Passive platform for controlling thickness and uniformity of crystalline sheets

Abstract

The present disclosure relates to a passive platform and process for controlling the thickness and uniformity of crystalline sheets grown from a melt. The described technology addresses the technical problem of achieving sub-50-micron thickness precision in direct sheet growth by isolating flow instabilities and employing multi-stage thermal management. The solution involves a process chamber with partitioning structures, insulating walls, and distinct thermal zones, including a thickness modulation zone to adjust mean sheet thickness and a uniformity control zone to passively correct local deviations. This approach facilitates scalable, reliable production of crystalline sheets suitable for electronic and photovoltaic applications.

Description

PASSIVE PLATFORM FOR CONTROLLING THICKNESS AND UNIFORMITY OF CRYSTALLINE SHEETSField of Invention

[0001] The present disclosure relates generally to materials science and manufacturing technologies, and more specifically to systems and methods for controlling the thickness and uniformity of crystalline sheets grown from their melt.Background

[0002] A single crystalline silicon sheet is a structural element employed in electronic devices and photovoltaic modules to convert or manage electrical energy. Conventional wafers are produced by slicing cylindrical boules obtained via Czochralski or float-zone processes, leading to significant kerf loss and high production costs. On the other hand, direct sheet growth from the melt offers a route to reduce material waste and lower manufacturing expenses. However, despite its promise, achieving consistent sheet dimensions remains a formidable challenge.

[0003] Different approaches have been pursued to address the thickness nonuniformity of as-grown sheets. These include variations in furnace design, alternative cooling schemes at the melt surface, and tailored material treatments of the solidifying front. Although each strategy has yielded incremental improvements, none has fully resolved the issue of thickness variation over practical sheet lengths.

[0004] Active control systems employing in situ thickness monitoring and feedback- adjusted cooling have been tested to combat fluctuations during growth. However, these approaches often struggle with measurement delays, control latency, and the unpredictable nature of thermofluid disturbances in the melt pool, limiting their ability to maintain tight tolerances.

[0005] During sheet growth, surface tension gradients (Marangoni effects) and buoyancy- driven convection in both the melt and surrounding gas can induce chaotic flow patterns that alter local heat transfer rates. Moreover, inert gas shear at the melt interface further exacerbates temperature and velocity variations near the solidification front. As a result, such unsteady transport phenomena routinely produce deviations of several hundred microns in thickness, well above the target variation of a few tens of microns. Efforts to mitigate one source of instability often shift sensitivity to another mechanism, thereby preventing robust uniformity.1 I P a g e22094251.V1-8 / 5 / 25

[0006] Passive strategies that segregate the initial crystallization zone and direct subsequent thermal management through multistage cooling and heating zones have been conceptually proposed. These schemes aim to confine high-gradient disturbances to a localized region and promote more uniform downstream solidification. Incorporating thermal partition elements and calibrated thermal resistances could, in principle, stabilize the thickness profile without active intervention. However, existing methods lack the precision and scalability needed to achieve sub-50 micron uniformity over practical sheet lengths.

[0007] Accordingly, there is a need in the art for a passive control platform capable of precisely regulating both the mean thickness and the thickness variations of crystalline silicon sheets grown directly from the melt.Summary

[0008] The present disclosure relates to passive platforms and methods for controlling the thickness and uniformity of crystalline sheets grown from a melt, particularly for applications in materials science and manufacturing technologies. The described technology provides systems and processes that enable precise, passive regulation of both the mean thickness and thickness variations of crystalline sheets, such as silicon, by isolating flow instabilities and employing multi-stage thermal management without the need for active feedback.

