Thickness Modulation Research Articles

Exploring the effect of dielectric screening on neutral and charged-exciton properties in monolayer and bilayer MoTe2

Dielectric engineering of heterostructures made from two-dimensional van der Waals semiconductors is a unique and powerful tool to tailor the electric and optical band gaps solely via the dielectric environment and the crystal thickness modulation. Here, we utilize high quality MoTe2 monolayer and bilayer crystals as a candidate for near-infrared photonic applications. The crystals are exfoliated on various technologically relevant carrier substrates: silicon/silicon dioxide, poly(methyl methacrylate), hexagonal boron nitride, silicon carbide, and silicon nitride. These substrates provide a large range of high frequency dielectric constants from 2.1 to 7.0 for MoTe2-containing heterostructures. We assess the relationship between the environmental dielectric function and Coulomb screening by combining detailed spectroscopic measurements, utilizing low-temperature and high-spatially resolved photoluminescence and contrast reflectivity, with microscopic many-body modeling, to explore the potential of this less-recognized material platform for applications in optoelectronics at photon wavelengths above 1 μm. We observe a redshift of the optical gap emission energy from the monolayer to bilayer regime on the order of 30 meV. Furthermore, the thickness controlled shift is slightly larger than the one induced by the local dielectric environment, which ranges on the order of 20 meV for the MoTe2 monolayers and on the order of 8 meV for the MoTe2 bilayers. We also show that the local dielectric screening barely affects the trion binding energy, which is captured by our microscopic model, accounting for the screened Coulomb potential for the heterostructures.

Tuning the mechanical properties of Mo-W alloyed Ni-based multilayered films upon post-annealing at 600 °C via modulation of individual layer thickness

Ni-based multilayered film is attractive due to its high good thermal conductivity, oxidation resistance and mechanical properties. However, the influence of individual layer thickness on the microstructure thermal stability and mechanical properties have seldom been investigated. Hence, the 5 at.% Mo and 5 at.% W co-added in Ni/NiAl multilayers with individual layer thicknesses ranging from 10 nm to 160 nm were synthesized using co-sputtering. Upon post-annealing at 600 °C, the phase separation of γ-Ni solid solution in multilayer occurs, precipitating dispersed nano-sized α-W phases in major when individual layer thicknesses are lower than 40 nm. The periodical layer interfaces of these multilayers are maintained with excellent thermal stability. The hardness of multilayer is enhanced with reduction of individual layer thicknesses due to grain boundary relaxation, increased layer interfacial barriers and W-related precipitations as obstruction for dislocations movement, showing anneal hardening significantly. Due to crack deflection at the layer interfaces, less brittle W-relative phase precipitation and bare columnar crystals growth, the superior toughness is achieved for 600 °C annealed multilayer with individual layer thicknesses of 40 nm. Therefore, 5 at.% MoW co-alloyed Ni-based multilayer are suitable for high-temperature applications with excellent mechanical properties by modulation of individual layer thicknesses.

Crystallinity and thickness modulation of polymeric carbon nitride by dual-functional lithium ions for boosting photocatalytic H2O2 production

The production of H2O2 through photocatalysis is a green and economical alternative to conventional methods. Here, we prepared poly (heptazine imide) (PHI) phase polymeric carbon nitrides (Li-PCN) by facile lithium ions-assistant post-condensation method. Lithium ions not only can optimize condensation process, but also exfoliate and tailor PCN, resulting in higher crystallinity, excellent photo-absorption range, which enhance surface adsorption of dioxygen, and increase the number of electron transfers in the reaction. Based on the above advantages, the Li-PCN exhibits excellent photocatalytic H2O2 (2680 μmol g-1h−1) production activity under visible light, which was about 35.7 times higher than that of PCN. Besides, we have increased the concentration of H2O2 through changing reaction solution to a final content of 4.8613 mM. Furtherly, the homemade H2O2 production was used to degrade methyl orange pollution by Fenton reaction. This work provides a new synthetic route to PHI and highlights the function of lithium ions, which can promote the development of more efficient photocatalysts for H2O2 production.

