration distributions for the first SiGe crystal growth experiment.12 The microgravity condition suppresses convections in a melt offering quiescent, diffusionlimited growth that eliminates unexpected striations in the grown crystals 13, 14 and homogeneous doping by unidirectional solidification in regime 1 < k (k ≡ CS/CL: segregation coefficient; CS and CL denote solid and liquid concentrations, respectively).15 Recently, microgravity experiments for a dilute solution demonstrated long-ranged and long-duration concentration fluctuations in the solutions caused by thermophoretic flux.16 The unexpected large radial segregations of dopants were observed for bulk semiconductor crystal growth experiments in microgravity that were reviewed by Carlberg.17 Furthermore, Rudolph et al. analyzed the effects of thermos-diffusion with respect to the zone concentration variations of semiconductor crystals grown by the THM methods under convectionless conditions.18 Direct measurements of the shape and concentration on crystal growth interfaces grown under the microgravity condition would be needed to understand the diffusion-limited growth. Striations in SiGe crystals were observed in the liquid phase diffusion crystal growth by Yildiz et al. on the ground.19 ,20 However, no growth striations were observed during SiGe crystal growth experiment by Armour et al. with direct current furnace and applying magnetic field. 21 The melt convection producing the growth striations can be depressed by an electro-magnetic force. Therefore, an alternative method is required for temperature fluctuation in microgravity instead of convection in a melt. We intentionally imposed temperature change by 1K during the TLZ growth in microgravity and were successful in producing striations during crystal growth.


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In this report, we will present the growth interface shape and the Ge concentration distribution of the melt on the interface of a space-grown SiGe crystal in detail. The SiGe single crystalline area around the Si seed was subject to analysis. The report also discusses the characteristic properties of the growth interface and melt in front of the growth interface under microgravity.

2. Experiments and results 2-1. Observation of crystal growth interface shape The detailed crystal growth procedures of the third SiGe crystal growth experiment in the ISS were described in our previous report. 9 Briefly, the growth conditions and results are as follows: A Si1-XGeX (X = 0.485 ± 0.015 mole fraction) crystal measuring 10 mm in diameter and 14.5 mm in length was grown. The duration of crystal growth was 117 hours. The averaged temperature gradient at the growth interface was estimated as 9 K/cm during growth. During the growth experiment, the 10-5 G level microgravity condition was achieved in the GHF. Stepwise temperature changes of ±1 K were adopted for a total of 42 times during growth via tele-commands sent from the Tsukuba Space Center at about one- or two-hour intervals, in order to maintain the predefined temperature profiles shown in Fig. 1 of Ref 9. The first 1 K stepwise temperature change was applied 5.2 hours after the start of crystal growth. After that, 21 successive 1 K commands were sent to the ISS, while -1 K commands were adopted for 21 times at the later stage of crystal growth. The fluctuations in temperature within ±0.2 K on the metal cartridge surface including a SiGe crystal were measured by W-Re type thermocouples. The SiGe crystal returned to the ground was cut into rectangular plates, parallel to the growth axis. The SiGe rectangular plate surface was polished by diamond slurry and colloidal silica.


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The SEM backscattered electron image (compo-mapping) of the SiGe crystal cross section from the Si seed to the remaining melt zone was taken by the JEOL-8230 Electron Probe Micro Analyzer (EPAM) with 20 kV and 20 nA settings, and using a probe measuring 20×20 μm2 in size as shown in Fig. 1 (a). The SiGe single crystalline area is in the region from the Si seed/SiGe interface to the dotted red line; the SiGe polycrystalline area is from the dotted red line to the pink line in Fig. 1 (a).9 A cylindrical Si seed with smaller diameter than that of the inner diameter of the BN crucible produced a gap between the seed and the crucible. The molten SiGe on the seed filled the gap thus the Si seed/SiGe interface shape at periphery area is not flat. 9

Figure 1. (a) SEM compositional image map of SiGe crystals 10 mm in diameter and 17 mm in length. (b) An enlarged and a high contrast view of the striations (growth interface) around the Siseed/SiGe area.


