基于自適應(yīng)非線性粒子群算法的光刻光源優(yōu)化方法

王 建，劉俊伯，胡 松*

基于自適應(yīng)非線性粒子群算法的光刻光源優(yōu)化方法

王 建1,2，劉俊伯1，胡 松1,2*

1中國(guó)科學(xué)院光電技術(shù)研究所，四川 成都 610209；2中國(guó)科學(xué)院大學(xué)，北京 100049

光刻光源優(yōu)化作為必不可少的分辨率增強(qiáng)技術(shù)之一，能夠提高先進(jìn)光刻成像質(zhì)量。在先進(jìn)光刻領(lǐng)域，光源優(yōu)化的收斂效率和優(yōu)化能力是至關(guān)重要的。粒子群優(yōu)化算法作為一種全局優(yōu)化算法，自適應(yīng)控制策略可以提高粒子的全局搜索能力，非線性控制策略可以擴(kuò)大粒子搜索范圍。本文提出一種基于自適應(yīng)非線性控制策略的粒子群優(yōu)化算法，將光刻光源優(yōu)化問(wèn)題轉(zhuǎn)換成多變量評(píng)價(jià)函數(shù)求解。對(duì)簡(jiǎn)單周期光柵圖形和不規(guī)則圖形進(jìn)行成像優(yōu)化仿真，通過(guò)粒子群優(yōu)化算法的全局迭代特性優(yōu)化光源形貌。利用圖形誤差(PEs)作為多變量評(píng)價(jià)函數(shù)，對(duì)迭代300次的仿真結(jié)果進(jìn)行評(píng)價(jià)，兩種仿真圖形的PEs分別降低52.2%和35%。與傳統(tǒng)粒子群優(yōu)化算法和遺傳算法相比，該方法不僅能提高成像質(zhì)量，而且具有更高的收斂效率。

光源優(yōu)化；光刻；分辨率增強(qiáng)技術(shù)；粒子群優(yōu)化算法

1 引 言

光刻技術(shù)作為超大規(guī)模集成電路制造必不可少的關(guān)鍵技術(shù)。目前，光刻分辨率成為約束集成電路圖形臨界尺寸的重要因素。根據(jù)瑞利準(zhǔn)則，波長(zhǎng)()和數(shù)值孔徑(numerical aperture，NA)是決定光刻技術(shù)分辨率(resolution)的兩個(gè)關(guān)鍵因素。縮短曝光波長(zhǎng)、擴(kuò)大數(shù)值孔徑成為提高光刻分辨率的有效方法。但由于設(shè)備溫度、裝配公差等因素的影響，會(huì)導(dǎo)致光刻成像質(zhì)量下降。此外，當(dāng)微納圖形特征尺寸小于曝光波長(zhǎng)時(shí)，受到衍射效應(yīng)的影響，產(chǎn)生光學(xué)鄰近效應(yīng)(optical proximity effect，OPE)，造成晶圓表面圖形發(fā)生畸變。因此，提高光刻成像質(zhì)量，分辨率增強(qiáng)技術(shù)(resolution enhance techniques，RETs)是解決這些負(fù)面效應(yīng)必不可少的手段[1-3]。

傳統(tǒng)RETs主要包含離軸照明技術(shù)(off-axis illumination technique，OAI)、光學(xué)鄰近校正技術(shù)(optical proximity correction technique，OPC)和相移掩模技術(shù)(phase-shift mask technique，PSM)[4]。隨著光刻工藝不斷發(fā)展，傳統(tǒng)RETs已無(wú)法滿足先進(jìn)節(jié)點(diǎn)復(fù)雜圖形的高成像質(zhì)量需求，比如，在離軸照明中的各種照明方式，環(huán)形、偶極子、四極等。然而，逆光刻技術(shù)(inverselithography techniques，ILTs)作為RETs的一種先進(jìn)方法，被廣泛應(yīng)用到先進(jìn)光刻成像質(zhì)量?jī)?yōu)化領(lǐng)域。其中，在ILTs方法中，基于像素表征的光源優(yōu)化(source optimization，SO)[5-6]具有靈活度高、易于調(diào)制的優(yōu)勢(shì)，被應(yīng)用于精確調(diào)制光源強(qiáng)度分布。