[0009] An apparatus is provided for passively controlling the thickness and uniformity of a crystalline sheet grown from a melt. The apparatus includes a process chamber configured to contain a melt and support the growth of the crystalline sheet, a heating system disposed below the melt to provide a controlled heating flux, and a first cooling system disposed above the melt surface to initiate crystallization by providing a cooling flux greater than the heating flux. The apparatus further includes a partitioning structure to isolate effects of unsteady flow and heat transfer associated with crystallization from downstream regions of the process chamber. Downstream of the first cooling system, a second cooling system is disposed above the crystalline sheet and comprises at least one thickness modulation zone for adjusting the average thickness of the crystalline sheet by providing a cooling flux different from the heating flux, and at least one uniformity control zone for reducing thickness variations by providing a cooling flux substantially equal to the heating flux when the crystalline sheet reaches a target thickness, such that local deviations in thickness are passively corrected. The process chamber, heating system,21 a g e22094251.V1-8 / 5 / 25and cooling systems are configured to suppress flow instabilities due to buoyancy and surface tension gradients, enabling control of sheet thickness and uniformity without active feedback.

[0010] The partitioning structure may include a first series of insulating walls disposed with a small clearance above the upper surface of the crystalline sheet to isolate unsteady cooling effects, and a second series of insulating walls disposed with a small clearance below the crystalline sheet within the melt to isolate unsteady heating effects.

[0011] The heating system may comprise one or more heat pipes configured to maintain a predetermined uniform temperature at the bottom of the melt. A temperature-equalizing plate made of a material having anisotropic thermal conductivity may be disposed between the crucible and the heating system.

[0012] The thickness modulation zone may comprise a cold plate fabricated from a material having a higher thermal conductivity in a direction perpendicular to a heat flux than parallel thereto, and the cold plate may be coated with a radiation layer having a uniform emissivity. An inert gas may be circulated between the second cooling system and an upper surface of the crystalline sheet to remove contaminants. The process chamber and cooling systems may be configured to maintain a Rayleigh number of the melt below 1700. The second cooling system may include one or more heat pipes thermally coupled to a finned heat sink cooled by forced air flow. The process chamber may be insulated on the lateral sides and bottom to suppress external thermal disturbances. The uniformity control zone may comprise a cold radiation surface having an emissivity selected to balance heating and cooling fluxes at a target sheet thickness. A layered structure may be disposed between the cold plate and the heat pipes in the second cooling system to achieve a gradual temperature change.

[0013] A method is also provided for passively controlling the thickness and uniformity of a crystalline sheet grown from a melt. The method includes initializing growth of the crystalline sheet by cooling a surface of the melt within a process chamber using a first cooling system that provides a cooling flux greater than a heating flux supplied to the melt from a heating system disposed below the melt, isolating effects of unsteady flow and heat transfer associated with crystallization from downstream regions of the process chamber using a partitioning structure, adjusting an average thickness of the crystalline sheet in a thickness modulation zone downstream of the first cooling system by providing a cooling flux different from the heating flux using a second cooling system disposed above the crystalline sheet, and reducing thickness31 a g e22094251.V1-8 / 5 / 25variations of the crystalline sheet in a uniformity control zone downstream of the thickness modulation zone by providing a cooling flux substantially equal to the heating flux using the second cooling system, such that local deviations in thickness are passively corrected. The method further includes suppressing flow instabilities due to buoyancy and surface tension gradients within the process chamber, wherein the thickness and uniformity of the crystalline sheet are controlled without active feedback.

[0014] The temperature or heat flux at the bottom of the process chamber may be adjusted to a predetermined value with a predetermined precision, thereby passively controlling the thickness and uniformity of the crystalline sheet and reducing sensitivity to design parameter variations. The method is applicable to crystalline sheets having a lower density than the melt.Brief Description of the Drawings

[0015] FIG. 1 is a perspective view of a process chamber for controlling the thickness and uniformity of a crystalline sheet grown from the melt.

[0016] FIG. 2 is a top view of a process chamber showing the arrangement of cooling, heating, and partitioning systems for crystalline sheet thickness control.

[0017] FIG. 3 is a cross-sectional view of a process chamber illustrating the configuration for controlling crystalline sheet thickness and uniformity.

