Abrupt Change of Bandgap Energy in Quantum System of Nanolayer on Silicon Surface

In the quantum system of nanolayer (NL) on silicon, the bandgap energy obviously increases with decreasing thickness of NL, in which the quantum connement (QC) effect plays a main role. In simulating calculation, the QC effect has been exhibited as the thickness of Si NL changes along with (100), (110) and (111) direction respectively. And the simulation result demonstrated that the direct bandgap can be obtained as the NL with (001) direction is thinner than 10nm on Si surface. However, it is discovered in the simulated calculation that the QC effect disappears as the NL thickness arrives at size of monoatomic layer, in which its bandgap sharply deceases, where the abrupt change effect in bandgap energy occurs near idea 2D-layer. In experiment, we fabricated the Si NL structure by using electron beam irradiation and pulsed laser deposition methods, in which a novel way was used to control the NL thickness by modulating irradiation time of electron beam. The new effect should have a good application on optic-electronic chip of silicon.


Introduction
The nanostructures have been stud ied, mainly involving nanoparticle, nanowire and nanolayer in the past decade [1][2][3][4][5]. Especially, scientists have made an attention to the nanolayer (NL) structure due to its unique properties and applications [6][7][8][9][10][11][12][13]. Recently, in the quantum system of Si NL, some interesting phenomena and new effects have been discovered. In last few years, scientists have invested strong effort to growth of 2D silicon material [14,15], which was expected to have a great impact on the development of future electronic devices and energy storage [16][17][18]. The molecular dynamics simulation was used to study the formation of double-layer silicon in slit pores, where their stability is further con rmed by rst principles calculation in the simulated calculation [19,20].
Here, it is interesting that the quantum con nement (QC) effect play a main role as the NL thickness is larger than 0.5nm. The energy bandgap obviously increases with decreasing thickness of NL by the QC effect in the quantum system of NL on silicon. In the article, the QC effect has been exhibited as the thickness of Si NL changes along with (100), (110) and (111) direction respectively in simulating calculation. And the simulation result demonstrated that the direct bandgap can be obtained as the NL diameter is smaller than 10nm in NL with (001) direction on Si surface. However, the bandgap energy of the NL changes in complicated ruler as the NL reaches to 2D Si material, where a new effect takes place on the energy change of NL bandgap. The bandgap energy in quantum system of NL on silicon surface abruptly changes as the NL is near 2D structure. It is discovered in the simulated calculation that the QC effect disappears as the NL thickness arrives at size of monoatomic layer, in which its bandgap energy sharply deceases where the abrupt change effect of bandgap energy occurs.

Fabrication of silicon nanolayer
Scientists usually used the self-assembly ways from silicon-rich silicon oxide matrices and plasma synthesis methods to fabricate various silicon nanostructures [21-27]. Here, the interesting method for fabricating silicon nanocrystal is growth under laser photons interaction [28][29][30]. We have taken the interesting and simplest method for fabricating silicon nanolayer (NL), in which Si NL crystal rapidly grows with irradiation of electron beam on amorphous silicon lm prepared by using pulsed laser deposition (PLD). The novel method of electron affection could be used to replace the traditional annealing methods in preparing process of silicon nanocrystals [31].
The coherent electron beam with 0.5 nA/nm 2 was used to irradiate on amorphous silicon lm for 10-30min in Tecnai G2 F20 system, in which the electron beam from eld-emission electron gun was accelerated by 200 KV and had higher energy and better coherent, where the silicon nanolayers with various thickness rapidly grew. The TEM image exhibits a geometry top viewed on the Si nanolayer as shown in Fig.1. Truly interesting, the several structures of silicene with quasi-2D lm were obtained through controlling irradiation time and density of the coherent electron beam, which are respectively related to growing along with (100), (110) and (111) direction.

Investigation on Si nanolayer in simulation
The dynamic stability of the nanolayer was investigated by using rst-principles calculations with consideration of three kinds of crystal structures observed in experiment, in which the crystal lattice grows respectively along with (100), (110) and (111) direction. The electronic behavior on the Si nanolayer was investigated by an ab initio nonrelativistic quantum mechanical analysis. The density functional theory (DFT) was used to calculate the density of states (DOS) on silicon nanolayers, which is carried out with the local density approximation (LDA) and gradient-corrected exchange-correlation function (GGA) for the self-consistent total energy methods.
It is interesting in the total energy calculations using DFT that the transformation from the indirect bandgap to direct bandgap can be obtained as the nanolayer thickness is smaller than 10nm, wholes simulated model of NL structure along with (001) direction and its direct bandgap are shown in Fig.2

