Department of Physics, Chemistry and Biology
Master’s Thesis
Structural and electronic properties of bare and
organosilane-functionalized ZnO nanopaticles
Linda Angleby
2008-12-05
LITH-IFM-EX--08/1933—SE
Linköping University Department of Physics, Chemistry and Biology SE-581 83 Linköping
Department of Physics, Chemistry and Biology
Structural and electronic properties of bare and
organosilane-functionalized ZnO nanopaticles
Linda Angleby
2008-12-05
Supervisor
Lars Ojamäe
Examiner
Lars Ojamäe
Avdelning, institution
Division, Department
Chemistry
Department of Physics, Chemistry and Biology Linköping University
URL för elektronisk version
ISBN
ISRN: LITH-IFM-EX--08/1933--SE
_________________________________________________________________ Serietitel och serienummer ISSN
Title of series, numbering ______________________________
Språk Language Svenska/Swedish Engelska/English ________________ Rapporttyp Report category Licentiatavhandling Examensarbete C-uppsats D-uppsats Övrig rapport _____________ Titel Title
Structural and electronic properties of bare and organosilane-functionalized ZnO nanopaticles Författare Author Linda Angleby Nyckelord Keyword Sammanfattning Abstract
A systematic study of trends in band gap and lattice energies for bare zinc oxide nanoparticles were performed by means of quantum chemical density functional theory (DFT) calculations and density of states (DOS) calculations. The geometry of the optimized structures and the appearance of their frontier orbitals were also studied. The particles studied varied in sizes from (ZnO)6 up to (ZnO)192
Datum
Date
.The functionalization of bare and hydroxylated ZnO surfaces with MPTMS was studied with emphasis on the adsorption energies for adsorption to different surfaces and the effects on the band gap for such adsorptions.
1. Abstract ... 1
2. Introduction ... 2
2.1 Properties of ZnO crystals ... 2
2.2 Electronic structure of ZnO ... 3
2.3 Functionalization with MPTMS ... 3
3. Method ... 4
3.1 Geometry optimization ... 4
3.2 Electronic structure ... 4
3.3 Functionalization ... 4
4. Results and Discussion ... 5
4.1 Bare ZnO clusters ... 5
4.1.1 Structure ... 6 4.1.2 Lattice energies ... 7 4.1.3 Electronic structure ... 11 4.2 Functionalized ZnO ... 17 4.2.1 Structure ... 17 4.2.2 Adsorption energies ... 18 4.2.3 Electronic structure ... 18 5. Conclusions ... 21
5.1 Optimization of bare ZnO particles ... 21
5.2 Functionalization with MPTMS ... 21
6. References ... 22
7. Acknowledgments ... 24
1. Abstract
A systematic study of trends in band gap and lattice energies for bare zinc oxide nanoparticles were performed by means of quantum chemical density functional theory (DFT) calculations and density of states (DOS) calculations. The geometry of the optimized structures and the appearance of their frontier orbitals were also studied. The particles studied varied in sizes from (ZnO)6 up to (ZnO)192. The functionalization of bare and hydroxylated ZnO surfaces with MPTMS was studied with emphasis on the adsorption energies for adsorption to different surfaces and the effects on the band gap for such adsorptions.
2. Introduction
2.1 Properties of ZnO crystals
Zinc oxide is a wide band gap semiconductor that exhibits a number of interesting electronic and optical properties such as piezoelectricity [12] and photo conductivity [13].
This material has many potential uses like gas sensors, light emitting diodes, thin film transistors and solar cells. It is also non-toxic and biocompatible, which makes it a candidate for a variety of in vivo applications [3] [14].
Figure 1. The two directions of the crystal structure that gives name to the surfaces perpendicular to the
directions in question. Zinc atoms are blue and oxygen atoms are red.
Bulk zinc oxide has a hexagonal (wurtzite) crystal structure and the experimental bulk lattice energy is 4142 kJ/mol [1]. Two of the most important crystal surfaces are denoted 0001 and 10-10 (Fig 1). These differ in the distribution of zinc and oxygen, and therefore provide different possibilities for coordinating adsorbed molecules.
The stability of a crystal structure can be described by the lattice energy, which is defined as the change in molar enthalpy for the process MX(s) M 2+(g) + X 2+(g). The larger the
enthalpy, the more stable the lattice.
To systematically study the dependence on cluster size and shape, a variety of clusters were prepared from an existing crystal structure. The structures were created by increasing the number of “rings” and “layers” to produce series of growing crystals (Fig 2), from sizes as small as (ZnO)6 up to (ZnO)192.
10-10
2.2 Electronic structure of ZnO
The difference in energy between the top of the valence band and the bottom of the conduction band is called the band gap. These energy levels may also be called HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital). For zinc oxide the LUMO corresponds to the 4s orbital of zinc and HOMO the 2p orbital of oxygen.