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Note that the compo-mapping contrast is usually proportional to the electron density per unit weight of an irradiated material. Actually, the JEOL-8230 EPMA’s compo-mapping contrast can resolve ΔZ, which denotes the averaged electron number difference between materials (Si atomic number of 14, Ge of 32). The applied ±1K stepwise temperature changes during crystal growth produce a Ge concentration difference of ±0.002 mole fraction (Si0.5000±0.0020Ge0.5000±0.0020), as calculated from the Si-Ge phase diagram. To detect striations on the SiGe polished-surface that were induced by the ±1 K stepwise temperature changes,9 we did not employ acid etching because the striations do not originate from impurities, but from the difference in Ge concentration. Figure 1 (a) shows the artifact striations due to the ±1 K changes in the single crystalline area and the polycrystalline area.9 Figure 1 (b) shows more detailed compo-mapping of the SiGe single crystal area on the Si seed in Fig. 1 (a). The map was enhanced in its contrast. The striations (white curves) across the right to left periphery were observed on a SiGe crystal. The right area from the center axis of the crystal did not include a large twin that appeared on the left side. We fit the striation curves (Nos. 1 to 12) by using polynomial functions, f(r), in the single crystal area in Fig. 1 as depicted in Fig. 2.

Figure 2. Polynomial function, f(r), fitting of the 12 striations (growth interface). r=0 denotes the crystal center axis.


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The No. 1 striation corresponds to the first stepwise temperature change (closest to the seed Si; 2.0 mm away from the seed/SiGe interface along the center axis). The No. 12 striation is 3.6 mm away from the seed/SiGe interface along the center axis in Fig. 1 (b). The interface shapes, f(r), in Fig. 2 were almost convex to the liquid zone. The modulated convex shape of interface No. 1 gradually varied into a smooth sine wave with growth. At the periphery, interfaces were concave to the melt zone. The freckle-like Ge-rich horizontal bars (marked as “Ge bars”) with a length of 2-3 mm and a width of 0.1 mm exist at 0.4 and 1.7 mm away from the right periphery in (a) and (b) of Fig. 1, respectively. The black vertical lines overlapping these Ge bars in Fig. 1 (b) were the artifact noise. These Ge bars indicate that the initial growth pattern (especially around the periphery area) is cellular growth. As a cellular growth interface could trap a melt between the cell, trapped melt in the crystal will migrate in a crystal toward the high temperature side due to the TGZM (Temperature Gradient Zone Melting) effect.22 The trajectory of the migrated Ge drops was white (Ge-enriched), as shown by the vertical lines in (a) and (b) of Fig. 1. The change in contrast of the triangle twin area, just dark contrast comparing with the other single crystal area, at the left periphery near the seed shown in Fig. 1 (a) is not due to a change in Ge concentration, but due to the electron channeling effect. In the following sections, we will analyze the right side from the center axis of the SiGe single crystal because the long twin boundary in the left side is across the striations shown in (a) and (b) of Fig. 1. Because the interface shape bends at the twin boundary, it is difficult to discuss shape and concentration on the interfaces. In Fig. 3, (a) to (c) show the radial dependence of df(r)/dr for each interface on the right side of the SiGe single crystalline area. Interface Nos. 1 to 6 have two peaks in df(r)/dr curves around r~1.5 and ~3.4 mm, and two minima around r~2.8 and 4.3 mm as


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shown in Fig. 3 (a). Both peak (minimum) intensities decreased (increased) with growth but maintained their peak (minimum) positions. The df(r)/dr curves of interface Nos. 7 to 10 in Fig. 3 (b) similarly show a broadened minimum around 3.5 mm and df(r)/dr ~ - 0.28. Interface No. 11 and No. 12 have a broad minimum around 3.0 mm in Fig. 3 (c).

