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Journal of Inorganic Materials

Abbreviation (ISO4): J Inorg Mat      Editor in chief: Lidong CHEN

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Journal of Inorganic Materials >

2024 , Vol. 39 >Issue 4: 416 - 422

DOI: https://doi.org/10.15541/jim20230392

RESEARCH ARTICLE

Heteroepitaxial Diamond Nucleation and Growth on Iridium: First-principle Calculation

  • Weihua WANG , 1 ,
  • Leining ZHANG 2 ,
  • Feng DING , 3 ,
  • Bing DAI , 4 ,
  • Jiecai HAN 4 ,
  • Jiaqi ZHU 4 ,
  • Yi JIA 1 ,
  • Yu Yang 5
Expand
  • 1. China Aerospace Science and Technology Innovation Research Institute, China Aerospace Science and Technology Corporation, Beijing 100176, China
  • 2. School of Chemistry and Chemical Engineering, Beijing Institute of Technology, Beijing 102488, China
  • 3. Faculty of Materials Science and Engineering/Institute of Technology for Carbon Neutrality, Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China
  • 4. National Key Laboratory of Special Environment of Composite Technology, Harbin Institute of Technology, Harbin 150001, China
  • 5. Beijing Institute of Control Engineering, Beijing 100190, China
DING Feng, professor. E-mail: ;
DAI Bing, professor. E-mail:

Received date: 2023-08-30

  Revised date: 2023-11-06

  Online published: 2024-04-25

Supported by

National Key R&D Program of China(2020YFA0709700)

National Key R&D Program of China(2016YFE0201600)

National Natural Science Foundation of China(52072087)

Guangdong Key Research and Development Program(2020B010169002)

Heilongjiang Natural Science Foundation(YQ2020E008)

The Fundamental Research Funds for the Central Universities(HIT.OCEF.2022048)

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Abstract

Heteroepitaxy provides an effective path for the synthesis of diamond wafers. After more than 20 years of development, the diamond nucleation and growth technology on iridium substrates has enabled to prepare crystals with a maximum diameter of 3.5 inches, which opens a door to application diamond as ultimate semiconductor in the future chip industry. However, a series of problems that occur on heterogeneous substrates, such as surface nucleation, bias process window, and diamond epitaxial growth, need to overcome from the perspective of growth thermodynamics. In this study, aiming at the key issue how diamond can achieve epitaxial nucleation and growth in chemical vapor deposition atmosphere, a simulation study was carried out on the nucleation and growth process of diamond at the atomic scale based on the first-principle calculation. The results show that the adsorption of C atoms on the surface of the Ir substrate is more stable than that on the bulk phase, which indicates that diamond nucleation can only occur on the substrate surface. The number of C atoms of sp3 hybridization in the amorphous hydrogenated carbon layer increases firstly and then decreases with the increase of ion kinetic energy under ion bombardment, confirming the existence of the ion kinetic energy or bias voltage window in the high-density nucleation of diamond. The interfacial binding energy is the lowest (about -0.58 eV/C) when diamond is epitaxially grown along the Ir substrate, meaning that the interface binding energy is the decisive thermodynamic factor for the epitaxial growth. In conclusion, this study clarifies the thermodynamic mechanism of single crystal diamond epitaxial growth under the bias-assisted ion bombardment, and points out a great significant guidance for the growth of diamond and other carbon based semiconductors.

Key words： diamond; heteroepitaxy; nucleation and growth; first-principle; binding energy

Cite this article

Weihua WANG , Leining ZHANG , Feng DING , Bing DAI , Jiecai HAN , Jiaqi ZHU , Yi JIA , Yu Yang . Heteroepitaxial Diamond Nucleation and Growth on Iridium: First-principle Calculation[J]. Journal of Inorganic Materials, 2024 , 39(4) : 416 -422 . DOI: 10.15541/jim20230392