[0018] FIG. 4 is a graph showing the required length of the thickness modulation zone as a function of cold plate emissivity and temperature.

[0019] FIG. 5 is a graph showing the reduction in thickness variations along the uniformity control zone as a function of the length of the uniformity control zone.

[0020] FIG. 6 is a flowchart depicting a method for controlling the thickness and uniformity of a crystalline sheet grown from the melt.Detailed Description

[0021] The following detailed description provides illustrative embodiments of the disclosed technology, which pertains to systems and methods for passively controlling the thickness and uniformity of crystalline sheets grown from their melt. The disclosed technology is particularly relevant to the field of materials science and manufacturing technologies, with specific applicability to the production of single crystalline silicon sheets for use in electronic devices and photovoltaic modules. While the embodiments described herein focus on certain configurations41 P a g e22094251.V1-8 / 5 / 25and methods, it is to be understood that these are provided for illustrative purposes only and are not intended to limit the scope of the disclosed technology.

[0022] For clarity and conciseness, certain well-known elements, processes, and techniques commonly understood by those skilled in the art may not be described in comprehensive detail. The described subject matter is intended to include various modifications, substitutions, and rearrangements of components or steps, provided they fall within the scope of the appended claims. Accordingly, the specific examples and embodiments disclosed herein are not to be construed as limiting, but rather as illustrative of the principles and features of the described subject matter.

[0023] The production of crystalline sheets, such as single crystalline silicon sheets, plays an important role in the manufacturing of electronic devices and photovoltaic modules.Conventional methods, such as slicing cylindrical boules produced via Czochralski or float-zone processes, result in significant material waste due to kerf loss and high production costs. Direct sheet growth from the melt, including methods like Horizontal Ribbon Growth (HRG), offers a promising alternative to reduce material waste and lower costs. However, achieving consistent thickness and uniformity in crystalline sheets grown directly from the melt has proven to be a persistent challenge.

[0024] In conventional HRG processes, the sheet is pulled horizontally as the material solidifies at the melt surface. This process is highly sensitive to thermofluid instabilities, including surface tension gradients (Marangoni effects), buoyancy-driven convection, and inert gas shear stresses at the melt interface. These instabilities lead to chaotic flow patterns, unsteady heat transfer, and significant variations in sheet thickness. Active control systems, which rely on in situ thickness monitoring and feedback mechanisms, have been explored to address these issues. However, such systems are limited by measurement delays, control latency, and the unpredictable nature of the disturbances, often exacerbating the problem rather than resolving the challenges. As a result, sheets produced using these methods frequently exhibit mean thicknesses of 1-2 mm with variations as large as 0.5 mm, far exceeding the target precision of sub-50 microns.

[0025] The present disclosure addresses these limitations by introducing a passive control platform that isolates and mitigates the effects of flow instabilities during the sheet growth process. The described system employs a process chamber with a specialized partitioning51 P a g e22094251.V1-8 / 5 / 25mechanism to confine unsteady heat transfer and fluid flow to the crystal initialization zone. This isolation prevents disturbances from propagating downstream, where the sheet undergoes further thermal management. The system incorporates a multi-stage heating and cooling architecture, including a thickness modulation zone and a uniformity control zone. In the thickness modulation zone, the average sheet thickness is adjusted by maintaining a controlled imbalance between the cooling flux from above and the heating flux from below. In the uniformity control zone, the cooling and heating fluxes are balanced when the sheet reaches its target thickness, passively correcting any local deviations and promoting uniformity.

[0026] Innovative features include the use of insulating walls to isolate flow instabilities, the design of cold plates with anisotropic thermal conductivity for improved temperature uniformity, and the application of materials with uniform radiative properties to reduce sensitivity to temperature and emissivity variations. Additionally, the system is designed to suppress buoyancy-driven convection in both the melt and the surrounding inert gas by maintaining Rayleigh numbers below specific thresholds. These aspects collectively enable the production of crystalline sheets with precise control over mean thickness and thickness variations, achieving target values of approximately 200 microns with variations as low as 30 microns. This passive approach eliminates the need for complex active control systems, offering a scalable and robust solution to longstanding challenges in direct sheet growth from the melt.

