超晶格材料superlattices_(graduate)
PLD
PLD目录1计算机硬件简介1分类1发展历程1组成1制膜技术简介1优点1对激光器要求1相关产品PLDPLD（普兰迪营销策划有限公司）展开编辑本段计算机硬件简介可编程逻辑器件PLD（programmable logic device) ：PLD是做为一种通用集成电路生产的，他的逻辑功能按照用户对器件编程来搞定。
一般的PLD的集成度很高，足以满足设计一般的数字系统的需要。
这样就可以由设计人员自行编程而把一个数字系统“集成”在一片PLD上，而不必去请芯片制造厂商设计和制作专用的集成电路芯片了。
分类目前使用的PLD产品主要有：1、现场可编程逻辑阵列FPLA（field programmable logic array);2、可编程阵列逻辑PAL（programmable array logic);3、通用阵列逻辑GAL（generic array logic);4、可擦除的可编程逻辑器件EPLD（erasable programmable logic device);5、现场可编程门阵列FPGA（field programmable gate array)。
其中EPLD和FPGA的集成度比较高。
有时又把这两种器件称为高密度PLD。
发展历程早期的可编程逻辑器件只有可编程只读存贮器(PROM)、紫外线可按除只读存贮器(EPROM)和电可擦除只读存贮器(EEPROM)三种。
由于结构的限制，它们只能完成简单的数字逻辑功能。
其后，出现了一类结构上稍复杂的可编程芯片，即可编程逻辑器件，它能够完成各种数字逻辑功能。
典型的PLD由一个“与”门和一个“或”门阵列组成，而任意一个组合逻辑都可以用“与一或”表达式来描述，所以，PLD能以乘积和的形式完成大量的组合逻辑功能。
这一阶段的产品主要有PAL和GAL。
PAL 由一个可编程的“与”平面和一个固定的“或”平面构成，或门的输出可以通过触发器有选择地被置为寄存状态。
PAL器件是现场可编程的，它的实现工艺有反熔丝技术、EPROM技术和EEPROM技术。
红外探测Ⅱ类超晶格技术概述(一)
第５１卷 第４期 激光与红外Ｖｏｌ．５１，Ｎｏ．４ ２０２１年４月 ＬＡＳＥＲ ＆ ＩＮＦＲＡＲＥＤＡｐｒｉｌ，２０２１ 文章编号：１００１ ５０７８（２０２１）０４ ０４０４ １１·综述与评论·红外探测ＩＩ类超晶格技术概述（一）尚林涛，王 静，邢伟荣，刘 铭，申 晨，周 朋（华北光电技术研究所，北京１０００１５）摘 要：本文简单归纳总结了红外探测ＩＩ类超晶格材料的发展历史、基本理论、相比ＭＣＴ材料的优势和材料的基本结构。
通过设计６１?系超晶格材料适当的层厚和不同层间应力匹配的界面可以构筑灵活合理的能带结构，打开设计各种符合器件性能要求的新材料结构的可能性（如各种同质结ｐ ｉ ｎ结构，双异质结ＤＨ、异质结Ｗ、Ｍ、Ｎ、ＢＩＲＤ、ＣＢＩＲＤ、ｐ π Ｍ Ｎ、ｐＢｉＢｎ、ｎＢｎ、ＸＢｐ、ｐＭｐ等结构），还可以在一个焦平面阵列（ＦＰＡ）像元上集成吸收层堆栈实现集成多色／多带探测。
Ｔ２ＳＬ探测器可以满足实现大面阵、高温工作、高性能、多带／多色探测的第三代红外探测器需求，尤其在长波红外（ＬＷＩＲ）和甚长波红外（ＶＬＷＩＲ）及双色／多带探测上可以替代ＭＣＴ。
关键词：ＩＩ类超晶格；Ｔｙｐｅ ＩＩ；Ｔ２ＳＬ；ＳＬＳ；材料结构中图分类号：ＴＮ２１５ 文献标识码：Ａ ＤＯＩ：１０．３９６９／ｊ．ｉｓｓｎ．１００１ ５０７８．２０２１．０４．００２Ｏｖｅｒｖｉｅｗｏｆｉｎｆｒａｒｅｄｄｅｔｅｃｔｉｏｎｔｙｐｅ ＩＩｓｕｐｅｒｌａｔｔｉｃｅｔｅｃｈｎｏｌｏｇｙ（Ｉ）ＳＨＡＮＧＬｉｎ ｔａｏ，ＷＡＮＧＪｉｎｇ，ＸＩＮＧＷｅｉ ｒｏｎｇ，ＬＩＵＭｉｎｇ，ＳＨＥＮＣｈｅｎ，ＺＨＯＵＰｅｎｇ（ＮｏｒｔｈＣｈｉｎａＲｅｓｅａｒｃｈＩｎｓｔｉｔｕｔｅｏｆＥｌｅｃｔｒｏ Ｏｐｔｉｃｓ，Ｂｅｉｊｉｎｇ１０００１５，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ：Ｔｈｅｄｅｖｅｌｏｐｍｅｎｔｈｉｓｔｏｒｙ，ｂａｓｉｃｔｈｅｏｒｙ，ａｄｖａｎｔａｇｅｓｏｖｅｒＭＣＴｍａｔｅｒｉａｌｓａｎｄｂａｓｉｃｓｔｒｕｃｔｕｒｅｏｆｉｎｆｒａｒｅｄｄｅｔｅｃ ｔｉｏｎｔｙｐｅ ＩＩｓｕｐｅｒｌａｔｔｉｃｅｍａｔｅｒｉａｌｓａｒｅｓｕｍｍａｒｉｚｅｄｉｎｔｈｅｐａｐｅｒ Ｔｈｒｏｕｇｈｔｈｅｄｅｓｉｇｎ６ １?ｓｕｐｅｒｌａｔｔｉｃｅｍａｔｅｒｉａｌｓｓｙｓｔｅｍｏｆａｐｐｒｏｐｒｉａｔｅｌａｙｅｒｔｈｉｃｋｎｅｓｓａｎｄｍａｔｃｈｉｎｇｉｎｔｅｒｆａｃｅｓｔｒｅｓｓｂｅｔｗｅｅｎｌａｙｅｒｓｃａｎｂｕｉｌｄｆｌｅｘｉｂｌｅｒｅａｓｏｎａｂｌｅｂａｎｄｓｔｒｕｃ ｔｕｒｅ，ｏｐｅｎｔｈｅｐｏｓｓｉｂｉｌｉｔｙｏｆｄｅｓｉｇｎｉｎｇｎｅｗｍａｔｅｒｉａｌｓｔｒｕｃｔｕｒｅｔｈａｔｃｏｎｆｏｒｍｔｏｔｈｅｒｅｑｕｉｒｅｍｅｎｔｓｏｆｔｈｅｄｅｖｉｃｅｐｅｒｆｏｒｍ ａｎｃｅ（ｓｕｃｈａｓａｖａｒｉｅｔｙｏｆｈｏｍｏｊｕｎｃｔｉｏｎｐ ｉ ｎｓｔｒｕｃｔｕｒｅ，ｄｏｕｂｌｅｈｅｔｅｒｏｊｕｎｃｔｉｏｎＤＨ，ｈｅｔｅｒｏｊｕｎｃｔｉｏｎＷ，Ｍ，Ｎ，ＢＩＲＤ，ＣＢＩＲＤ，ｐ π Ｍ Ｎ，ｐＢｉＢｎ，ｎＢｎ，ＸＢｐ，ｐＭｐ，ｅｔｃ），ａｌｓｏｃａｎｉｎｔｅｇｒａｔｅｍｕｌｔｉｌａｙｅｒａｂｓｏｒｐｔｉｏｎｌａｙｅｒｓｔａｃｋｏｎｏｎｅｆｏｃａｌｐｌａｎｅａｒｒａｙ（ＦＰＡ）ｐｉｘｅｌｔｏｒｅａｌｉｚｅｉｎｔｅｇｒａｔｅｄｍｕｌｔｉｃｏｌｏｒ／ｍｕｌｔｉｂａｎｄｄｅｔｅｃｔｉｏｎ Ｔ２ＳＬｄｅｔｅｃｔｏｒｃａｎｍｅｅｔｔｈｅｒｅｑｕｉｒｅｍｅｎｔｓｏｆｔｈｅｔｈｉｒｄ ｇｅｎｅｒａｔｉｏｎｉｎｆｒａｒｅｄｄｅｔｅｃｔｏｒｗｉｔｈｌａｒｇｅａｒｒａｙ，ｈｉｇｈｏｐｅｒａｔｉｎｇｔｅｍｐｅｒａｔｕｒｅ，ｈｉｇｈｐｅｒｆｏｒｍａｎｃｅ，ｍｕｌｔｉｂａｎｄ／ｍｕｌｔｉｃｏｌｏｒｄｅｔｅｃｔｉｏｎ，ｅｓｐｅｃｉａｌｌｙｃａｎｒｅｐｌａｃｅＭＣＴｉｎｔｈｅｌｏｎｇｗａｖｅｉｎｆｒａｒｅｄ（ＬＷＩＲ），ｔｈｅｖｅｒｙｌｏｎｇｗａｖｅｉｎｆｒａｒｅｄ（ＶＬＷＩＲ）ａｎｄｔｈｅｔｗｏ ｃｏｌｏｒ／ｍｕｌｔｉ ｂａｎｄｄｅｔｅｃｔｉｏｎＫｅｙｗｏｒｄｓ：ｃｌａｓｓＩＩｓｕｐｅｒｌａｔｔｉｃｅ；ｔｙｐｅ ＩＩ；Ｔ２ＳＬ；ＳＬＳ；ｍａｔｅｒｉａｌｓｔｒｕｃｔｕｒｅ作者简介：尚林涛（１９８５－），男，硕士，工程师，研究方向为红外探测器材料分子束外延技术研究。
vctic超晶格薄膜的微结构及超硬效应
Trans. Nonferrous Met. Soc. China 25(2015) 2581−2586Microstructure and superhardness effect of VC/TiC superlattice filmsXue-chao DONG 1, Jian-ling YUE 1,2, En-qing WANG 1, Miao-lei LI 1, Ge-yang LI 31. School of Aeronautics and Astronautics, Central South University, Changsha 410083, China;2. State Key Laboratory of Powder Metallurgy, Central South University, Changsha 410083, China;3. State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200030, ChinaReceived 22 September 2014; accepted 23 April 2015Abstract: Vanadium carbide/titanium carbide (VC/TiC) superlattice films were synthesized by magnetron sputtering method. The effects of modulation period on the microstructure evolution and mechanical properties were investigated by EDXA, XRD, HRTEM and nano-indentation. The results reveal that the VC/TiC superlattice films form an epitaxial structure when their modulation period is less than a critical value, accompanied with a remarkable increase in hardness. Further increasing the modulation period, the hardness of superlattices decreases slowly to the rule-of-mixture value due to the destruction of epitaxial structures. The XRD results reveal that three-directional strains are generated in superlattices when the epitaxial structure is formed, which may change the modulus of constituent layers. This may explain the remarkable hardness enhancement of VC/TiC superlattices. Key words: superlattice films; carbide films; microstructure evolution; superhardness effect; epitaxial growth1 IntroductionHard films have been successfully applied for theprotection of materials and particularly to increase theefficiency and extend the lifetime of cutting tools sincethe 1970s [1]. With the development of modern high-speed cuttings, it is demanded for protective hardfilms that both hardness and wear resistance should becontinuously increased. It was found in 1987 that superlattices deposited alternately by two kinds of materials at nanometer-scale thickness, i.e., superlatticefilms, could exhibit an anomalous increase of hardness ascompared with the monolayer films [2]. Therefore, tosynthesize superlattice