得益于独特的晶体结构和优异的物理性质, 金刚石被称作“终极半导体”[1]和电子材料的“珠穆朗玛峰”[2], 在功率器件[3-4]、探测器[5⇓-7]、二极管[8]、量子传感[9-10]、热管理[11⇓-13]等电子信息产业领域具有巨大的应用潜力。大尺寸、高品质晶圆制备是金刚石广泛应用的前提。与同质外延技术[14-15]或高温高压法[16⇓-18]相比, 异质外延技术不受金刚石籽晶尺寸品质或高温高压极端环境影响, 在异质衬底上经过外延形核-生长阶段后直接获得单晶金刚石[19⇓-21], 为金刚石晶圆合成提供了一个有效的实现路径。
异质外延技术[19⇓-21]涉及异质衬底选择、外延形核和织构生长等多个方面。经过一系列研究[22⇓⇓⇓⇓⇓⇓⇓⇓⇓-32], Ir衬底[27-28]和偏压增强形核技术[29⇓-31]被证明是目前最优的异质衬底和外延形核增强手段。2017年至今, 通过异质外延技术已陆续成功制备1~3.5英寸(2.54~8.89 cm)的金刚石晶圆[21,33⇓⇓-36], 这表明经过20多年的发展, 异质外延技术在制备大尺寸金刚石晶体方面已经取得了比较显著的进展与突破。高质量异质衬底制备[37⇓-39]、偏压技术窗口确定[40-41]、织构生长技术[19,42-43]、位错与应力控制技术[44⇓⇓-47], 甚至于电子器件性能验证[5,8,33,45]都得到了比较充分的研究。
然而, 技术的巨大发展却掩饰机理认识上的滞后。从金刚石生长理论的角度看, 除了一些关于衬底优异性的新认识[48⇓-50]外, 金刚石异质外延形核与生长机理近年来并未取得显著的进步。表面形核、偏压技术窗口、金刚石外延生长等一系列发生在异质衬底上的现象都需要从生长热力学角度给予解释。具体至少包括以下三个方面的问题: (1)无偏压条件下, 碳原子吸附在衬底表面进行形核是否有利?(2)有偏压条件下, 金刚石形核与偏压大小的关系如何?(3)金刚石外延生长的热力学驱动力如何?受第一性原理成功解释二维材料生长的启发[51⇓⇓-54], 化学气相沉积气氛中金刚石如何实现外延形核与生长这一关键问题似乎找到了一个新的解释路径。
本研究以Ir衬底上金刚石异质外延技术为研究对象, 基于第一性原理和形核生长原子尺度过程, 通过实验与计算相结合的手段, 确定了C原子在Ir(001)表面的吸附行为, 模拟了离子轰击作用下的体相形核过程, 最后揭示了决定金刚石外延形核生长的主要因素。

1 实验与计算方法

Ir衬底上金刚石外延形核与生长实验已在前期研究工作[41,43,55-56]中详细报道, 其中Ir复合衬底的制备利用电子束蒸镀设备, 金刚石形核与生长实验通过集成有直流偏压电源的微波等离子体化学气相沉积设备来完成。
本研究中计算过程是基于第一性原理——密度泛函理论, 采用VASP软件包(Vienna Ab-initio Simulation Package, VASP)来完成的[57-58]。交换相关函数采用广义梯度近似(Generalized Gradient Approximation, GGA)处理[59], 价电子与原子核之间的相互作用采用广义波函数(PAW)方法计算[60]。下文2.1和2.3节中截断能设置为400 eV, 2.2节中截断能设置为250 eV。k点网格采用Gamma方法, 2.1和2.2节计算中设置为3×3×1, 2.3节计算中设置为2×2×1。真空层厚度设置为2 nm, 结构优化的收敛标准是原子间力小于0.1 eV/nm, 能量收敛为10-4 eV。
为了比较C原子吸附在Ir衬底不同位置的稳定性, 需要计算C原子吸附在Ir衬底不同位置时的吸附能(Adsorption energy, Ea)[61], 其表达式如式(1):
${{E}_{a}}={{E}_{Ir}}+{{E}_{C}}-{{E}_{total}}$
式中, ${{E}_{total}}$——整个吸附体系的能量; ${{E}_{C}}$——C原子在真空中的能量; ${{E}_{Ir}}$——Ir（001）衬底体系的能量。
为了模拟微波等离子体CVD中偏压增强形核过程, 本研究做出以下假设: (1)假设CH3是等离子体中的主要反应粒子, 在电场作用下轰击衬底表面的带正电离子是CH3+离子; (2)对等离子体施加直流偏压可以认为CH3+离子在直流外加电场下加速获得初始动能, 故本研究设置离子速率分别为0.005、0.011、0.019、0.025、0.030和0.035 nm/fs, 离子动能${{E}_{k}}=\frac{1}{2}{{m}_{C{{H}_{3}}}}{{v}^{2}}$经过计算分别为2、10、30、50、70和100 eV; (3)Ir衬底表面积为1.09 nm×1.09 nm, 且每隔2 ps施加6个CH3+离子, 直到Ir衬底表面吸附的C原子数量不再增加或者开始形成C链结构为止; (4)每隔2 ps过程中产生的H2、CH4和其他脱离表面的粒子都直接予以除去; (5)CH3+离子距离Ir(001)衬底表面0.5 nm, 每步步长为0.00125~ 0.00165 nm。
生长过程中, 为了比较金刚石团簇沿着Ir(001)衬底表面不同取向排布时的稳定性, 需要计算金刚石团簇与Ir(001)衬底之间的相互作用力——二者之间的结合能大小(Binding energy, ${{E}_{b}}$)。金刚石团簇在Ir(001)衬底上的结合能${{E}_{b}}$的表达式如式(2)[51]:
${{E}_{b}}=({{E}_{total}}-{{E}_{Ir}}-{{E}_{dia}})/{{N}_{\mathrm{C}}}$
式中, ${{E}_{dia}}$——金刚石团簇的能量; ${{N}_{C}}$——金刚石团簇所含的C原子数目。

