Land use structure in Drazevac, Konatice and Poljane.
\\n\\n
Released this past November, the list is based on data collected from the Web of Science and highlights some of the world’s most influential scientific minds by naming the researchers whose publications over the previous decade have included a high number of Highly Cited Papers placing them among the top 1% most-cited.
\\n\\nWe wish to congratulate all of the researchers named and especially our authors on this amazing accomplishment! We are happy and proud to share in their success!
\\n"}]',published:!0,mainMedia:null},components:[{type:"htmlEditorComponent",content:'IntechOpen is proud to announce that 179 of our authors have made the Clarivate™ Highly Cited Researchers List for 2020, ranking them among the top 1% most-cited.
\n\nThroughout the years, the list has named a total of 252 IntechOpen authors as Highly Cited. Of those researchers, 69 have been featured on the list multiple times.
\n\n\n\nReleased this past November, the list is based on data collected from the Web of Science and highlights some of the world’s most influential scientific minds by naming the researchers whose publications over the previous decade have included a high number of Highly Cited Papers placing them among the top 1% most-cited.
\n\nWe wish to congratulate all of the researchers named and especially our authors on this amazing accomplishment! We are happy and proud to share in their success!
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Nonlinear optical phenomena such as self-focusing, self-phase modulation, soliton formation and propagation, higher harmonic generation, different types of stimulated light scattering, and four-wave mixing have attracted interest from the fundamental point of view of the investigation of light/matter interaction, and as a basis for applications in contemporary optical communications and optical signal processing. Nonlinear Optics - Novel Results in Theory and Applications contains novel results concerning the mathematical methods of nonlinear optical phenomena analysis, soliton formation and propagation in optical fibers, and peculiarities of nonlinear optical phenomena in micro- and nanostructures. The book may be interesting for researchers and engineers interested in nonlinear optics, lasers, and optical communications.",isbn:"978-1-78985-164-9",printIsbn:"978-1-78985-163-2",pdfIsbn:"978-1-83962-009-6",doi:"10.5772/intechopen.77311",price:119,priceEur:129,priceUsd:155,slug:"nonlinear-optics-novel-results-in-theory-and-applications",numberOfPages:154,isOpenForSubmission:!1,hash:"a3ad4a3553a3ec59f7992d4f6495ac07",bookSignature:"Boris I. Lembrikov",publishedDate:"February 6th 2019",coverURL:"https://cdn.intechopen.com/books/images_new/7582.jpg",keywords:null,numberOfDownloads:4367,numberOfWosCitations:0,numberOfCrossrefCitations:2,numberOfDimensionsCitations:2,numberOfTotalCitations:4,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"April 18th 2018",dateEndSecondStepPublish:"May 9th 2018",dateEndThirdStepPublish:"July 8th 2018",dateEndFourthStepPublish:"September 26th 2018",dateEndFifthStepPublish:"November 25th 2018",remainingDaysToSecondStep:"3 years",secondStepPassed:!0,currentStepOfPublishingProcess:5,editedByType:"Edited by",kuFlag:!1,biosketch:null,coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"2359",title:"Dr.",name:"Boris",middleName:"I.",surname:"Lembrikov",slug:"boris-lembrikov",fullName:"Boris Lembrikov",profilePictureURL:"https://mts.intechopen.com/storage/users/2359/images/system/2359.jpg",biography:"Boris I. Lembrikov is a senior lecturer at the Faculty of Electronics, Electrical and Communication Engineering of the Holon Institute of Technology (HIT), Holon, Israel. B. I. Lembrikov received his Ph.D. in Nonlinear Optics at the Technion – Israel Institute of Technology in 1996. Since then he was an invited researcher at the Haifa University, at the Max Planck Institute High Magnetic Field Laboratory at Grenoble, France, at the Technion, Haifa, Israel. Dr. B. I. Lembrikov is an author of the book \\Electrodynamics of Magnetoactive Media\\, a number of chapters in scientific books, a large number of papers in international peer reviewed journals and reports delivered at the international scientific conferences. He actively participated in a number of research projects concerning optics of nanoparticles, optical communications, UWB communications. The main research fields of interest of Dr. B. I. 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The results showed that, the level of the landscape degradation and modification of geomorphologic processes by human activities has been increased in the past decades [4], and it was initiated by very fast demographic, socio-economic and technological changes in Serbia, likewise in the region [5-7], and in the world [8-11].
According to level and type of degradation, the Kolubara River basin belongs to the most endangered areas in Serbia. Due to the lignite exploitation in the Kolubara River basin, human impact led to morphological change of the entire area, as well as to the changes of the intensity of different geomorphologic processes: changes in river course [12,13], the intensity of bank erosion [14,15], sediment deposition [16] and environmental problems [17,18].
Unlike the other rivers with similar hydrological characteristics, the river network in the lower part of the Kolubara River basin were changed rapidly during the XX century because of direct human impact. Anthropogenic influences on the hydrological network in the study area were very intensive since 1959, when the huge river regulation works were done in the lower part of the Kolubara River. Spatial planning of the area, which included diverting of the Kolubara’s river bed, had an aim to prepare the site for the lignite exploitation within the Kolubara mining basin. The Kolubara River divides the mining basin in two parts: eastern and western part. The productive area of the basin (geologic contours of lignite deposits) is 520 km2. Kolubara mining basin is situated about 40 km south-southeast of Belgrade and represents the largest lignite deposits in the central part of Serbia; the annual production is 30 million tons of lignite, and it is the opencast mine. The mine expansion caused the need for technical solutions of diverting and removing river beds in this area. According to “General project of diverting the Kolubara River and its tributaries for the purpose of lignite exploitation”, the Kolubara’s riverbed was diverted into the Pestan’s riverbed (its right tributary). This caused many problems which were not predicted by the General project.
In this way, anthropogenic factor modified existing natural conditions: the process of fluvial erosion was changed; bank erosion became stronger and resulted in soil loss, larger amounts of sediment load deposition, cutting off the meanders and fossilization of certain parts of the riverbed, floods, land use changes, landscape degradation, sediment load pollution, etc.
Regarding to natural conditions, the Kolubara River basin is similar to the other river basins in the area. Tectonic movements had an influence on a morphological evolution of the river network in the past. During the Paleogene and the Early Neogene a small bay of the Pannonian Sea named the Kolubara’s bay existed in the area of the Kolubara River basin. After the sea recession, the fluvial erosion started in this bay and it formed today’s hydrological network of the Kolubara River. Tectonic characteristics of this area, more precisely Kolubarsko-pestanski fault and Posavski fault had influenced the orientation of the hydrological network in the Kolubara River basin. But today the Kolubara’s hydrological network is influenced by fluvial erosion and anthropogenic factors.
The Kolubara River Basin encompasses the western part of Serbia and covers 4.12% of Serbia’s surface area. The highest point of the drainage basin is at 1,346 m, and the lowest has altitude of 73 m. The Kolubara River is the last large right tributary of the Sava River, and according to the flow length (86.4 km) and the basin area (3,641 km2) it is classified as a middle-sized river on the territory of Serbia [3].
The lower part of the Kolubara River basin is called the Donjokolubarski basin (area of 1,810 km2) and is situated in the municipality of Obrenovac. The Donjokolubarski basin encompasses the catchment area of the Kolubara’s confluences (the Pestan River, the Turija River with the Beljanica River, the Tamnava River with the Ub River and the Kladnica River) and the lower part of the Kolubara’s valley. The average altitude of the Donjokolubarski basin is 168 m, the highest point is at 695 m, and the lowest has an altitude of 73 m.
According to the nearest meteorological station in Obrenovac, this area is characterized by continental climate, the average temperature was 11°C, and the mean annual precipitation from year 1925 to 2000 was 722 mm [12]. The average annual runoff of the Kolubara River (at Drazevac gauging station) for the period 1961-2005 was 21.8 m3/s.
Position of the Kolubara River basin in Serbia (right) and study area (left)
In this research we used diffrent methods that can be devided into the field and lab work methods. The GIS methods were used for the modeling of terrain evolution and landscape changes, which represents the base for bank erosion intensity quantification.
Analysis of topographical maps, aerial photo and orthophoto images were used in the previous researches aiming to determine the evolution of the riverbed [6,15,19-23]. The results showed that the application of GIS has an advantage in quantification of river migration processes.