[0027] Referring to FIG. 1 and FIG. 2, the process chamber layout and functional zones are illustrated in perspective and top views, respectively. The feed 100 is introduced into the process chamber through the feed channel 102 to maintain the melt surface 104 at a consistent level. The melt is contained within the crucible 206, which is supported by the crucible holder 108 to provide structural support and thermal insulation. Below the crucible holder 108, the heating system 112 supplies controlled heat to the melt, ensuring uniform temperature distribution and suppressing buoyancy-driven convection. Adjacent to the feed channel 102, the insulating wall 114 isolates disturbances caused by the feed introduction, preventing unsteady flow and heat transfer effects from propagating downstream. Above the melt surface 104, the crystal forming cooling system 116 initiates crystallization by providing a cooling flux significantly higher than the heating flux from below, setting the primary thickness of the crystalline sheet. Downstream of the crystal forming cooling system 116, the insulating wall 122 isolates the initial growth zone from subsequent thermal management zones. The thickness modulation cooling system 134,61 P a g e22094251.V1-8 / 5 / 25located further downstream, adjusts the average thickness of the crystalline sheet by creating a controlled imbalance between the cooling flux from above and the heating flux from below. The insulating wall 136 separates the thickness modulation zone from the uniformity control zone, preserving the modulation process. The uniformity control cooling system 144 balances the cooling and heating fluxes when the crystalline sheet reaches the target thickness, passively correcting local deviations and promoting uniformity. The insulating wall 146 isolates the uniformity control zone from external disturbances, while the sheet upper surface 128 represents the interface of the crystalline sheet as the crystalline sheet advances through the chamber.

[0028] Referring to FIG. 3, the cross-sectional view of the process chamber provides a detailed depiction of the feed channel 102, melt surface 104, crucible 206, crucible holder 108, temperature equalizing plate 310, and heating system 112. The feed 100 is introduced into the chamber through the feed channel 102 to maintain the melt surface 104 at a constant level. The melt is contained within the crucible 206, which is supported by the crucible holder 108. Between the crucible 206 and the crucible holder 108, the temperature equalizing plate 310, made of a material with anisotropic thermal conductivity such as pyrolytic graphite, ensures uniform temperature distribution at the bottom of the crucible. Below the crucible holder 108, the heating system 112 provides controlled heat to the melt, maintaining stable thermal conditions and suppressing buoyancy-driven convection.

[0029] Referring further to FIG. 3, the crystal growth zone is isolated by the insulating wall 114, positioned adjacent to the feed channel 102, and the insulating wall 320, located with a small clearance below the crystalline sheet 318. Above the melt surface 104, the crystal forming cooling system 116 provides a cooling flux significantly higher than the heating flux from below, promoting solidification and setting the primary thickness of the crystalline sheet 318. The insulating wall 122 isolates unsteady flow and heat transfer effects associated with the initial growth zone, ensuring stable downstream conditions for subsequent thermal management.

[0030] The thickness modulation zone is depicted with the thickness modulation cooling system 134, which includes the cold radiation surface 326, the radiation layer 330, and the cold plate 332. The cold plate 332, fabricated from a material with anisotropic thermal conductivity, improves temperature uniformity, while the radiation layer 330, coated with a material having uniform radiative properties, reduces sensitivity to temperature and emissivity variations. An inert gas 324, such as helium, flows between the cold radiation surface 326 and the sheet upper71 P a g e22094251.V1-8 / 5 / 25surface 128, removing contaminants and aiding in thermal management. The insulating wall 136 separates the thickness modulation zone from the uniformity control zone, preserving the integrity of the modulation process.