The influence of device structure on resistance switching in PbS QDs film inserted RRAM

The introduction of PbS QD (quantum dot) films has been proved, dramatically, to optimize the resistive switching (RS) performance in oxide resistive random access memory. In order to optimize parameters to a greater extent, the necessity of in-depth understanding of the resistance switching mechanism is self-evident. In this paper, PbS QD layers were inserted into a Ta/AlOxNy/Pt structure device in different positions in order to investigate the influence of the device structure in the PbS QD film inserted device. The Ta/PbS QDs/AlOxNy/Pt device with a Ta anion reservoir and a PbS QD film anion reservoir in the same direction exhibits excellent optimization of parameters, which is ideal for low-power devices. A model is constructed to elaborate the resistive switching process. Moreover, modulation of PbS QD film thickness on RS has been studied. A device with middle thickness of the PbS QD films combines low voltage, low current, and excellent stability, which is believed to be a favorable structure for the PbS QD inserted device.

Investigating the strain controlled epitaxial growth of Mn3Ge films through thickness modulation

Mn3Ge, a typical member of the Heusler family, has a high spin polarization and large spin Hall angle, making it a potential material for spintronic devices. Regarded as a topological Weyl semi-metal, Mn3Ge could be applied in topological spintronics owing to its special Fermi-arc-type surface states and various spin transport properties. In this study, we grew high-quality perpendicularly magnetized Mn3Gefilms through magnetron sputtering. X-ray diffraction (XRD) showed that hexagonal antiferromagnetic Mn3Ge was mixed with tetragonal ferromagnetic Mn3Ge. Thickness-dependent double-phase Mn3Ge films with large magnetic anisotropy and robust anomalous Hall effect (AHE) were obtained. The triangular spin structure of hexagonal Mn3Ge enhances the AHE; however, it shrinks the coercivity of the tetragonal ferromagnetic property. This manipulation of coexisting multi-phases comes from the strain of the substrate during growth, achieved by controlling the film thickness. Structural, magnetic, and transport measurements demonstrated stress modulation of the defect pinning, magnetic anisotropy, and spin transport properties. The coexistence of antiferromagnetic and ferromagnetic Mn3Ge provides the possibility of a new generation of Mn3X-based devices for applications in spin-torque memories.

Machine Learning Approach to Delineate the Impact of Material Properties on Solar Cell Device Physics.

In this research, solar cell capacitance simulator-one-dimensional (SCAPS-1D) software was used to build and probe nontoxic Cs-based perovskite solar devices and investigate modulations of key material parameters on ultimate power conversion efficiency (PCE). The input material parameters of the absorber Cs-perovskite layer were incrementally changed, and with the various resulting combinations, 63,500 unique devices were formed and probed to produce device PCE. Versatile and well-established machine learning algorithms were thereafter utilized to train, test, and evaluate the output dataset with a focused goal to delineate and rank the input material parameters for their impact on ultimate device performance and PCE. The most impactful parameters were then tuned to showcase unique ranges that would ultimately lead to higher device PCE values. As a validation step, the predicted results were confirmed against SCAPS simulated results as well, highlighting high accuracy and low error metrics. Further optimization of intrinsic material parameters was conducted through modulation of absorber layer thickness, back contact metal, and bulk defect concentration, resulting in an improvement in the PCE of the device from 13.29 to 16.68%. Overall, the results from this investigation provide much-needed insight and guidance for researchers at large, and experimentalists in particular, toward fabricating commercially viable nontoxic inorganic perovskite alternatives for the burgeoning solar industry.

Interfacial‐Modulated Growth of Nanostructured Bi2Te3 Films for Enhancing Thermoelectric Performance

Little room remains for further reducing lattice thermal conductivity (κL) which cannot be reduced below the amorphous limit. Further improvements in the thermoelectric (TE) figure of merit should rely on enhancing the TE power factor (PF) with low electrical thermal conductivity (κe). Layered Bi2Te3 exhibits anisotropic TE properties and modulation of its growth behavior can effectively modify the transport of electrons and phonons and thus enhance its TE properties. Herein, Bi2Te3 films are grown by molecular beam epitaxy with the modulation of substrates, seed layer, and thickness. The nanopillars‐dominated film without seed layer changes to nanoplates dominated after the seed layer is predeposited, and the grain size ratio of the (006)/(015) plane increases. The room temperature PF of the stoichiometric Bi2Te3 grown on SiO2 with seed layer reaches 34 μW cm−1 K−2 with a low κe of 0.39 W m−1 K−1. This strategy can be applied in other layered materials with specific growth behavior and properties for nano–micro devices.