For the purposes of this study, comparative analyses have been made on the base of Cadastral maps scale 1:2500 from 1967 and orthophoto images from 2004; reconstruction of the hydrological system has been done for the periods from 1967 to 2004. By comparing the data from two periods, we determined the evolution of the Kolubara River course in 37 years. River bank lines were digitized and the extent of bank erosion was calculated under Geomedia professional. The same software was used for the estimation of the Kolubara River lateral migration rate. This rate was estimated using the calculated area between river positions in 1967 and in 2004 (area of river migration), which was divided by the total length of the river course in 1967. The loss of land (S) is expressed as the ratio between area of endangered land parcels (ha) in 1967 (P1967) and area of endangered land parcels (ha) in 2004 (P2004) [15]:
River erosion and frequent floods make great material damages to people, villages and economy. The owners of the arable land parcels on the Kolubara River banks loose the parts of the parcels that river carries away. The reduction of parcels on the Kolubara River banks, land loss and land use changes were estimated comparing the cadastral maps from 1967 and orthophoto images from 2004.
Land use structure in the area of villages: Drazevac, Konatice and Poljane are characterized by: arable land (which people used for farming mostly wheat and corn-crop rotation practice), forests (alluvial forests of willows and poplars) and few pastures. The river dynamic is intensive in the Kolubara’s alluvial zone, which influenced sandbank formation, mostly on the concave side of the river. By statistical analysis of a land use structure [24] in the three villages with degraded land parcels on the river banks, we obtained the results which show significant reduction in arable land. And by analyses of the questionnaire carried out among the owners of degraded land parcels in the villages Drazevac, Konatice and Poljane, it can be concluded that it was significant decrease in the agricultural production. The risks from the floods and further soil loss influenced the land owners’ decision making about farming the degraded land parcels.
The change of fluvial erosion intensity was analyzed regarding to changes in water balance and sediment load transport on two hydrological profiles. Тhe results of water balance that D. Dukic [25] has made in his research for the period of 1925-1960 and the results obtained in this study were analyzed and compared. This comparative analysis appoints to the amount of water which Donjokolubarski basin disposed before regulatory changes of Kolubara in 1959/60 and after them. River flow regimes of different periods were compared because that could be a factor which has a significant influence on the observed process. All these efforts should confirm or eliminate the influence of natural factors on the river banks degradation in the Donjokolubarska valley.
Having data of extreme discharges, in order to estimate the impact of future floods on bank erosion, we have made a probability curve of maximum discharges of the Kolubara River and its tributaries.
Because of intense anthropogenic impacts in the Donjokolubarska valley, we have sampled the suspended sediments from the Kolubara’s riverbed and later analyzed the pollution of the accumulated load. Since the processes of bank erosion and sediment accumulation occur close to the villages and that endangered land parcels are used for food production, such approach points to ecological aspect of researched problem.
The sediment samples were taken on two locations in the Kolubara’s riverbed. For heavy metals and carbon analysis the soil was milled to a fine powder. Heavy metals were determinate by AAS method.
On the research sector (Fig. 1) the Kolubara River length in 1967 was 8.2 km and 10.6 km in 2004. This fact appoints to the river course evolution through the landscape. In the period between 1967 and 1981 the Kolubara River has migrated 50 m, actually 27 m into left and 23 m into right, and the average migration of the Kolubara River was 3.6 m per year. By further comparison of aerial photo image from 1981 and orthophoto image from 2004 it can be observed that the Kolubara’s riverbed was stabilized and during 23 years migrated only 26 m. So, the Kolubara River average migration in this period was 1.1 m per year which is three times less comparing to the previous period of observation (1967-1981) [13].
The rate of the Kolubara river lateral migration along the research sector is 47 m in average for the period of 37 years, which means 1.27 m per year. At the most endangered part (in the area of Drazevac village) the most intensive migration rate of the riverbed was 224 m in 37 years, with the average of 6.05 m per a year [15].
The changes of fluvial erosion intensity may result from changes in climatic-hydrological characteristics of the river basin (which are manifested in discharge regime changes) and various human impacts. Therefore, the natural factors of the Donjokolubarski basin were analyzed to determine whether they have influenced the stronger bank erosion.
The results showed that average mean annual discharge of the Kolubara River measured in Drazevac was 22.3 m3/s in the observation period 1961-1990, and 21.3 m3/s in the observation period 1991-2005. Amplitude of average high and low flows in the period 1961-1990 was 77.94 m3/s, and in the period 1991-2005 it was 64.66 m3/s [13].
To study water balance of the Donjokolubarski basin we used the following periods: 1925-1960, 1961-1990 and 1991-2005. With this approach it was possible to determine the changes that may be occurred after diverting the Kolubara River into the Pestan’s riverbed in 1959. Briefly, precipitation analysis showed that the second period was a bit wetter than the first, actually about 60 mm in the Pestan River basin and 80 mm in the Turija River basin and the Tamnava River basin. Meanwhile, higher air temperatures and higher evaporation caused almost the same specific discharges of these rivers. The last period was in mean values similar to the second, apart from intensified variation of extreme values of all climatic elements. The discharges were influenced by more frequent alternation of wet and dry periods, which could be seen on figure 2.
Monthly coefficients of variation of the period 1991-2005 are higher in all river sub basins except in July and August. These differences are significant, the variation of discharges in eight months are higher than the highest coefficients of variation of the period 1961-1990, which is 1.5. The more important is the fact that the period of appearances of unstable discharges is March-April (over 2.5), which is related to snow melting. That is the period of maximum discharges and any sudden disturbance of soil moisture resulting in serious disorder of river bank stability. Some of the natural factors have been changed in the last two decades, for example, March used to be, in Serbia, the month with the most stable discharges (and the highest). The differences in March discharges during the observed periods are over 20 m3/s (almost twice reduced), and it was followed by extreme discharge variations. These are the significant changes since the area of the Kolubara River basin is bigger than 3500 km2 and maximum discharges are higher than 500 m3/s. Although the mean values are not of crucial importance, they indicate some disturbances which should be kept in mind; particularly because the last period of observation is twice shorter than the previous one and all analyses in the world indicate that extreme values of natural phenomena are more pronounced and more frequent.
Mean monthly discharges (Q) and coefficients of variation (Cv) of the Kolubara River measured in Drazevac gauging station for the both periods of observation
Preliminary results of the Donjokolubarski basin annual flow variation show discrepancy in spring and summer monthly flow among two studied periods (Figure 2 - right). Further research should examine correlation of monthly flow and bank erosion intensity.
The erosion control works in the river channel can cause changes in river morphology, since they influence the changes in river regimes, river bank characteristics and amount of sediment transport [26]. The consequences of these interventions are numerous, and often lead to riverbed widening and undermining concave sides of the river banks. The processes of river bank collapsing and erosion are complex since they are results of several factors, including sediment transport, ground lithology, stratigraphy, slope, flow geometry and anthropogenic activities [27].
Opencast lignite exploitation in Kolubara mining basin started in 1952 when the mining field “A” was open (it was exploited till 1966). Mining field “B“ was opened in 1952, mining field “D” in 1961, “Tamnava-East Mining Field” in 1979, “Tamnava-West Mining Field” in 1994 and mining field “Veliki Crljeni” in 2008 [28].
Plan of the mining fields in Kolubara mining basin [28]
Beogradsko-posavska water community “Beograd” has made a project „Regulation of the Kolubara River and its right tributaries from Ćelije to Poljane (km 23+200 – km 55+506)“ in 1957. Regulation works on the Kolubara River and its tributaries had begun in 1959/60. The diverting of the Kolubara River was done to clear the area for lignite exploitation, actually for opening new mining fields.
From that moment the Kolubara River flows through the Pestan\'s riverbed (its right tributary), and previous Kolubara\'s riverbed is abandoned with the periodic flow. The length of the Kolubara River was shortened by 20 km because of diverting its riverbed, while the length of the Pestan River was also shortened because its confluence was moved to the South. By diverting the Kolubara\'s riverbed into the Pestan\'s riverbed, which morphologically was not predisposed for kinetic energy of stronger flow, bank erosion became a dominating geomorphological process in the area and initiated processes of digging the riverbanks, transportation and deposition of eroded material. It is obvious that river system changes in lower part of the Kolubara River are demonstrated in domination of fluvial (lateral) erosion on one hand, and in cutting the meanders and fossilization of certain parts of the riverbed, on the other hand.
