Modeling and Control of SiNX Thin Film Surface Morphology Using Kinetic Monte Carlo Method

Recently, considerable attention has been devoted to silicon nanocrystals (Si-nc) from both the experimental and the theoretical perspectives [1-4], due to its potential nanoelectronic and optoelectronic device applications as well as their interesting physical properties. Many researchers have investigated the production of the light emission from Si-nc embedded in silicon (Si) oxide films [5,6]. Indeed, silicon oxide presents a low efficiency of carrier injection owing to its too large barrier height, which reduces the properties of the devices. In order to increase the injection efficiency of carriers, SiNx thin films have attracted a great deal of attention, as they have a lower barrier height than silicon oxide.


INTRODUCTION
Recently, considerable attention has been devoted to silicon nanocrystals (Si-nc) from both the experimental and the theoretical perspectives [1][2][3][4] , due to its potential nanoelectronic and optoelectronic device applications as well as their interesting physical properties.Many researchers have investigated the production of the light emission from Si-nc embedded in silicon (Si) oxide films [5,6] .Indeed, silicon oxide presents a low efficiency of carrier injection owing to its too large barrier height, which reduces the properties of the devices.In order to increase the injection efficiency of carriers, SiN x thin films have attracted a great deal of attention, as they have a lower barrier height than silicon oxide.
In general, there are two methods used for the formation of silicon nanocrystals, one is the crystallization of nitrogen doped silicon (SiN x ) films [3] and the other is direct deposition [7] .Various fabrication techniques, such as plasma-enhanced chemical vapor deposition (PECVD) [2,8] , low-pressure chemical vapor deposition (LPCVD) [4] , and catalytic chemical vapor deposition (Cat-CVD) [1] have been examined for the fabrication of Si-nc in SiN x thin films with different silicon sources; i.e.SiH 4 [1,2,8] and Si 2 H 6 [4] .
In preparation of SiN x films, various deposition process parameters have a strong influence on the structure and morphology as well as properties of the films [4,7] .Some of the reports [4,7] indicated that both the size and density of Si crystallites could be controlled by the substrate temperature.Consequently, the simulation of the deposit step plays an important role in defining the required properties of the obtained films.
In a SiN x thin film deposition process, the obtained film is automatically shaped by microscopic random processes (e.g., adsorption, desorption, migration, and surface reactions) [4] .Indeed, a good control at the nano-and micro-scale of the film growth process is critical to the performance of materials.Therefore, it is necessary to understand and control the microscopic processes that describe nitrogen doped silicon film deposition.

ABSTRACT
This work focuses on the study of the formation of amorphous silicon clusters embedded in SiN x thin films prepared by low-pressure chemical vapor deposition technique at a temperature of 1023 K by using a mixture of silane (SiH 4 ) and ammonia (NH 3 ).The deposition process is modeled via kinetic Monte Carlo simulation on a triangular lattice.The distribution of ammonia molecules in the simulation matrix is described using our previous pattern.This pattern includes adsorption and migration microscopic processes.The influences of the NH 3 /SiH 4 gas flow ratio and the deposition time on the deposition kinetics are analyzed.The obtained results describe well the different stages of the nitrogen doped silicon deposition process.Indeed, an increase in the gas flow ratio leads to the formation of a high density of smaller amorphous silicon clusters.Moreover, larger clusters can be formed by increasing the deposition time.Simulation results are also compared to our previous results to better understand, on the one hand, the interest of using disilane instead of silane in order to make such deposits, and on the other hand to evaluate the role of ammonia in the SiN x film deposition process.

e-ISSN: 2321-6212 p-ISSN: 2347-2278
Kinetic Monte Carlo (KMC) methods have been widely and successfully used to simulate thin film microscopic processes as well as the influence of deposition parameters on the evolution of film microstructure, since they can describe the different stages of the film growth process and contain the surface morphology information [4] .
In this work, we investigate via the KMC method the influence of deposition parameters, namely gas flow ratio and deposition time, on the deposition kinetics of nitrogen doped silicon films deposited by LPCVD technique from silane (SiH 4 ) and ammonia (NH 3 ).We focus on a SiN x thin film deposition process governed by two microscopic processes including particle adsorption and migration.In order to simulate this process, the distribution of the NH 3 molecules in the simulation matrix is described using our previous simulation pattern [4] .