films has become an importantapproach to obtain the films with high hardness andexcellent wear resistance.For superlattice films, their constituent layers can bemetal layers, nitrides, carbides or oxides of differentmaterials or a combination of one layer made of nitride,carbide, or oxide of one metal and the second layer madeof another metal [3]. However, less attention has beenpaid to carbide superlattice films compared with thosesuperlattices consisting of nitrides, oxides ormetals [4−8]. Generally, the carbide films have the samecrystal structure as nitride films and even higher hardness, lower friction coefficient and superior wear resistance performance. This supplied an alternative kind of material to obtain the superlattice films with excellent properties. Although some carbide superlattice films, e.g., VC/TiC [9,10], TiC/NbC [11] and VC/SiC [12], have been reported, further studies on the relationshipbetween the microstructure and mechanical properties of these superlattices are still required. For instance, there exist different results regarding whether the superhardness effect can be obtained in the VC/TiCsuperlattices [9,10], indicating that the strengthening mechanism also needs to be further investigated. This study intends to clarify the relationship between the microstructure and the superhardness effect of VC/TiC superlattices. A series of VC/TiC superlattice films with different modulation periods were prepared by magnetron sputtering method. Then, the microstructure and mechanical properties of these superlattice films were investigated. TiC/VC superlattices were chosen in this study for two reasons. First, both TiC and VC have already been applied practically due to their excellent properties. Second, they both exhibit the same structure (NaCl-type) and have smaller lattice mismatch (a VC =0.4160 nm, a TiC =0.4328 nm), which is believed toFoundation item: Project (51201187) supported by the National Natural Science Foundation of China Corresponding author:Jian-lingYUE;Tel:+86-731-88877495;E-mail:*****************.cn DOI: 10.1016/S1003-6326(15)63878-XXue-chao DONG, et al/Trans. Nonferrous Met. Soc. China 25(2015) 2581−2586 2582be favorable to obtaining high hardness increment by forming epitaxial structures.2 ExperimentalVC/TiC superlattices and TiC, VC monolayer films were prepared by SPC−350 multi-target magnetron sputtering system. VC (99.8% in purity) and TiC (99.8% in purity) targets were placed on two radio frequency cathodes, while the metallic Ti target (99.99%) was placed on the DC cathode. Mirror polished stainless steel substrates were ultrasonically cleaned in acetone and absolute alcohol before being mounted on a rotatable substrate holder in the vacuum chamber and the distance between target and substrate was about 5 cm. The base pressure was pumped down to 2×10−4 Pa before deposition. Ar (99.99% in purity), whose pressure was kept at 0.6 Pa, was introduced into the chamber. The VC/TiC superlattice films were prepared at 300 °C by alternating deposition of TiC and VC layers. In order to improve the adhesion, Ti transition layer with 100 nm in thickness was deposited before depositing superlattices.A series of superlattices with different modulation periods but the modulation ratio of about 1:1 were prepared by controlling the target power and the resident time that substrates were exposed to the target. And the VC and TiC monolayers were deposited under the same conditions as that of VC/TiC superlattices. The total thickness of each specimen was about 2 μm.The composition of the films was determined by energy dispersive X-ray spectrometry analysis (EDXA). The microstructures of all the films were characterized by Rigaku D/max−2550/PC X-ray diffraction (XRD) with Cu Kα excitation radiation, and high-resolution transmission electron microscopy (HRTEM) using a Philips CM200−FEG. The hardness (HV) and elastic modulus (E) of all the samples were measured by a Fischerscope H100VP nanoindenter equipped with a Vicker’s indenter and the values for specimen were evaluated by an average of at least 20 measurements.3 Results and discussion3.1 Microstructure of VC/TiC superlattice filmsEDXA results show that the C/Ti mole ratio of the TiC monolayer films is 52.8:47.2, and the C/V mole ratio of the VC monolayers is 47.6:52.4. This indicates that both TiC and VC monolayers in this work are near stoichiometric.The low-angle XRD patterns of the VC/TiC superlattice films with different modulation periods (Λ) are shown in Fig. 1. The low-angle diffraction peaks, which clearly appear to be systematically distributed in the diffraction patterns, can be attributed to the modulation period Λ of the superlattices. This indicates an obvious layered structure for all superlattices. Correspondingly, the modulation period of the superlattices can be figured out from [13]()1sinsin2−−=nnΛθθλ(1)where λ is the X-ray