2 结果与讨论

2.1 C原子在Ir衬底上的吸附行为

本研究首先计算了单个C原子吸附在Ir体相结构不同位点时的吸附能, 其中Ir衬底为3×3×3晶胞结构, C原子分别吸附在八面体间隙位(O)、四面体间隙位(T)及Ir原子取代位(S), 如图1(a)所示。不同吸附位点的吸附能如图1(b)所示: (1)当吸附在八面体间隙位时, 吸附能为-5.18 eV; (2)当吸附在四面体间隙位时, 吸附能为-4.33 eV; (3)当取代了1个Ir原子时, 吸附能为-2.04 eV。结果表明: 当C原子吸附在八面体间隙时吸附能最低, 因此八面体间隙位属于最稳定的吸附位点。
图1 C原子在Ir衬底上的吸附模型及行为

Fig. 1 Adsorption modes and behaviors of C atom on Ir substrate

(a) Adsorption modes of C atom in octa-site (O), tetra-site (T) and subs-site (S) of the surface; (b) Adsorption energy when one C atom is adsorbed on different sites of Ir substrate; (c) Adsorption energy variation of C atoms adsorbed on different depths from Ir (001) surface

控制吸附位点为八面体间隙位, 逐渐改变C原子吸附位置从Ir(001)表面到体相内不同位置, 研究计算了不同位置的C原子吸附能, 结果如图1(c)所示。在该模型中, 真空层厚度为2 nm, Ir(001)结构为6×6×10超胞。由图可知: (1)当C原子吸附在Ir(001)表面时, Ea为-8.26 eV; (2)随着吸附深度的增加, C原子吸附位置逐渐从表面变化到体相内, 吸附能骤然升高到-5.60 eV, 随后逐渐稳定在-5.50 eV附近。该结果清晰地表明, 当C原子吸附在Ir(001)结构表面时, 表面吸附的吸附能最低, 意味着表面吸附比体相吸附更稳定。同时, 该结果还表明在吸附原子无初始动能的前提下, 吸附原子进入体相内不是自发的过程, 体相吸附其实是极不稳定的状态。

