Experimental and theoretical study of the effect of bombardment with Ar + ions on the spectrum of valence electrons of a Si (111) single crystal

. The paper studies the effect of disordering of the surface layers on the electronic and optical properties of single-crystal silicon.An analysis of the photoelectron spectra shows that with complete amorphization of the surface density, the condition of Si valence electrons of changes significantly. In particular, the positions of the main maximum of the electrons of the valence band of Si (111) shift by ~ 0.4 eV towards higher binding energies and the band gap E g increases by 0.1-0.15 eV. The energy of a valence electron in amorphized silicon, which at low impurity concentrations, i.e. at low bombardment doses (D <10 15 cm –2 ), the potential M kk and, therefore, the shift of the maximum of the density of states vary linearly with respect to concentration. At high impurity concentrations (at doses D> 10 15 cm –2 ), corresponding to the transition to amorphous silicon, the concentration dependence of M kk is very weak. Therefore, upon amorphization, the peak A of the density of states of the silicon valence band under consideration is shifted to the region of lower electron binding energies. The theoretical substantiation of the obtained experimental results is given.


Introduction
Experimental and theoretical studies presented in [1][2][3][4][5] have shown that atom deposition, ion implantation, laser irradiation and other effects in different crystals lead to a sharp change in the electronic and crystal structure of their surface region, and these changes are mainly due to the formation of nanoscale structures, changes in the stoichiometric composition and phase structure of the near-surface layer. In this case, it is of particular interest to study the processes of formation of nanocrystals and the dependence of their physical properties on the size and the presence of structural defects in them [1][2][3][4][5]7].
Any change in the physicochemical state of the surface (the appearance of vacancies and interstitial atoms, the introduction or substitution of an implanted impurity, the appearance of active centers, disordering, the formation of compounds, etc.) first of all leads to a change in the density of state of valence electrons, which is well reflected in the experimental spectrum of photoelectrons: change in the intensity, shape and energy position of existing peaks or their disappearance and the appearance of new peaks [6,[8][9][10][11][12][13][14][15][16][17][18][19][20][21][22].
The study of these changes is very important in the development of multilayer nanofilm metal-dielectricsemiconductor (MDS) and semiconductor dielectric semiconductor (SDS) structures, electronic and optical devices, including solar cells.
The main purpose of this work was to experimentally study the effect of the disordering of the crystal lattice of the surface of single-crystal Si(111) on its electronic structure and optical properties, as well as to provide a theoretical explanation of the experimental results obtained.

The method of the experiment
Basic experiments were performed using the universal setup with several chambers under high vacuum (P∼10 -6 Pa). The given setup was based on a universal ultrahighvacuum facility (Chernogolovka, Moscow oblast) [19][20][21] The object of the study was p type single crystal Si(111) in the form of disks with a diameter of 10 mm and a thickness of 1 mm. The disordering of the Si(111) surface was carried out by bombardment with Ar + ions with an energy of E0= 1 keV with a variation in the ion dose within the range of 10 13 to 10 16 cm -2 . Before ion implantation, the Si surface was cleaned by heating to T = 1200 -1300 K for 10 -12 hours and pulsed heating to T = 1500 K. The surface composition was controlled by Auger electron spectroscopy (AES) and high-energy electron diffraction (RHEED) methods.
To study the changes in the parameters of the energy zones and the density of state of valence electrons Si(111) during ion bombardment, we used the methods The study of the atomic depth distribution profiles was carried out using the (AES) method in combination with surface etching with Ar + c E0=1 keV ions at an angle of ~80 relative to the normal.
Annealing, ion bombardment, atom deposition, and all measurements were carried out in the same experimental setup at a vacuum no worse than 10 -6 Pa. The degree of disordering of the surface was estimated from the fast electron diffraction patterns.

