Pub Date : 2025-12-04DOI: 10.1007/s12633-025-03578-z
Wuju Qin,, Xu Zhang, Xuefeng Han, Yuan Liu, Yingchao Zhou, Zhongshi Lou, Shuai Yuan, Deren Yang
With the advancement of packaging technologies, wafer bonding has become increasingly critical in the fabrication of microelectronic devices, and stress concentration during this process has been recognized as a key factor affecting device reliability. To elucidate the stress response characteristics of wafers with different edge profiles and thicknesses during bonding, finite element simulations were conducted on R-type (rounded) and T-type (beveled) wafers with varying thinning thicknesses and chamfer angles. The simulations were performed under vertically applied uniform loads ranging from 15 to 60 MPa. The results indicate that while the stress distribution remains relatively uniform across the central wafer region, pronounced stress concentrations emerge in the edge regions, particularly near geometric discontinuities such as notches. T-type edges showed relatively better stress mitigation performance when thinned to an intermediate thickness (~ 562 μm), and larger chamfer angles were found to reduce stress concentrations associated with thinning. Further analysis of the stress concentration factor K revealed that R-type wafers exhibited a marked increase in K following thinning, whereas T-type structures demonstrated enhanced tolerance to thinning as chamfer angles increased. These findings indicate notable differences in stress adaptation between edge geometries under varying thicknesses and clarify the coupled influence of edge design and thinning on wafer stress behavior. The results may offer useful guidance for optimizing wafer edge structures to improve bonding performance and enhance the mechanical reliability of chip packages.
{"title":"Finite Element Simulation of Bonding-Induced Stresses in Thinned Wafers with Varying Edge Geometries","authors":"Wuju Qin,, Xu Zhang, Xuefeng Han, Yuan Liu, Yingchao Zhou, Zhongshi Lou, Shuai Yuan, Deren Yang","doi":"10.1007/s12633-025-03578-z","DOIUrl":"10.1007/s12633-025-03578-z","url":null,"abstract":"<div><p>With the advancement of packaging technologies, wafer bonding has become increasingly critical in the fabrication of microelectronic devices, and stress concentration during this process has been recognized as a key factor affecting device reliability. To elucidate the stress response characteristics of wafers with different edge profiles and thicknesses during bonding, finite element simulations were conducted on R-type (rounded) and T-type (beveled) wafers with varying thinning thicknesses and chamfer angles. The simulations were performed under vertically applied uniform loads ranging from 15 to 60 MPa. The results indicate that while the stress distribution remains relatively uniform across the central wafer region, pronounced stress concentrations emerge in the edge regions, particularly near geometric discontinuities such as notches. T-type edges showed relatively better stress mitigation performance when thinned to an intermediate thickness (~ 562 μm), and larger chamfer angles were found to reduce stress concentrations associated with thinning. Further analysis of the stress concentration factor <i>K</i> revealed that R-type wafers exhibited a marked increase in <i>K</i> following thinning, whereas T-type structures demonstrated enhanced tolerance to thinning as chamfer angles increased. These findings indicate notable differences in stress adaptation between edge geometries under varying thicknesses and clarify the coupled influence of edge design and thinning on wafer stress behavior. The results may offer useful guidance for optimizing wafer edge structures to improve bonding performance and enhance the mechanical reliability of chip packages.</p></div>","PeriodicalId":776,"journal":{"name":"Silicon","volume":"18 1","pages":"381 - 389"},"PeriodicalIF":3.3,"publicationDate":"2025-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147336459","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-04DOI: 10.1007/s12633-025-03576-1
Ananda Sankar Chakraborty
A novel, accurate charge-based MOSFET long-channel computational model is presented, which is portable and can be used across the electrical engineering domains ranging from sensing to power electronics, both under sub-threshold as well as super-threshold regime of MOSFET operation. The proposed physics-based model can be universally used to any long-channel MOS-transistor as it does not depend on any empirical factor and features extremely good computational efficiency. The model uses a novel two-step charge linearization, resulting into accurate drain current and charge model – valid for both the subthreshold and super-threshold regime of long-channel MOSFET operation. Another salient feature of the proposed model is a novel SPICE-compatible numerical solution strategy for the principal branch of the Lambert W function ((varvec{W}_{varvec{0}}varvec{(x)}) for (varvec{{x in {mathbb {R}} | x ge 0 }})). The algorithm is faster than present industry standard implementations, computationally efficient, accurate with maximum percentage error (varvec{approx O(10^{-14}%)}) and therefore may be incorporated in a SPICE engine for electrical design and optimization. The proposed computationally efficient long channel MOSFET model is validated against thorough TCAD simulations upto the fourth derivative and has been found to have fast convergence along with much higher degree of accuracy (maximum error (varvec{approx O{(10^{-14}%)}})) compared to existing MOSFET models.