Map of the Kolubara\'s basin first trend of relief energy [2] shows that almost whole area of the Donjokolubarska valley is under tectonic movements of slowly sinking. For this reason the sediments are accumulated in the riverbed, river velocity decreases which cause the riverbed meandering and stronger bank erosion. This natural process became more intensive since the Kolubara River was diverted into the riverbed of Pestan. In the Donjokolubarski basin there are numerous sectors with abandoned riverbeds and cut off meanders.
Forming of meanders and cutting the “necks” are recent geomorphologic-hydrological process, which is dominated in the study area. According to results of the recent researches [13], there are 89 abandoned parts of the riverbeds and cut off meanders in the area of the Donjokolubarski basin. The Kolubara and its tributaries tend to move to the east because of the Kolubarsko-pestanski fault, which indicate more abandoned riverbeds and cut off meanders on the left side of the Kolubara valley (64), compared to the right side (25).
In the study area there are 40 cut off meanders with total length of 20.30 km while the number of abandoned parts of the riverbeds is 49 with total length of 76.03 km. Hence, the total length of all abandoned riverbeds and cut off meanders in the Donjokolubarski basin is 96.33 km, and their total surface is 3.35 km2. The longest cut off meander is 1.7 km long and the shortest is 185.7 m long. The longest abandoned riverbed is 6.49 km long.
The length of the Kolubara’s riverbed is influenced by stronger bank erosion and formation of meanders, which is clearly perceived in the field. According to orthophoto image from 2004 and satellite image (Google Earth) the Kolubara River length (in the Donjokolubarska valley) is 66.52 km, while according to topographical map from 1970 it was 67.5 km, and according to topographical map from 1925 it was 87.6 km.
After cut off meander, the riverbed itself morphologically adjusts to the new state [29]. Morphological changes of the rivers are reflected in digging the concave river banks and sediment accumulation on the convex river banks.
As we earlier indicated, river erosion and frequent floods can make great material damages to people, villages and economy. Since the lateral erosion has more intensity, the river banks on concave side of the Kolubara River often collapse and farmers who have arable land parcels on the river bank (in the area of three villages the Kolubara flows through) loose the parts of the parcels which were carried away by the river. Based on Cadastral maps from 1967 and orthophoto images from 2004 we have estimated the area of diminished land parcels and their land loss.
Farmers who have land parcels in three villages (Drazevac, Konatice and Poljane) on the Kolubara river bank cannot farm them in whole, because the river has changed its course and took some parts of the land parcels away. The cadastral maps of the researched area scale 1:2500 from 1967 and orthophoto images from 2004 were compared. Using the results of this comparative analysis, the evolution of the hydrological system in the period from 1967 to 2004 was presented. The previous research showed that 60.37 ha was lost and degraded by the river bank erosion, which means that the land loss is 50.57 % of the land parcels from 1967 [15].
Land use | Total | Arable land | Woods | Pastures | Meadows | Sand banks | Other (roads…) |
Drazevac | |||||||
number of endagered parcels | 95 | 39 | 16 | 1 | 5 | 34 | - |
area in 1967 (ha) | 57.76 | 34.96 | 5.56 | 0.25 | 2.93 | 14.07 | - |
area in 2004 (ha) | 28.23 | 21.76 | 2.48 | 0.02 | 1.30 | 2.67 | - |
loss of land (ha) | 29.53 | 13.20 | 3.08 | 0.23 | 1.63 | 11.40 | - |
Konatice | |||||||
number of endagered parcels | 86 | 56 | 2 | 2 | - | 25 | 1 |
area in 1967 (ha) | 50.44 | 42.73 | 0.49 | 1.02 | - | 6.12 | 0.09 |
area in 2004 (ha) | 32.13 | 29.57 | 0.34 | 0.55 | - | 1.60 | 0.06 |
loss of land (ha) | 18.31 | 13.16 | 0.15 | 0.47 | - | 4.52 | 0.03 |
Poljane | |||||||
number of endagered parcels | 66 | 41 | 3 | - | - | 21 | 1 |
area in 1967 (ha) | 40.09 | 33.91 | 0.82 | - | - | 5.11 | 0.25 |
area in 2004 (ha) | 26.26 | 25.15 | 0.19 | - | - | 0.89 | 0.03 |
loss of land (ha) | 13.83 | 8.76 | 0.63 | - | - | 4.22 | 0.22 |
Land use structure in Drazevac, Konatice and Poljane.
On the basis of the recent and more accurate data from Obrenovac Municipality Cadastre we have determined land use structure of degraded land parcels on the Kolubara River banks. According to these data, total area of all 247 endangered land parcels was 148.3 ha in 1967, and 86.62 ha in 2004. Therefore, 61.68 ha of soil were lost within 37 years [13].
Land use changes in total area (left) and area of arable land (right) in Drazevac, Konatice and Poljane between 1967 and 2004
Land use changes in area of woods (left) and area of pastures (right) in Drazevac, Konatice and Poljane between 1967 and 2004
From 247 endangered land parcels, 136 are arable land with the area of 111.6 ha in 1967, and 76.48 ha in 2004, which means that within 37 years 35.12 ha of arable land was lost for farming, and it is 31.5 % of the initial area (in 1967). The woods comprise 21 of all endangered land parcels with area of 6.87 ha in 1967, and 3.01 ha in 2004, which means that it has been lost 3.86 ha of woods. There are only the three endangered land parcels with pastures, and their area was 1.27 ha in 1967, and 0.57 ha in 2004. All five endangered land parcels with meadows are in the area of Drazevac village.
Analyzing the area of endangered parts in the three villages, one can conclude that erosion was the most intensive in the period 1967-1981, when 50.9 ha of soil was lost within 14 years. The riverbed was stabilized later and the erosion decreased. This appoints to the fact that diverting the Kolubara River into the Pestan’s riverbed caused more intensive bank erosion since in time erosion was diminished which brought to the riverbed stabilization.
Three villages on the Kolubara River banks (Drazevac, Konatice and Poljane) were characterized by agricultural production and agricultural population. Analyzing the land use structure of endangered parcels one can conclude that arable land parcels are the most endangered and degraded by intensified lateral erosion of Kolubara.
In Serbia there is 4.25 million ha of arable land, and each year 500000 ha (which means 11.74 %) of arable land remain uncultivated [30]. In the above mentioned three villages 33.47 % of arable land (on the Kolubara River banks) remain uncultivated, which is three times more than the average in Republic of Serbia. During the field work, the interviewed owners of endangered arable land parcels pointed that they do not farm their land on the river banks because of flood risks. The Kolubara River floods almost every year and crop is ruined. Therefore, besides the loss of arable land, frequent floods are huge problem in this area.
The economic consequences of bank erosion in the area of the Donjokolubarski basin could be analyzed through losses that the owners of endangered arable land parcels had (because the arable land parcels were reduced). The area of arable land (on the river banks) was diminished by 35.12 ha within 37 years. In the research area the average annual yield is 3-4 t per hectare, so the annual losses of crops (mostly wheat and corn) in recent years are between 100 and 140 t per year.
Changes of land use structure and changes in sediment regimes are the direct consequences of the bank erosion [22]. The calculation of one-day sediment load discharge at the monitored hydrological profile includes the values of mean daily flow (Q – m3/s) and the relevant concentration of the suspended load (C–mg/l). The assessment of sediment deposition rate is based on the results of RHMSS [31] measurements and the results of own daily measurements of suspended load concentration during the period (1985-2004). The results show that 193253.8 tons of material was accumulated between two hydrological profiles. And the riverbed itself was raised for 36 cm, which is nine times enlarged comparing to previous research when it was raised for 4.2 cm (with a shorter time series) [2]. The extraction of the river deposited sediments from the Kolubara’s riverbed was stopped. Although the river deposits were hand extracted with low intensity, it certainly had great positive effects from the aspect of maintaining the surface of riverbed profile. Simple solutions, like the river deposit extraction, do not need huge investments for the implementation and they can be carried out without limitation of the natural conditions.
