Study Of 3D Fabrication And Proximity Effect Technique In Electron Beam Lithography

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.