[0031] Referring further to FIG. 3, the uniformity control zone is illustrated with the uniformity control cooling system 144, which includes the cold radiation surface 338, the radiation layer 340, and the cold plate 342. The cold plate 342 and radiation layer 340 are designed similarly to those in the thickness modulation cooling system, maintaining consistent temperature and radiative properties. The uniformity control cooling system 144 balances the cooling and heating fluxes when the crystalline sheet 318 reaches the desired thickness, passively correcting local deviations and promoting uniformity. The insulating wall 146 isolates the uniformity control zone from external disturbances.

[0032] The downstream end of the process chamber is depicted with the roller 150 and the meniscus 348. The roller 150 supports and pulls the crystalline sheet 318, facilitating the movement of the crystalline sheet 318 to subsequent processing zones for cooling, trimming, and removal. The meniscus 348 forms at the downstream edge of the crucible 206 as the crystalline sheet 318 exits the process chamber, completing the sheet growth process. Referring to FIG. 4 is a graph illustrating the required length of the thickness modulation zone 406 as a function of cold plate emissivity and temperature. The thickness modulation zone 406 is an important region within the process chamber wherein the average thickness of the crystalline sheet 318 is adjusted by establishing a controlled imbalance between the cooling flux from above and the heating flux from below. The graph provides insights into the design parameters necessary to achieve the desired modulation of sheet thickness.

[0033] The horizontal axis of FIG. 4 represents the cold plate temperature in Kelvin, while the vertical axis corresponds to the cold plate emissivity. Contour lines on the graph indicate the required length of the thickness modulation zone 406 in meters for various combinations of cold plate temperature and emissivity. These contours demonstrate how the cooling flux — governed by the radiative properties and temperature of the cold plate 332 — affects the spatial exposure required to reach the target thickness.

[0034] At lower emissivities and temperatures, the required length of the thickness modulation zone 406 increases, indicating that the cooling flux is less effective in modulating the sheet thickness. Conversely, higher emissivities and temperatures result in shorter required8 I P a g e22094251.V1-8 / 5 / 25lengths, as the cooling flux becomes more efficient. For example, a cold plate 332 with an emissivity of 0.85 and a temperature of approximately 1,465 K requires a thickness modulation zone 406 length of about 0.20 m when the sheet 318 is pulled at a rate of 1 mm / s.

[0035] Accordingly, the graph highlights the trade-offs between temperature and emissivity in achieving the desired cooling flux. At higher emissivities and temperatures, the sensitivity of the cooling flux to emissivity decreases, making the system more robust to variations in radiative properties. Similarly, at lower emissivities and temperatures, the sensitivity to temperature decreases, providing greater stability in thermal management. This graphical representation serves as a design tool for optimizing the thickness modulation zone 406.

[0036] By selecting appropriate cold plate 332 emissivity and temperature values, one can achieve precise control over the average thickness of the crystalline sheet 318 while minimizing the required length of the modulation zone 406. This optimization reduces the overall size and energy consumption of the process chamber, which contributes to the scalability and operational effectiveness of the passive control platform.

[0037] Referring to FIG. 5 is a graph illustrating the reduction in thickness variations of a crystalline sheet 318 as a function of the length of the uniformity control zone 144. In some embodiments, the uniformity control zone 144 defines a region within the process chamber where cooling and heating fluxes are balanced to passively address local deviations in sheet thickness by imposing a uniform temperature below the melt. Accordingly, this adjustment mechanism facilitates the sheet 318 reaching and sustaining the target thickness with minimal variations.

[0038] FIG. 5 further depicts the coordinate system for the data, wherein the horizontal axis represents the length of the uniformity control zone 144 in meters, and the vertical axis corresponds to the thickness variations of the crystalline sheet 318 in microns. The graph demonstrates a monotonic decrease in thickness variations as the length of the uniformity control zone 144 increases. This behavior highlights the effectiveness of the passive correction mechanism in progressively reducing deviations in sheet thickness over the control region’s extent.