NITROGEN DOPED SILICON THIN FILM DEPOSITION PROCESS
Kinetic Monte Carlo is a good tool to study the evolution of systems at the nano-and micro-scale.KMC methods arise naturally in the modeling of the surface morphology evolution of thin films in many deposition processes, such as the LPCVD process of nitrogen doped silicon films [4] .In this section, a SiN x thin film deposition process is described and modeled on a two-dimensional triangular lattice via KMC methods.The thin film deposition process considered in this work includes two microscopic processes: particle adsorption and surface migration.

Description and Modelling
The aim of this work is to model the deposition process of SiN x thin films deposited on a triangular lattice representing the surface structure of the film, as shown in Figure 1.In the modeling of the deposition process, one assumed that all molecules and radicals occupy discrete lattice sites and that the diameter of a Si atom is 0.25 nm [9] .A fixed number of sites (N=40,000) is available during the simulation.In order to deposit a molecule (or a radical), an empty site is first randomly selected among all lattice sites.The corresponding deposition rate is calculated as follows [10] : where 0 d V parameter depends only on the deposition total pressure P and on the wafer-to-wafer distance δ, E a = 1.5 eV [10] represents the deposition activation energy, K B is the Boltzmann constant, and T is the deposition temperature.
We consider two types of microscopic processes (Monte Carlo events in the KMC simulation) taking place in the deposition process of SiN x films: an adsorption process and a migration process.In the adsorption process, incident molecules and radicals are incorporated into the SiN x thin film from the gas phase.However, in a migration process, Si adatoms on the thin film move to their adjacent vacant sites.
The number of nearest neighbors of a Si adatom in the simulation matrix ranges from zero to six, the coordination number of the triangular lattice.During the simulation, a Si adatom with one to five nearest neighbors is possible to jump to an unoccupied neighboring site with a rate that depends on its local environment; i.e. the number of the nearest neighbors of the Si adatom chosen for a migration event.Moreover, a Si adatom with only one nearest neighbor is considered to be unstable in the lattice [9,11] and migrates to its most stable neighboring vacant site, which is defined as the site with the most nearest neighbors [11] .The migration rate of the ith silicon adatom was given by the following expression [9,11] : where υ 0 is the pre-exponential factor, E 0 represents the contribution to the activation energy barrier, and n i is the number of the nearest neighbors of the ith silicon adatom.Note that the migration rate is zero when n i =6 since this Si adatom is fully surrounded by other adatoms and cannot migrate.Calculation of the migration rate necessitates selection of the parameters υ 0 and E 0 in eqn.(2).In this work, υ 0 and E 0 take the following values 10 13 s -1 and 0.6 eV, respectively [12] .

Simulation Algorithm
In this paper, the KMC method is used to simulate the deposition process of SiN x thin films due to its high efficiency in simulations of the process of chemical vapor deposition, which involves the adsorption, desorption, migration, and surface reactions [4] .
According to the KMC method, a list of events is created for all possible events including adsorption and migration [13] and the events are executed instantaneously upon selection.During the simulation, sites for deposition and migration are chosen randomly in the simulation lattice, in such a way that individual events are separated [4] .
Basing on these considerations, the following KMC algorithm is used to simulate the deposition process of SiN x thin films: 1.A triangular lattice (N=40,000) representing the surface structure of the film is considered.

Select a random number µ
] in order to determine the type of the next event whether it is an adsorption event (0<µ< V d ) or a migration event ( ), where M is the total number of Si adatoms on the lattice at the specific time instant.4. Execute and carry out the selected event from the list of events formed in step 2. 7. Return to step 2 until the preset deposition time has been reached.