本文提出一種基于自適應(yīng)非線性控制策略(adaptive nonlinear control strategy，ANCS)的PSO算法優(yōu)化光刻光源形貌。自適應(yīng)策略能夠降低粒子陷入局部最優(yōu)的概率，非線性控制策略能夠擴(kuò)大粒子的搜索范圍?；谙袼氐腟O模型中，采用光刻膠圖形布局與目標(biāo)圖形之間的圖形誤差作為評(píng)價(jià)函數(shù)，對(duì)光源優(yōu)化結(jié)構(gòu)進(jìn)行評(píng)價(jià)。對(duì)簡(jiǎn)單陣列圖形與較復(fù)雜不規(guī)則圖形進(jìn)行仿真。與傳統(tǒng)粒子群優(yōu)化算法及遺傳算法對(duì)比，ANCS-PSO具有更優(yōu)越的收斂效率。

2 部分相干成像模型

根據(jù)光刻成像理論，光刻成像模型是典型的部分相干成像模型，如圖1所示。光刻照明光源經(jīng)匯聚鏡組形成經(jīng)典科勒照明，均勻入射掩模表面，受掩模透射率影響，產(chǎn)生帶有掩模圖形頻譜信息的衍射光，并入射投影物鏡系統(tǒng)。在光刻成像模型中，由于光瞳的低通濾波效應(yīng)，只有低頻衍射光通過(guò)投影物鏡，在理想焦面形成空間像。光線入射晶面表面與光刻膠發(fā)生光化學(xué)反應(yīng)，經(jīng)過(guò)烘烤顯影等處理后，特征圖形顯示在晶圓上。根據(jù)瑞利準(zhǔn)則，光刻成像系統(tǒng)的極限分辨率為

圖1 光刻成像模型

其中：1表示工藝因子。在光刻成像系統(tǒng)中，照明模式與系統(tǒng)光瞳為關(guān)于光軸圓對(duì)稱結(jié)構(gòu)，故光源相干因子()可定義為照明模式圓半徑大小(s)與系統(tǒng)光瞳半徑大小(p)的比值，即：

在部分相干成像系統(tǒng)中，空間像強(qiáng)度分布可由阿貝成像理論與霍普金斯成像理論計(jì)算獲得[15]。而根據(jù)阿貝成像理論，部分相干成像系統(tǒng)近似等于一系列完全相干成像系統(tǒng)在不同點(diǎn)光源處衍射相干光的疊加。對(duì)于光刻光源優(yōu)化，采用阿貝成像方法，能夠降低計(jì)算復(fù)雜度。在完全相干成像系統(tǒng)中，照明光源為理想點(diǎn)光源，則完全相干成像模型可表示為

3 光源優(yōu)化模型

在基于像素的SO模型中，采用一定數(shù)量像素點(diǎn)的方式離散光源圖形。將搜尋評(píng)價(jià)函數(shù)全局最優(yōu)解轉(zhuǎn)換成求解多變量函數(shù)問(wèn)題。對(duì)于ANCS-PSO模型，優(yōu)化變量的數(shù)量決定計(jì)算的復(fù)雜度。在光刻成像模型中，光刻光源為關(guān)于光軸圓對(duì)稱結(jié)構(gòu)，可將光源劃分為四個(gè)相等的部分，如圖2所示，為典型環(huán)形照明模式。因此，按照笛卡爾坐標(biāo)系將光源圖形劃分為四個(gè)象限，僅利用第一象限的有效光源像素點(diǎn)作為優(yōu)化變量，可沿著水平垂直方向反轉(zhuǎn)第一象限像素點(diǎn)分布得到最終光源形貌[17]。out表示環(huán)形光源最大半徑，in表示環(huán)形光源最小半徑。