REIK Kolubara has a negative ecological impact on the Donjokolubarska valley. There are lots of waste waters after the ore production. Waste waters from the mine “REIK Kolubara” are discharged without any treatment into the Kolubara River. Therefore, the Kolubara River contains waste waters from the mine and after each flood the soil on the river banks is contaminated by substances from the waste waters. The results of soil analysis in the Kolubara river basin show increased concentration of nickel, arsenic and lead in the area of the Donjokolubarski basin [18].
The eroded material from the river banks is accumulated downstream. The accumulated sediments can contain considerable concentrations of heavy metals and that is threat for the aquatic habitats and for the people [8, 32-34].
Ecological aspects of mechanical water pollution by suspended sediment, chemical water pollution by organic and mineral fertilizers used in plant production in the catchment, nutrients found in the soil as well as chemical pollution of water and sediment by pesticides and heavy metals are very important ecological problem in the study area. On two locations we have sampled the accumulated material from the Kolubara’s riverbed to examine the transport of contamination and accumulation of contaminated sediments due to bank erosion processes.
Distribution of Ni (left) and As (right) in the soil of the Donjokolubarski basin [18].
Sampling of deposited sediments on location 1 (left) and 2 (right)
The deposited sediments have sandy-clay texture. Chemical characteristics of deposited sediments from Kolubara’s riverbed are: mildly alkaline reaction, high bases saturation degree and low humus content. The average heavy metal concentration in sediments decreased in the order: Ni > Cr > Zn > Pb > Cu > Cd.
In Serbia there is no law defining limitation of heavy metals in suspended sediments. Some European countries have such laws [34], but the differences between countries are significant. In most of the cases the critical values are obtained using the equilibrium method and maximum acceptable concentration (MAC) for the surface waters with regard to direct and indirect effects on living organisms in the water-sediments systems. According to these data, the range for different elements is as follows: 15 - 100 mg.kg-1 for Pb; 0.6 – 2.4 mg.kg-1 for Cd; 36 - 120 mg.kg-1 for Cu; 123 - 1050 mg.kg-1 for Zn; 10 - 180 mg.kg-1 for Ni and 37 - 120 mg.kg-1 for Cr. These ranges are bigger then estimated ecotoxic criteria [35], which are: 5 - 50 mg.kg-1 for Pb, Ni i Cu; 0.1 – 1.0 mg.kg-1 for Cd; 50 - 500 mg.kg-1 for Zn; 10 - 100 mg.kg-1 for Cr.
Sample | Zn | Cu | Pb | Cd | Cr | Ni |
mg.kg-1 | ||||||
Location 1 | 39.3 | 15.9 | 23.0 | 0.0 | 94.0 | 198.3 |
Location 2 | 41.0 | 20.2 | 27.9 | 0.1 | 103.0 | 210.9 |
Heavy metal contents in the deposited sediment load.
Respecting the above mentioned criteria, mean measured concentration of Pb, Zn and Cr are within the limits (after de Vries and Bakker [35]), while concentration of Cu and Cd are below the limits and concentration of Ni are above the limits. According to OSPAR limitation values [36], average concentrations of Pb, Cu and Cd are below the limits, average concentrations of Cr and Zn are within the limits, while average concentrations of Ni are above the limits.
The Kolubara River is a good example which represents the existence of all conditions for frequent and large scale floods. As an indirect consequence of the anthropogenic influence on the hydrological system in the lower part of the Kolubara valley, once a year (sometimes twice a year) the Kolubara River overflows, and the area of lower part of the Kolubara River basin is endangered by floods. Catastrophic floods of the Kolubara River and its tributaries spread over the area of lower part of the Kolubara River basin during the spring of 1937, and they lasted two months approximately (from March to May). In this area large scale floods also happened in 1965, 1975, 1981, 1996, 1998, 1999, 2001, 2004, 2006, 2008 and 2010.
The highest discharge of the Kolubara River in the period of 1959-2000 was 646 m3/s and it was registered on Drazevac hydrological station. According to probability curve of high discharges the discharge of 646 m3/s may occur once in a 46 years. The lowest value of annual maximum discharge would be about 25 m3/s, the highest discharge in a hundred years would be 740 m3/s, and the highest discharge in a thousand years would be 960 m3/s. During the first decade of XXI century almost every two years the flood wave was bigger than the biggest one which occurs once in a fifty years. Huge flood waves were occurred in 2001, 2004, 2006, 2008 and 2010. The last flood in December 2010 had already reached the maximum value which occurs once in a hundred years (according to probability calculation (until and including) year of 2000)). Since the floods are directly and indirectly related to bank erosion these data should be included in bank erosion analysis because their analogy is proved, although there is no quantification of their correlation. Therefore, researches should be focused on causes of floods, and on reduction of bank erosion uncertainties. Many factors that influence the Kolubara River floods are already known. Firstly, there is a difference in flows in the upper and lower part of the Kolubara River basin. The drainage conditions in the upper part are more favorable. The area of hydrological profile Slovac is less than 1/3 of the whole basin, but it drains a half of all waters in the Kolubara River basin. Downstream hydrological profile Beli Brod encompasses a half of the basin, and its discharge is 3/4 of Kolubara\'s discharge. In the Donjokolubarski basin the drainage conditions are different, and the most significant factor is slope (the slope of the river flow and the slope of the river basin). The distance between Beli Brod and the Kolubara’s confluence with the Sava River is 50 km and the altitude difference is 20 m. The present slope of 40 cm/km (0.4 ‰) is declining every year due to intensive sediment accumulation in the riverbed. Relating these processes with the shape of the river basin and rapid concentration of water downstream of the Beli Brod, it does not surprise that Kolubara River “ramp” over its alluvial plain. Moreover, in the last decade there is simultaneity of frequent rains of high intensity with extended duration and sudden snowmelt, and that is the reason for increased concern. Considering that rivers in the sub basins are mostly torrential, this concern is even more enhanced. Additionally, in this area rivers were diverted to bring the economic benefits. Because of all these reasons, the life in the coastal zone of the Kolubara River basin is gloomy but real with lot of uncertainties.
In order to prevent the frequent floods there are a several plans to deal with the actual situation in the area. Construction of several small accumulations on the Kolubara’s tributaries is at its first phase, but there is no indication for solving the existing water problems. There is an idea to channelize the Kolubara’s riverbed for sailing (i.e. for the transportation of lignite from the Kolubara mine), but it is still in the early phase of planning, although the initiative appeared long time ago. The height difference between the Kolubara’s River confluence with Sava River and the location of lignite exploitation in the Kolubara mine basin is 23 m [12]. This height difference and the wideness of the Kolubara’s riverbed would facilitate its riverbed training works, enabling cheaper lignite transportation from the Kolubara mine basin. Training works the Kolubara’s riverbed and its preparation for lignite transportation could easily be carried out, so the invested means would be economically justified. Thus, the meandering flow would be straightened, and the strong bank erosion in the riverbed would be regulated which means that some factors of flooding would be eliminated.
Bank erosion, soil loss, sediment load deposition, changes in the river course, floods, landslides, soil and water pollution are the major environmental problems in the Kolubara River basin which could be aggravated by the land-use changes. The solutions for all mentioned environmental problems demand a complex analysis of the area characteristics and development of the strategy for solving the existing water problems in this area, but in the same time they have to provide necessary conditions for the further lignite exploitation. Some villages are located in the lower part of the Kolubara River basin, in the area which is planned for the expansion of the Kolubara mining basin, so it is an important factor for the future sustainable landscape planning.
Hydrological network of the Donjokolubarski basin is constantly changing due to natural factors and anthropogenic impacts. The damage which is done cannot be compensated, but even worse is the fact that no one feels responsible and that the population in this area is still left to the mercy of torrential river. Numerous calls for helping endangered people and goods were sent to the different addresses, but no one tried to help. Apparently, the problem goes beyond the “values” of a few villages and the state interest (lignite exploitation) has absolute priority, like in the case of neighboring Dubrava and unique sources of Obrenovac Municipality [34]. This situation lasted till the catastrophic floods in June 2010, when the shocking images of flood damage terrified the publicity, and problem could not be ignored anymore. As an attempt to repair the flood consequences, during 2010 two dikes were constructed with the length of 200 m in total. The first location was repaired for bridge protection, and the second one for household protection. The total cost of construction works was 100 000 euros. Since, the total length of all degraded river banks of first category is about 5 km; the economic profitability of this repairing method is questioned. It made sense in the initial phase of degradation, but now it goes beyond the reality of existing situation. It seems that, after the construction of two dikes, somebody tries to justify the negligence, because it is obvious that these two dykes are insufficient to solve the problem. In cases like this one, even not doing anything for protection of degraded areas represents a serious violation of principles of sustainable management of natural resources, actually that is an offence. The responsible for effects of the changes in the Kolubara River basin is still unknown, is it nature or man?