Figure 3. (a) Radial dependences of df(r)/dr of interfaces 2 to 6. (b) Radial dependences of df(r)/dr of interfaces 7 to 10. (c) Radial dependences of df(r)/dr of interfaces 11 and 12.

2-2. Ge concentrations on the growth interface The ±1 K stepwise temperature changes in the GHF heaters simultaneously produce stepwise Ge concentration variations of the SiGe crystal growth interface. We successfully measured the Ge concentrations, CGe(r), on the interfaces shown in Fig. 2 by using the EPMA. The electron beam setting was 20 kV, 30 nA, using just the focus probe size and TAP/LIF crystals for detecting Si Kα and Ge Kα radiation. The measured radiation peak counts were on the order of 10 7. Such huge peak counts produced ±0.0002 mole fraction with a statistic error for the Ge concentration. Figure 4 shows the measured Ge mole fraction changes across striation No. 2 at r=0.2 mm with 50


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μm pitch. The measured Ge mole fraction decreased about 0.002 mole fraction across the striation in Fig. 4.

Figure 4. Germanium concentration distribution across striation No. 2 at r=0.2 mm. The arrow shows the Ge concentration on the interface.

We can define the Ge concentration of the interfaces as depicted by an arrow as being just before the decrease in Ge concentration due to the stepwise temperature change in Fig. 4. The radial dependence of the Ge concentrations, CGe(r), on each interface was measured from the center to the right side (r ~ 4.3 mm) with about 0.5 mm step. The measured Ge concentration depends on the specimen surface roughness and tilting geometrical position of the X-ray detectors in the EPMA. The periphery region was unsuitable for the precise measurements, as edge drooping caused by mechanical polishing of the SiGe plate was about 0.5 mm from the periphery. Figure 5 shows the radial dependence of the Ge concentrations, C Ge(r), on each interface. The solid or open symbols are the measured data, and the dotted or solid lines denote the least mean


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square fitted curves. The CGe(r) curves do not change

monotonically. The Ge concentration

distributions of interface Nos. 3, 5, 9 and 11 were very homogeneous within ±0.0005 (corresponding to the ±0.25 K temperature difference calculated using the phase diagram). In interface No. 6 and No. 7, homogeneous Ge concentration was restricted at 1 < r < 4 mm (No. 6) and the periphery area at 0 < r < 2 mm (No. 7). The maximum concentration difference on interface Nos. 2 to 12 is 0.003 mole fraction of interface No. 4.

Figure 5. Open and filled markers denoting the measured radial dependences of the Ge concentrations, CGe(r), on interfaces 1 to 12. And the solid and dotted lines are fitted polynomial functions.


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3. Discussion 3-1. Crystal growth rate calculation The averaged radial dependence of the SiGe crystal growth rates, ∂f(r)/∂t ≡ Lij(r)/T, of the interfaces in Fig. 2 can be calculated by the distance, Lij(r), between neighboring interfaces i and j (i>j) along the normal direction of i-th interface, and the stepwise temperature-change duration, T, between sending commands from the ground to the ISS. We assumed that the interface moved toward its normal direction and was parallel to a polished SiGe crystal surface in Fig. 1. The first 1 K temperature change was applied 5.2 hours after the start of crystal growth and the 12th change was commanded 20.1 hours later. The average growth rate from interface Nos. 1 to 12 along the center axis was 0.107 mm/hr. (14.9 hrs. for a growth length of 1.6 mm). The averaged growth rate is calculated under the assumption with the interface growth with parallel to the z axis. Since the normal direction of the interfaces does not always coincide with the z axis, the calculated ∂f(r)/∂t would be lower than the averaged growth rate. The calculated growth rates ∂f(r)/∂t of interface Nos. 2 to 6 shown in Fig. 6 (a) are almost constant at 0.08 mm/hr. in the 0 < r < 3 mm region, and 0.05 mm/hr. for minimum ∂f(r)/∂t around r=4.0 mm. For interface Nos. 7 to 12, the ∂f(r)/∂t curves vary abruptly with r in (b) and (c) of Fig. 6. The ∂f(r)/∂t minimum rate in interface No. 2 in Fig. 6 (a) is about 0.05 mm/hr. at r=4.0 mm, which is about half the average growth rate of 0.107 mm/hr. calculated above. The ∂f(r)/∂t curves in (a) to (c) of Fig. 6 are closely related to the df(r)/dr curves in Fig. 3. For example, the modulated ∂f(r)/∂t curve of interface No. 10 is caused by the change in shape from interface No. 9 and No. 10.