Pressure-Induced Superconductivity in HgTe Single-Crystal Film.

HgTe film is widely used for quantum Hall well studies and devices, as it has unique properties, like band gap inversion, carrier‐type switch, and topological evolution depending on the film thickness modulation near the so‐called critical thickness (63.5 Å), while its counterpart bulk materials do not hold these nontrivial properties at ambient pressure. Here, much richer transport properties emerging in bulk HgTe crystal through pressure‐tuning are reported. Not only the above‐mentioned abnormal properties can be realized in a 400 nm thick bulk HgTe single crystal, but superconductivity is also discovered in a series of high‐pressure phases. Combining crystal structure, electrical transport, and Hall coefficient measurements, a p‐n carrier type switching is observed in the first high‐pressure cinnabar phase. Superconductivity emerges after the semiconductor‐to‐metal transition at 3.9 GPa and persists up to 54 GPa, crossing four high‐pressure phases with an increased upper critical field. Density functional theory calculations confirm that a surface‐dominated topologic band structure contributes these exotic properties under high pressure. This discovery presents broad and efficient tuning effects by pressure on the lattice structure and electronic modulations compared to the thickness‐dependent critical properties in 2D and 3D topologic insulators and semimetals.

Dual-channel asymmetric convolutional neural network for an efficient retinal blood vessel segmentation in eye fundus images

The morphological properties of retinal vessels are closely related to the diagnosis of ophthalmic diseases. However, many problems in retinal images, such as complicated directions of vessels and difficult recognition of capillaries, bring challenges to the accurate segmentation of retinal blood vessels. Thus, we propose a new retinal blood vessel segmentation method based on a dual-channel asymmetric convolutional neural network (CNN). First, we construct the thick and thin vessel extraction module based on the morphological differences in retinal vessels. A two-dimensional (2D) Gabor filter is used to perceive the scale characteristics of blood vessels after selecting the direction of blood vessels; thereby, adaptively extracting the thick vessel features characterizing the overall characteristics and the thin vessel features preserving the capillaries from fundus images. Then, considering that the single-channel network is unsuitable for the unified characterization of thick and thin vessels, we develop a dual-channel asymmetric CNN based on the U-Net model. The MainSegment-Net uses the step-by-step connection mode to achieve rapid positioning and segmentation of thick vessels; the FineSegment-Net combines dilated convolution and the skip connection to achieve the fine extraction of thin vessels. Finally, the output of the dual-channel asymmetric CNN is fused and coded to combine the segmentation results of thick and thin vessels. The performance of our method is evaluated and tested by DRIVE and CHASE_DB1. The results show that the accuracy (Acc), sensitivity (SE), and specificity (SP) of our method on the DRIVE database are 0.9630, 0.8745, and 0.9823, respectively. The evaluation indexes Acc, SE, and SP of the CHASE_DB1 database are 0.9694, 0.8916, and 0.9794, respectively. Additionally, our method combines the biological vision mechanism with deep learning to achieve rapid and automatic segmentation of retinal vessels, providing a new idea for diagnosing and analyzing subsequent medical images.

Modulation effect on mechanical properties of nanolayered MoN/MoSiN coatings

The combination of molybdenum nitride, MoN, and molybdenum silicon nitride, MoSiN, to be a naolayered MoN/MoSiN film was developed by the reactive radio frequency, r.f., magnetron sputtering system. The MoN and MoSiN building layers were designed and fabricated with a crystalline and an amorphous/nanocrystalline feature, respectively. The effect of thickness modulation of the c-MoN and a-MoSiN layers on microstructure and mechanical properties of the MoN/MoSiN coatings were investigated. With a fixed 50.0 nm crystallines MoN building layer, the amorphous/nanocrystalline MoSiN building layer with a designed thickness of 25.0 nm would suppress the continuous growth of crystalline phases. For mechanical characterization, the change in modulation did not lead to significant influence on hardness and Young's modulus. When a large thickness ratio of c-MoN/a-MoSiN was applied, phenomenal increase in scratch and wear resistance was observed due to higher volumetric ratio of hard crystalline MoN layer and discontinuity of crystalline phase growth through building layers in the nanolayered MoN/MoSiN coatings.

Telluride Nanocrystals with Adjustable Amorphous Shell Thickness and Core-Shell Structure Modulation by Aqueous Cation Exchange.