wavelength, θn and θn−1 are the diffraction angles, n is diffraction series. Fitting of the 2θvalues for the diffraction peaks into Eq. (1) resulted in the Λ of superlattices, which are shown in Fig. 1.Fig. 1 Low-angle XRD patterns of VC/TiC superlattices with modulation ratio of 1:1Figure 2 displays the cross-sectional HRTEM image and selected area electron diffraction (SAED) pattern of the VC/TiC (Λ=5.2 nm) superlattice film. The SAED pattern on the top-left corner is indexed as a NaCl-type structure, and the low-magnification image on the bottom-left corner of Fig. 2 clearly shows that this superlattice specimen possesses a well-defined composition modulation structure consisting of VC (dark layers) and TiC (light layers). The high-magnification image on the right side shows that the lattice fringes continuously go through several modulation layers and interfaces. This indicates that the two constituent layers,Fig. 2 Selected area election diffraction (SAED) pattern, low-magnified and high-magnified cross-sectional HRTEM images of VC/TiC superlattice with Λ=5.2 nmXue-chao DONG , et al/Trans. Nonferrous Met. Soc. China 25(2015) 2581−2586 2583VC and TiC, grow coherently each other and the epitaxial structure is therefore formed in this superlattice film.Figure 3 shows the high-angle XRD patterns of the VC/TiC superlattices along with VC and TiC monolayers. As can be seen, NaCl-type VC and TiC monolayer films present relatively broad (111) diffraction peaks. By contrast, the VC/TiC superlattices with modulation period ranging from 1.9 to 12 nm only present one fundamental peak, which is located between TiC (111) and VC (111) peaks and thus can be regarded as VC/TiC superlattice (111) peak. Additionally, when Λ is less than 6.8 nm, the VC/TiC superlattice (111) peaks are much higher and sharper than those of VC or TiC monolayers. With the increase of Λ, the superlattice (111) peaks gradually decrease in the intensity and also broaden. After Λ exceeds 12 nm, the superlattice (111) peaks become quite diffusive and are divided into two peaks, as shown in the local amplification figure on the left side of Fig. 3.Combined with the HRTEM results in Fig. 2, the higher (111) peak intensity of VC/TiC superlattices with Λ less than 6.8 nm compared with that of VC or TiC monolayers, as shown in Fig. 3, indicates that these superlattices form an epitaxial structure and their crystal integrity is greatly improved. Similar phenomena have also been observed in some other superlattice systems such as ZrO 2/TiN [14], VC/AlN [15], HfN/Si 3N 4 [16] and TiAlN/AlON [17], and the corresponding reasons have also been explained from both thermodynamics and kinetics factors of film growth in these studies [14−17].Furthermore, the VC/TiC superlattice (111) peaks are located between the VC (111) and TiC (111) peaks when Λ is lower than 12 nm, which can be attributed to the fact that the two (111) peaks from VC and TiC sublayers in superlattices approach each other and then overlap when the epitaxial structure is formed. Correspondingly, the (111) interplanar spacings (d 111) of TiC and VC sublayers also approach each other. That is, d 111 of VC layers increases along the direction perpendicular to the superlattice interface (out-of-plane), while d 111 of TiC decreases along the same direction. Therefore, it can be inferred that the uniaxial tensile strains in VC and the uniaxial compressive strains in TiC sublayers along the out-of-plane direction are induced from epitaxial structure. When Λ increases to 25.1 and 26.9 nm, the superlattice (111) peaks are divided into two parts, i.e., VC (111) and TiC (111) peaks, suggesting that the strains start to be relaxed in superlattices due to the destruction of epitaxial structure.On the other hand, in order to grow epitaxially on the VC sublayers (a VC =0.4160 nm) in superlattices, the TiC sublayers with bigger lattice constant (a TiC = 0.4328 nm) will be subjected to the biaxial compressive strains in the (111) plane (i.e., parallel to the superlattice interface, in-plane). In contrast, the VC sublayers will be under the biaxial tensile in-plane strains. Combined with the above discussion for the out-of-plane strains in superlattices, the strain states of VC/TiC superlattices with epitaxial structure are shown in Fig. 4. It reveals that when the epitaxial structure is formed in superlattices, three directional strains are generated in the different sublayers, for example, the TiC sublayers are under the biaxial (in-plane) and uniaxial (out-of-plane) compressive strains, while the VC sublayers are under biaxial and uniaxial tensile strains, respectively.3.2 Hardness and elastic modulus of VC/TiCsuperlattice filmsFigure 5 demonstrates the nanoindentation hardness (HV) and elastic modulus (E ) of VC/TiC superlattices as a function of modulation period. The hardness and modulus of VC and TiC monolayers are also shown in Fig. 5. As can be seen, the hardness and modulus ofVC/TiC superlattices can be significantly increasedcompared with VC and TiC monolayers. With theincrease of modulation period (1.9 nm≤Λ ≤ 5.2 nm), the HV and E increase rapidly and reach peak values ofFig. 