提出了一种新颖、精确的基于电荷的MOSFET长沟道计算模型,该模型便于携带,可用于从传感到电力电子等电气工程领域,无论是在MOSFET的亚阈值还是超阈值下工作。所提出的基于物理的模型不依赖于任何经验因素,具有极高的计算效率,可普遍应用于任何长沟道mos晶体管。该模型采用了一种新颖的两步电荷线性化方法,得到了精确的漏极电流和电荷模型,适用于长沟道MOSFET的亚阈值和超阈值工作。提出的模型的另一个显著特征是一种新颖的spice兼容的兰伯特W函数主干的数值解策略((varvec{{x in {mathbb {R}} | x ge 0 }})为(varvec{W}_{varvec{0}}varvec{(x)}))。该算法比目前的行业标准实现更快,计算效率高,准确,最大百分比误差(varvec{approx O(10^{-14}%)}),因此可以纳入SPICE引擎进行电气设计和优化。与现有的MOSFET模型相比,所提出的计算效率高的长沟道MOSFET模型经过了全面的TCAD仿真验证,直至四阶导数,并且已经发现具有快速收敛以及更高程度的精度(最大误差(varvec{approx O{(10^{-14}%)}}))。
{"title":"Efficient Long-Channel MOSFET Model with SPICE-enabled Lambert W Function for Universal Application","authors":"Ananda Sankar Chakraborty","doi":"10.1007/s12633-025-03576-1","DOIUrl":"10.1007/s12633-025-03576-1","url":null,"abstract":"<div><p>A novel, accurate charge-based MOSFET long-channel computational model is presented, which is portable and can be used across the electrical engineering domains ranging from sensing to power electronics, both under sub-threshold as well as super-threshold regime of MOSFET operation. The proposed physics-based model can be universally used to any long-channel MOS-transistor as it does not depend on any empirical factor and features extremely good computational efficiency. The model uses a novel two-step charge linearization, resulting into accurate drain current and charge model – valid for both the subthreshold and super-threshold regime of long-channel MOSFET operation. Another salient feature of the proposed model is a novel SPICE-compatible numerical solution strategy for the principal branch of the Lambert W function (<span>(varvec{W}_{varvec{0}}varvec{(x)})</span> for <span>(varvec{{x in {mathbb {R}} | x ge 0 }})</span>). The algorithm is faster than present industry standard implementations, computationally efficient, accurate with maximum percentage error <span>(varvec{approx O(10^{-14}%)})</span> and therefore may be incorporated in a SPICE engine for electrical design and optimization. The proposed computationally efficient long channel MOSFET model is validated against thorough TCAD simulations upto the fourth derivative and has been found to have fast convergence along with much higher degree of accuracy (maximum error <span>(varvec{approx O{(10^{-14}%)}})</span>) compared to existing MOSFET models.</p></div>","PeriodicalId":776,"journal":{"name":"Silicon","volume":"18 1","pages":"427 - 436"},"PeriodicalIF":3.3,"publicationDate":"2025-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147336468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-04DOI: 10.1007/s12633-025-03543-w
Amit Mandal, Sarvesh P. S. Rajput
This study elucidates the early-age reaction mechanisms governing strength development in ceramic waste powder (CWP) concrete activated with 6% potassium silicate (K₂SiO₃) solution. Microstructural evolution at three cement replacement levels (0%, 15%, 30%) was investigated through SEM–EDS analysis coupled with 7-day mechanical testing. Progressive pozzolanic activation was confirmed by decreasing Ca/Si ratios from 4.51 in control specimens to 2.61 at 15% CWP and 0.92 at 30% CWP replacement. Optimal strength development occurred at 15% CWP, achieving 7-day compressive strength of 42.05 MPa compared to 38.86 MPa for control specimens, with flexural strength reaching 5.90 MPa versus 5.70 MPa and split tensile strength of 5.33 MPa versus 4.20 MPa. At this replacement level, Ca/Si ratios approached ideal C-S–H stoichiometry (1.5–2.0) with balanced microstructural heterogeneity. EDS mapping revealed potassium silicate activation enhanced aluminosilicate dissolution, promoting C-A-S–H gel formation through localized Si enrichment and K-ion distribution at reaction interfaces. The 30% replacement level exhibited excessive microstructural heterogeneity, compromising mechanical performance despite continued pozzolanic activity. These findings demonstrate that controlled potassium silicate activation enables effective partial cement replacement with CWP, providing mechanistic insights for developing sustainable alternatives to conventional sodium-based activation systems while maintaining early strength requirements critical for construction applications.