環(huán)形照明光源內(nèi)外半徑大小分別為

在笛卡爾坐標(biāo)系中，光源圖形中心點(diǎn)位置為

圖2 光源表示方式

4 仿真結(jié)果

圖4顯示為逆光刻光源優(yōu)化仿真結(jié)果。當(dāng)目標(biāo)圖形布局類似單周期光柵時(shí)(圖3(b))，光源模式近似水平方向偶極照明，如圖4(a)，4(e)，4(i)所示。而目標(biāo)圖形布局接近水平方向光柵結(jié)構(gòu)時(shí)(圖3(c))，照明光源模式近似于垂直方向偶極照明，如圖4(c)，4(g)，4(k)所示。根據(jù)優(yōu)化后的光源形貌，對(duì)兩種目標(biāo)圖形進(jìn)行部分相干成像仿真，并通過(guò)sigmoid函數(shù)(式(5))得到光刻膠圖形，分別為圖4(b)，4(f)，4(j)和4(d)，4(h)，4(l)。與初始PEs相比，三種算法兩種成像圖形誤差值降低，分別為：Pattern 01：52.2%，41.7%，37.4%；Pattern 02：35%，25.3%，25.3%。

圖5顯示三種優(yōu)化算法模型收斂曲線效率。經(jīng)過(guò)多次仿真實(shí)驗(yàn)，當(dāng)?shù)螖?shù)為300次時(shí)，收斂曲線已保持穩(wěn)定狀態(tài)。兩種目標(biāo)圖形的仿真PEs初始值均由相同光源強(qiáng)度分布計(jì)算得到，其中有效光源像素點(diǎn)值為隨機(jī)數(shù)。在兩種PSO模型中，為了保證仿真結(jié)果有效性，其學(xué)習(xí)因子及慣性權(quán)重系數(shù)最大最小值相同。此外，在PSO模型中，優(yōu)化模型計(jì)算復(fù)雜度與粒子種群個(gè)數(shù)相關(guān)，為保證模型的收斂效率，設(shè)置粒子種群p=50。迭代結(jié)果顯示，ANCS-PSO相比其他兩種算法具有更快迭代速度和效率。

圖3 (a) 環(huán)形光源形貌；(b) 簡(jiǎn)單陣列圖形；(c) 不規(guī)則光柵

圖4 光源優(yōu)化仿真結(jié)果

圖5 仿真收斂曲線

5 總 結(jié)

本文提出了一種改進(jìn)的PSO算法應(yīng)用于逆光刻技術(shù)的光源優(yōu)化中，即自適應(yīng)非線性粒子群優(yōu)化算法(ANCS-PSO)。通過(guò)仿真兩種目標(biāo)圖形布局，驗(yàn)證了該算法的有效性。此外，為了驗(yàn)證ANCS-PSO的優(yōu)越性，與傳統(tǒng)粒子群優(yōu)化算法和遺傳算法對(duì)比。仿真結(jié)果表明，兩種仿真圖形誤差PEs值降低，分別Pattern 01：52.2%，41.7%，37.4%；Pattern 02：35%，25.3%，25.3%，有效地提高光刻成像質(zhì)量。三種算法仿真結(jié)果進(jìn)行了對(duì)比，本文所提方法不僅具有更高的收斂效率，而且在提高光刻成像質(zhì)量中更具有優(yōu)勢(shì)。隨著仿真圖形復(fù)雜度的提高，圖形誤差降低百分比有所降低，在后續(xù)的工作中，將采用多目標(biāo)函數(shù)優(yōu)化的方式來(lái)提高優(yōu)化表現(xiàn)結(jié)果。

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Source optimization based on adaptive nonlinear particle swarm method in lithography

Wang Jian1,2, Liu Junbo1, Hu Song1,2*

1Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, Sichuan 610209, China;2University of Chinese Academy of Sciences, Beijing 100049, China