The band gap of ZnO is of interest because of its importance for the conductivity of the materials. Bulk zinc oxide has an experimental band gap of 3.37 eV [2], but the HOMO-LUMO difference varies with cluster size and also when different molecules become adsorbed to the surface.
Another approach to study the electronic structure is to calculate the density of states (DOS). This is a plot of the number of states available for occupation by electrons at each energy level. The higher the DOS at an energy level, the more states are available. A DOS of zero means that there are no states available, which is the case within the band gap. In the DOS plot you may also study the effective band gap, which is the difference in energy between the edges of the dominant parts of the DOS in the valence a conduction bands, ignoring small DOS in the band gap that would otherwise constitute the HOMO and LUMO energy levels.
2.3 Functionalization with MPTMS
MPTMS (mercaptopropyltrihydroxysilane) (Fig 3) is a potential linker for the immobilization of biomolecules that may realize different biosensing and bioelectronic applications [3] [14]. The attractive features of MPTMS are the silane that may form self-assembled monolayers on metal oxide surfaces, and the organic tail with a free thiol that can link to biomolecules by a disulfide bridge [4].
This study mainly concentrates on the changes in structure and band gap of the surface on which MPTMS adsorbs. For this application the methyl groups have been omitted to leave only the hydroxyl groups to interact with the ZnO surface. It was proposed by Petoral et al. in the study of MPTMS on semiconductor surfaces [4] that the preferred orientation of the adsorbed MPTMS was to bind with oxygen to zinc in the surface, and that the adsorbed molecules condensate to form the self-assembled monolayer. Petoral et al. also discussed how the MPTMS may attach to a hydroxylated ZnO surface.
Si O O O SH a Si HO OH OH SH b c
3. Method
3.1 Geometry optimization
The clusters studied were sculpted in Cerius2 [15] from crystal coordinates. Each series of clusters consisted of a base structure to witch were added layers to increase the cluster size. These structures were then geometry optimized in the Gaussian 03 software [5], by DFT calculations, using the B3LYP hybrid functional [6] and a double-zeta basis set [7].
3.2 Electronic structure
To calculate the molecular orbitals of the optimized clusters, the double zeta basis set was again used. The 6-31G(d,p) basis set [8] gives more accurate results but the calculation time is considerably longer due to the heavier calculations. Therefore only a few of the smaller structures were studied using this basis set. The Molekel software [16] was used to visualize the HOMO and LUMO of the different clusters.
3.3 Functionalization
The functionalizations were studied by energy optimization of the geometry of adsorbent in proximity to an already optimized ZnO cluster surface, followed by calculations of the
electronic structure and the density of states, to evaluate the impact on the band gap. For these calculations, the double zeta basis set and B3LYP functional were used.
4. Results and Discussion
4.1 Bare ZnO clusters
The results of the optimization of the bare zinc oxide clusters are shown in figure 4. The optimized structures are divided into groups that display structural similarities. The first of these groups are the hexagonal clusters, the second group is the triangular shapes, and the fourth show the flat series and the fifth group are rhombic in their appearance. The clusters in the series of triangular shapes, h to k in figure 4, have an uneven number of zinc and oxygen atoms in each layer. Energy optimizations were therefore only performed on particles with an even number of layers for this series.
a b c d e f g k j i h l m
Figure 4. Optimized structures of ZnO clusters.
Structures are named (a) rod, (b) snowflake, (c) large snowflake, (d) elliptic, (e) 3flat, (f) 4flat, (g) 5flat, (h) rope, (I) prism, (j) large prism, (k) blunted prism, (l) rhombic and (m) large rhombic.
4.1.1 Structure
In general the optimizations of the structures gave similar results. The bulk structure were lost in the cluster surfaces, where the individual zinc and oxygen became more aligned in the 0001 direction, although oxygen tends to protrude a bit more from the surface than zinc. The
different Zn-O bond lengths became almost equal, and the O-O and Zn-Zn bond lengths were shortened. Figure 5 show the relative structures and bond lengths before and after
optimization.
Figure 5. (a) Starting structure for elliptic (ZnO)10, (b) optimized structure for elliptic (ZnO)10, (c) starting
structure for rod (ZnO)9, (d) optimized starting structure for rod (ZnO)9.
For the series of flat clusters, seen in figure 6, there was partial loss of the wurtzite structure. Instead the lattice assumed a more compressed geometry. Only the flat cluster with four rings maintains a hexagonal structure, however severely flattened.
1..992 Å 3. 217 Å 1.973Å 5.205 Å 2.044 Å 1.924 Å 1.98 Å 3.92 Å 4.087 Å 3.801 Å 3.819 Å a b c d
Figure 6. Geometry optimization of ZnO flat series. (a) Starting structure for 3flat (ZnO)14, (b) optimized
structure for 3flat (ZnO)14, (c) starting structure for 4flat (ZnO)18, (d) optimized structure for 4flat (ZnO)18, (e)
starting structure for 5flat (ZnO)22, (f) optimized structure for 5flat (ZnO)22
4.1.2 Lattice energies
.
