【作者】 郝慧娟；

【导师】 张玉林；

【作者基本信息】 山东大学 ， 控制理论与控制工程， 2007， 博士

【摘要】 微机电系统器件的制造要求微三维加工工艺。当前制作三维微结构的技术主要有体硅微加工技术、LIGA(Lithographie，Galvanoformung and Abformung)技术、IH(Integrated Harden Polymer Stereo Lithography)工艺等。体硅微加工技术和LIGA技术能够制作高精度、高深宽比的陡直微细结构，但是难于加工各种微曲面和结构较为复杂的器件；IH三维光刻技术从理论上能加工出任意曲面和任意高深宽比的复杂结构，但因其工艺中X、Y向的扫描是靠X／Y工作台的机械移动来完成的，加工精度较低，分辨率目前仅为亚微米级。为了满足微机电系统的快速发展，需求精度更高的加工手段。电子束光刻技术是目前公认的最好的高分辨率图形制作技术，目前主要用于0.1～0.5μm精密二维掩模制造，而难于生产高深宽比的三维结构。本学位论文围绕着电子束光刻技术直接在基片上产生高精度的垂直、曲面、微尖等三维结构等问题，对电子束光刻、邻近效应校正、显影过程模拟等问题进行了较全面和较深入的研究，提出了多种新的计算方法；根据抗蚀剂吸收能量密度的计算结果，对三维结构进行了邻近效应校正；结合显影模型，模拟了三维结构的显影轮廓。在准确模拟曝光、显影过程的基础上，研究了不同曝光、显影条件对抗蚀剂吸收能量分布、显影线宽、边墙陡度的影响。论文的主要工作集中于电子束三维光刻方法、曝光的计算机模拟、工艺优化，概括如下：1、首次提出了电子束重复增量扫描方式，为通用电子束曝光系统提供了一种新的三维加工方法。曝光实验得到了轮廓清晰的正梯锥1、圆锥、梯锥1的三维结构，验证了该扫描方式的可行性和正确性。重复增量扫描方式无需改变曝光剂量，通过重复、重叠的多次曝光，使光刻图形不同的位置得到不同的曝光总剂量，实现对图形的三维加工；该扫描方式也无需进行复杂的图形分割，避免了图形分割带来的数据量过大的问题，降低了数据传输时间，从而可以降低曝光总时间，提高曝光效率；该扫描方式也不用在光刻过程中改变束斑参数，克服了系统内部扫描频率的限制，为通用电子束光刻系统进行曲面图形的加工提供了条件。2、根据光刻胶的反差的经验公式，提出了曝光剂量与刻蚀深度关系的计算方法，减少了实验次数和由于测量带来的误差，而且为电子束光刻的三维加工提供了重要参数。3、提出了抗蚀剂灵敏度、反差的计算方法，为电子束三维加工和曝光剂量与刻蚀深度关系的计算提供了重要参数。对不同入射电子束能量、抗蚀剂厚度的反差的计算显示：随着入射电子束能量的增加，反差不断减小；随着抗蚀剂厚度的增加，反差不断增大。4、提出了邻近函数的改进形式，并用于计算抗蚀剂吸收能量密度分布，克服了解析法和Monte Carlo模拟法无法克服的局限性，使吸收能量密度的计算真正用于软件中。对不同曝光条件下的抗蚀剂吸收能量密度分布的计算获得了其分布规律，而且得出了优化电子束光刻的工艺条件：(1)随着入射电子束能量的增加，电子的横向分布范围增大，但抗蚀剂的吸收能量密度分布曲线越来越陡峭，即：抗蚀剂单位体积内沉积的能量也越大。因而，高入射电子束能量有利于邻近效应的降低。(2)抗蚀剂厚度对吸收能量密度分布的影响不是很明显，主要影响前散射电子的能量密度分布。抗蚀剂越薄，电子的沉积能量密度分布曲线越陡峭。因而，薄抗蚀剂层有利于邻近效应的降低。(3)低原子序数的衬底产生的背散射电子数目较少，而且电子在衬底中的能量损失率较高，从而由衬底返回胶中的背散射电子在抗蚀剂中的能量沉积密度较小，有利于邻近效应的降低。(4)束斑直径越小，抗蚀剂吸收能量密度分布曲线越陡峭，越有利于邻近效应的降低，提高分辨率。因而，适量的高束能、薄胶层、低原子序数衬底、小束斑有利于邻近效应的降低、分辨率的提高。5、采用了最小二乘非线性曲线拟合的方法确定邻近函数参数，克服了直线拟合带来的α误差较大的问题，比单高斯拟合得到的结果更精确。对不同曝光条件下的参数(α、β、η)的计算获得了其分布规律，不仅能为电子束曝光条件的优化、邻近效应的降低提供理论指导，而且能为邻近效应校正快速地提供精确的参数。(1)随着入射电子束能量的增加，α不断减小，β不断增大，而η几乎不变，表明提高入射电子束能量有利于邻近效应的降低。(2)随着抗蚀剂厚度的增加，α不断增大，β、η变化不明显，说明薄抗蚀剂有利于分辨率的提高和邻近效应的降低。(3)衬底材料对α的影响较小，随着衬底材料原子序数的增大，β减小，η增大，说明低原子序数的衬底材料，有利于邻近效应的降低。6、研究了邻近效应产生的机理，引入累积分布函数计算各关键点的有效曝光剂量。通过预先建立计算过程中需要的各种规则表，计算过程中需要的参数通过查表直接获得，快速、准确地实现曝光图形能量分布的计算。7、提出了水平和深度两个方向分别对三维结构邻近效应进行校正的方法。水平方向采用最大矩形法校正，同时考虑了抗蚀剂不同深度处吸收能量密度分布不同。深度方向的校正从吸收能量密度与曝光剂量的关系上考虑。校正后的曝光过程无需改变曝光剂量，为剂量无法改变的系统提供了三维结构的校正方法。通过预先建立校正过程中需要的各种规则表，校正过程中需要的参数直接查表获得，快速、准确地实现了校正，提高了曝光效率。校正结果显示，邻近效应已大大降低。8、采用了基于遗传算法的最小二乘法确定显影速率参数，与传统的Gauss-Newton迭代法比较显示，基于遗传算法拟合的残差平方和较小，拟合效果更好，而且与参数初始值的选取无关，具有较强的鲁棒性。9、对光线追迹模型中的射线前进算法进行了改进，采用了递归的射线前进算法计算射线轨迹，降低了显影模拟中射线间的不连续性，光线追迹算法也更加精确。研究了不同曝光条件、显影时间对显影线宽W_b、边墙陡度θ的影响，得出了参数的分布规律，不仅为优化电子束曝光和显影工艺提供了参数，也为改进图形设计提供了参数依据。(1)在给定的曝光剂量下，随着加速电压的增大，W_b不断减小，θ值先减小，后增大。(2)在给定的加速电压下，随着曝光剂量增大，W_b、θ不断增大。(3)在给定的加速电压、曝光剂量下，随着抗蚀剂厚度的增加，W_b值不断减小，θ不断增加。(4)随着显影时间的增加，W_b逐渐增大，θ在开始时处于逐渐增加的趋势，当达到一定的最大值时又表现出下降的趋势。更多还原

【Abstract】 The fabrication technics of three dimension microstructures is demanded to manufacture devices in micro electro mechanical system(MEMS). Now the methods of three-dimensional microfabrication are mainly bulk-silicon micromachining, LIGA (Lithographie, Galvanoformung and Abformung) and IH(Integrated Harden Polymer Stereo Lithography), etc. Bulk-silicon and LIGA can produce steep microstructure with high-precision and high-aspect-ratio, but it is difficult for them to create micro devices with curved surface and complex structures; theoretically, IH can produce devices with arbitrary curved-surface and high-aspect-ratio, but its scan in X-Y is finished by the moving of X-Y stations mechanically, the precision is low and only submicron resolution can be achieved. In order to satisfy the rapid progress of the MEMS, higher precision micro-fabrication methods should be developed.Electron beam lithography(EBL) is considered as the best technique to offer the higher patterning resolution, and it is generally used to make precise masks with resolution 0.1～0.5μm, while it is difficult to fabricate three dimensional microstructures. In order to produce three-dimensional structures with high precision