Engineering the structure of core-shell colloidal semiconductor nanoparticles (CSNPs) is attractive due to the potential to enhance photo-induced charge transfer and induce favorable optical and electronic properties. Nonetheless, the sensitivity of telluride CSNPs to high temperatures makes it challenging to precisely modulate their surface crystallinity. Herein, we have developed an efficient strategy for synthesizing telluride CSNPs with thin amorphous shells using aqueous cation exchange (ACE). By changing the synthesis temperature in the range of 40-110 °C, the crystallinity of the CdTe nanoparticles was controllable from perfect crystals with no detectable amorphous shell (c-CdTe) to a core-shell structure with a crystalline CdTe NP core covered by an amorphous shell of tunable thickness up to 7-8 nm (c@a-CdTe). A second ACE step transformed c@a-CdTe to crystalline CdTe@HgTe core-shell NPs. The c@a-CdTe nanoparticles synthesized at 60 °C and having a 4-5 nm thick amorphous shell exhibited the highest surface-enhanced Raman scattering activity with a high enhancement factor around 8.82 × 105, attributed to the coupling between the amorphous shell and the crystalline core.

Improvement in carrier mobility through band-gap engineering in atomic-layer-deposited In-Ga-Zn-O stacks

This paper reports the performance improvement of heterojunction channel field-effect transistor using an atomic-layer-deposited InGaZnO (IGZO) channel on basis of a band alignment. The heterojunction stack consisted of a 5 nm-thick In0.61Ga0.16Zn0.23O confinement layer (CL) and a 2 nm-thick In0.52Ga0.32Zn0.15O barrier layer (BL). Band-gap engineering through cation composition and thickness modulation of each layers allowed free electron diffusion from the In0.52Ga0.32Zn0.15O BL to the In0.61Ga0.16Zn0.23O CL and carriers confinement in CL, leading to the improvement in field-effect mobility. The control transistor with 5 nm-thick IGZO CL layer had a mobility of 33.4 cm2/Vs, whereas the heterojunction transistor with 2 nm-thick IGZO BL exhibited a higher mobility of 50.7 cm2/Vs as well as low gate swing of 89 mV/decade as a result of carrier transporting boosting. Moreover, the corresponding heterojunction channel transistors exhibited better gate bias stability due to the mitigation of gap states creation and passivating behavior by introducing the 2 nm-thick IGZO BL.

Thickness modulations enable multi-functional spin valves based on Van der Waals hetero-structure

Spintronic devices serve as important components of the next-generation large scale integrated circuits, but until today, spintronic devices of different kinds can only be realized by using different materials and structures, methods of controlling device properties and realizing different functions of devices are still wanted. Here, we report on the first realization of spin valves with three distinct magnetoresistance behaviors in a single hetero-structure of Fe3GeTe2 (FGT)/Nb-doped MoS2 (MoS2: Nb)/FGT by varying the thickness of the sandwiched MoS2: Nb layer. We propose a possible scenario for the spacer layer’s functions and corresponding mechanisms of three different types of spin valves, where the MoS2: Nb layer works as a tunneling barrier, a spin-filter, and a spin potential keeper, respectively. This work demonstrates a novel and promising method for controlling the spin valve properties and functions in a single material and structure system, which significantly benefits the integration of spin devices on a single micro-chip. More importantly, we propose a novel method to tune the properties of different types of spintronic devices.

Two-Dimensional Semiconductor Heterojunctions for Optoelectronics and Electronics

Two-dimensional (2D) layered semiconductors are current research hotspots on account of their wide variety of applications in electronics and optoelectronics due to their particular ultrathin nature. In this review, the band alignment engineering in heterojunctions composed of 2D van der Waals (vdW) layered semiconductors and their device applications in optoelectronics are provided. Various approaches that induced adjustability of vdW heterojunctions are summarized, mainly including composition and thickness modulations, strain, and electric fields. Furthermore, their perspectives on future developments in optoelectronics and electronics devices based on the newly unique physical and chemical properties are outlined.