3 High-angle XRD patterns of VC, TiC monolayer and VC/TiC superlattice filmsXue-chao DONG , et al/Trans. Nonferrous Met. Soc. China 25(2015) 2581−25862584Fig. 4 Strain states in VC /TiC superlattices with epitaxial structureFig. 5 Dependence of hardness and elastic modulus of VC/TiC superlattices on modulation period41.9 GPa and 330 GPa when Λ is 5.2 nm. However, after Λ exceeds 5.2 nm, the HV and E begin to decrease by further increasing Λ and finally tend to be near the rule-of-mixture value.3.3 Strengthening of superlattice filmsSo far, there exist two main theories, the Koehler’s modulus-difference strengthening theory [18] and the alternating-stress strengthening theory [19], which are always used to explain the superhardness effects of superlattices. Both of these theories are based on the model of dislocations being blocked at interfaces.According to the Koehler’s strengthening theory, the modulus difference between two superlattice constituents is the key factor to restrict the dislocations from gliding across the interfaces and thus determine whether the superhardness effect could be obtained in superlattices. The hardness increment (∆H max ) of superlattices compared with the constituent material with lower hardness can be calculated by this theory asA max 3sin =8πRG H mθΔ (2)where θ is the smallest angle between the interface andthe dislocation slip plane of constituent material with smaller elastic modulus; m is the Taylor factor, calculated as 0.3 for TiC and VC [20]; R =(G B −G A )/(G B +G A ), where G A and G B are shear moduli of two constituents, respectively, and G B >G A , G =E /[2(1+υ)] (E is the elastic modulus and υ is the Poisson ratio). Fitting of the elastic modulus of TiC and VC (E TiC =255 GPa, E VC =245 GPa), and υ of 0.25 for TiC and VC [20], and θ of 45° for NaCl-type VC/TiC superlattices into Eq. (1), yields a ∆H max of 0.6 GPa compared with VC monolayer. This value is much lower than the measured ∆H max of about 12.6 GPa in this study, indicating that it is not enough for the Koehler’s strengthening theory to directly explain the hardness enhancement of VC/TiC superlattices.In reference to the alternating-stress theory [19], it is known that when the dislocations go across the interfaces in superlattices, they are resisted not only by the potential barriers coming from the change of line energy of dislocations due to the two different modulus layers (Koehler’s strengthening theory), but also by that from the alternating-stress field. The maximum hardness increase from the alternating-stress field can be estimated asmax max 10τ≅ΔH (3)where τmax =(2/π2)A ηE [21] is the maximum shear stress at the interface; A is the modulation amplifying factor that is closely correlated to structural parameters of superlattices such as modulation period, modulation ratio, roughness and width of interface; E is the weighted average elastic modulus of two constituents of superlattices; and η is the lattice mismatch between two layers of superlattices.Based on the studies from MIRKARIMI et al [22] and SHINN and BARNETT [23], A takes the value of 0.5 for calculation in this study. Using the data of E of TiC and VC, 250 GPa, and η of 0.04 (a VC =0.4160 nm, a TiC =0.4328 nm), we can roughly estimate ∆H max as ~10.1 GPa. However, this estimation is not enough to explain the actual hardness enhancement. It should beXue-chao DONG, et al/Trans. Nonferrous Met. Soc. China 25(2015) 2581−2586 2585noted that even the sum of the hardness increase from the alternating-stress field model and modulus-difference model, 10.7 GPa, is still lower than the measured value (12.6 GPa).Actually, the discrepancy between the estimated value from these two strengthening theories and the actual result is due to approximation made when not considering any changes in the modulus of constituent layers in the superlattices under epitaxial strains. It is noted that the modulus changes have an important influence on the hardness increment based on these two theories. Some studies [24,25] have demonstrated that an applied elastic strain can significantly change the in-plane biaxial modulus of thin films, that is, the biaxial modulus increases with compressive strains, and reduces with tensile strains. As shown in Fig. 5, the remarkable increase of elastic modulus of superlattices is closely related to the epitaxial strains when the modulation period is less than a critical thickness. Thus, the biaxial modulus of TiC sublayers with relatively high modulus in the presence of VC/TiC superlattices should increase, while the corresponding biaxial modulus of VC sublayers with lower modulus