directly in base plate, such as vertical, curvilinear and micro tip array, EBL, proximity effect correction, and development simulations are studied comprehensively in this paper, and many new calculation methods are proposed. Also the proximity effect of three dimension structures is corrected according to the calculation results of resist absorbed energy density distribution. Even the development profiles are simulated in terms of development models. Moreover, the impact of different exposure and development on resist absorbed energy density distribution, line width and side degree is investigated. The main work of this dissertation includes three dimensional microfabrication, computer simulation, and the optimization of the exposure conditions. The main achievements can be summed up as follows:1. The increment overlapped scanning method in EBL is proposed firstly, which provides a new method of three dimension microfabrication for universal electron beam system. The distinct three dimensional profiles of positive trapozid 1, the conic and the conic trapezoid prove the feasibility and validity of the new method. Different total doses can be obtained through the repeated and overlapped exposure without changing every dose in the method. Also, the scanning method does not need the complex division of patterns, so the data is decreased, and the data transmission time is shorted, the total exposure time is reduced, the exposure efficiency is improved. The beam parameters need not be changed, which gets over the limit of inner frequency and provides favorable condition for curvilinear microstructure.2. The calculation method of relation between the dose and depth is proposed according to the experiential formula of resist contrast. The calculation not only reduces experimental time and measurement error, but also provides significant parameters for 3D microfabrication.3. The calculation methods of resist sensitivity and contrast are respectively proposed, which provides important parameters for EBL and calculation of relation between the dose and depth. The contrast calculations for different incident energy and resist thickness show: the contrast continuously reduces with the increasing of incident energy; and it increases with the reducing of resist thickness.4. The improved form of proximity function is proposed and applied to the calculation of the resist absorbed energy density distribution. The calculation gets over the limit of analytical method and Monte Carlo simulation, and can be really used to software. The distribution rule of absorbed energy density distribution and the optimization processing of EBL are obtained through the calculations on different exposure condition. It can be summarized as: (1)With the increase of incident electron beam energy, the lateral distribution of electron becomes larger, but the distribution curve of energy deposition becomes sharper, deposited energy of resist in volume is higher. So higher electron beam voltage can reduce the proximity effect.(2)The effect of resist thickness on absorbed energy density distribution is not serious. It mainly affects forward electron scattering. The thinner the resist film is, the sharper the curve of energy deposition distribution is. Therefore, thinner resist film can reduce the proximity effect.(3)The lower atomic number of substrate material produces fewer backward scattered electrons, and the loss ratio of electron in substrate is higher, the energy deposition of backward scattered electron in resist is smaller. So lower atomic number of substrate material results in less proximity effect.