[0039] At shorter control-zone lengths, the thickness variations are relatively high, exceeding 100 microns. By comparison, as the length increases toward 1 meter, the variations decrease significantly to approximately 30 microns. This reduction is attributed to the balance of9 | P a g e22094251.V1-8 / 5 / 25net cooling or heating flux within the uniformity control zone 144: regions thicker than the target experience a higher heating flux, leading to localized melting and thinning, whereas regions thinner than the target experience a higher cooling flux, promoting localized thickening.

[0040] The data further underscore the significance of optimizing the length of the uniformity control zone 144 to achieve the desired precision in sheet thickness. However, longer uniformity control zones 144, while providing reductions in thickness variations, also increase the overall size and energy requirements of the process chamber. As a result, the length needs to be carefully selected based on the target thickness precision and the operational constraints of the system.

[0041] The results presented in FIG. 5 demonstrate that the disclosed passive control platform is capable of achieving sub-50-micron thickness variations over practical sheet lengths. This level of precision addresses longstanding challenges in the direct growth of crystalline sheets 318 from the melt, offering a scalable and robust solution for applications in electronics and photovoltaics.

[0042] Referring to FIG. 6, there is shown a flowchart illustrating a method for controlling the thickness and uniformity of a crystalline sheet grown from the melt. The method comprises several sequential steps, each addressing specific aspects of sheet growth and thermal management to enable precise control over both the mean thickness of the sheet and variations in thickness. In some embodiments, this approach leverages passive control mechanisms to mitigate longstanding challenges associated with direct sheet growth from the melt.

[0043] Accordingly, at block 400 the method begins with initializing the growth of a crystalline sheet from the melt inside a process chamber by cooling the melt surface 104 to promote solidification and the formation of the crystalline sheet. The cooling flux applied at this stage is significantly higher than the heating flux from the heating system 112 below, thereby ensuring the initiation of crystallization at the melt surface 104 under stable conditions.

[0044] At block 402, the crystalline sheet is pulled at a uniform rate equal to the growth rate of the sheet. By comparison to active pulling schemes, this synchronization ensures that the sheet advances through the process chamber in alignment with the sheet's formation. As a result, consistent growth conditions are maintained.

[0045] FIG. 6 further depicts isolation of the crystal growth zone at block 404. In this step, the growth zone is confined from the remainder of the process chamber by insulating walls 11410 | P a g e22094251.V1-8 / 5 / 25and partitioning mechanisms. These measures confine unsteady heat transfer and fluid flow effects — such as surface tension gradients, buoyancy-driven convection, and inert gas 324 shear stresses — to the initial growth zone, thereby ensuring stable downstream conditions for subsequent thermal management.

[0046] At block 406, the crystalline sheet enters the thickness modulation zone. In this zone, the average thickness of the sheet is reduced to a predetermined value by applying a uniform temperature at the top and bottom of the process chamber. The cooling flux from the top is deliberately set to be significantly less than the heating flux from the heating system 112 at the bottom, creating a controlled thermal imbalance that rapidly modulates the mean thickness toward the target value.

[0047] Thereafter, at block 408, the crystalline sheet progresses into the uniformity control zone. In this zone, thickness variations of the crystalline sheet are reduced to a predetermined value by applying a uniform temperature at the top and a uniform heat flux at the bottom of the process chamber. When the thickness of the crystalline sheet reaches the target value, the cooling flux from the top balances with the heating flux from the heating system 112 at the bottom. Any local deviations from the target thickness result in either localized melting, thinning, or solidification, thickening, passively correcting the variations and thereby promoting uniformity throughout the crystalline sheet.

[0048] These steps, as illustrated in FIG. 6, enable precise regulation of both the mean thickness and thickness variations of the crystalline sheet, thereby addressing and overcoming difficulties naturally associated with direct sheet growth from the melt.