should decrease. This leads to the fact that the modulus difference, R, between TiC and VC sublayers in superlattices would be increased under the epitaxial strains. Therefore, the hardness enhancement in VC/TiC superlattices should increase in reference to the Koehler’s strengthening theory as well as the alternating-stress field theory, when taking into account the modulus change of constituent layers coming from the epitaxial strains.According to the (111) peak positions of TiC, VC monolayers and VC/TiC superlattices in Fig. 3, it can be calculated that the out-of-plane compressive strain in TiC sublayers is about 2.5%, and the out-of-plane tensile strain in VC sublayers is about 1.5%. Also, the calculations from Refs. [24,25] revealed that ~2.5% compressive strain could increase the biaxial modulus of materials by about 100%, and about 1.5% tensile strain could lead to 30% decrease in biaxial modulus. It is noted that these calculations agree well with the measured maximum modulus of VC/TiC superlattices, as shown in Fig. 5. If it is presumed that the in-plane strain is equal to the out-of-plane strain in constituent layers, we can accordingly obtain ΔH max of 9.7 GPa by the Koehler’s theory, and 13.8 GPa by the alternating-stress field theory in VC/TiC superlattices. Here, it can be found that the sum of hardness increase from the Koehler’s theory and alternating-stress field theory, 23.5 GPa, seems to be quite competent to explain the actual experimental results in this work.From the present VC/TiC superlattices, it can be deduced that in order to synthesize the superlattices with superhardness effect, the epitaxial structure should be formed primarily. On the other hand, the three- directional strains induced from the epitaxial structures should increase the modulus difference between two constituent layers in superlattices. Otherwise, the superhardness effect could not even be obtained in some superlattice systems with epitaxial structure, for example, our previously reported ZrO2/TiN superlattices [14], in which the modulus difference between two constituent layers was found to be decreased by the epitaxial strains.4 Conclusions1) The VC/TiC superlattices can form an epitaxial structure when the modulation period is less than a critical value (~5.2 nm), resulting in that their hardness and elastic modulus are significantly increased. Further increasing the modulation period, the hardness and elastic modulus of VC/TiC superlattice films gradually decrease to be close to the rule-of-mixture value due to the destruction of epitaxial structure.2) The hardness enhancement of the VC/TiC superlattices is closely related to the three-directional strains, which are induced from the epitaxial structure and may change the interplanar spacing and thus the modulus of constituent layers when the epitaxial structure is formed.3) It is found that when taking into account the modulus change of VC and TiC sublayers in superlattices under the three-directional strains, the remarkable hardness enhancement of VC/TiC superlattices could be interpreted by combining the Koehler’s theory and the alternating-stress field theory.References[1]KANG M S, WANG T G, SHIN J H, NOWAK R, KIM K H.Synthesis and properties of Cr−Al−Si−N films deposited by hybridcoating system with high power impulse magnetron sputtering(HIPIMS) and DC pulse sputtering [J]. Transactions of NonferrousMetals Society of China, 2012, 22(S3): s729−s734.[2]HELMERSSON U, TODOROV A S, BARNETT S A. Growth ofsinglecrystal TiN/VN strainedlayer superlattices with extremely highmechnical hardness [J]. Journal of Applied Physics, 1987, 62(2):481−485.[3]MUSIL J. Hard and superhard nanocomposite coatings [J]. Surface &Coatings Technology, 2000, 125(1−3): 322−330.[4]MARULANDA D M, OLAYA J J, PIRATOBA U, MARIÑO A,CAMPS E. The effect of bilayer period and degree of unbalancing onmagnetron sputtered Cr/CrN nano-multilayer wear and corrosion [J].Thin Solid Films, 2011, 519(6): 1886−1893.[5]SUN P L, SU C Y, LIOU T P, HSU C H, LIN C K. Mechanicalbehavior of TiN/CrN nano-multilayer thin film deposited byunbalanced magnetron sputter process [J]. Journal of Alloys andCompounds, 2011, 509(6): 3197−3201.[6]LAO J J, SHAO N, LI G Y, MEI F H, GU M Y. Mutual promotioneffect of crystal growth in TiN/SiC nanomultilayers[J]. Appl PhysLett, 2005, 86(1): 011902.Xue-chao DONG, et al/Trans. Nonferrous Met. Soc. China 25(2015) 2581−2586 2586[7]KALIARAJ G S, RAMADOSS A, SUNDARAM M,BALASUBRAMANIAN S, MUTHIRULANDI J. Studies of calcium-precipitating oral bacterial adhesion on TiN, TiO2 singlelayer, and TiN/TiO2 multilayer-coated 316L SS [J]. Journal ofMaterials Science, 2014, 49(20): 7172−7180.[8]LI W, LIU P, ZHAO Y S, MA F C, LIU X K, CHEN X H, HE D H.Crystallization of amorphous SiC and superhardness effect inCrAIN/SiC nanomultilayered films [J]. Surface & CoatingsTechnology, 2013, 214: 168−172.