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Figure 6. (a) Radial dependences of the calculated growth rate, ∂f(r)/∂t mm/hr., of interfaces 2 to 6. (b) ∂f(r)/∂t mm/hr. of interfaces 7 to 9. (c) ∂f(r)/∂t mm/hr. of interfaces 10 to 12.


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3-2. Calculation of the melt concentration gradient on the growth interface The mass balance equation of Ge at the crystal growth interface is given as follows.9 

f r  CL r , z   CS r , z   D  f r  CL r , z   CL r , z  t r z   r

(1)

Here, CL(r,z), CS(r,z), D and t are the liquid and solid Ge concentrations on the interface, the diffusion coefficient and time, respectively. The concentration gradient along the tangent, s, on the interface is expressed by Eq. (2). CL r , z   s

 CL r , z  f r  CL r , z      r r z   f r    1    r  1

2

(2)

From Eqs. (1) and (2), the Ge concentration gradients in the radial and axial directions on the interface are respectively derived as follows.  CL r , z       r int

2   f r  f r  CL r , z   CS r , z    CL r , z   f r   1      2 r t D  r   f r    s  1    r 

1

f r   CL r , z   f r  CL r , z   CS r , z   CL r , z         r  r t D  z int int

(3)

(4)

To calculate (∂CL/∂r)int and (∂CL/∂z)int using Eqs. (3) and (4), ∂f(r)/∂r and CL(r,z) on the interface were obtained from Figs. 3 and 5, respectively. CS(r,z) are the corresponding solidus concentration to CL(r,z) in the phase diagram, and D was set to 9.5×10-9 m2/s.9 The growth rate at the position r on the interface, ∂f(r)/∂t is in (a) to (c) of Fig. 6. The first term on the right-hand side of Eq. (3), CL r , z  s  1  f r  r 2 , was estimated as the derivative of r for the fitted curve of CGe(r) in Fig. 5, i.e., dCGe(r)/dr.


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In Fig. 7, (a) to (f) show the calculated radial dependences of (∂CL/∂r)int and (∂CL/∂z)int. The (∂CL/∂r)int curves of all interfaces were close to zero at the crystal’s center axis (r=0) in (a) to (c) of Fig. 7. The (∂CL/∂r)int curves almost change from minus to plus with increasing r.

Figure 7. (a) Calculated radial dependences of the radial axis concentration gradient at interfaces 2 to 5. (b) at interfaces 6 to 9. (c) at interfaces 10 to 12. (d) The calculated radial dependences of the z axis concentration gradient at interfaces 2 to 5. (e) at interfaces 6 to 9. (f) at interfaces 10 to 12.

The melt Ge concentration on the interface monotonically decreases with increasing r of interface Nos. 6, 9 and 11. In the r > 4 mm region, the (∂CL/∂r)int values were considerably different by interfaces. The (∂CL/∂r)int curves of interface No. 3 and No. 5 in Fig. 7 (a) are very similar as well as their f(r) in Fig. 2, df(r)/dr in Fig. 3, and R(t) in Fig. 6 (a). In Fig. 7, the maximum and minimum values of (∂CL/∂r)int are 1.0×10-3 mole fraction/mm at r=3.4 mm of interface No. 4 and -1.34×10-3 mole fraction/mm at r=0.6 mm of interface No. 6, respectively.