2.2 直流电场作用下CH3+离子轰击Ir衬底过程

金刚石偏压技术窗口在Si衬底[25]、3C-SiC衬底[62]和Ir衬底[40-41]上都存在, 既有时间窗口, 也有偏压大小窗口。虽然窗口区间不尽相同, 但也表明偏压形核窗口是金刚石形核技术中一个较为普遍的现象。
a-C:H层中自发形成大量sp3杂化的C原子(sp3-C原子)是金刚石形核的前提。Lifshitz等[63]认为sp3-C原子团簇中大概只有万分之一到百万分之一的C原子能形成金刚石晶核, 因此估算a-C:H层中形成的sp3-C原子个数是必要的。表1所示为不同速率离子轰击表面后形成a-C:H层中C原子个数及sp3-C原子个数。结果如下: (1)当离子速率为0.005 nm/fs时, 经过7500步MD(Molecular Dynamics, MD)后, 表面的C原子个数为6, 相比5000步MD时开始减少, 计算此时的sp3-C原子个数为0(比例为0); (2)当离子速率为0.011 nm/fs时, 经过15000步MD后, 表面的C原子个数为17, 比运行12500步MD后表面C原子个数有所减少, 计算此时sp3-C原子个数为5(比例为29.4%); (3)当离子速率为0.019 nm/fs时, 经过12500步MD后, 加入的C原子开始成为碳链, 计算此时表面的C原子个数为22, 但sp3-C原子个数为1(比例为4.5%); (4)当离子速率为0.025, 0.030和0.035 nm/fs时, 经过12500步MD后, 表面的C原子个数分别为18, 23和26, 但sp3-C原子个数分别为2, 0和1(比例依次为11.1%, 0%和3.8%)。图2所示为不同速率CH3+离子轰击表面后所有C原子(包括a-C:H层和其他脱离表面的含C粒子)的成键类型。其中最大尺寸原子代表Ir, 中等尺寸原子为C, 最小尺寸原子为H; 从蓝色到红色依次代表C原子成键的个数从0到4。通过排除生成的CH4分子和脱离表面的含C粒子外, 可以清晰地计算出形成的sp3-C原子依次为0, 5, 1, 2, 0和1。结果表明: (1)当离子速率很低时, 几乎无法有效沉积a-C:H层和形成足够的sp3-C原子, 即金刚石形核难以发生; (2)当离子速率增大时, a-C:H层中C原子个数及sp3-C原子个数均有所增加; 离子速率进一步增大时, 沉淀平衡时a-C:H层中sp3-C原子个数以及比例整体呈现减少的趋势; (3)随着离子轰击时间的延长, a-C:H层中C原子个数及sp3-C原子个数逐渐增加。这表明轰击时间存在一个最低阈值, 离子速率存在一个最优区间, 与所认知的形核存在诱导期及偏压大小窗口所一致。
表1 不同速率CH3+离子轰击表面后形成a-C:H层中C原子个数及sp3-C原子个数.

Table 1 Carbon atom number and sp3-bonded carbon number in the a-C:H layer after the CH3+ ion bombardment with different rates

Ion rate 0.005 nm/fs 0.011 nm/fs 0.019 nm/fs 0.025 nm/fs 0.030 nm/fs 0.035 nm/fs
Number
Step		 C
atom		 sp3-C
atom		 C
atom		 sp3-C
atom		 C
atom		 sp3-C
atom		 C
atom		 sp3-C
atom		 C
atom		 sp3-C
atom		 C
atom		 sp3-C
atom
2500 4 0 4 0 6 0 6 0 6 0 6 0
5000 9 0 7 1 9 0 11 0 11 0 11 0
7500 6 0 13 1 15 0 15 0 17 0 17 1
10000 - 16 3 21 1 17 2 20 2 23 1
12500 21 4 22 1 18 2 23 0 26 1
15000 17 5 - - - - -
图2 不同速率CH3+离子轰击表面后所有C原子的成键类型

Fig. 2 Bonding types of C atoms after the CH3+ ion bombardment with different ion rates

(a) 0.005 nm/fs; (b) 0.011 nm/fs; (c) 0.019 nm/fs; (d) 0.025 nm/fs; (e) 0.030 nm/fs; (f) 0.035 nm/fs

Atoms with the atomic size from large to small representing Ir, C and H, and C atom with the color from blue to red representing the bonding number of C atom from 0 to 4. Colorful figures are available on website

2.3 金刚石外延生长的能量分析

建立了8×8×3的Ir(001)超晶格结构, 该结构有下述特点: (1)共包含有192个Ir原子, 晶格矢量方向分别为[110]、$[\bar{1}10]$和[001]三个取向, 且对底层C原子进行了固定; (2)金刚石(001)团簇包含5层, 共计96个C原子, 除了团簇底层C原子与Ir衬底相互作用外, 其他C原子均进行了H原子钝化; (3)金刚石团簇与Ir(001)表面的最初距离设定为0.251 nm, 且为消除[001]方向上因周期性原因所导致的金刚石团簇与Ir衬底的作用干扰, 对表面结构施加了2 nm的真空层。
通过改变金刚石团簇与Ir衬底之间的夹角θ为0°、5°、10°、15°、20°、25°、30°、35°、40°和45°, 分别获得了金刚石(001)团簇沿着Ir(001)衬底不同取向排列的模型结构。图3所示为夹角θ=0°、10°、25°和45°时的模型结构: 当θ=0°时, 面内取向关系为金刚石(001)[010]//Ir(001)[010]; 当θ=45°时, 面内取向关系为金刚石(001)[110]//Ir(001)[010]。
图3 金刚石(001)团簇与Ir(001)衬底夹角θ=0°、10°、25°和45°时的结构