Making the constant pressure on state institutions through various appeals, indicating to unsustainability of current situation and stand by position of constant fear, this paper is one of many attempts to help the endangered population. In this context, the monitoring of the Kolubara River in the Donjokolubarski basin is a logical solution and our contribution, with particular results and recommendations, to fight for the basic human right to live without fear from hazards.
What kind of message can be sent to people living in this area and dealing with above mentioned problems? As they say, finding that the state does not protect them from the problems that come upon them, they give up farming the parcels of endangered area (along the river). The even more irrational, is the fact that they still pay taxes on the parcels, which does not exist anymore or they are significantly reduced, because the taxes calculation is made according to Cadaster from 1967! The estimation of all unnecessary loss of land, land values, personal losses of individuals and damage done to whole community is in the course. At the time when the personal status is far beyond collective responsibility due to difficult economic situation, this scientific approach is the only way to inspire the responsible ones in finding the solution.
This research could be the warning for the future anthropogenic activities on the river system since the new changes on the hydrological network were planned in this area. The four new mining fields should be opened, and if it happens, the hydrological network will be changed again and new problems will appear in the river basin.
This paper was realized as a part of the projects "Studying climate change and its influence on the environment: impacts, adaptation and mitigation" (43007) and "The Democratic and National Capacities of Serbia’s Institutions in the Process of International Integrations" (179009) financed by the Ministry of Education and Science of the Republic of Serbia within the framework of integrated and interdisciplinary research for the period 2011-2014. Translation and language correction was performed by Ljiljana Stanarevic.
In statistical physics only a few problems can be solved exactly. For complex problems, numerical methods can give exact results for problems that could only be solved in an approximate way. Numerical simulation can be a way to test the theory. The numerical results can be compared to the experimental results. The numerical simulation is placed between the fundamental and the experimental treatment; it has a quasi-experimental character (numerical experience). For problems of statistical physics, the most widely used simulation methods are the Monte Carlo method and the molecular dynamics method.
The first Monte Carlo simulation (MCS) was proposed by Metropolis et al. in 1953 [1]. The second Monte Carlo simulation was proposed by Wood and Parker in 1957 [2]. The obtained results were in good agreement with the experimental results of Bridgman [3] and those of Michels et al. [4]. In this method we attribute a series of initial positions chosen randomly to a system of N particles interacting through a defined potential. A sequence of particle configurations is generated by giving successive displacements to particles; we only retain configurations to ensure that the probability density is that of the chosen.
Molecular dynamics simulation (MDS) has been first introduced to simulate the behavior of fluids and solids at the molecular or atomic level. MDS was used for the first time by Alder and Wainwright in the late 1950s [5, 6] to study the interactions of hard spheres. The principle is the resolution of equations of motion for a hard sphere system in a simulation cell. The basic algorithm is Verlet’s algorithm [7].
In this chapter, we will present techniques of numerical simulations using the Monte Carlo method. We will present an application on the gas phase during plasma-enhanced chemical vapor deposition (PECVD) of thin films. The application concerns collisions between particles. Particles are in Brownian motion. Collisions, elastic or inelastic, are considered to be binary. Non-elastic collisions result in effective chemical reactions.
In Section 2, we cite some MCS and MDS works on PECVD processes. Section 3 presents general rules on numerical simulation methods. Section 4 presents how to simulate a physical problem using MCS? We present the Metropolis algorithm as a scheme to trait random configurations and different modules related to elaborate an MCS code. In Section 5, we apply the MCS on SiH4/H2 gas mixture during a PECVD process. Finally the conclusion summarizes the contents of the chapter.
The PECVD is the most widely used technique to produce hydrogenated amorphous silicon thin films (a-Si:H) for solar cells and for film transistors and electronic devices [8, 9]. Reactions during plasma deposition are complex and are not understood completely.
Gorbachev et al. [10, 11, 12] have developed a model that is based on chemical reactions and different processes in a PECVD reactor. The model takes into account the formation of SinHm oligomers (n ≤ 5). It presents a simulation of the growth of the films. Gorbachev et al. found that Si2H5 and Si3H7 strongly influence the growth of the film [11].
Valipa et al. [13] calculated the β reactivity of the SiH3 radical on a surface of a silicon lattice plane during the growth of a-Si:H using MDS. The mechanisms of physical and chemical interactions of low temperature plasmas with surfaces can be explored using MDS [14].
For a CH4/H2 mixture, Farouk et al. used the Monte Carlo method (PIC/MC); they calculated the ionization rate of the plasma and the deposition rate of the thin layer [15]. Rodgers et al. [16] have developed three-dimensional Monte Carlo simulations of diamond (100) surface CVD. Other works on MCS are in [17, 18, 19].
In our previous works [20, 21, 22, 23, 24], we were interested in the study of the gas phase and the interaction of plasmas with the surface, for SiH4/H2 and CH4/H2 gas mixtures during PECVD processes. The used numerical simulation techniques were MCS and MDS. To complete the studies, we used the fluid model [25].
The starting point of numerical simulation is a physical phenomenon; its purpose is to obtain useful physical results. Between these two points, several steps can be identified. These steps are general and they are applicable for MCS. The steps can be summarized as follows:
The physical phenomenon must be defined by the description of the dominant domain of physics. The main assumptions and simplifying approximations are necessary to understand the physical phenomenon and the design of the first model.
Mathematical model requires a mathematical formulation of the problem. It may be a problem of elements or discrete object or a problem of a continuous medium; it may be a spatiotemporal problem or frequency problem and may be a deterministic or probabilistic problem.
It would be interesting to know the mathematical equations that govern the phenomenon:
The forces between particles and elements
The potential interaction
The determination of a time scale
The determination of a length scale
Definition of constant magnitudes of motion and equilibrium magnitudes
Continuity equations, balance equations, transfer equations, etc.
The MCS technique has been chosen for this work; knowing its basic algorithm is necessary for elaborating the simulation. This step requires some actions:
Validation of the model on simple cases
Simulation calculation on complex phenomena
The MCS is based on a probabilistic process with a random choice of configurations and samples of the situation of the physical system. The two pedagogical examples most cited in the literature are the integration of a single variable function and Ising’s model of spin. In the following subsection, we define the integration of a single variable function. We introduce the Ising model at the end of Section 4.2.2.
Calculation of the definite integral for a function f(x) of a single variable x on domain {a, b} has been proposed (Figure 1):
The integral of a function f(x).
Let:
Let xi and yi be real random numbers (i = 1, 2,…, N), and let H be a real number greater than the f(x) for x belonging to the domain {a, b} (or x ∈ {a, b}).
Let r1 and r2 be two random numbers belonging to the domain {0, 1} according to a uniform distribution law. Generators (e.g., Ran, RANDOM, RANDUM, or other IMSL mathematical libraries) of random numbers can be used:
where xi and yi are random numbers (xi ∈ {a, b} and yi ∈ {0, H}).
The Monte Carlo (MC) method is based on a probabilistic process. Let N be the total number of cases chosen (possible cases). It is necessary to count the number of favorable cases (or the number of points below the curve y = f(x)); let yi ≤ f(xi)). The number of favorable cases is Nfav. When N➔∞, the value I of the integral is [26]:
An example [26] is the calculation of the value π by calculating the integral I on a quarter circle of unit radius (R = 1.0). The pairs of random numbers (xi, yi) satisfying the condition: xi2 + yi2 ≤ 1. The function f(x) is equal to
We take a = 0.0, b = 1.0, and H = 1.0.
For different values of N, we show that the numerical solution tends to π = 4I.
Although this integral is simple, it shows the strength and simplicity of the method. The technique can be generalized for the integration of multivariate functions.
We note that integration by the MC method is based on:
The choice of random configurations according to a uniform distribution law
Each configuration chosen is either favorable or unfavorable (the “or” is exclusive).