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In Fig. 7 (d), the (∂CL/∂z)int curves of interface Nos. 2 to 4 at about −0.80×10-3 mole fraction/mm at r < 3 mm indicate that a uniform z-axis Ge concentration gradient existed. The (∂CL/∂z)int curves of interface Nos. 10 to 12 in Fig. 7 (f) vary from a minimum of -1.20×10-3 mole fraction/mm around the center area (r < 1.0 mm) to a maximum of -0.70×10-3 mole fraction/mm around r ~ 2.5 mm. These interfaces were smooth in Figs. 2 and 3, but their growth rates in Fig. 6 (c) were modulated. The low (high) ∂f(r)/∂t values such as 0.08 (0.12) mm/hr. at r=3.0 (0.6) mm of interface No. 11 correspond to high (low) (∂CL/∂z)int values. The (∂CL/∂r)int and ∂f(r)/∂t curves of each interface in Fig. 7 would not correlate with each other. The average temperature gradient in the melt, 9 K/cm, is almost constant during the experiment, and the slightly bended concave interface shapes are from interface Nos. 1 to 12, as shown in Fig. 2. The maximum temperature difference on the interfaces is 1.5 K (corresponding to 0.003 mole fraction) at interface No. 4 as calculated by the CGe(r) curve in Fig. 5. In these situations, we usually expect small (∂CL/∂r)int and constant (∂CL/∂z)int values on the interface in steady state growth. The modulated interface in Fig. 2 and CGe(r) curves in Fig. 5 would thus reflect fluctuations of the concentration gradients of (∂CL/∂r)int and (∂CL/∂z)int on the interfaces in Fig. 7.

3-3. Evaluation of melt saturation around the center axis It is worth to compare the calculated magnitude of the grad (C L(r, z))int vector represented as χ which consists of the (∂CL/∂r)int and (∂CL/∂z)int around the center area with the averaged concentration gradient calculated at 9 K/cm from the start to end of growth. The averaged temperature gradient was calculated by the one-dimensional TLZ growth method based on a stable and saturated melt zone.9 The interface shapes around the center area are almost flat from (a) to (c) in Fig. 3. Thus, the first term of Eq. (4) is almost small around the center area from Figs. 3 and


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7. Therefore, we assume the growth around the center area is comparable with one-dimensional growth. The averaged temperature gradient is converted to (∂CL/∂z)int divided by m: (∂TL/∂z)int = (1/m)(∂CL/∂z)int (where m denotes dCL/dT calculated by the liquidus curve of the Si-Ge phase diagram) under the assumption of a saturated melt. Here, 9K/cm corresponds to −1.31×10-3 mole fraction/mm dotted line in Fig. 8. The averaged χ values around the center area at r = 0.2, 0.6 and 1.0 mm of interface Nos. 2 to 12 are plotted in Fig. 8. The solid red line in Fig. 8 is a visual guide. In Fig. 8, the χ gradually decreased from −0.88×10-3 mole fraction/mm of interface No. 2 to −1.19×10-3 mole fraction/mm of interface No. 10. In contrast, the averaged χ of interface No. 11 and No. 12 increased slightly. This suggest that the melt in front of the interfaces around the center area would be unsteady and unsaturated until interface No. 10 (at about 16 hours after the start of growth).

Figure 8.

χ of the interfaces 2 to 12. The red line is a visual guide. The dotted line is the calculated ∂CL(r)/∂z from the averaged temperature gradient at 9 K/cm.

The interface temperature and heater temperature were gradually increasing from the interface No. 1 to 12 in Fig. 5. The successive 1K stepwise temperature changes for 1 hour interval makes


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the melt slightly unsaturated state, which would contribute to elongate the melt unsaturation duration. The other origin of the long-time unstable and unsaturated melt state (i.e. a transient state) might be the unexpectedly high growth rate (0.4 mm/hr) exhibited by interface No. 1 (5.2 hours after the start of growth).11 In this experiment, the programmed heater temperature profile based on the TLZ growth model was adjusted under an assumed growth rate of 0.1 mm/hr. The excess Ge ejected from the interface due to the high growth rate would be stagnant in the melt, thus resulting in a long-time unstable and unsaturated melt state around the interface. The interface that becomes smooth with growth in Figs. 2 and 3 would denote the mitigation of the melt’s constitutional undercooling that was numerically calculated using phase field simulations and experimentally observed.23, 24