{"title":"Early-Age Strength Development and Microstructural Evolution in Potassium Silicate-Activated Ceramic Waste Concrete","authors":"Amit Mandal, Sarvesh P. S. Rajput","doi":"10.1007/s12633-025-03543-w","DOIUrl":"10.1007/s12633-025-03543-w","url":null,"abstract":"<div><p>This study elucidates the early-age reaction mechanisms governing strength development in ceramic waste powder (CWP) concrete activated with 6% potassium silicate (K₂SiO₃) solution. Microstructural evolution at three cement replacement levels (0%, 15%, 30%) was investigated through SEM–EDS analysis coupled with 7-day mechanical testing. Progressive pozzolanic activation was confirmed by decreasing Ca/Si ratios from 4.51 in control specimens to 2.61 at 15% CWP and 0.92 at 30% CWP replacement. Optimal strength development occurred at 15% CWP, achieving 7-day compressive strength of 42.05 MPa compared to 38.86 MPa for control specimens, with flexural strength reaching 5.90 MPa versus 5.70 MPa and split tensile strength of 5.33 MPa versus 4.20 MPa. At this replacement level, Ca/Si ratios approached ideal C-S–H stoichiometry (1.5–2.0) with balanced microstructural heterogeneity. EDS mapping revealed potassium silicate activation enhanced aluminosilicate dissolution, promoting C-A-S–H gel formation through localized Si enrichment and K-ion distribution at reaction interfaces. The 30% replacement level exhibited excessive microstructural heterogeneity, compromising mechanical performance despite continued pozzolanic activity. These findings demonstrate that controlled potassium silicate activation enables effective partial cement replacement with CWP, providing mechanistic insights for developing sustainable alternatives to conventional sodium-based activation systems while maintaining early strength requirements critical for construction applications.\u0000</p></div>","PeriodicalId":776,"journal":{"name":"Silicon","volume":"18 1","pages":"391 - 410"},"PeriodicalIF":3.3,"publicationDate":"2025-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147336604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Adopting sustainable and cleaner fuels has become imperative in light of the rapid depletion of petroleum reserves and escalating vehicular emissions. Biodiesel produced from agricultural and food-waste oils presents a promising alternative; however, its application in contemporary CRDI diesel engines is hindered by intrinsic drawbacks such as elevated viscosity, diminished volatility, and lower energy density. This study explores the synergistic potential of silicon dioxide (SiO₂) nanoparticles as energy catalytic additives to enhance the performance, combustion behavior, and emission profile of an Agri & Food-Waste Mixed Biodiesel (MME20) blend. Nanofuel formulations MME 20, MME20+SIO40, MME20+SIO80, and MME20+SIO120 were developed using CTAB-assisted ultrasonication for superior stability and uniformity. Experimental assessments were conducted on a single-cylinder CRDI diesel engine (3.7 kW, 1500 rpm, 18:1 compression ratio). The addition of SiO₂ nanoparticles led to a reduction in brake specific fuel consumption (BSFC) from 0.355 to 0.31 kg/kWh and an improvement in brake thermal efficiency (BTE) from 24.2% to 25.8% compared to neat biodiesel. Combustion analysis indicated elevated peak in-cylinder pressure (72 bar) and heat release rate (63 J/°CA), which are attributed to enhanced fuel atomization, micro-explosion phenomena, and catalytic oxidation mechanisms induced by SiO₂. Emission studies revealed marked decreases in hydrocarbon (20%), carbon monoxide (~18%), and smoke opacity (~25%), with a slight increase in nitrogen oxides (10%) likely resulting from higher in-cylinder flame temperatures. The findings underscore the effectiveness of SiO₂ nanoparticles in ameliorating the limitations of biodiesel, enabling improved engine performance, superior combustion, and cleaner exhaust emissions in CRDI diesel engines. Alongside the experimental evaluation, a comprehensive Artificial Neural Network (ANN) model was developed using MATLAB to predict engine performance, combustion, and emission parameters. The ANN was configured as a feedforward backpropagation network with input neurons representing engine operational variables and SiO₂ nanoparticle concentrations. The model was trained and validated using experimental data from varying nanoparticle blend levels (0, 40, 80, and 120 ppm) under different engine loads. The ANN predicted key outputs including brake thermal efficiency, brake-specific fuel consumption, hydrocarbon emissions, carbon monoxide emissions, nitric oxide emissions, and smoke opacity with high accuracy, achieving regression coefficients (R2R2) exceeding 0.98 and low mean squared error values. This predictive modeling complements the experimental results by enabling rapid parameter estimation and optimization without exhaustive engine testing, demonstrating the ANN's potential as an effective tool in biodiesel fuel engine studies.