For statistical physics problems, the probabilistic choice of configurations is not always deterministic; the favorable and unfavorable cases are not exclusive. According to the Metropolis algorithm [26, 27], the steps of the simulation are:
Choice of a simulation cell of adequate shape to the studied phenomena. The size of the simulation cell is related to a scale of length characteristic of the forces and interaction potential of the studied phenomenon. This cell may contain Npc particles (and/or elements).
Choice of an initial configuration that responds to some physical and thermodynamic properties. The total or internal energy of the system is Ei.
Infinitesimal random displacement of a particle (or element of the system) and calculation of the new internal energy of the system Ef. This displacement is related to the physical magnitudes: time scale and length scale. The physical system tends toward a minimization of the internal energy of the system with some fluctuation. Let ΔE = Ef-Ei the fluctuation.
If ΔE ≤ 0; the new configuration is retained (favorable) and the different averages can be obtained; go to step (c).
If ΔE > 0; a random number ε is chosen such that 0 < ε < 1. Let the probability Pr equal to: Pr = exp. (−ΔE/kBT) (where kB is the Boltzmann constant and T is the temperature).
If ε < Pr, accept the move and in any case go back to step (c) for a new choice of an infinitesimal displacement (new configuration). Note that if such a trial move is rejected, the old configuration is again counted in the averaging with probability Pr.
Figure 2 shows how to choose between the selected configurations. Let ε be a random number following a uniform law; If ε1 ≤ Pr the configuration is retained, and if ε2 > Pr the configuration is rejected.
Configuration choice according to Metropolis scheme.
Numerical simulation using the MC method is a very important tool for the study of static properties. The basic algorithm is based on probability notions. Understanding of the distribution function and/or interaction potentials is the heart of the calculation.
In equilibrium statistical physics, the system has a certain probability that can be in any states. The probability of being in a state μ with energy H(μ) is given by the Boltzmann distribution P(μ):
where T is the absolute temperature and kB is called Boltzmann’s constant. It is conventional to denote the quantity (kBT)−1 by the symbol β. The normalizing factor Z, or partition function, is given by:
The average of a quantity Q fora system in equilibrium is:
The internal energy U, is given by:
which can be written in terms of a derivative of the partition function:
From thermodynamics we have expressions for the specific heat C, the entropy S, and the Helmholtz free energy F:
or
and
and
We can calculate other parameters affecting the system.
The Monte Carlo method is an excellent technique for estimating probabilities, and we can take advantage of this property in evaluating the results. The simplest and most popular model of a system of interacting variables in statistical physics is the Ising model. It consists of spins σi which are confined to the sites of a lattice and which may have only the values (+1) and (−1). These spins interact with their nearest neighbors on the lattice with interaction constant J; they can interact with an external magnetic field B coupling to the spins. The Hamiltonian H for this model is [26]:
The Ising model has been studied in one and two dimensions to obtain results of thermal properties, phase transition, and magnetic properties [26, 27, 28]. For chosen values of J and/or B, different steps may be taken for the calculations (simulation cell, initialization, configurations, boundary conditions, calculation algorithms). For any configuration, each spin takes the two possible directions. The detail of the calculation procedure is not the purpose of this chapter.
We give a system of N particles (atoms, molecules, ions or particles) placed in a cell of fixed volume, generally of cubic form. The initial positions may, depending on the case, be distributed randomly according to a certain law (uniform or otherwise) or have a given symmetry. In a fluid, a gas, or a plasma, the particles may have random positions in general; in a solid or surface, with a crystal structure, the particles take ordered positions. The choice of random initial positions allows great freedom on the choice of the number of particles in the cell.
At the first step, the particles are given velocities that are generally selected to have a zero total momentum. If the system is in thermodynamic equilibrium, the initial velocities will be randomly chosen according to a Maxwell-Boltzmann law. In the general case, the velocity distribution is according to the problem dealt with. All other phase properties can be initialized to the particles; the main thing is the conservation of the total quantities of the system.
The particles interact with each other according to chosen interaction potentials. Since the interaction potentials are specific for each “numerical experiment,” the main part of the work consists in calculating the interaction energies for each proposed configuration.
The choice of interaction potentials is directly related to the mathematical formulation of the problem according to the state of the medium: fluid, gas, plasma, or solid. It can be Lennard-Jones potential, Coulomb potential, Debye potential, Morse potential, Stillinger-Weber potential, Born-Mayer potential, Moliere potential, or others.
In general, two main boundary conditions are used: periodic boundary conditions (PBC) and minimum image convention (MIC) [29].
To minimize the surface effect, periodic boundary conditions (PBC) [30] are invariably imposed. The simulation cell is reproduced throughout the space to form an infinite mesh. We can simulate the properties of an infinite system. The particles that we follow are in the central cell; if a particle crosses a wall with a certain velocity, its image returns with the same velocity by the opposite wall. Under these conditions, the number of particles in the central cell, and consequently the density, is constant. These conditions also allow the conservation of the energy and the momentum of the system and do not introduce periodic effects (because of the interaction between particles).
According to the hypotheses and according to the geometry of the problem, other boundary conditions are proposed [26]. For example, in order to model thin films, the simulation cells are longitudinal and parallel to the film; one uses PBC in the directions parallel to the film. In the direction normal to the film, free edge boundary conditions can be used. In such cases, it may be appropriate to also include surface fields and surface interactions. In this way, one can study phenomena such as wetting, interface localization-delocalization transitions, surface-induced ordering and disordering, etc.
The core of the program includes calculating the potential energies of particle configuration and particle collisions. The interactions and collisions between particles can be elastic or inelastic; they can be binary or collective. For computation, the interaction energy of a particle with its neighbors is carried out by refocusing a base cell on the particle. This particle only interacts with particles in this region. This is called the “minimal image convention” (MIC) [1].
Generally, a RANDOM generator of real random numbers ri belonging to the domain {0, 1} (or ri ∈ {0, 1} is available. This distribution law is uniform.
To have a real random number xi belonging to the domain {a, b} (or xi
To have a real random number xi belonging to the domain {a, b} (or xi ∈ {a,b}) according to a formula (or law) of nonuniform distribution f(x), a histogram technique is used. Let Nm be the number of intervals. If the mesh is regular (Figure 3):
Random number selection according to f (x) distribution.
We define:
We define the sequence:
and the sequence:
Hence each real random number ri belongs to the domain {0, 1} (where ri ∈ {0, 1}) (according to the uniform law); this number belongs to the domain {rxj-1, rxj}. It corresponds to a random value xran of the domain {xj-1, xj}; this number satisfies the formula (or the law) of nonuniform distribution f(x).
This technique can be generalized for a nonuniform distribution law f(x) with an irregular mesh Δxi, or with tabular data f(xi) with i = 1,…, m.
The technique can be generalized, too, for a discrete distribution law f(i) with i = 1,…, m.
In the literature, the reader can find simple algorithms for the choice of random numbers of some simple functions (Gaussian, etc.).
It is necessary to find some parameters allowing the control of the smooth course of the evolution of the system. We must look for the constants of movement. For example for an isolated system, we have the conservation of the total energy and the quantity of matter.
By using the numerical simulation, it is possible to calculate many spatiotemporal quantities F(r,t). These quantities can be positions, speeds, kinetic moments, particle energies, concentrations, transport coefficients, etc. It would then be possible to calculate all other quantities related to F(r,t).
For the calculation of the averages, one can note the quantities on the space, on the time or on both. The histogram methods can be used. Static or dynamic distribution functions and spatial or temporal correlation functions can be calculated. It should be noted that the SMC is much more adequate for static properties because of the probabilistic choice of configurations.
Any calculated function or parameter F(r,t) can be used for another application in another calculation program.
In the MCS model discussed extensively in this chapter, it’s more about collisions between particles. It’s particle-particle MCS or PP-MCS. In many problems of physics, the general idea is the same, but the applications and proposed models are numerous.
Other MCS models, named particle-in-cell MCS (PIC-MCS), are based on particle-cell interactions. In these last models, we also use a probabilistic choice of configurations and small variations in the state of the system (following the Metropolis algorithm); the interaction is between the particle with a cell, a mesh, or a drop. The parameters and variables of the cell, although local and instantaneous, are macroscopic. These parameters and variables can be thermodynamic, fluid, or electromagnetic. An example of the model based on PIC-MCS is described by Mattei et al. [31] for simulation of electromagnetic particle-in-cell collision in inductively coupled plasmas. Several works can be found in the literature on this same line of work. Other MCS models using particles may be considered. [32].