3-4. Evaluation of Ge concentration gradient on interfaces Figure 9 (a) shows a schematic image of (∂CL/∂r)int, -(∂CL/∂z)int, the concentration gradient (grad(CL(r)) vector, interface normal vector n and angle (θi) between the horizontal axis and grad(CL(r)) of the i-th interface in Fig. 2. Both (∂CL/∂r)int and (∂CL/∂z)int are also shown in Fig. 7. Figure 9 (b) shows the distributions of the grad(CL) vector as arrows superimposed on each interface represented by dotted lines. The θi values at the nine r positions on each interface are plotted in (c) to (e) of Fig. 9. The Ge ejected from the interface would diffuse to the melt in the grad(CL(r)) vector direction around the interface. As the angles between the horizontal axis and interface normal direction are distributed in the range from about 70 to 100 deg. The θi is not always parallel to the normal direction of the growth interface. The θi curves at r=0.2, 0.6 and 1.0 mm are over 90 deg in Fig. 9 (c). Thus, ejected Ge would diffuse to the center axis. The θ i curves in the middle area (r= 1.7, 2.2 and 2.9 mm) are located around 90 deg until interface No. 8 in Fig.


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9 (d). The θi curves in the periphery (r= 3.4, 4.0 and 4.3 mm) are smaller than 90 deg until interface No. 6, and after that interface the θi curves fluctuate around 90 deg in Fig. 9 (e). On the interface Nos. 2 to 4, the grad(CL(r)) directions are separated around r~2 mm: θi > 90 deg in r < 2.0 mm region and θi < 90 deg in r > 3.4 mm. All the θi values on interface No. 6, 9 and No. 11 are over 90 deg. The collective Ge diffusion behaviors with a millimeter scale are clearly observed in Fig. 9 (b).

Figure 9. (a) Interface normal vector n and grad(CL). (b) grad(CL) vectors on each interface (f(r), dotted line). (c-e) the angles of the grad(CL) of interfaces 2 to 12 at each radial position.

If the isoconcentration line is consist with the interface, the two vectors, n and grad(CL(r)), in Fig. 9 (a) coincide with each other. The grad(CL(r)) on the interface is calculated by the CGe(r) in


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Fig. 5 measured on the interface. It is difficult to define the n and grad(CL(r)) in the inter-interface region, the averaged grad(CL(r)) direction should accord with the averaged interface normal direction, n. In this sense, no steady Ge diffusive flow exists in front of the interface. These grad(CL(r)) fluctuations on the interface vary the growth rate from Eq. (1). That changes the shape and temperature distribution of the interface. The demixing behavior of equilibrium liquid SiGe has been studied by using ab-initio simulation 25 and thermodynamic properties, 26 such as Scc(0) (long wavelength limit of concentration-concentration fluctuations calculated by the Gibbs free energy of mixing and also by partial atomistic structure factors). The Scc(0) curve of the liquid silicon-germanium system is over the ideal mixture Scc(0) curve for the entire Ge concentration. Therefore, SiGe melt tends to result in demixing.25, 26 Under convectionless conditions, the intrinsic demixing behavior of SiGe melt would thus tend to prolong unstable/unsaturated states and cause Ge concentration gradient fluctuations on the interface.

5. Conclusion We have simultaneously defined the Ge concentrations and shapes of SiGe crystal growth interfaces by using the EPMA. Based on the detailed measurements of growth interface shapes and Ge concentrations on the interface, growth conditions were precisely analyzed. Calculated axial and radial concentration gradients on the interface show that SiGe crystals grown by the TLZ method under the microgravity condition do not always realize steady-state growth and quiescent melt on the interface, but would slowly close to a stable state.


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AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] Tel: +81 50 3362 7986.