Description of the Pattern
During the thin film deposition process, the microstructure of a SiN x film is the result of a complex interplay between adsorption and migration processes.Motivated by this consideration, this work focuses on the study of the formation of smaller amorphous silicon clusters in a SiN x matrix.For this, a SiN x thin film deposition process which involves molecules and radicals adsorption and Si adatoms migration is considered and is modeled using a triangular lattice-based KMC simulation.The distribution of NH 3 molecules in the simulation matrix is described using our previous approach [4] .In fact, for a randomly selected site from the matrix to be occupied by a SiH 2 radical (or a SiH 4 molecule), the neighbor sites are reserved for NH 3 molecules (Figure 1) that allows for SiN x thin film growth.Thus, the SiH 2 radicals and SiH 4 molecules are surrounded by NH 3 molecules in all directions, thereby allowing the formation of smaller amorphous silicon clusters.Furthermore, by increasing the number of NH 3 molecules in the simulation matrix, a nitrogen (N) compound is created with the formation of strong Si-N bonds.Using this model, the deposition process of smaller amorphous silicon clusters can be simulated using the KMC method [4] .
Figure 1.Schematic design of the deposition process of a SiN x thin film [4] .A: SiH 2 (SiH 4 ) site enclosed by NH 3 molecules in all directions.B: SiH 2 (SiH 4 ) site having less than six nearest neighbors.C: SiH 2 (SiH 4 ) site enclosed by SiH 2 radicals and/or SiH 4 molecules in all directions.
In order to better understand the formation process of amorphous silicon clusters, the chemical reactions describing the deposition kinetic of SiN x films from SiH 4 and NH 3 were studied [14] by introducing the influences of radical species like silylene (SiH 2 ), monoaminosilane (SiH 3 NH 2 ), and silylamine (SiHNH 2 ):  (10)   It can be seen from these equations that, on the one hand, each SiH 4 molecule promotes the deposition of a Si atom into the SiN x film thanks to either the dissociative adsorption of SiH 4 (eqn.( 4)) or SiH 2 (eqn.( 5)) or SiHNH 2 (eqn.( 9)) species on the simulation matrix and, on the other hand, each NH3 molecule ensures the deposition of a N atom into the obtained film thanks to either the dissociative adsorption of SiHNH 2 (eqn.( 9)) or NH 3 (eqn.( 10)) species on the matrix.
For no NH 3 flows, Si films are deposited thanks to both SiH 4 and SiH 2 species (eqns.( 4) and ( 5)).However, for low flows of NH 3 in comparison with the flows of SiH 4 , NH 3 molecules react with both SiH 4 and SiH 2 species to form SiH 3 NH 2 and SiHNH 2 radicals in the gas phase (eqns.( 6)-( 8)).In fact, the adsorption of SiH 4 (eqn.( 4)) and SiH 2 (eqn.( 5)) is high compared to the adsorption of SiHNH 2 (eqn.( 9)) and NH 3 (eqn.( 10)), which corresponds to the case of nitrogen doped silicon thin films.In this case, the density of Si-N bonds is negligible in comparison with that of Si-Si allowing the deposition of larger silicon clusters.
Finally, for high flows, NH 3 has opposite influences on the formation kinetic of amorphous silicon clusters.Indeed, NH 3 controls completely the deposition process of films.Moreover, the adsorption of SiH 4 (eqn.( 4)) and SiH 2 (eqn.( 5)) is insignificant in comparison with that of SiHNH 2 (eqn.( 9)) and NH 3 (eqn.( 10)) leading the deposition of silicon nitride (Si 3 N 4 ) films.Thus, more N-containing species are available in the lattice.Therefore, the formation of Si-N bonds is naturally favored over that of Si-Si.In fact, the presence of strong Si-N bonds impedes the coalescence of smaller silicon clusters into larger clusters.

SIMULATION RESULTS AND DISCUSSION
In this work, the LPCVD process of SiN x thin films was simulated by using the KMC method.A mixture of SiH 4 and NH 3 was used as the source gas.The gas flow ratio R (defined as R=f(NH 3 )/f(SiH 4 ) where f(NH 3 ) is NH 3 flow and f(SiH 4 ) is SiH 4 flow) and the deposition time (tKMC) were chosen to be the main influent parameters.During the deposition process, the deposition temperature T and the total pressure P were, respectively, fixed to 1023 K and 26.66 Pa.