[0049] The apparatus described above achieves precise control over the thickness and uniformity of a crystalline sheet grown from a melt by employing a passive system that eliminates the need for active feedback mechanisms. The process chamber, heating system, and cooling systems are configured to suppress flow instabilities caused by buoyancy and surface tension gradients, which are common sources of thickness variations in conventional systems. The inclusion of a partitioning structure isolates unsteady flow and heat transfer effects associated with crystallization, preventing disturbances from propagating downstream. This arrangement ensures that the downstream regions of the process chamber operate under stable thermal conditions, enabling consistent sheet growth.11 | P a g s22094251.V1-8 / 5 / 25

[0050] The second cooling system, featuring distinct thickness modulation and uniformity control zones, offers a structured method for thermal management. The thickness modulation zone adjusts the average thickness of the crystalline sheet by creating a controlled imbalance between the cooling flux and the heating flux, enabling rapid convergence to a target thickness. The uniformity control zone further refines the crystalline sheet by balancing the cooling and heating fluxes when the sheet reaches the target thickness, passively addressing local deviations. This configuration removes the latency and inaccuracies commonly associated with active feedback systems, leading to a more dependable and scalable approach for producing crystalline sheets with sub-50-micron thickness variations.

[0051] By maintaining the Rayleigh number of the melt below 1700, the apparatus suppresses buoyancy-driven convection, ensuring uniform heat transfer and minimizing chaotic flow patterns. This contributes to the production of crystalline sheets with improved dimensional precision, making the system suitable for high-performance applications such as electronics and photovoltaics.

[0052] The method associated with as aspect of the invention described above provides a systematic approach to passively controlling the thickness and uniformity of a crystalline sheet grown from a melt. By initializing the growth process with a first cooling system that provides a cooling flux greater than the heating flux, the method ensures stable crystallization at the melt surface. The use of a partitioning structure to isolate unsteady flow and heat transfer effects associated with crystallization prevents disturbances from affecting downstream thermal management zones, thereby maintaining consistent growth conditions.

[0053] The method's sequential thermal management strategy, involving a thickness modulation zone and a uniformity control zone, enables precise control over the sheet's dimensions. In the thickness modulation zone, the average thickness of the crystalline sheet is adjusted by applying a cooling flux different from the heating flux, allowing rapid convergence to a target thickness. In the uniformity control zone, the cooling and heating fluxes are balanced when the sheet reaches the target thickness, passively correcting local deviations. This passive correction mechanism ensures that any perturbations in thickness are automatically mitigated, resulting in a uniform sheet.

[0054] The suppression of flow instabilities due to buoyancy and surface tension gradients within the process chamber further enhances the method's effectiveness. By maintaining stable12 | P a g s22094251.V1-8 / 5 / 25thermal and flow conditions, the method achieves sub-50-micron thickness variations without the need for active feedback systems. This approach reduces system complexity, improves reliability, and supports scalability for industrial applications, making the approach particularly advantageous for the production of crystalline sheets used in electronics and photovoltaic modules.13 | P a g &22094251.V1-8 / 5 / 25

Claims

Claims:What is claimed is:

1. An apparatus for passively controlling the thickness and uniformity of a crystalline sheet grown from a melt, comprising: a process chamber configured to contain a melt and to support growth of the crystalline sheet; a heating system disposed below the melt and configured to provide a controlled heating flux to the melt; a first cooling system disposed above a surface of the melt and configured to initiate crystallization of the crystalline sheet by providing a cooling flux greater than the heating flux; a partitioning structure configured to isolate effects of unsteady flow and heat transfer associated with crystallization from downstream regions of the process chamber; a second cooling system disposed downstream of the first cooling system and above the crystalline sheet, the second cooling system comprising: at least one thickness modulation zone configured to adjust an average thickness of the crystalline sheet by providing a cooling flux different from the heating flux; and at least one uniformity control zone configured to reduce thickness variations of the crystalline sheet by providing a cooling flux substantially equal to the heating flux when the crystalline sheet reaches a target thickness, such that local deviations in thickness are passively corrected; wherein the process chamber, heating system, and cooling systems are configured such that flow instabilities due to buoyancy and surface tension gradients are suppressed, and the thickness and uniformity of the crystalline sheet are controlled without active feedback.