(4)The smaller the beam spot diameter, the sharper the curve of energy deposition distribution is. So smaller beam spot diameter is good to reduce proximity effect and improve the resolution.In conclusion, high beam energy, small beam spot diameter, thin resists and low atomic number substrate can reduce proximity effect and improve exposure resolution.5. The parameters of proximity function are obtained through nonlinear least-squares curve fitting. The linear fitting results in the bigger error ofα, the nonlinear fitting gets over the problem, and it is exacter than the single gauss fitting. The distribution rule ofα,βandηis obtained through the calculation for different exposure conditions, which not only provides academic instruction for optimization of EBL, but also provides precise parameters for proximity effect correction.(1) The increment of electron beam energy leads to the decrease ofαand increase ofβ, whileηis almost constant. It shows that higher electron beamvoltage can reduce the proximity effect.(2)The increasing of resist thickness results in the increment ofα, whileβ andηare almost invariable. So thinner resist film can reduce the proximity effect and improve the resolution.(3)The increase of substrate’s atom number causes decrease ofβand increment ofη, whileαis unchangeable. Therefore, smaller beam spot diameter is good to reduce proximity effect and improve the resolution.6. The mechanism of the proximity effect has been studied. The effective energy received by critical points is calculated through the cumulation distribution function (CDF). The different regular tables are founded in advance, thus the parameters needed in calculation can be looked up in the tables. The calculation of absorbed energy density distribution of points in pattern can be achieved quickly and exactly.7. The new method that proximity effect of 3D structrues are corrected in the horizontal and the vertical respectively is proposed. The maximal rectangle correction is introduced in the horizontal correction, also considering that the resist absorbed energy density distribution is different at different depth. The relation between resist absorbed energy density distribution and dose is taken into account in vertical correction. The dose keeps unchangeable after correction, which provides new correction method for EBL. The rule tables needed in correction are founded before. The parameters are looked up in the tables directly in correcting, so the correction can be finished quickly and exactly, and the exposure efficiency is improved. The AFM figures show that the proximity effect is greatly reduced.8. The development rate equation parameters are determined through the genetic algorithm-based least square. The comparison with the traditional Gauss-Newton iterative method indicates that the remained square sum of genetic algorithm-based method is smaller, and the effect is better. And the initialized parameters is irrelative to the genetic algorithm-based method, so it has the stronger robust.9. The advancing approach is improved in the ray tracing algorithm model. The recursive advancing method is applied to the calculate ray trajectories, which lessens the discontinuity of ray in simulation. So, the ray tracing algorithm is more accurate. The three dimensional profile is obtained through simulation. The rules of development linewidth W_b and the sidewall degree 9 are achieved through simulation for different exposure condition and development time,which not only offers parameters for optimization of exposure and development, but also provides referrence for improvement of pattern design.(1)At given dose, W_b decreases with the increment of accurate voltage, whileθdecreases firstly, then increases.(2)With the increasing of exposure dose, W_b andθincrease at given accurate voltage.(3)The increase of resist thickness results in the increment ofθand decreasing of W_b at given accurate voltage and dose.(4)With the increment of development time, Wb increases continually, andθincreases gradually at the beginning, but has the decrease trend when arriving at the maximal value.更多还原