The imaging model of lithography

Overview:With the continuous reduction of critical dimension (CD) of semiconductors, lithography technology has gradually become a key technology in the field of integrated circuit manufacturing. Resolution enhancement technologies (RETs) is to improve the resolution of lithography by modifying the incident angle of the light source and the mask mode under the premise that the wavelength and numerical aperture (NA) remain the same. Due to the influence of experimental conditions, such as temperature, assembly tolerance, and other factors, the aberration is introduced, leading to the deformation of the aerial image. In addition, the optical proximity effect (OPE) will be introduced, if the CD of the pattern is smaller than the illumination wavelength. Therefore, it is very important to solve the above problems to improve the imaging quality and image fidelity. Recently, many researchers have proposed the optimization algorithm based on pixelated representation of illumination source for inverse lithography optimization. This method has not only achieved high modulation and flexibility, but also has great advantages in improving lithography resolution. In this paper, a particle swarm optimization algorithm (PSO) combing with adaptive nonlinear control strategy (ANCS) is proposed to optimize the shape of lithography illumination source based on pixel representation. According to the unique symmetry characteristics of the light source, the light source is characterized by equal separation and dispersion, which can reduce the optimization complexity and improve the iteration efficiency. A simple grating array pattern and a complex and irregular grating array pattern are selected to verify the simulation results, and the pattern errors (PEs) between the photoresist pattern and the ideal pattern are used as the cost function to evaluate the simulation results. The effectiveness of the improved algorithm is verified by simulation of the two grating structures. In order to verify the superiority of ANCS-PSO, it is compared with the traditional particle swarm optimization algorithm and genetic algorithm. The simulation results show that the errors of the two kinds of simulation patterns are reduced by Pattern 01: 52.2%, 41.7%, 37.4%, and Pattern 02: 35 %, 25.3%, 25.3%, respectively, which effectively improves the photoresist image assurance. The comparison of the simulation results of the three algorithms shows that the proposed method not only has higher iteration efficiency, but also has more advantages in improving the quality of lithographic imaging and image fidelity.

Wang J, Liu J B, Hu SSource optimization based on adaptive nonlinear particle swarm method in lithography[J]., 2021, 48(9): 210167; DOI:10.12086/oee.2021.210167

Source optimization based on adaptive nonlinear particle swarm method in lithography

Wang Jian1,2, Liu Junbo1, Hu Song1,2*

1Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, Sichuan 610209, China;2University of Chinese Academy of Sciences, Beijing 100049, China

As an essential resolution enhancement technique, source optimization can improve the quality of advanced lithography. In the field of advanced lithography, the convergence efficiency and optimization ability of the source optimization are very important. Particle swarm optimization (PSO) is a global optimization algorithm. The adaptive control strategy can improve the global search ability of particles, and the nonlinear control strategy can expand the search range of particles. In this paper, a PSO algorithm based on adaptive nonlinear control strategy (ANCS) is proposed to solve the problem of source optimization by transforming it into a multivariable evaluation function. The image optimization simulation is carried out with a brief periodic grating image and an irregular image, and the source shape is optimized by the global iteration property of the proposed method. By using the pattern errors (PEs) as a multivariate merit function, the results of 300 iterations are evaluated, and the PEs of the two kinds of simulation patterns are reduced by 52.2% and 35%, respectively. Compared with the traditional PSO algorithm and genetic algorithm, the proposed method not only improves the imaging quality, but also has higher convergence efficiency.

source optimization; lithography; inverse lithography optimization techniques; particle swarm optimization algorithm

王建，劉俊伯，胡松. 基于自適應(yīng)非線性粒子群算法的光刻光源優(yōu)化方法[J]. 光電工程，2021，48(9): 210167

Wang J, Liu J B, Hu SSource optimization based on adaptive nonlinear particle swarm method in lithography[J]., 2021, 48(9): 210167

TP391

A

10.12086/oee.2021.210167

2021-05-21；

2021-08-26

國(guó)家自然科學(xué)基金資助項(xiàng)目(61604154，61875201，61975211，62005287)

王建(1981-)，男，博士，副研究員，主要從事微電子裝備關(guān)鍵技術(shù)的研究。E-mail：wangjian@ioe.ac.cn

胡松(1965-)，男，博士，研究員，主要從事微電子裝備關(guān)鍵技術(shù)的研究。E-mail：husong@ioe.ac.cn

National Natural Science Foundation of China (61604154, 61875201, 61975211, 62005287)

* E-mail: husong@ioe.ac.cn