2. The apparatus of claim 1, further comprising at least one thickness modulation zone configured to adjust an average thickness of the crystalline sheet by providing a cooling flux different from the heating flux.

3. The apparatus of claim 1, wherein said partitioning structure comprises: a first series of insulating walls disposed with a small clearance above an upper surface14 | P a g s22094251.V1-8 / 5 / 25of said crystalline sheet to isolate unsteady cooling effects; and a second series of insulating walls disposed with a small clearance below said crystalline sheet within said melt to isolate unsteady heating effects.

4. The apparatus of claim 1, wherein said heating system comprises one or more heat pipes configured to maintain a predetermined uniform temperature at a bottom of said melt.

5. The apparatus of claim 1, wherein the apparatus further comprises a temperatureequalizing plate made of a material having anisotropic thermal conductivity disposed between said crucible and said heating system.

6. The apparatus of claim 1, wherein said thickness modulation zone comprises a cold plate fabricated from a material having a higher thermal conductivity in a direction perpendicular to a heat flux than parallel thereto.

7. The apparatus of claim 6, wherein said cold plate is coated with a radiation layer having a uniform emissivity.

8. The apparatus of claim 1, wherein an inert gas is circulated between said second cooling system and an upper surface of said crystalline sheet to remove contaminants.

9. The apparatus of claim 1, wherein said process chamber and said cooling systems are configured to maintain a Rayleigh number of said melt below 1700.

10. The apparatus of claim 1, wherein said second cooling system includes one or more heat pipes.

11. The apparatus of claim 10, wherein the one or more heat pipes are thermally coupled to a finned heat sink cooled by forced air flow.

12. The apparatus of claim 1, wherein the process chamber is insulated on the lateral sides and bottom to suppress external thermal disturbances.

13. The apparatus of claim 1, wherein said uniformity control zone comprises a cold radiation surface having an emissivity selected to balance heating and cooling fluxes at a target sheet thickness.

14. The apparatus of claim 1, wherein the apparatus further comprises a layered structure disposed between said cold plate and said heat pipes in said second cooling system to achieve a gradual temperature change.

15. A method for passively controlling the thickness and uniformity of a crystalline sheet grown from a melt, the method comprising:15 | P a g e22094251.V1-8 / 5 / 25initializing growth of the crystalline sheet by cooling a surface of the melt within a process chamber using a first cooling system, wherein the first cooling system provides a cooling flux greater than a heating flux supplied to the melt from a heating system disposed below the melt; isolating effects of unsteady flow and heat transfer associated with crystallization from downstream regions of the process chamber using a partitioning structure; reducing thickness variations of the crystalline sheet in a uniformity control zone downstream of the thickness modulation zone by providing a cooling flux substantially equal to the heating flux using the second cooling system, such that local deviations in thickness are passively corrected; and suppressing flow instabilities due to buoyancy and surface tension gradients within the process chamber, wherein the thickness and uniformity of the crystalline sheet are controlled without active feedback.

17. The method of claim 15, further comprising adjusting an average thickness of the crystalline sheet in a thickness modulation zone downstream of the first cooling system by providing a cooling flux different from the heating flux using a second cooling system disposed above the crystalline sheet.

18. The method of claim 15, wherein a temperature at a bottom of the process chamber is adjusted to a predetermined value with a predetermined precision, thereby passively controlling the thickness and uniformity of the crystalline sheet.

19. The method of claim 15, wherein a heat flux at a bottom of the process chamber is adjusted to a predetermined value with a predetermined precision, thereby reducing sensitivity of the thickness of the crystalline sheet to variations of design parameters.

20. The method of claim 15, wherein the crystalline sheet has a lower density than the melt of the crystalline sheet.1 6 | P a g s22094251.V1-8 / 5 / 25

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