For statistical physics problem solving (such as thin film deposition problems), MCS models use experimental, numerical, or theoretical data from other methods and models. Models can be improved to hybrid models. In the hybrid models, connections between two modules can be realized. The first module is MCS; the second module is fluid, electromagnetic, or other. An example of a three-module hybrid model is presented by Mao and Bogaerts [33] to study gas mixtures in PECVD system. The three modules are MCS, fluid, and electromagnetic. The first module EM calculates the electromagnetic fields by solving Maxwell equations. These fields are used as inputs in the module MCS, where the electron density, electron temperature, electron energy distribution function, and electron impact reaction rates can be computed with a Monte Carlo procedure. Subsequently, the module fluid calculates densities and fluxes of the various plasma species (i.e., heavy particles and electrons) with continuity equations and the electrostatic field with Poisson’s equation. This electrostatic field is used as input again in the EM. This cycle is iterated until convergence. The schematic of the hybrid model is given in Figure 4.
Schematic of a hybrid model of three modules used to study gas mixtures in the PECVD [33].
To solve statistical physics problems with evolutions as a function of time, kinetic models of MCS (kMCS) are used. Using kMCS, Battaile and Srolovitz [17] described kinetic phenomena of the diffusive motion of a single interstitial atom in a close-packed metal crystal. The motion of the interstitial atom is usually limited to two types: vibration of the atom around the center of the interstitial hole in which it resides and hops to nearest-neighbor interstitial sites. The atom can hop into any of the nearest-neighbor interstitial sites; it executes a random walk. In an MC simulation of this diffusion process, the new position of the interstitial atom is chosen at random from a list of the adjacent interstitial sites.
Other CVD and PECVD works on MCS are presented in Ref.s [15, 34, 35, 36, 37, 38]. They show how MCS methods can study properties of gas mixtures and properties of the growth of thin films.
In this section, we present an example of PP-MCS of collisions and reactions in gas phase of SiH4/H2 mixture used in PECVD process. Some paragraphs have been treated in previous works [21, 24].
We use a MCS to study collisions and chemical reactions in gas phase of SiH4/H2 mixture used in the PECVD process. In this phase, important reactions have been identified that contribute to the production and the consumption of hydrogen (H), silylene (SiH2), and silyl (SiH3). The hydrogen consumption reactions SiH4 + H → SiH3 + H2 and SiH3 + H → SiH2 + H2 are found to play a central role in deciding the distribution of hydrogen [39].The plasma chemistry indicates that H atoms and SiH3 radicals play an important role in the a-Si:H deposition process [40]. Experimentally, it is generally accepted that SiH3 radicals dominate a-Si:H and μc-Si film growth from SiH4 plasmas in the PECVD; it is the key precursor of a-Si:H deposition [41]. The proposed MCS allowed to get the ratio SiH2/SiH3 and mean value of densities of species. It provides information on SiH4 dissociation and on the production of SiH3, H, SiH2, and Si2H6 and other important parameters.
The plasma in the PECVD reactor is weakly ionized. For our study, the mixture gas contains 22% of SiH4 and 78% of H2; the pressure is 100 mtorr, the temperature of the gas ranges from 373 to 723 K, the electron temperature is about 2.5 eV, and the electron density is 3. 108 cm−3. The process is considered to be stationary. We take into account electrons and eight neutral species (SiH4, SiH3, SiH2, H, H2, Si2H6, Si2H5, SiH). Reactions taken into account include seven electron-neutral and 14 neutral-neutral reactions. Table 1 shows the 21 reactions and rate constants Kreac. At low temperature, the neutrals interact occasionally with each other and move under the effect of thermal agitation; their velocity distribution function is Maxwell-Boltzmann distribution. Electrons have the mean velocity with kinetic energy Te.
Symbol | Reactions | Kreac (cm3/s) |
---|---|---|
R1 | SiH4 + e→SiH3 + H+e | k1 = 3 × 10−11 [42] |
R2 | SiH4 + e→SiH2 + 2H + e | K2 = 1.5 × 10−10 [42] |
R3 | SiH4 + e→SiH + H + H2 + e | K3 = 9.34 × 10−12 [42] |
R4 | SiH4 + e→SiH2 + H2 + e | K4 = 7.19 × 10−12 [42] |
R5 | H2 + e→2H + e | K5 = 4.49 × 10−12 [42] |
R6 | Si2H6 + e→SiH3 + SiH2 + H + e | K6 = 3.72 × 10−10 [42] |
R7 | Si2H6 + e→SiH4 + SiH2 +e | K7 = 1.1 × 1010× (1.(1./(1. + (0.63 × P)))) [43] |
R8 | SiH4 + H→SiH3 + H2 | K8 = 2.8 × 10−11 × exp.(−1250/T) [44] |
R9 | SiH4 + SiH2→Si2H6 | K9 = 1.1 × 1010 × (1.−(1./(1. + (0.63 × P)))) [43] |
R10 | SiH3 + SiH3→SiH4 + SiH2 | K10 = 0.45 × 1.5 × 10−10 [44] |
R11 | SiH4 + Si2H5→SiH3 + Si2H6 | K11 = 5 × 10−13 [42] |
R12 | SiH3 + H→SiH2 + H2 | K12 = 2 × 10−11 [44] |
R13 | SiH3 + Si2H6→SiH4 + Si2H5 | K13 = 4 × 10−10 × exp. (−2500/T) [44] |
R14 | SiH2 + H→SiH + H2 | k14 = 2 × 10−11 [44] |
R15 | Si2H6 + H→Si2H5 + H2 | K15 = 0.66 × 2.4 × 10−10 × exp. (−1250/T) [43] |
R16 | Si2H6 + H→SiH4 + SiH3 | K16 = 0.34 × 2.4 × 10−10 × exp. (−1250/T) [44] |
R17 | SiH + H2→SiH3 | K17 = 2 × 10−12 [43] |
R18 | SiH2 + SiH3→Si2H5 | K18 = 3.77 × 10−13 [43] |
R19 | SiH2 + H2→SiH4 | K19 = 3 × 10−12 × (1. + (1./1. + (0.03 × P))) [43] |
R20 | 2SiH3→Si2H6 | K20 = 0.1 × 1.5 × 10−10 [43] |
R21 | SiH4 + SiH→Si2H5 | K21 = (1.−(1./(1. + (0.33 × P)))) × (6.9 × 10−10) [43] |
List of gas phase reactions and corresponding rate constants [24].
Let
And chemical reaction for the production of A is as:
Rate production and consumption for any species A are taken as:
The MCS is based on binary collisions at the microscopic level. Elastic collisions are between all particles, and inelastic collisions (or effective collisions) are those that result in a chemical reaction. A chemical reaction needs a collision involving at least two particles (atoms, ions, electrons, or molecules). According to kinetic theory, gases consist of particles in random motion. These particles are uniformly distributed in a cell which has a parallelepiped form of sizes Lx, Ly, and Lz (Figure 5). These particles move in a straight line until they collide with other particles or the walls of their container. Dimensions and volume of Monte Carlo cell must take into consideration the mean free path of species.
Form of the simulation cell.
Let ni be the density of neutral spice i (i = 1,…, 8). The first particle i is randomly chosen according to a probability of neutral species Prsp,I (nonuniform discrete distribution) given by:
The chosen particle takes randomly three components of space in cell ri(xi, yi, zi) according to the normal distribution (nonuniform distribution). It takes also randomly three components of velocity vi (vxi, vyi, vzi) according to Maxwell-Boltzmann distribution.
Let ni and nj be the densities of species i and j in the gas and Vij the relative velocity between the two species i and j.
According to the kinetic theory of gases, we have for an incident particle i on a target particle j the average collision frequency νij as:
where <sij> is the cross section of the particle j.
The mean free path <λι> of species i is:
The time between two collisions τij is then:
For chemical effective reactions (inelastic collisions) between two reactive species i and j giving products i’ and j’, the rate constant reaction verifies [45]:
General rules of collision theory are applied:
The new velocities of the colliding particles are calculated using conservation of energy and momentum for elastic collisions.