[9]HÖGBERG J, BIRCH J, JOHANSSON M P, HUTMAN L,JANSSON U. Deposition of epitaxial transition metal carbide filmsand superlattices by simultaneous direct current metal magnetronsputtering and C60 evaporation [J]. Journal of Materials Research,2001, 16(3): 1301−1310.[10]BELGER A, REIBOLD M, PAUFLER P. Modulus and hardnesschange of silicon and sapphire substrates by TiC/VC multilayercoatings [J]. Materials Sciences and Applications, 2012, 3: 185−194. [11]SEKKAL W, ZAOUI A, SCHMAUDER S. Nanoindentation study ofthe superlattice hardening effect at TiC(110)/NbC(110) interfaces [J].Applied Physics Letters, 2005, 86(16): 163108.[12]LI G Y, LI G Q, YANG D. Li. Microstructure evolution andmechanical properties in VC/SiC nanomultilayers [J]. Applied Surface Science, 2012, 258(24): 9856−9858.[13]KIM C, OADRI S B, SCANLON M R, CAMMARATA R C.Low-dimension structural properties and microindentation studies ofion-beam-sputtered multilayers of Ag/Al films [J]. Thin Solid Films,1994, 240(1−2): 52−55.[14]YUE J L, LIU Y, ZHAO W J, LI G Y. Template-induced coherentgrowth and mechanical properties of ZrO2/TiN nano-multilayers [J].Scripta Materialia, 2006, 60(4): 240−243.[15]LI G Q, LI Y G, LI G Y. Crystallization of amorphous AlN andsuperhardness effect in VC/AlN nanomultilayers [J]. Thin SolidFilms, 2012, 520(6): 2032−2035.[16]LI G Q, LI Y G, LI G Y. Crystallization of amorphous Si3N4 andsuperhardness effect in HfC/Si3N4 nanomultilayers [J]. Applied Surface Science, 2011, 257(13): 5799−5802.[17]LI W, LIU P, WANG J T, MA F C, LIU X K, CHEN X D, HE D H.Investigation on microstructure and mechanical properties of reactively synthesized TiAlN/AlON nanomultilayers [J]. Vacuum, 2012, 86(9): 1300−1304.[18]KOEHLER J S. Attempt to design a strong solid [J]. Physical ReviewB, 1970, 2(2): 547−551.[19]KATO M, MORI T, SCHWARTZ L H. Hardening by spinodalmodulated structure [J]. Acta Metall, 1980, 28: 285−291.[20]CHU X, BARNETT S A. Model of superlattice yield stress andhardness enhancements [J]. Journal of Applied Physics, 1994, 77(9):4403−4407.[21]XU J H. Studies on microstructure and superhardness effects ofceramic nano-multilayer films [D]. Shanghai: Shanghai Jiao TongUniversity, 2000: 79−100. (in Chinese)[22]MIRKARIMI P B, BARNETT S A, HUBBARD K M, JERVIS T R,HULTMAN L. Structure and mechanical properties of epitaxialTiN/V0.3Nb0.7(100) superlattices [J]. Mater Res, 1994, 9: 1456−1463.[23]SHINN M, BARNETT S A. Effect of superlattice layer elasticmoduli on hardness [J]. Appl Phys Lett, 1994, 64: 61−63.[24]JANKOWSKI A F, TSAKALAKOS T. The effect of strain on theelastic constants of noble metals [J]. J Phys F: Met Phys, 1985, 15:1279−1292.[25]CAMMARATA R C, SIERADZKI K. Eff'ects of surface stress on theelastic moduli of thin films and superlattices [J]. Physical ReviewsLetters, 1989, 62(17): 2005−2008.VC/TiC超晶格薄膜的微结构及超硬效应董学超1，岳建岭1,2，王恩青1，李淼磊1，李戈扬31. 中南大学航空航天学院，长沙 410083；2. 中南大学粉末冶金国家重点实验室，长沙 410083；3. 上海交通大学金属基复合材料国家重点实验室，上海 200030摘 要：采用磁控溅射工艺制备VC/TiC超晶格薄膜，并采用EDXA 、XRD、HRTEM和纳米力学探针研究调制周期对超晶格薄膜的微结构和力学性能的影响。
《超晶格A2B7型La-Ce-Y-Ni-Mn-Al储氢合金的设计与性能研究》范文
《超晶格A2B7型La-Ce-Y-Ni-Mn-Al储氢合金的设计与性能研究》篇一一、引言随着人们对能源危机和环境问题的认识不断加深，寻求可替代传统能源的清洁能源成为科学研究的重要方向。
其中，储氢合金作为一种能够储存大量氢气的重要材料，其研究和应用得到了广泛关注。
本篇论文旨在探讨一种新型的A2B7型超晶格La-Ce-Y-Ni-Mn-Al储氢合金的设计及其性能研究。
我们将详细讨论合金的设计理念、合成过程、性能特点及其在新能源技术中的应用。
二、合金设计超晶格A2B7型La-Ce-Y-Ni-Mn-Al储氢合金的设计基于对现有储氢材料性能的深入理解，以及通过元素替代和结构调整来优化其性能的策略。
我们选择了La、Ce、Y作为主要的稀土元素，这些元素在储氢过程中具有较高的活性。
同时，Ni、Mn、Al的加入能够提供良好的结构稳定性和电子特性。
我们设计的合金由两种主要元素组分构成，即A组分和B组分。
A组分主要由稀土元素La、Ce和Y组成，这些元素具有较大的储氢容量和良好的热力学性能。
B组分则主要由过渡金属元素Ni、Mn和Al组成，它们提供了良好的结构支撑和电子传导性。
这种设计既保证了储氢的容量，又提高了合金的稳定性。
三、合成过程合成超晶格A2B7型La-Ce-Y-Ni-Mn-Al储氢合金的过程主要包括原料准备、熔炼、淬火和退火等步骤。
首先，将选定的元素按照设计比例混合成原料，然后在高温下进行熔炼，使元素充分混合并形成均匀的液态合金。
接着进行淬火处理，使液态合金迅速冷却形成固溶体。
最后，通过退火处理来改善合金的微观结构和性能。
四、性能特点本论文主要研究的新型超晶格A2B7型La-Ce-Y-Ni-Mn-Al储氢合金在以下几个方面表现出了良好的性能：首先，本合金的储氢容量大。
由于其具有丰富的活性位点和优秀的晶格结构，能够吸附更多的氢气。
其次，该合金的稳定性好。
其组成元素之间的相互作用以及独特的超晶格结构使得合金在充放电过程中具有较好的稳定性。
自组装纳米结构
一、纳米尺度自组装的体系概述
（2）纳米薄膜磁存储材料有更小的体积，更高的存储密度和更永久的 存储能力。
比如单磁畴Fe、Fe-Co合金和氮化 铁等纳米颗粒具有较高的矫顽力， 用在磁记录介质材料中不仅可以提 高音质和图像的质量，而且还具有 很好的信噪比，磁记录密度比γFe2O3高出几十倍。
一、纳米尺度自组装的体系概述
杨生春 理学院材料物理系
Tel: 82663034 Email: ysch1209@ Web: /web/ysch1209
主要内容
一．纳米尺度自组装的体系概述 二．分子自组装的有序纳米结构薄膜
1. 2. 分子自组装的基本原理 分子自组装的驱动力
S. Griessl, et al. Single Mol., 2002, 3, 25.
氢键驱动形成超分子网络
基于芳烃分子中胺基间形成的氢键自组装形成的网络状结构
氢键驱动形成超分子网络
通过对分子浓度的控制，可由构建出不同的网格结构
M. Stöhr, M. Wahl, C. H. Galka, T. Riehm, T. A. Jung and L. H. Gade, Angew. Chem., Int. Ed., 2005, 44, 7394.
4 nm magnetic particles
一、纳米尺度自组装的体系概述
4. 有序纳米结构薄膜材料在高科技领域中的作用 （1）纳米薄膜传感器具有更小的体积和更高的分辨率
Diarylethene分子修饰的金纳米粒子自组装薄膜开关
S. J. van der Molen et al. , Nano Lett. 2009, 9, 76-80.
由4 nm FePt纳米粒子形 成的自组装薄膜的磁通的 线密度可以达到 5000fc/mm,因而可以获得 更高的磁存储密度，并且 展现出良好的存取特性。
超晶格材料superlattices_(graduate)
表示。 两边同时乘以电子浓度n,同时乘以ab
abneveBabn
于是c有I：cBU H eUHebIbnBnR cHI
这里
RH
B ebnc
B
b G aA s I
AlGaAs a
称为霍耳电阻。 注意到 ns nb 为面电子浓度。
RH
霍RH耳电e阻nBsc与磁感应强度成线性关系。 0,0
成正比,与电子空穴复合所需要的
时间 成反比,即
VnI
这里 V 是结的体积.
与材料性质有关.
