1 引言
纳米计量不仅在测量和表征纳米材料及器件方面提供基础支撑,还在纳米制造工艺控制和质量管理领域扮演重要角色[1]。在纳米计量过程中,受工作原理及测试环境等因素的影响,测试结果可能会截然不同。因此,研究准确适用的纳米传递标准具有重要意义[2]。基于原子光刻技术[3-4]制备得到的纳米光栅,其节距直接溯源于激光半波长,因此可以作为纳米级长度计量的传递标准,实现对于扫描探针显微镜(SPM)和扫描电子显微镜(SEM)等纳米测量仪器非线性特征的高精度校准。原子光刻技术的基本原理是:原子与激光驻波场的相互作用使原子周期性地会聚至激光驻波场的波腹或波节位置,从而形成节距为激光半波长的纳米光栅[5-6]或网格结构[7-8]。
1978年,Bjokholm等[9]首次提出原子光刻技术的概念。1992年,Timp等[10]利用钠原子首次在实验中验证该技术,并在硅基板上得到节距为294 nm的纳米光栅。1993年, McClelland等[5]利用铬原子也成功获得周期为212.78 nm的光栅结构。之后,利用Al[11]、Yb[12]、Fe[13]等元素制备得到特定节距纳米光栅的研究均不断出现。然而,在原子光刻纳米光栅研制过程中,普遍面临的挑战是光栅的峰谷高度(PTVH)难以得到稳定的提升,这不仅在某种程度上限制了其研制的稳定性与复现性,还会对光栅节距测试与节距表征精度产生不利影响。一般来讲,影响原子光刻制备纳米光栅PTVH的主要因素有原子通量、激光光强以及切光比例等,原子通量直接决定了光栅峰谷高度的上限,因此在所有影响因素中尤为重要。研究提高原子通量的理论与方法对于提升原子光刻纳米光栅质量至关重要。
原子光刻实验中,一般将工作物质放置入原子炉管中进行加热,并以泻流的方式将原子束引出。经验表明,不同的原子炉管构型对应不同的泻流模式与原子通量,受此启发,本文应用原子炉管喷发量理论模型,对比研究了三类典型原子炉管构型下的原子通量水平,并基于最优原子炉管构型将研制的铬纳米光栅峰谷高度提升到100 nm,同时解决了炉管使用过程中炉管喷口堵塞的问题,使原子光刻光栅峰谷高度、原子炉管的使用稳定性和光栅研制质量的复现性等均得到进一步优化。
2 基本原理与理论模型
原子光刻的基本原理如图1所示[14]。中性原子在原子炉中加热到一定温度时喷发而出,经过小孔预准直和激光冷却[15-16]后,垂直入射到激光驻波场中。原子在驻波场中受到偶极力的作用,向驻波波节(负失谐)或波腹(正失谐)位置移动,最后沉积到硅基片上,形成周期为激光半波长的纳米光栅。由于铬(Cr)原子在大气中具有很好的稳定性以及表面黏附性[17],因此选择Cr元素作为原子源。实验选择的激光波长为λ=425.6 nm,对应于铬原子7S3→7的跃迁谱线。因此,实验制备得到的纳米光栅周期为λ/2=212.8 nm。
图 1. 原子光刻原理示意图
Fig. 1. Schematic of atom lithography
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在原子光刻实验中,一定量的铬元素放置于原子炉管中,通过加热将温度到达一定程度,铬原子气体在腔体内形成饱和蒸气压,经炉管中的一个小的开口喷发而出。其理论模型根据Knudsen系数可以分成三种情况。Knudsen系数定义为炉腔内气体原子的平均自由程
与炉管喷口直径ds的比值[18]。
1)
/ds<0.01,此区域称之为黏滞流体区。此时炉腔内原子间的碰撞频率高于原子与炉内壁的碰撞频率,由流体力学描述。
2)
/ds>1,此区域称之为原子泻流区。此时炉腔内原子间的碰撞频率低于原子与炉内壁的碰撞频率,由泻流公式描述。
3) 0.01</ds<1,此区域称之为由黏滞流体向原子泻流的过渡区,由半经验方程描述。
密闭炉管内铬蒸气的饱和蒸气压与温度的关系为[19]
式中P为炉管内铬蒸气的饱和蒸气压,T为铬蒸气的温度。为计算铬原子气体平均自由程,假设炉管完全密闭,铬蒸气处于热平衡状态,则满足关系
式中kB为气体玻尔兹曼常数,当原子加热温度为1923 K时,可得炉管内铬蒸气原子数密度为n=1.603×1021 m-3。
一定温度和压强下,容器内热平衡态气体中的原子平均自由程可表示为
式中δ=π
为原子的碰撞截面,R0为原子半径,实验中铬原子半径为R0=1.25×10-8 cm,由此计算可得炉管内铬气体原子的平均自由程为
=0.225 cm。而实验所用炉管喷口直径为0.1 cm,因此,实验中原子喷发模型满足泻流条件。
在一定温度和压强的泻流条件下,原子通量可表示为[20]
式中As为炉管喷口处面积,v为炉管内铬蒸气原子平均速度(当温度为1923 K,v=960 m/s[21]),
为Knudsen公式,其中L为喷口处壁的厚度,A为壁厚l处的横截面积,C为此横截面对应的周长。
3 实验对比与讨论
为比较不同原子炉管构型对于原子喷发量以及实验结果的影响,对比实验中保持其他主要影响实验结果的条件不变,包括原子炉温度1923 K、会聚光功率30 mW、切光比例50%、冷却光功率15 mW等。
第一类与第二类原子炉管构型如图2所示,其中,图2(a)中原子炉管壁厚L=1 mm,开口大小为d=1 mm,因为炉管喷口为圆柱形,因此Knudsen公式可以简化为K=×,将L和d代入得K=1.33,再代入n和v可得N1=4.03×1017 s-1。第一类炉管在实际使用中存在的典型问题是炉管使用不久后出现炉管喷口处堵塞现象。炉管喷口的堵塞会导致两个问题:1)原子喷发通量大幅下降(稳定后喷发量缩减到N1/10,即4.03×1016 s-1),导致纳米光栅PTVH明显降低,此种情况下PTVH一般在30 nm左右即达到饱和状态;2)原子束出射方向发生改变,这会引起光栅节距的改变[22]。一般认为,造成原子炉管堵塞的最大问题是炉管喷口处内外存在温度差,导致原子气体在喷口处沉积,最终形成堵塞现象。