{"title":"Effect of Metal-Based SiO2 Nanoparticles Blended Concentration on Performance, Combustion and Emission Characteristics of CRDI Diesel Engine Running on Agri & Food Waste Biodiesel and ANN Prediction Using MATLAB","authors":"Deepankumar S, Barun Haldar, Vishal Shukla, Sivapragasam Alagesan","doi":"10.1007/s12633-025-03528-9","DOIUrl":"10.1007/s12633-025-03528-9","url":null,"abstract":"<div><p>Adopting sustainable and cleaner fuels has become imperative in light of the rapid depletion of petroleum reserves and escalating vehicular emissions. Biodiesel produced from agricultural and food-waste oils presents a promising alternative; however, its application in contemporary CRDI diesel engines is hindered by intrinsic drawbacks such as elevated viscosity, diminished volatility, and lower energy density. This study explores the synergistic potential of silicon dioxide (SiO₂) nanoparticles as energy catalytic additives to enhance the performance, combustion behavior, and emission profile of an Agri & Food-Waste Mixed Biodiesel (MME20) blend. Nanofuel formulations MME 20, MME20+SIO40, MME20+SIO80, and MME20+SIO120 were developed using CTAB-assisted ultrasonication for superior stability and uniformity. Experimental assessments were conducted on a single-cylinder CRDI diesel engine (3.7 kW, 1500 rpm, 18:1 compression ratio). The addition of SiO₂ nanoparticles led to a reduction in brake specific fuel consumption (BSFC) from 0.355 to 0.31 kg/kWh and an improvement in brake thermal efficiency (BTE) from 24.2% to 25.8% compared to neat biodiesel. Combustion analysis indicated elevated peak in-cylinder pressure (72 bar) and heat release rate (63 J/°CA), which are attributed to enhanced fuel atomization, micro-explosion phenomena, and catalytic oxidation mechanisms induced by SiO₂. Emission studies revealed marked decreases in hydrocarbon (20%), carbon monoxide (~18%), and smoke opacity (~25%), with a slight increase in nitrogen oxides (10%) likely resulting from higher in-cylinder flame temperatures. The findings underscore the effectiveness of SiO₂ nanoparticles in ameliorating the limitations of biodiesel, enabling improved engine performance, superior combustion, and cleaner exhaust emissions in CRDI diesel engines. Alongside the experimental evaluation, a comprehensive Artificial Neural Network (ANN) model was developed using MATLAB to predict engine performance, combustion, and emission parameters. The ANN was configured as a feedforward backpropagation network with input neurons representing engine operational variables and SiO₂ nanoparticle concentrations. The model was trained and validated using experimental data from varying nanoparticle blend levels (0, 40, 80, and 120 ppm) under different engine loads. The ANN predicted key outputs including brake thermal efficiency, brake-specific fuel consumption, hydrocarbon emissions, carbon monoxide emissions, nitric oxide emissions, and smoke opacity with high accuracy, achieving regression coefficients (R2R2) exceeding 0.98 and low mean squared error values. This predictive modeling complements the experimental results by enabling rapid parameter estimation and optimization without exhaustive engine testing, demonstrating the ANN's potential as an effective tool in biodiesel fuel engine studies.</p></div>","PeriodicalId":776,"journal":{"name":"Silicon","volume":"18 1","pages":"437 - 455"},"PeriodicalIF":3.3,"publicationDate":"2025-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147336469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-04DOI: 10.1007/s12633-025-03563-6
E. Balakrishnan, G. Yuvaraj, Trinath Keerthipalli, Raghuram Pradhan, S. K. Karthikeyan, Srinivas Tadepalli
Fiber Metal Laminates (FMLs) have emerged as advanced hybrid materials that combine the lightweight advantages of fiber composites with the structural stability of metal layers, making them attractive for automotive, aerospace, defense, and construction applications. However, achieving strong interfacial adhesion between natural fibers, fillers, and metal layers remains a significant challenge. This study focuses on enhancing the performance of natural fiber–based FMLs reinforced with prestressed areca nut fibers, SS316 foil, and nanosilica fillers through silane surface treatment. The 3-aminopropyltriethoxysilane (3-APTES) coupling agent was employed to promote Si–O–Si bonding and improve compatibility within the epoxy matrix. Laminates were fabricated using vacuum bagging and post-cured at 130 °C to achieve improved stability. Among all compositions, the laminate containing 40 vol.% silane-treated prestressed areca fiber, SS316 foil, and 2.0 vol.% nanosilica exhibited superior performance, achieving tensile and flexural strengths of 162 MPa and 182 MPa, along with enhanced shear properties and reduced drilling-induced damage. SEM analysis confirmed uniform nanosilica dispersion, reduced voids, and stronger fibre–matrix interaction. Overall, the combined use of surface treatment, nanosilica reinforcement, and natural fibers effectively improves the mechanical, shear, and machining performance of FMLs.