四. 半导体超晶格激光器 1.半导体激光的工作原理
空带
空带
h
h
2h
满带
受激吸收过程
满带
受激辐射过程
2. 超晶格激光器
AlGaGAasAAs lGaGAasAAs lGaGAasAAslGaAs GaAs
光子沿平行界面层的方向发射出来。GaA层s又起到 光波导的作用。
于是电流密度为
jvz
Jd
s
ineD tdU
电流强度为
It 应S理v解z 成S电 子Jd 的s迟i豫n e 时D t间d。U 当 这e里tDdS是U界2面面时积，，
电流开始变小。这就解释了为什么当电压超过某一值后
出现负阻的原因。用这种方法，我们还能确定电子迟豫
时间值。 负阻的出现是电子在垂直于界面的方向电子 运动受到超晶格周期场的调制所致。
对d动p量x 的2三Lx个d分nx量d表py达式2L两y边d微ny 分，d然pz后乘2L到z一d起nz
dx d py d pz p2 L x 2 L y 2 L z dx d ny d nzn
dxd nyn dzn L 2 xL yL 3 zdxd pyp dzp
超晶格结构与特性
超晶格结构与特性作者：张海瑞来源：《价值工程》2014年第28期摘要：本文简要论述了半导体超晶格的分类，结构特性，能带结构与应变超晶格，以及它们的发展与应用。
Abstract： This paper briefly discusses the classification， structural characteristics and the band structure of semiconductor superlattice， strained-layer superlattice， and their development and application.关键词：超晶格；结构；类型；特征Key words： superlattice；structure；types；characteristics中图分类号：O431.2 文献标识码：A 文章编号：1006-4311（2014）28-0318-021 超晶格的定义及结构超晶格是指周期性交替生长的两种或多种材料构成的人造晶体。
相邻两层不同材料的厚度合称为超晶格的周期长度，一般来说这个周期长度比各层单层的晶格常数大几倍或更长，因此，这种结构获得了“超晶格”的名称。
下面对半导体超晶格的结构进行简单的介绍。
Ga1-xAlxAs/GaAs半导体超晶格结构是在半绝缘的GaAs衬底上，外延生长GaAs薄层，再在上面交替的生长厚度为几埃甚至上百埃的Ga1-xAlxAs和GaAs薄层而构成的。
掺杂时的Ga1-xAlxAs/GaAs的能带图如图2所示，GaAs的禁带宽度Eg1为1.424eV，Ga1-xAlxAs的禁带宽度Eg2则随组分x而变，其关系为：Eg2=Eg1+1.247x。
两种材料的禁带宽度之差ΔEg为：ΔEg=Eg2-Eg1=1.247x，可见，ΔEg也随Al组分x而变化。
从图2中可以看到，在Ga1-xAlxAs和GaAs的交界处，能带是不连续的，二者的导带底能量差为ΔEc，价带顶能量差为ΔEν，而且ΔEc+ΔEν=ΔEg。
ZnMgO超晶格的结构和光学特性
ZnO/Mg0.2Zn0.8O超晶格的结构和光学特性带隙偏移为0.5ev的ZnO/Mg0.2Zn0.8O超晶格在蓝宝石沉底（方向0001）使用氧化锌缓冲层的激光分子束外延生长而成。
用截面透射电子显微镜，俄歇深度剖析和X -射线衍射验证得该超晶格结构为8nm到18nm。
当井层厚度下降小于5 nm时，光致发光峰和吸收边的光致发光激发光谱显示出蓝移，显示出量子尺寸效应。
氧化锌作为宽禁带氧化物半导体正日益受到人们的注意。
在室温下氧化锌带隙为3.34电子伏特，在紫外线光的发射方面具有潜在应用价值。
我们已经证明光泵ZnO薄膜（由六角形晶体紧密结合在一起的蜂巢结构组成）低阈值(24 kW/cm2）的室温激光行为。
这里有三个有趣的发现。
第一，由激子-激子碰撞引起的受激发射过程，在室温下也会发生，是因为非常大的激子束缚能（60meV）。
第二，当纳米晶的尺寸调整为50nm时，这种受激发射过程的阈值非常低。
第三，纵腔（longitudinal cavity）通过六角形晶体间的晶界（grain boundaries 如同镜子般）自动形成。
最近，我们报告，MgxZn1-xO合金膜可以通过脉冲激光沉积制备，这显示出较高的带隙（最大为x=0.33时的4电子伏特）和相似的晶格常数。
激子重组的激子发射过程能够进一步被加强，如果这种低维结构如同量子井，线，点那样建造。
在这里，我们报告ZnO/Mg0.2Zn0.8O超晶格的结构和光学特性。
从光致发光和光致发光激发光谱中发现量子禁闭效应（quantum confinement Effect）。
MgxZn1-xO超晶格通过激光分子束外延（MBE）即在超真空室内对陶瓷靶进行脉冲激光沉积（期间，利用高能电子衍射的影像进行观察）.阻隔层的Mg组分为x=0.20，相当于在纯净的ZnO异质结面（heterointerface）上0.5ev的带偏移（band offset）。
在沉积过程中，氧气压力保持在1×10-6托。
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于是电流密度为
电流强度为 S J d etdU 这里S是界面面积， I Svz sin D etdU t 应理解成电子的迟豫时间。当 D 2 时， 电流开始变小。这就解释了为什么当电压超过某一值后 出现负阻的原因。用这种方法，我们还能确定电子迟豫
2 dV (r , t ) dV
Vd 内发现电子的概率为:
若粒子在运动过程中能量守恒，波函数可以写成
( x, y, z, t ) ( x , y, z ) T (t )
于是含时间薛定谔方程可以写成
2 [ U ( x, y, z )]( x, y, z ) E( x, y, z ) 2m 称为定态薛定谔方程
GaAs
U
AlGaAs
GaAs AlGaAs GaAs
d 70A0 发现大于2V后 出现负微分电阻。
I (m A)
100
I
50
0,0
1
2
3
4
U (V )
下面解释一下为什么这样？ 按照电流密度的表达式： j vz vz 为电子在 为电荷密度，
I (mA)
100
50
在z轴方向的 运动速度。
于是
ˆ i ( r , t ) H (r , t ) t
2
(r , t ) 表示粒子所处的状态，属微观量
2 * ( r , t ) ( r , t ) ( r , t ) 表示
t
时刻
在空间 r 处单位体积内发现电子的概率.