Influence of Gas Flow Ratio
In this section, in order to study the influence of the gas flow ratio on the LPCVD process of amorphous silicon clusters embedded in SiNx thin films, eight values of this input parameter were used (0, 0.26, 0.36, 0.50, 1, 1.2, 1.4, and 1.6).All Deposits were carried out at a deposition duration (tKMC) of 2 h.The KMC simulation results are shown in Figures 2-4.  Figure 3 shows the surface structure of the SiN x thin films according to the gas flow ratio R for a deposition temperature of 1023 K. Thus, an increase in R provokes a decrease in the size of amorphous silicon clusters along with an increase in their density, as shown in Figure 4.The size of amorphous silicon clusters is observed to decrease from 0.85 nm to 0.28 nm whereas their density increases from 5 × 10 12 clusters/cm 2 to 10 13 clusters/cm 2 as R goes from 0 to 1.6.
From these results, it is clear that nitrogen in silicon influences considerably the internal microstructure during the film deposition phase.In fact, the presence of strong Si-N bonds prevents the coalescence of smaller amorphous silicon clusters into larger clusters.Several authors have shown that NH 3 gas has a crucial role in the deposition process of SiN x thin films [14,15] .Compared to our previous work [4] in which SiN x thin films were deposited by LPCVD technique from Si 2 H 6 and NH 3 , the role of NH 3 was reduced thanks to the silicon excess in the matrix came from the use of Si 2 H 6 as the source gas.During the simulation, the SiH 2 radicals (SiH 4 molecules) must be surrounded by NH 3 molecules in all directions; consequently, the formation of smaller amorphous silicon clusters can occur.Hence, a nitrogen compound is created with the formation of strong Si-N bonds in the lattice.Therefore, the simulation pattern describes well the formation of smaller amorphous silicon clusters by the use of SiH 4 and NH 3 as the source gas.

Influence of Deposition Time
A series of eight SiNx thin films was prepared by LPCVD technique from SiH 4 and NH 3 , whereas the deposition time (tKMC) was chosen to be the main parameter.All films were grown using different values of this input parameter, while keeping all other input parameters the same (T=1023 K and P=26.66 Pa).The flow rates of NH 3 and SiH 4 were fixed at 36 and 100 sccm, respectively.The KMC simulation results are shown in Figures 5-7. Figure 5 shows the surface morphology of the SiN x thin films prepared with different values of tKMC.Indeed, an increase in tKMC causes an increase in the surface coverage of SiN x thin films, as clearly shown in Figure 6.Qualitatively, this relationship between the deposition time and the morphology of the SiNx thin films has been demonstrated via the work of Karabacak et al. [16] .This work reported that the surface morphology of amorphous silicon nitride films prepared by plasma-enhanced chemical vapor deposition technique enlarged with the increase in growth time.

Figure 2 .
Figure 2. Variation of the percentage of the surface coverage of SiN x thin films as a function of the gas flow ratio R with N=40,000, tKMC=2 h, T=1023 K, and P=26.66 Pa.

Figure 2 Figure 3 .
Figure2represents the variation in the SiNx film surface coverage as a function of the NH 3 /SiH 4 gas flow ratio R. Indeed, an increase in the gas flow ratio leads to a decrease in the surface coverage of the obtained films, as clearly shown in Figure3.

Figure 4 .
Figure 4. Variation of amorphous silicon cluster size and density as a function of the gas flow ratio R with N=40,000, tKMC=2 h, T=1023 K, and P=26.66 Pa.

Figure 5 .
Figure 5. Surface structure evolution of SiN x thin films as a function of the deposition time (tKMC) with N=40,000, R=0.36, T=1023 K, and P=26.66 Pa.The black color represents the amorphous silicon clusters while gray color is for regions occupied by nitrogen.

Figure 6 .
Figure 6.Variation of the percentage of the surface coverage of SiNx thin films as a function of the deposition time (tKMC) with N=40,000, R=0.36, T=1023 K, and P=26.66 Pa.With the increase of deposition time from 15 min to 6 h the density of amorphous silicon clusters increases, reaches its maximum at 4 h and then decreases, whereas their size increases from 0.1250 nm to 0.7800 nm with increase of tKMC, as shown in Figure7.

Figure 7 .
Figure 7. Variation of amorphous silicon cluster size and density as a function of the deposition time (tKMC) with N=40,000, R=0.36, T=1023 K, and P=26.66 Pa.