{"title":"Effect of Interfacial Adhesion Enhancement on SS316 Foil/Prestressed Areca Fiber–Nanosilica Fiber Metal Laminate Composites","authors":"E. Balakrishnan, G. Yuvaraj, Trinath Keerthipalli, Raghuram Pradhan, S. K. Karthikeyan, Srinivas Tadepalli","doi":"10.1007/s12633-025-03563-6","DOIUrl":"10.1007/s12633-025-03563-6","url":null,"abstract":"<div><p>Fiber Metal Laminates (FMLs) have emerged as advanced hybrid materials that combine the lightweight advantages of fiber composites with the structural stability of metal layers, making them attractive for automotive, aerospace, defense, and construction applications. However, achieving strong interfacial adhesion between natural fibers, fillers, and metal layers remains a significant challenge. This study focuses on enhancing the performance of natural fiber–based FMLs reinforced with prestressed areca nut fibers, SS316 foil, and nanosilica fillers through silane surface treatment. The 3-aminopropyltriethoxysilane (3-APTES) coupling agent was employed to promote Si–O–Si bonding and improve compatibility within the epoxy matrix. Laminates were fabricated using vacuum bagging and post-cured at 130 °C to achieve improved stability. Among all compositions, the laminate containing 40 vol.% silane-treated prestressed areca fiber, SS316 foil, and 2.0 vol.% nanosilica exhibited superior performance, achieving tensile and flexural strengths of 162 MPa and 182 MPa, along with enhanced shear properties and reduced drilling-induced damage. SEM analysis confirmed uniform nanosilica dispersion, reduced voids, and stronger fibre–matrix interaction. Overall, the combined use of surface treatment, nanosilica reinforcement, and natural fibers effectively improves the mechanical, shear, and machining performance of FMLs.</p></div>","PeriodicalId":776,"journal":{"name":"Silicon","volume":"18 1","pages":"457 - 469"},"PeriodicalIF":3.3,"publicationDate":"2025-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147336605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Deficit irrigation presents significant potential for water savings, making it increasingly popular worldwide as a method to reduce freshwater consumption over time. The low water productivity of strawberries is often attributed to excessive water use and the limited ability of cultivars to optimize fruit set and yield in hydroponic systems. This study aimed to evaluate three management strategies cultivar selection, irrigation frequency, and potassium silicate application frequency on the growth, water conservation, and production efficiency of hydroponically grown strawberries.
Methods
The experiment followed a split-plot design, with 'Albion' and 'Chandler' cultivars as the main plot treatments, and a factorial arrangement of irrigation frequency (once/day vs. twice/day) and potassium silicate (AgSil16H) application frequency (6, 9, 12, 15 weeks) randomly assigned to the subplots.
Results
Results indicated that foliar application of potassium silicate enhanced plant vigor and contributed to water conservation (34%) in hydroponically grown strawberries compared to the control, where no potassium silicate was applied. Notably, a 12-week potassium silicate application boosted photosynthetic rates and improved water conservation, thereby enhancing plant productivity and water use efficiency. For 'Chandler' cultivar, potassium silicate treatment led to a 23% increase in net assimilation rate, a 29% rise in stomatal conductance, and a 33% reduction in transpiration loss. Additionally, electrolyte leakage decreased by 25%, while maintaining steady intercellular CO2 concentrations. Strawberry plants treated with potassium silicate and irrigated once daily reduced water usage by 34% compared to untreated plants. Furthermore, flowering occurred 4 days earlier in treated plants, while fruit set increased by 16% and flower drop decreased by 13% compared to controls. Among all treatments, the 'Chandler' cultivar, irrigated once per day and treated with potassium silicate for 12 weeks, showed superior growth and significant water savings over the control group. Potassium silicate treatment for 12 weeks also resulted in a 28% higher marketable fruit yield compared to the control.
Conclusion
Therefore, potassium silicate (AgSil16H) demonstrated its potential as a promising fertilizer under deficit irrigation conditions, effectively conserving water and improving productivity in hydroponically grown strawberries.