在体元
AlGaAs
GaAs AlGaAs
GaAs
二.制备方法
1. 分子束外延技术MBE
Molecular beam epitaxy
2. 金属有机化合物汽相沉积技术（MOCVD)
Matal organic compound chemical vapor deposition
三. 超晶格材料性质
以GaAs/AlGaAs超晶格为例
此方程的解可设为：
2 2 2 2 E 2 2 2 2m x y z i
( p x x p y y pz z )
( x, y, z) ( x Lx , y, z)
( x, y, z) ( x, y Ly , z)
2 px nx Lx
2 ny 同理： p y Ly
2 pz nz Lz
动量取离散值
nx n y 0, 1, 2, 3... nz
含时间的波函数为
Ae Ae
i i ( p x x p y y pz z ) Et
（4）.于是得到
i ( x, t ) ( 2 2 2 )( x, t ) U ( x, t ) ( x, t ) t 2m x y z
2 2 2
2
此为薛定谔方程。
i ( x, t ) ( 2 2 2 )( x, t ) U ( x, t ) ( x, t ) t 2m x y z
二. 粒子微观态的三种等价描述
力学量 粒子的状态可以用三种描述：波函数 量子数 以粒子作自由运动为例
2
z
y
电子运动的定态薛定锷方程为：
Байду номын сангаас
2 2 2 2 2 2 E 2 2m x y z
Lz
x
Lx
Ly
Ae 利用周期性边界条件： z
单独GaAs或AlGaAs的能级结构
呈带状。
2
AlGaAs
GaAs
AlGaAs
GaAs
AlGaAs
AlGaAs 层中导带中的电子流入 GaAs 层，该层中的
电子浓度加大，导电性增强。
通过求解薛定谔方程，可解得超晶格材料的电子能带。 其中导带能级表达式为
2 2 2 E J0 (k x k y ) J cos(k z d ) 2m
时间值。 负阻的出现是电子在垂直于界面的方向电子 运动受到超晶格周期场的调制所致。
j vz
Jd
etdU sin D
三.发光二极管 LED (Light-emitting diode) h
空带
n
P
n
h
满带
p
半导体中电子和空穴的复合从而释放出光子来. 电源可以将电子从p型半导体经电源拉到n 型半导体, 增大了电子空穴复合的机会,也就增大了发射出的光子数.
2
t
nx ,ny ,nz
n ,
x
ny , nz nx ,ny ,nz
量子数每取定一组值，就对应一种形式的波函数 也就对应粒子的一个微观态。
n ,
x
ny , nz nx ,ny ,nz
量子数的取值花样个数等于粒子所具有的总的微观态数。 2 2 2 p n pz nz px nx y y Ly L L
GaAs
AlGaAs GaAs AlGaAs GaAs
这里 k x , k y , k z 是三个坐标轴方向
的波矢量分量。它们同动量的关系为
J 0 , J 是两个常数，与原子间电子
云的交叠程度有关。 d 为超晶格的
P k
z
y
周期。
x
二. 超晶格材料的伏安特性 GaAs/AlGaAs超晶格材料 测量电压和电流间的关系。
2 3
波矢空间单位面积内拥有的微观态 Lx Ly 数为 2 2
Ly
Lx
第二节 超晶格材料的伏安特性
一.超晶格材料的能带结构特点
描述电子微观运动的方程-薛定谔方程
GaAs
AlGaAs
GaAs AlGaAs GaAs
2 [ U ( x, y, z)]( x, y, z) E( x, y, z) 2m
2
2 n i 2 n 2 n i 2n x y x z x y z L Lx Ly Lz 2 m x
2n y Ly
2nz Lz
2
（1）在垂直于界面方向电子运动受限。
GaAs
AlGaAs
GaAs AlGaAs GaAs
（2）GaAs层中电子浓度较高，电子
在平行界面方向迁移率较大
v电子速度, E电场强度， 电子迁移率。 （3）界面效应比较明显。 （4）低温时出现量子Hall效应，电子气体出现复杂的相， 如条纹相等。
v E
建立薛定谔方程的步骤： (1).写出能量表达式 1 E Px2 Py2 Pz2 U 2m （2).两边乘以波函数Ψ
1 2 2 2 E Px Py Pz U 2m
（3）.将能量和动量算符化 Px i E i Py i Pz i x t y z
( x, y, z) ( x, y Lz , z)
可得到：
y
Lz Lz
x
Ly
Lx Ly
Lx
Ae
i ( p x x p y y pz z )
Ae
i p x ( x Lx ) p y y pz z )
1 e
i p x Lx
p x Lx 得到： 2n x
AlGaAs GaAs AlGaAs GaAsAlGaAs AlGaAs GaAs
GaAs
层又起到 光子沿平行界面层的方向发射出来。 GaAs
光波导的作用。
第三节 量子霍耳（Hall）效应
B
一. 经典霍耳效应 用一个周期来分析
1879年霍耳（A.H.Hall） 发现：在匀强磁场中通电 的金属导体板或半导体板 的两个侧面出现横向电势 差，这一现象称为霍耳效应 实验发现：
2
3
dpx dpy dpz
px px dpx py py dpy pz pz dpz
内粒子具有的微观态数 Lx Ly Lz dN dnx dny dnz dpx dpy dpz 3 2 由于 px kx , py k y , pz kz
2 2 2 dpz dnz dpx dnx dpy dny Lz Lx Ly 对动量的三个分量表达式两边微分，然后乘到一起 2 2 2 dpx dpy dpz dnx dny dnz Lx Ly Lz
x
z
dnx dny dnz
这是动量区间
Lx Ly Lz
2 2 2
2
2 或写成 i ( r , t ) [ U ( r , t )] (r , t ) t 2m 2 2 2 2 2 2 2 这里 x y z 2 2 ˆ 令 H U (r , t ) 称为粒子的哈密顿量 2m
四. 主要应用 （1）场效应管, (2) 激光器工作物质，（3）传感器 （4）光波导, （5）自旋电子器件. 由于这种材料作成的器件主要靠电子工作，量子效应 起主要作用。所以下面的内容，先简单介绍一下量子 力学知识，然后介绍超晶格的伏安特性和量子Hall 效应
第一节 量子力学简介
量子力学用来描述微观粒子在小尺度(〈0.1m)内运动， 已经成为材料科学和高技术的基础理论。半导体器件、 激光器的工作原理都源于量子力学。超晶格材料的物性 也需要用量子力学知识来解释。 一. 量子力学方程-薛定谔方程
超晶格材料
参考文献：
冯澎
夏建白：超晶格物理，（科学出版社，1995）。 李铭复：半导体物理学， （科学出版社，1991）。
引言
超晶格材料