精微線材彎壓成形產品檢測之模擬分析與預測公式建立

Abstract

科技產業的蓬勃發展使晶片備受重視，各家廠商積極投入研究更創新、更微型的IC產品；為確保晶片品質，半導體設備的檢測產業成為重要一環，通過晶圓測試與檢驗，確保實用性與可靠性，使產品在競爭中脫穎而出，本論文利用有限元素分析方法建立分析模型，還原實際檢測端行為並予以預測分析。 本論文研究不同溫度下精微線材的性質以提供產品電性參數，並將實驗結果用於模擬，重現耐電流曲線；此外，本論文亦對待測物凹痕進行分析，待側物依據其外觀分為鋁墊和錫球兩部分，最終透過模擬和回歸分析建立耐電流與凹痕樣態的預測公式。 藉由建立耐電流與待測物凹痕樣態預測公式可以協助合作企業對產品應用之接觸品質進行掌控，提供更加完善的規格需求給客戶，並能針對模擬做雙重確認，對企業與其客戶皆能達成益處。 本論文前半部分主要探討不同溫度下線材的耐電流性能，參考學長的拉伸實驗平台，將其改造為高溫實驗平台，為突破不同實驗機台夾具限制，設計了以鋁箔包覆線材的鋁箔試片，並驗證其可行性，最終獲取材料在不同溫度下的機械性能。 接著建立了耐電流模擬模型，模型分為兩階段：電熱模擬和熱固模擬；在電熱模擬中，利用材料電性參數和高溫拉伸實驗結果，還原了產品通電後的溫度分布；而熱固模擬則考慮了溫度對材料機械性能的影響，進而探討對於產品與待測物間接觸力的影響。 確認模型設計與實際結果一致後，本論文根據電阻公式等相關電性定律推導出預測公式，藉由單因子分析確認產品特徵值與溫度在公式中的項數冪次，並分析其敏感度，最終以實際耐電流測試結果驗證預測公式的準確性，結果顯示公式誤差低於5%。 論文後半部分針對待測物凹痕進行探討，首先針對鋁墊探討，透過收斂性分析確認模型之元素種類與尺寸，並驗證模擬結果在凹痕深度和凹痕直徑方面均能在實際量測範圍內；為節省模擬時間，簡化了分析模型，並確認簡化結果與原模型差距低於1%，最終將預測公式與實際結果比對，顯示鋁墊凹痕預測公式可信度高。 另一種待側物類型為錫球，透過比較選擇了合適的元素類型與材料擬合修正式並確認收斂尺寸；模型簡化方面，探討了銅柱對錫球凹痕樣態的影響，發現有無銅柱影響不大，因此後續模擬中以無銅柱錫球作為分析主題，並將模型壓縮量以接觸力值取代，減少模擬時間；預測公式建立方面，確認接觸力與凹痕壓縮量成正比，通過該關聯性和凹痕面積比尺寸效應，將接觸力與凹痕壓縮量無因次化，最終預測公式與實際結果比對，誤差低於3%，顯示錫球凹痕預測公式的完整性。 整體而言，本論文通過實驗、模擬和回歸分析，建立了精微線材耐電流和待測物凹痕的預測公式，驗證了公式的高準確性和實用性，為未來產品設計和質量控制提供了重要參考。

The rapid growth of the technology industry has significantly emphasized the importance of chips. Companies are investing in research to develop more innovative and miniaturized IC products. Ensuring chip quality has made semiconductor equipment testing a crucial component. Through wafer testing and inspection, functionality and reliability are assured, helping products stand out in a competitive market. This thesis employs uses finite element analysis to establish a model that replicates actual testing behaviors and provides predictive analysis. This thesis examines the properties of fine wires at different temperatures to provide electrical parameters for the product. Experimental results are used for simulations to reproduce the current carrying capacity curve. Additionally, this thesis analyzes indentations on test objects, categorized into aluminum pads and tin solder balls based on appearance, ultimately deriving predictive formulas for current carrying capacity and indentation patterns through simulation and regression analysis. By establishing prediction formulas for current carrying capability and probe mark patterns, we can help partner companies control product contact quality, provide more comprehensive specification requirements to customers, and conduct dual verification of simulations. This approach will be beneficial both internally and externally. The first part of this thesis focuses on the current carrying performance of wires at various temperatures. Using a modified tensile test platform from previous research, a temperature-variable platform was developed. An aluminum foil specimen was designed to overcome the limitations of different testing machine fixtures, and its feasibility was verified, resulting in the acquisition of the material’s mechanical properties at different temperatures. A current carrying simulation model was then established, divided into two stages: electrothermal coupling simulation and thermo-mechanical coupling simulation. In the electrothermal coupling simulation, the electrical parameters of the material and high-temperature tensile test results were used to recreate the temperature distribution after electrification. The thermo-mechanical coupling simulation considered the effect of temperature on the material’s mechanical properties, influencing the contact force between the product and the test object. After confirming the consistency between the model design and actual results, this thesis derived predictive formulas based on electrical resistance and other relevant electrical laws. Single-factor analysis was used to determine the exponent of terms in the formula related to product characteristic values and temperature, analyzing their sensitivity. Finally, the predictive formula was validated against actual current carrying test results, showing an error of less than 5%. The latter part of this thesis focuses on the indentations of the test objects. For aluminum pads, convergence analysis was used to determine the model’s element size and type, verifying that the simulation results for indentation depth and diameter were within the actual measurement range. To save simulation time, the analysis model was simplified, confirming that the difference between the simplified and original models was less than 1%. The predictive formula for aluminum pad indentations was compared with actual results, showing high reliability. For tin solder balls, appropriate element types and material fitting formulas were selected through comparison, confirming the convergence size. The model was simplified by studying the impact of copper columns on tin solder ball indentations, finding minimal influence, thus focusing subsequent simulations on tin solder balls without copper columns. The model’s compression amount was replaced with contact force values to reduce simulation time. The predictive formula established showed that contact force and indentation compression amount are proportional. By non-dimensional zing the contact force and indentation compression amount through their correlation and the size effect of the indentation area, the predictive formula was compared with actual results, with an error of less than 3 %, demonstrating the completeness of the tin solder ball indentation predictive formula. Overall, this thesis establishes predictive formulas for the current carrying capacity of fine wire products and indentations of test objects through experiments, simulations, and regression analysis. It verifies the high accuracy and practicality of these formulas, providing essential references for future product design and quality control.