Fig. 3 Structure of cluster model of diamond (001) and Ir (001) surface as a function of the alignment angle θ=0°, 10°, 25° and 45°

When θ are 0° and 45°, the in-plane orientation relationships are diamond(001)[010]//Ir(001)[010] and diamond(001)[110]//Ir(001)[010], respectively

当夹角θ为0°、5°、10°、15°、20°、25°、30°、35°、40°和45°时, 上述体系结构优化后的结合能Eb分别约是-0.58、-0.54、-0.54、-0.53、-0.54、-0.54、-0.52、-0.53、-0.52和-0.53 eV/C。需要指出的是, 金刚石具有四重对称性, 因此当夹角从45°增大到90°时的金刚石结构及体系结合能与夹角从45°减少到0°时的金刚石结构及体系结合能具有明显的对称性。通过比较上述结果(如图4(a)所示), 不难发现: (1)当θ=0°时, Eb最小为-0.58 eV/C, 这意味着当金刚石晶核与Ir衬底原子按照金刚石[110]// Ir[110]方向(也就是金刚石[010]//Ir[010]方向)排列时, 二者之间的结合作用最强, 表明界面结合能是决定金刚石外延形核生长的主要热力学因素。(2)对于尺寸在2.2 nm×2.2 nm的金刚石团簇, 最小结合能与最大结合能之差高达5.21 eV, 这表明大概含有6个晶胞的纳米晶金刚石吸附在Ir(001)衬底表面时, 不同的取向之间具有如此大的能量差, 从而有力保证了金刚石团簇稳定的外延生长过程。(3)对于不同取向关系下结合能差异的原因可以通过比较差分电荷密度差异进行解释。Dong等[54]计算后发现在薄膜与衬底保持外延取向时, 界面处衬底原子与薄膜原子之间的化学键键能最大、结合力最强。
图4 金刚石-Ir体系结合能随夹角θ的变化关系(a), 及金刚石在Ir(001)衬底上进行形核生长后获得的SEM表面形貌(b)

Fig. 4 Binding energy for the diamond-Ir system as a function of the alignment angle θ (a), and SEM surface morphology of diamond grains on Ir (001) surface (b)

No.1-4 represent grains with different sizes and shapes

图4(b)所示为金刚石在Ir(001)衬底上形核生长后获得的SEM表面形貌, 其中标号为1~4的区域包含了不同尺寸、不同形态的金刚石晶粒。这些晶粒具有以下特征: (1)晶粒呈现八面体金字塔或者立方八面体结构, 暴露出(001)或者(111)晶面; (2)晶粒都是沿着<110>晶向族分布, 包括[110]和$[\bar{1}10]$晶向等; (3)晶粒大小不一, 尺寸相对较小的晶粒呈现八面体金字塔结构, 尺寸较大的晶粒呈现立方八面体结构, 不同形态可能是由织构生长所致, 也可能是晶粒合并的缘故。实验结果表明, 金刚石晶粒在形核生长时的面内取向关系为金刚石(001)[010]//Ir(001)[010], 这与上文的结合能计算结果完全一致。同时需要指出的是, 金刚石与Ir衬底之间的外延关系还可通过X射线衍射分析或者高分辨透射电子显微镜等手段获得, 在本团队或其他团队的前期实验工作中可确认[21,24,30,43], 故在此只对SEM形貌予以阐述, 对其他表征结果不在此展开赘述。

3 结论

针对化学气相沉积气氛中金刚石外延形核与生长这一问题, 基于第一性原理和形核生长原子尺度过程, 本研究系统模拟了金刚石形核生长过程。
(1)通过计算C原子在Ir衬底表面不同吸附位点的吸附能, 发现当C原子吸附在八面体间隙位时, 相比吸附在四面体间隙位和Ir原子取代位时, 吸附能更低、吸附更稳定, 且表面吸附的吸附能低于晶格内吸附的吸附能, 因此表面吸附比体相吸附更稳定。
(2)通过改变离子速率进而改变离子动能模拟偏压大小对金刚石形核的影响, 发现a-C:H层中形成sp3-C原子个数随着离子动能增加呈现先增加后减少的变化规律, 证实了偏压窗口的存在。
(3)通过改变金刚石团簇与Ir衬底之间的夹角, 计算不同夹角时二者的界面结合能, 发现当金刚石与衬底之间取向关系为外延取向——金刚石(001) [010]/Ir(001)[010]时界面结合能最小(约为-0.58 eV/C), 进而提出了界面结合能是决定外延形核生长的热力学机制。

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