Low power multilevel resistive switching in titanium oxide-based RRAM devices by interface engineering

The stochastic nature of conductive filament formation and dissolution always leads to large fluctuations of key device parameters that hinder the practical applications of resistive random-access memories (RRAMs). Here, we report a simple bilayer oxide-based device structure of Al/TiOx/TiOy/FTO (x < y) employed to address this variability issue and improve the overall performance of the memory device. The bipolar resistive switching performance remarkably improved in these bilayer devices with lower forming voltage (~1 V), set/reset voltages of 0.4/-0.6 V, a programming current of 10 μA, an enlarged ON/OFF ratio (>103), longer retention (>103 s), and better uniformity as compared to the control Al/TiOy/FTO device. Moreover, the modulation of TiOx layer thickness enables tunability of switching voltages, currents, and the resistance window. In addition, reliable and reproducible multiple resistance states, more specifically different low resistance states, can be achieved in bilayer devices by controlling the programming current down to 10 μA, which is in contrast to the binary states of the control devices. These improved switching parameters with multilevel storage capability in bilayer devices are attributed to the incorporation of an oxygen vacancy-rich interfacial layer, namely TiOx, which serves as an oxygen vacancy reservoir and facilitates effective conductive filament formation inside the switching layer. Furthermore, the thermodynamics involving the dielectric constant and Gibb's free energy of oxide formation at the Al/TiOx and TiOx/TiOy interfaces play a pivotal role in the associated switching mechanism. The spatial variability of the operating voltage across these devices is found to be as low as 8%. These findings pave the way for low power, low cost, and high density data storage applications.

Heterostructural tailoring of blue ZnSeTe quantum dots toward high-color purity and high-efficiency electroluminescence

Ternary ZnSeTe quantum dots (QDs) are regarded as the most promising non-Cd blue emitters, which can be exploited for the fabrication of self-emissive QD display device or QD-light-emitting diode (QLED). We report extensive synthesis of high-quality blue ZnSeTe QDs with a double shell scheme of ZnSe inner and ZnS outer shell in a unique two-step approach. In such ZnSeTe/ZnSe/ZnS heterostructure, the thickness modulation of ZnSe inner shell leads to the variations in not only the thickness of ZnS outer shell but Photoluminescence (PL) characteristics such as peak wavelength, color purity-associated bandwidth, and Quantum yield (QY). The Te/Se ratio in ZnSeTe core is precisely tailored to demonstrate moderate PL tunability in deep-blue territory and the thickness of ZnS outer shell is further independently varied to examine its effects on the performance of QLED. All the QDs that possess outstanding PL QYs up to near-unity (96%) along with an appropriate deep-blue emissivity are individually employed for solution-processed QLED fabrication. The resulting blue QLEDs produce high electroluminescence performances in the ranges of 6107–12654 cd/m2 in luminance and 5.3–18.6% in external quantum efficiency, depending on ZnSe inner, ZnS outer shell dimensions and ZnSeTe core composition.

Deformable and Robust Core–Shell Protein Microcapsules Templated by Liquid–Liquid Phase‐Separated Microdroplets

AbstractMicrocapsules are a key class of microscale materials with applications in areas ranging from personal care to biomedicine, and with increasing potential to act as extracellular matrix (ECM) models of hollow organs, tissues, or biomolecular condensates. Such capsules are conventionally generated from non‐ECM materials including synthetic polymers. Here, robust microcapsules with controllable shell thickness from physically‐ and enzymatically‐crosslinked gelatin are fabricated, and a core–shell architecture is achieved by exploiting a liquid–liquid phase‐separated aqueous system in a one‐step microfluidic process. Microfluidic mechanical testing reveals that the mechanical robustness of thicker‐shell capsules could be controlled through modulation of the shell thickness. Furthermore, the microcapsules demonstrate environmentally‐responsive deformation, including buckling driven by osmosis and external mechanical forces. A sequential release of cargo species is obtained through the degradation of the capsules. Stability measurements show the capsules are stable at 37 °C for more than 2 weeks. Finally, through gel–sol transition, microgels function as precursors for the formation of all‐aqueous liquid–liquid phase‐separated systems that are two‐phase or multiphase. These smart capsules that can undergo phase transition are promising models of hollow biostructures, microscale drug carriers, and building blocks or compartments for active soft materials and robots.