(a)
and (b) after simulated calculation. It is originated from the Heisenberg principle related to ⊿hK x h/⊿x, in which the wave vector will relax from X region to Γ region as the ⊿x decreases to nanoscale (relaxing relation: ⊿x↓ →⊿K x ↑), where higher electronic speed is obtained in nanolayer.
In the experimental result, the nanolayer of silicon crystal growing along with (100) direction was prepared, as shown in Fig.3(a), where the TEM image exhibits its structure. In the simulated calculation, the DMol3 mode is used to make optimum atomic structure for obtaining the lowest combining energy, and the CASTEP mode is used to simulate for obtaining the energy band structure after optimum process. In Fig.3(b), the simulation model of the Si nanolayer has been built along with (100) direction according to the experimental result. After optimization process in simulation, the quasi-2D structure of silicon crystal with the rectangular lattice occurs in the lowest energy of optimum structure, as shown in Fig.3(c). The structural transformation from the ideal model of 2D structures to the optimal quasi-2D structures of Si crystal along with (100) direction should be noted in the simulation process, where the convex bonding angles take place on silicon lm. The Fig.3(d) exhibits the change curve of bandgap energy with various thicknesses of Si NL along with (100) direction in the simulation result, where it is interesting that the quantum con nement (QC) effect plays a main role as the nanolayer thickness is lager, but the QC effect disappears as the nanolayer thickness is smaller than 0.4nm near monoatomic layer, when its bandgap energy abruptly decreases. Truly interesting, the QC effect disappears as the nanolayer thickness reaches to size of monoatomic layer, where its bandgap sharply deceases. This abrupt change effect in bandgap energy may be originated from transforming between different dimensions at the symmetry broken point, in which the quasi-2D shape of NL is transformed to the two dimensional quantum layer. Here, the abrupt change effect in bandgap energy was observed and studied at rst.
The nanolayer structure of the Si crystal growing along with (110) direction was obtained, as shown in the TEM image of Fig.4(a), from whom we can build the simulation model of the Si nanolayer in this direction, as exhibited in Fig.4(b). The idea model structure with the hexagonal lattice is transformed to the real quasi-2D structure with convex atomic bonds after simulated optimum process, as shown in Fig.4(c). In the same way, the abrupt change effect in bandgap energy takes place as the nanolayer thickness reaches to size of monoatomic layer, where the QC effect disappears, as shown in Fig.4(d).
Here, it is interesting to make a compression between the quasi-2D silicene with the hexagonal lattice and the graphite. The simulation result demonstrates that the indirect bandgap can be transformed to the direct bandgap as the nanolayer thickness along with (110) direction is smaller than 3nm.
In the same way, the TEM image in Fig.5(a) shows the nanolayer structure of the Si crystal growing with (111) direction, according to whom the simulated model of the Si nanolayer in this direction can be built, as shown in Fig.5(b). The real quasi-2D structure along with Si crystal (111) direction can be obtained after simulated optimum process, as exhibited in Fig.5(c). The result of simulated calculation demonstrates that the QC effect plays a main role as the nanolayer thickness is larger, in which the indirect bandgap is almost kept in thickness changing. In the same manner, the abrupt change effect in bandgap energy was discovered in the simulated calculation, where the bandgap energy deeply decreases as the nanolayer thickness arrives near monoatomic layer, as shown in Fig.5(d). Here, it is should be noted that the bandgap rapidly disappears in the process.
The abrupt change effect in bandgap energy may be originated from transforming between different dimensions at the symmetry broken point. In the picture (c) of Fig.3, Fig.4 or Fig.5, the structure near monoatomic layer belongs to the fractional dimension of 2.1~2.5 in quasi-2D situation, and the bandgap will disappear to become a semi-metal, where new quantum phenomena and effects will appear in the process from the 3D layer to the quasi-2D shape and to the idea quantum surface.

Preparation of silicon nanolayers
Preparation of silicon nanolayers involves two steps: fabrication of Si amorphous nanolayer by using PLD process and growth of Si nanolayer by using electron beam irradiation. At rst, a silicon wafer (100), (110) or (111) oriented substrate was taken on the sample stage in the combination fabrication system with pulsed laser etching (PLE) and pulsed laser deposition (PLD) devices. A pulsed Nd:YAG laser (wavelength: 1064nm, pulse length: 60ns FWHM, repetition rate: 1200) was used to etch lines on Si substrate in PLE process. Then, a third harmonic of pulsed Nd:YAG laser at 355nm was used to deposit the silicon amorphous nanolayer in PLD process. And second, we accelerate the electron beam from eldemission electron gun by 200 KV and make it have higher energy and better coherent. The coherent electron beam with 0.5 nA/nm 2 was used to irradiate on amorphous Si nanolayer for 10-30min in Tecnai G2 F20 system, where the silicon nanolayers with various thickness rapidly grow, while the TEM images of nanolayers were taken at the same time. The thickness change of the Si NL can be controlled by modifying irradiation time and density of the coherent electron beam.

Transmission electron microscope (TEM) analysis
In the TEM (FEI Tecnai G2 F20) image, the various nanolayer structures of silicon are detected in vacuum , in which the electron beam from eld-emission electron gun is accelerated by 200 KV, and the compositions are measured on the samples by using analysis in X-ray energy spectra.

Simulated calculation
First-principles total-energy calculations are used to optimize the equilibrium geometries and the relative energies of the simulation models on the silicon nanolayers. The simulated calculation is performed in the surface geometry with various nanolayer thickness along with the reconstructed top surface layer (100), (110) or (111), and vacuum region of at least 0.5nm. All atomic positions are relaxed, except the bottom Si layer and its passivating hydrogen layer. The electronic behavior is investigated by an ab initio non-relativistic quantum mechanical analysis in this work. Total energies and forces are calculated within the local density approximation (LDA) and generalized gradient approximation (GGA) for the selfconsistent total energy methods to DFT, as implement in the CASTEP.

Conclusion
In summary, we have prepared the nanolayer structures on silicon in the experiment. In the simulated calculation, the change ruler of bandgap energy with nanolayer thickness has been explored, where the abrupt change effect in bandgap energy was discovered as the nanolayer thickness deceases to arrive near monoatomic layer, in which the Dirac-cone shape gradually occurs and the bandgap disappears in K space on quasi-2D silicene. The new effects will be explored deeply in the process from the 3D layer to the 2D structure of silicon. In the experiment, the thickness change can be controlled by manipulating irradiation time and density of the coherent electron beam, which will provide an investigation platform on quantum system of silicon. The results of experiment and calculation demonstrate that the transformation from the indirect bandgap to the direct bandgap can be obtained really in the nanolayer of silicon growing along with (100) direction as the thickness is smaller than 10nm, which has a good application on optic-electronic material and devices.