ACKNOWLEDGMENT The SiGe analysis work was supported by MEXT/JSPS KAKENHI Grant No. 15K04671 and by Matching Planner Program No. MP27115661170.

REFERENCES (1) Pillarisetty, R.; Chu-Kung, B.; Corcoran, S.; Dewey, G.; Kavalieros, J.; Kennel, H.; Kotlyar, R.; Le, V.; Lionberger, D.; Metz, M.; Mukherjee, N.; Nah, J.; Rachmady, W.; Radosavljevic, M.; Shah, U.; S. Taft, S.; Then, H.; Zelick, N.; Chau, R. High Mobility Strained Germanium Quantum Well Field Effect Transistor as the P-Channel Device Option for Low Power (Vcc = 0.5 V) III-V CMOS Architecture. Proceedings of the 2010 International Electron Devices Meeting, San Francisco, CA, December 6-8. 2010. (2) Miceli, J. J.; Naughton, D. P. Model for gradient formation in polycrystalline germaniumsilicon alloy GRIN crystals via Czochralski crystal growing. Appl. Opt., 1988, 27, 500-504.


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(3) Hedegaard, E. M. J.; Johnsen, S.; Bjerg, L.; Borup, K. A.; Iversen, B. B. Functionally Graded Ge1–XSiX Thermoelectrics by Simultaneous Band Gap and Carrier Density Engineering. Chem. Mater., 2014, 26, 4992–4997. (4) Wagner, A. C.; Cröll, A.; Gonik, M.; Hillebrecht, H.; Binetti S.; LeDonne, A. Si1-XGeX (x≥0.2) crystal growth in the absence of a crucible. J. Cryst. Growth, 2014, 401, 762–766. ( 5 ) Yonenaga, I. Growth and Characterization of Silicon – Germanium Alloys. In Silicon, Germanium, and Their Alloys. Growth, Defects, Impurities, and Nanocrystals; Kissinger, G., Pizzini, S., Eds.; CRC Press, Boca Raton, 2014, pp 23-60. (6) Sekhon, M.; Lent, B.; Dost, S.; Numerical study of liquid phase diffusion growth of SiGe subjected to accelerated crucible rotation. J. Cryst. Growth, 2016, 438, 90–98. (7) Maeda, T,; Hattori, H.; Chang, W. H.; Arai, Y.; Kinoshita, K. Hole Hall mobility of SiGe alloys grown by the traveling liquidus-zone method. Appl. Phys. Lett., 2015, 107, 152104. (8) Adachi, S.; Kinoshita, K.; Takayanagi, M.; Miyata, H.; Numerical analysis of two-dimensional model of the traveling liquidus-zone method. J. Cryst. Growth, 2011, 334, 67–71. (9) Kinoshita, K.; Arai, Y.; Inatomi, Y.; Tsukada, T.; Miyata, H.; Tanaka, R.; Yoshikawa, J.; Kihara, T.; Tomioka, H.; Shibayama, H.; Kubota, Y.; Warashina, Y.; Ishizuka, Y.; Harada, Y.; Wada, S.; Ito, T.; Nagai, N.; Abe K.; Yoda, S. Compositional uniformity of a Si0.5Ge0.5 crystal grown on board the International Space Station. J. Cryst. Growth, 2015, 419, 47-51. ( 10 ) Kinoshita, K.; Arai, Y.; Inatomi, Y.; Tsukada, T.; Miyata, H.; Tanaka, R. Effects of temperature gradient in the growth of Si0.5Ge0.5 crystals by the traveling liquidus-zone method on board the International Space Station. J. Cryst. Growth, 2016, 455, 49-54. ACS Paragon Plus Environment

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(11) Kinoshita, K.; Arai, Y.; Inatomi, Y.; Tsukada, T.; Miyata, H.; Tanaka, R.; Abe, K.; Sumioka, S.; Kubo, M.; Baba, S. SiGe Crystal Growth by the Traveling Liquidus-Zone Method aboard the International Space Station. Int. J. Microgravity Sci. Appl., 2016, 33, 330213. (12) Abe, K.; Sumioka, S.; Sugioka, K.; Kubo, M.; Tsukada, T.; Kinoshita, K.; Arai, Y.; Inatomi, Y.; Numerical simulations of SiGe crystal growth by the traveling liquidus-zone method in a microgravity environment.