Discrete wavelengths observed in electroluminescence originating from Al1/2Ga1/2N and Al1/3Ga2/3N created in nonflat AlGaN quantum wells

When nonflat Al x Ga1−x N quantum wells (QWs) for producing 285 nm light emitting diodes (LEDs) were fabricated on n-AlGaN on AlN templates with dense macrosteps on c(0001) sapphire substrates with a 1.0° miscut relative to the m[1–100] axis, composite electroluminescence (EL) spectra from both inclined and terrace zones in Al x Ga1−x N QWs (x∼ 1/3) were generated owing to compositional and thickness modulations. The shoulder or main peaks in composite EL spectra tended to locate at fixed discrete wavelengths of ∼287, ∼292, and ∼296 nm from 12 nonuniform 285 nm LED wafers that were involved in nonnegligible run-to-run drift, even though these wafers were fabricated using the same source gas flow parameters for metal-organic vapor phase epitaxy. The discrete wavelengths of ∼287, ∼292, and ∼296 nm were attributed to EL from Al1/3Ga2/3N QWs with thicknesses of 8, 9, and 10 monolayers (ML), respectively, by referring to the results of cathodoluminescence (CL) analysis. Also, when nonflat Al x Ga1−x N QWs (x∼ 1/2) for 265 nm LEDs were grown, single-peak-like EL spectra were mainly generated from the inclined zones in nonflat QWs. The EL spectra taken from four nonuniform 265 nm LED wafers tended to show weak structures or main peaks at ∼257, ∼261, ∼266, and ∼271 nm, which were also attributed to emissions from Al1/2Ga1/2N QWs with thicknesses of 5, 6, 7, and 8 ML, respectively, by referring to CL analysis results. The creation of Al1/3Ga2/3N and Al1/2Ga1/2N in nonflat QWs in this work was in agreement with the results of our previous studies that indicated the creation of metastable Al n /12Ga1−n/12N (n: consecutive natural numbers). Furthermore, QW thicknesses of consecutive n ML may imply that Al1/3Ga2/3N and Al1/2Ga1/2N have 1 ML configurations of Al and Ga atoms on a c(0001) plane.

Solution process of selective color-gamut perovskite solar cell modulated with organic Fabry-Perot electrode for building-integrated photovoltaic

The modulation of the organic Fabry-Perot electrodes was considered to develop the selective color-gamut perovskite (PVK) solar cells, and the solution-based processes were used to develop large, rapid and economic colorful solar cells referred to as building-integrated photovoltaic (BIPV) systems. An planar p-i-n perovskite solar cell structure of ITO/PEDOT:PSS/PVK/PCBM/Ag/PCBM/Ag were synthesized with different precursor concentrations ranging from 0.75, 1, 1.25, 1.5, to 1.75 M. The selective color-gamut for Fabry-Perot electrodes was simulated with different thickness of n-type PCBM and p-type PEDOT:PSS. The results showed that the surface coverage increased from 48.91% to 54.47% when the precursor concentration increased from 0.75 to 1.5 M. However, the surface coverage reduced to 47.05% when the precursor concentration was 1.75 M. The color gamut of the PCBM cavity was more reddish than that of PEDOT:PSS cavity in the CIE1931 colorimetric diagram, and the color gamut could be modulated with blue and green colors for PCBM and PEDOT:PSS cavities, respectively. Interestingly, although p-type PEDOT:PSS causes danger to the hydrolysis, n-type PCBM is suitable for spin coating, and the conversion gain could be enhanced to 122, 118 and 123% for the brown, yellow and red colors, respectively. • Solution process of selective color perovskite solar cell for building-integrated photovoltaic (BIPV). • The selective color was made by organic Fabry-Perot electrode. • Thickness modulation by n-type PCBM and p-type PEDOT:PSS cavities. • Color gamut of PCBM was reddish than that of PEDOT:PSS in CIE1931 diagram.

Generation of adjustable femtosecond double pulses by diffraction of a chirped femtosecond pulse from volume Bragg gratings

Based on Kogelnik’s coupled wave theory, femtosecond double pulses with adjustable pulse shape and interval are generated by diffraction of a chirped femtosecond pulse from transmitted volume Bragg gratings (VBGs). It is found that duration of the diffracted double pulses depends on the chirped parameter of the incident femtosecond pulse. When the chirp parameter is larger than zero, the double pulses are compressed. However, when it is less than zero, the double pulses are broadened. The degree of compression and broadening of the double pulses are different from each other. Moreover, the pulse interval between the double pulses is determined mainly by thickness and refractive index modulation of the VBG. This paper provides a theoretical foundation to design proper VBGs for generating femtosecond double pulses with different waveform.