Conservation of total energy as isolated system.
Movement of the center of mass and relative motion around the center of mass.
The reader can refer to some fundamental physics books that deal with general notions of collisions and corresponding parameters [45, 46, 47, 48].
The plasma in the PECVD reactor is weakly ionized. At low temperature, particles interact occasionally with each other and move under the effect of thermal agitation. In reality, only a small fraction of collisions are effective (result in a chemical reaction) [21].
In our MCS, after traveling a random walk given by a Gaussian distribution, the first chosen particle collides with a second particle (molecule, atom, radical, or electron). The last particle j is randomly chosen according to a (i-j) collision probability Prcol,j (nonuniform discrete distribution) given by:
where
The activation energy is given by:
where the pre-exponential factor is assumed to be the collision frequency factor and Kreac is the rate constant of the gas phase reaction.
The two colliding particles (e.g., the electron and SiH4 molecule) can interact by several reactions (R1, R2, R3, and R4 in Table 1); we choose randomly one of gas phase reactions occurring according to a, nonuniform discrete distribution reaction probability Prreac (i,j):
where
All chemical systems go naturally toward states of minimum Gibbs free energy [21, 24]. A chemical reaction tends to occur in the direction of lower Gibbs free energy. To determine the direction of the reaction that is taking place, we use the old and new values of Kreac and the equilibrium constant with reactants and product concentrations. Each set of binary collisions can be related or converted into time. As cited in section (a), Table 1 gives gas phase reactions and corresponding rate constants used in this MCS.
To continue the simulation, after the elastic collision, particle i takes new values of components velocity and new mean free path; mean free path is taken from a normal (nonuniform) distribution (Gaussian distribution). If the collision is inelastic, we have to take a new particle.
From Metropolis algorithm, the scheme of this MCS is as follows:
Choices of particle of spice i with random position, velocity, and mean free path; periodic boundary conditions are used to keep particles in the elementary cell.
Choices of random collision with a spice j.
Study of collision type (elastic, inelastic). If the collision is elastic the particle i move with a new velocity and mean free path, and we return to step (b). If the collision is inelastic particles i and j give new particles i’ and j’, according to Metropolis scheme, and we return to step (a) or (b). Periodic boundary conditions are used to keep particles in the elementary cell.
At each step, we can note the different statistics.
Once the species are selected for the simulation model, an estimate of species densities should be made. Following the model of interaction and collisions between particles (binary, collective, etc.), a first choice of the minimum number Ni of particles of each species is made. A first estimate of the sizes (Lx, Ly, Lz) of the elementary cell is made.
The study of the types of interaction potentials and the calculation of the approximate values of the force ranges, the kinetic energies, the internal energies, and the energies of activation make it possible to correct the minimal numbers Ni of particles and the sizes (Lx, Ly, Lz) of the elementary cell.
Let kp be the number of a species, kp = 1,…, 9. The minimal numbers Qnp(kp) and the sizes (Lx, Ly, Lz) have to be discussed for statistical calculations.
For numerical programming, according to the programming language used and according to the size (or the computational capacity) of the computer, it is necessary to find a judicious choice of the tables of integer or real values and which values would be useful to save all during simulation. Let Ncol,m be the maximum number of elastic collisions per particle, and let Ncycle be the number of cycles to average the simulation calculations.
For this MCS, the numerical chosen values are in Table 2.
Cell dimensions and steps for collisions | Number of species Kp | Initial number of particles in cell | ||
---|---|---|---|---|
Lx (m) | 4.68 10−6 | 1 | Qnp(SiH4) | Qnp1 |
Ly (m) | 4.68 10−6 | 2 | Qnp(SiH3) | 10 |
Lz (m) | 20.0 10−3 | 3 | Qnp(SiH2) | 10 |
4 | Qnp(H) | 10 | ||
Ncol,m | 500 | 5 | Qnp(H2) | Qnp5 |
Ncycle internal cycle | 2000 | 6 | Qnp(Si2H6) | 10 |
Ncycle external cycle | 200,000 | 7 | Qnp(SiH) | 10 |
8 | Qnp(Si2H5) | 10 | ||
9 | Qnp(e) | Qnp9 |
Used quantities and parameters in calculations for the gas temperature Tg = 520 K.
For radicals (e.g., SiH3), particle numbers Qnp(k) are very small; we take Qnp(k) = 10. These numbers cannot take value 1 or 0, even if a species k is in trace form in the gas. The value 0 for a species k means that any other species k’ does not make a collision with the species k; and the value 1 means that we have no collisions between particles of the same species in the cell.
Qnp1, Qnp5, and Qnp9 are calculated from the volume of cell, the pressure, the temperature, and the total number of particles in the cell (Qnp1 = 0.81187824 * 109; Qnp5 = 0.20296956 * 109; Qnp9 = 131).
As we have chosen a stationary regime, we must reach the values and properties at equilibrium. The results of the simulation show this trend. In MCS, averaged values, distribution functions, autocorrelation functions, and correlation functions can be calculated. To ensure rapid convergence of calculations, it would be useful to look for statistically symmetric (or stationary or unsteady) parameters [26, 50].
As an example for our MCS calculation, we have:
The number of Si2H6, SiH, and Si2H5 particles reaching the surface is negligible.
Let Ns,i and Ns, H2 be the densities of a species i and H2 reaching the surface. The ratios Ns,i/Ns, H2 are too small (Table 3).
Let Ns,i be the density of a species i reaching the surface and Nv,i the density of same species i in volume. The ratios Ns,i/Nv,i are too small (Table 4); the surface effect is negligible.
The reactions begin with the dissociation (consumption) of H2 and SiH4 by R5, R1, and R2 reactions.
The production of SiH3 is done by R8, and then there is production of SiH2 by R12.
The reaction R2: SiH4 + e → SiH2 + 2H + e plays the central role in SiH4 dissociation by electron impact [24]. This result is compatible with [39].
The second important chemical reaction in the SiH4 dissociation is R1: SiH4 + e → SiH3 + H + e [24]. This result is compatible with that of Perkins et al. [51] and that of Doyle et al. [52].
Type | H2 | SiH4 | H | SiH3 | SiH2 |
---|---|---|---|---|---|
Ns,i/Ns, H2 | 1 | 0.23 | 1.67 10−4 | 8.60 10−5 | 9.86 10−6 |
Ratios Ns,i/Ns, H2 of particles reaching the surface compared to H2.
Type | SiH4 | SiH3 | SiH2 |
---|---|---|---|
v, j | 6.695 10−6 | 7.965 10−6 | 775 10−6 |
Ratios Ns,i/Nv,i of particles reaching the surface compared to volume.
MCS is a widely used method in statistical physics to study thermodynamic, structural, or phase properties. It is based on random and probabilistic processes. The purpose of this chapter is to present the technique for general use in physics for the study of thin film deposition problems. The technique can be generalized to other fields of science: biology, economics, transportation, and social sciences.
We started by presenting general rules for numerical simulation methods. Metropolis algorithm has been considered as the basic algorithm. After, we presented the different steps for the realization of a MCS code. We chose the particle-particle model MCS (PP-MCS) to explain the different steps and procedures to be applied in the deposition of thin layers by PECVD processes. We have shown that this technique can be generalized to the particle-in-cell MCS (PIC-MCS) case or kinetic MCS (kMCS), as it can be joined with other modules to give hybrid models. It is important to know how to choose random configurations from the laws or probability distributions in the system.
A numerical application is presented for collisions in a SiH4/H2 gas mixture in the PECVD process. A preliminary work of determination of the chemical reactions between molecules and radicals is made. A choice of the simulation cell is made, and the definition of the probabilities of the collisions between peers is made. The Metropolis algorithm makes it possible to follow the various elastic and inelastic collisions; it also makes it possible to make the statistics of the interactions with the surface. The results are compatible with [39, 51, 52].
Other questions may be asked to account for molecular ions, surface and volume kinetics, or thin film formation. The techniques and different models of the MCS (PP-MCS, MCS-PIC, kMCS) allow taking care of these questions.
The interconnection of the MCS with other models (MDS, hybrid model, fluid model, electromagnetic model, etc.) would allow answering more questions. The methods can be applied to other specialties than the physical sciences.
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