J. Cryst. Growth, 2014, 402, 71-77.

(13) Müller, G. Crystal Growth from the Melt; Springer-Verlag Berlin Heidelberg, Berlin, 1988 ; pp. 112. ( 14 ) Nishinaga, T. Mechanism of macrostep formation in solution growth of compound semiconductor and the evidence given by space experiment. Cryst. Res. Technol., 2013, 48, 200– 207. (15) Ostrogorsky, A. G.; Marin, C.; Volz, M.; Duffar, T. Initial transient in Zn-doped InSb grown in microgravity. J. Cryst. Growth, 2009, 311, 3243-3248. (16) Vailati, A.; Cerbino, R.; Mazzoni, S.; Takacs, C. J.; Cannell, D. S.; Giglio, M.; Fractal fronts of diffusion in microgravity. Nat. Commun., 2011, 2, 290. (17) Carlberg, T. A review of radial segregation in crystal growth during microgravity. Prog. Cryst. Growth Charact. Mater., 2006, 52, 213-222. ( 18 ) Rudolph, P.; Boeck, T.; Schmidt, P. Thermodiffusion and Morphological Stability in Convectionless Crystal Growth Systems from Melts and Melt-Solutions. Cryst. Res. Technol., 1996, 31, 221-229. (19) Yildiz, M.; Dost, S.; Lent, B. Growth of Bulk SiGe Single Crystals by Liquid Phase ACS Paragon Plus Environment

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Diffusion. J. Cryst. Growth, 2005, 280, 151-160. (20) Yildiz, M.; Dost, S. A Computational Model for the Liquid Phase Diffusion Growth of SiGe Single Crystals. Int. J. Eng. Sci., 2005, 43, 1059-1080. (21) Armour, N.; S, Dost. Effect of an applied static magnetic field on silicon dissolution into a germanium melt. J. Cryst. Growth, 2009, 311, 780-782. (22) Anthony, T. R.; Cline, H. E. Random walk of liquid droplets migrating in silicon. J. Appl. Phys., 1976, 47, 2316. (23) Miller, W.; Rasin, I.; Stock, D. Evolution of cellular structures during Ge1−XSiX single-crystal growth by means of a modified phase-field method. Phys. Rev. E. 2010, 81, 051604. (24) Yonenaga, I.; Taishi, T.; Ohno, Y.; Tokumoto, Y. Cellular structures in Czochralski-grown SiGe bulk crystal. J. Cryst. Growth, 2010, 312, 1065–1068. (25) Ko, E.; Jain, M.; Chelikowsky, J. R. First principles simulation of SiGe for the liquid and amorphous state. J. Chem. Phys., 2002, 117, 3476. (26) Amore, S.; Giuranno, D.; Novakovic, R.; Ricci, E.; Nowak, R.; Sobczak, N.; Thermodynamic and surface properties of liquid Ge–Si alloys. CALPHAD: Comput. Coupling Phase Diagrams Thermochem., 2014, 44, 95-101.


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“For Table of Contents Use Only” Study of SiGe crystal growth interface processed in microgravity Yasutomo Arai, Kyoichi Kinoshita, Takao Tsukada, Masaki Kubo, Keita Abe, Sara Sumioka, Satoshi Baba and Yuko Inatomi

We succeeded in determining the concentration gradient, grad(CL), on the modulated SiGe crystal/melt interface (blue line) processed in, convectionless, microgravity condition. The black and red arrows on the interface represent the grad(CL) vector and interface normal vector. The grad(CL) and interface normal directions on the interface are not always similar.


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Study of SiGe crystal growth interface processed in microgravity

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