图2(b)所示为第二类原子炉管构型,在喷口处增加了一段高温胶(HTG)保护层,有效地解决了原子炉管堵塞的问题。但是由图2(b)可知,这种改动变相地增加了炉管喷口厚度L,此时炉管喷口可以分为两段:第一段L'=1 mm,d'=1 mm;第二段L″=9 mm,d″=2 mm。将其代入Knudesen公式得到K=0.15,计算得到N2=4.48×1016 s-1,原子通量减少,直接影响了实验所得纳米光栅的高度。在相似实验条件下的对比实验表明,第二类原子炉管研制的原子光刻光栅PTVH同样在30 nm左右饱和。
图 2. 原子炉管构型。(a)第一类;(b)第二类
Fig. 2. Atomic furnace tube configuration. (a) First kind; (b) second kind
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为了增加原子通量,设计了第三类原子炉管构型,如图3(a)所示。炉管喷口去掉了保护层,同时将喷口处设计成刀口状。以原子炉管喷口中心为原点,刀口处切角为θ,如图3(b)所示,则d=1+2Ltanθ,考虑到原子炉管内径为7 mm,tanθ≤3,因此θ的取值范围是0≤θ≤71°。将上述关系式代入Knudsen公式和(4)式可计算得到原子通量N3,如图4所示。
图 3. 第三类原子炉管构型及其坐标系。(a)构型; (b)坐标系
Fig. 3. Atomic furnace tube and its coordinate system. (a) Configuration; (b) coordinate system
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图 4. 喷口刀口切角与原子通量关系图
Fig. 4. Relationship between nozzle blade angle and atom flux
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考虑到加工工艺和喷发量已经满足实验要求,实际制备的炉管喷口角度选择为θ=45°,此时d=1+2L,代入Knudsen公式可得K=6.00,N3=1.81×1018 s-1。将三类原子炉管构型的原子喷发量作比较(由于第一类炉管很快会有堵塞问题,因此比较的是堵塞以后稳定情况下的原子通量),结果如图5所示。相比于第一类和第二类,第三类原子炉管的原子通量增加了约40倍,同时也不存在炉管喷口堵塞的问题。
图 5. 三类原子炉管对应的喷发量比较
Fig. 5. Eruption volume comparison among three kinds of atomic furnace tubes
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由于炉管喷口为刀口状,其对原子束出射方向的稳定性以及束流形状、直径等均有影响。实验中,原子束从原子炉管喷出后经过预准直小孔、沉积狭缝以及冷却激光的作用,可以极大地减弱因炉管喷口形状改变而带来的影响,装置示意图如图6所示。预准直小孔尺寸与泻流小孔尺寸相当,测量表明,该种情况下原子束沿喷射方向的水平发散角小于2.7 mrad,具有良好的平行性与准直性[23]。
图 6. 原子束准直示意图
Fig. 6. Schematic of atomic beam collimation
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基于第三类炉管的原子光刻实验制备得到的纳米光栅形貌与轮廓测试结果如图7(a)所示,图7(b)展示了基于三类炉管研制的原子光刻光栅典型轮廓对比结果,该系列对比实验过程中保持实验条件(如会聚激光功率、切光比例、沉积时间等)一致。由图7(b)可知,通过改进原子炉管构型增加原子通量,原子光刻光栅PTVH从30 nm增加到了100 nm,并且光栅周期保持严格统一,始终与使用会聚光的半波长保持一致。峰谷高度达到100 nm的铬原子光刻光栅与美国国家标准技术研究所(NIST)利用原子光刻制备得到的纳米光栅的峰谷高度相当,满足作为纳米量级标准物质对于峰谷高度上的要求。
图 7. 第三类炉管研制的纳米光栅形貌与轮廓实验结果。(a)光栅原子力显微镜图像;(b)光栅截面对比
Fig. 7. Experimental result of morphology and profile of nano-grating fabricated by third kinds of furnace tube. (a) Atomic force microscope image of nano-grating; (b) profile comparison of nano-grating
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在图7(b)中,值得注意的是,虽然第三类原子炉管的原子通量增加了40倍,但是光栅的峰谷高度只增加了3倍左右,说明此时原子通量已经达到饱和,此时影响光栅峰谷高度的主要因素将变为激光功率和切光比例等,这也是今后优化实验需要进一步研究的重点内容。
4 结论
利用原子束喷发的理论模型,结合具体实验研究,优化了原子炉管构型,从而使原子通量增加了一个数量级,在其他实验条件相当的情况下,所研制的纳米光栅峰谷高度可以提升至100 nm。通过优化原子通量实现原子光刻光栅峰谷高度的提升,不仅有利于提升原子光刻实验的稳定性与复现性和光栅节距提取的精度,而且优化了光栅质量,降低了测试噪声对于测试结果的影响,同时为该光栅申请标准物质,以及研制更小周期纳米光栅标准物质奠定了基础。
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