Results and discussion
Before ion bombardment, the surface of Si (111) was cleaned by prolonged heating at T=1200 K and shortterm heating to T=1500 K in combination with soft etching of the surface with Ar + ions.
At the same time, the total concentration of impurity C and O atoms on the surface did not exceed 0.5-1 at.% and practically did not affect the structure of the photoelectron spectrum. Figure 1 shows the dynamics of changes in the spectrum (energy distribution curve -EDK) of photoelectrons and the RHEED of the image (in the insert) of the Si (111) surface when bombarded with Ar + ions with E0=1 keV at different doses.
The Ar + bombardment was conducted perpendicular to the surface. In the based one, we will consider the change in the position and shape of the main peak A of Si. It can be seen from Fig. 1 that, with an increase in the radiation dose, the peak A broadens, its amplitude decreases, and its position mixes towards higher energies (the upper edge of the valence band Ev).
In this case, the Si surface gradually transitions from a single crystal structure to a highly disordered amorphous state (insert Fig.1).
Under ion bombardment, the composition of the Si surface is practically unchanged, therefore, the observed changes are mainly explained by the disordering of the surface and near-surface layers.
At D=6•10 15 cm -2 complete amorphization occurs. However, all the features characteristic of amorphous Si was established at D=6•10 16 cm -2 and a further increase in D practically does not lead to a change in the spectrum of photoelectrons.
The table shows the values of the band gap Eg and the light transmission coefficient K for the Si(111) single crystal, measured before and after the amorphization of the surface.
The table shows that when the surface is disordered the band gap Eg increases slightly.
Despite this, the value of K at h<Eg significantly decreases (hence, the absorption coefficient increases), which is mainly due to the appearance and increase in the concentration of different energy levels in the band gap due to disordering of the surface.
Change in the density of the state of the valence band Si (111), in the process of disordering the surface from a theoretical point of view. On the basis of Fig. 1, the dependence of the energy shift ΔE of the main Si peak A on the dose of Ar + ions is constructed (Fig. 2). It is seen that the largest shift of the peak A due to the amorphization of the near-surface layer is 0.4-0.45 eV. It is known [9,10] that the state of an electron in a Si single crystal is described in the Bloch representation by the Green's function G0(,k). Where  is the frequency of the incident light, K is the quasiimpulse of an electron in the extended zone scheme.
The Green's function of an electron in an amorphous substance Gkk satisfies the Schredinger integral equation: where ̂ is the matrix element of a random potential acting on an electron from the side of randomly located atoms of a substance, while the summation over K is performed over all states of electrons in the crystal. K-describe the valence band of single-crystal Si, and K-describes the band corresponding to ion-bombarded (amorphous) Si. -Dirac delta function expressing the law of conservation of energy when absorbing a photon.
Averaging equation (1) over the chaotic distribution of impurities, we obtain the equation for the Green's function G=<G of the valence band of Si Where Mkk is the mass operator, which is the averaged effective complex potential acting on an electron from the side of chaotically located atoms.
The real part of this potential determines the shift of the maximum of the density of states, and the minimum part determines the broadening of the peaks. Peak broadening is not discussed in this article.
In the second order, perturbation theory, the shift of the maxima resulting from amorphization is proportional to the mean square of the modulus of the random potential V: where N is the concentration of defects, < |̂| 2 > is the mean-square fluctuation of the random interaction potential, the integral in (3) is understood in the sense of the main value. The energy of the valence electron in amorphized Si ′ is equal to where is the electron energy in the valence band of pure crystalline Si. The offset in the position of the peaks is determined by the value Mkk calculated by the formula (3).
The estimate shows that at low impurity concentrations, i.e. at low bombardment doses (D <10 15 cm -2 ), the potential Mkk and, consequently, the shift of the maximum density of states change linearly in concentration.At high impurity concentrations (at doses D>10 15 cm -2 ), corresponding to the transition to amorphous silicon, the concentration dependence of Mkk is very weak.
It is important to note that the value of Mkk is positive, since the main contribution to the integral (3) gives the state K, whose energy is less than the energy .Therefore, during amorphization, the peak A of the density of states of the silicon valence band under consideration is shifted to the region of lower electron binding energies.
These theoretical results are consistent with the experimental data shown in Figs. 1 and 3. The energy shift is ~0.4 eV.

Conclusion
Thus, we experimentally established a significant change in the density of the electronic states of the valence band of single-crystal Si(111) upon amorphization of its surface by ion bombardment.
In particular, ion bombardment leads to a displaced position of the main maximum A of the energy spectrum of Si(111) by ~0.4-0.45eV towards higher energies, which is consistent with theoretical concepts.
It is shown that the complete disordering of the surface layers of Si leads to some increase in Eg, an increase by 15-20% of the light absorption coefficient at h≤Eg, and a significant decrease (1.5 times or more) in