The lattice energies calculated for the geometry optimized structures have been plotted against the number of layers and the number of ZnO in the clusters. Figure 7 and 8 show how the lattice energy depends on cluster size. The lattice energy will increase with cluster size until it reaches the value for the structure in question with an infinite number of layers. From figure 8 you can see that the structure called snowflake has larger lattice energy than the other structures. This indicates that this is the most stable form of the nanostructural ZnO particles, and this stability may make this structure a good candidate for nanowires. On examination of lattice energies for the structures called large snowflake and blunted prism, if extrapolated, they may be more stable than the snowflake structure.
a b
c d
4,32 4,34 4,36 4,38 4,4 4,42 4,44 4,46 4,48 4,5 4,52 1 10 100 log(Number of layers) L at ti ce en er g y* 10^ -3 ( kJ/ m o l) Rod Elliptic Rope 3Flat 4Flat Rhombic 5Flat Prism Snowflake Large rhombic Large prism Blunted prism Large snowflake
Figure 7. Lattice energy plotted against the log of the number of layers in cluster.
4,32 4,34 4,36 4,38 4,4 4,42 4,44 4,46 4,48 4,5 4,52 0 50 100 150 200 n L at ti ce en er g y* 10^ -3 ( kJ/ m o l) Rod Elliptic Rope 3Flat 4Flat Rhombic 5Flat Prism Snowflake Large rhombic Large prism Blunted prism Large snowflake
To try and find the lattice energy for an infinite one, two or three dimensional cluster a number of plots were devised. To accomplish this, the lattice energies for different series of clusters were plotted against 1/n, 1/n1/2 or 1/n1/3
Figure 9. Examples of series of clusters for extrapolation to find the lattice energy of an infinite growth in (a)
one dimension, (b) two dimensions, (c) three dimensions.
Figure 10 show the lattice energies for each cluster series and the function of the fitted straight lines. You can see that for a structure that increases in size in one dimension, the mean value for the lattice energy would be 4461.5 kJ/mol. For the infinitely grown two-dimensional cluster the mean lattice energy would be 4529.8 kJ/mol. The infinite tree-dimensional cluster, i.e. the bulk of ZnO, would be 4594.9 kJ/mol, which is not far from the experimental lattice energy for bulk ZnO at 4142 kJ/mol [1].
depending on the nature of the series. Here n equals the number of ZnO units in the particle. The variables were deduced from the equation for the energy of a particle, and the calculations are accounted for in the appendix. To make a series of clusters that extends in one, two or three dimensions, layers or rings were added to a suitable structure. Examples of some of these series are shown in figure 9.
a
b
(a) y = -0,6129x + 4,4454 4,32 4,34 4,36 4,38 4,4 4,42 0 0,05 0,1 0,15 0,2 1/n Lat ti ce ener gy* 10 -3 (kJ/ mo l) (b) y = -0,7466x + 4,469 4,32 4,34 4,36 4,38 4,4 4,42 4,44 4,46 4,48 0 0,05 0,1 0,15 0,2 1/n Lat ti ce ener gy* 10 -3 (kJ/ mo l) (c) y = -0,4363x + 4,5217 4,32 4,34 4,36 4,38 4,4 4,42 4,44 4,46 0 0,1 0,2 0,3 0,4 0,5 1/n1/2 Lat ti ce ener gy* 10 -3 (kJ/ mo l) (d) y = -0,4734x + 4,5299 4,39 4,4 4,41 4,42 4,43 4,44 4,45 4,46 0 0,1 0,2 0,3 1/n1/2 Lat ti ce ener gy* 10 -3 (kJ/ mo l) (e) y = -0,472x + 4,5379 4,32 4,34 4,36 4,38 4,4 4,42 4,44 4,46 4,48 0 0,2 0,4 0,6 1/n1/2 Lat ti ce ener gy* 10 -3 (kJ/ mo l) (f) y = -0,4556x + 4,595 4,3 4,35 4,4 4,45 4,5 4,55 0 0,2 0,4 0,6 1/n1/3 Lat ti ce ener gy* 10 -3 (kJ/ mo l) (g) y = -0,4595x + 4,5952 4,38 4,4 4,42 4,44 4,46 4,48 4,5 4,52 0 0,1 0,2 0,3 0,4 0,5 1/n1/3 Lat ti ce ener gy* 10 -3 (kJ/ mo l) (h) y = -0,4551x + 4,5946 4,3 4,35 4,4 4,45 4,5 0 0,2 0,4 0,6 1/n1/3 Lat ti ce ener gy* 10 -3 (kJ/ mo l)
Figure 10. Crystal growth. (a) rod (ZnO)6, elliptic (ZnO)10, 3flat (ZnO)14, 4flat (ZnO)18. (b) rod (ZnO)6, rod
(ZnO)9, rod (ZnO)12, rod (ZnO)15, rod (ZnO)18, rod (ZnO)24, rod (ZnO)48, rod (ZnO)96, rod (ZnO)192. (c) rod (ZnO)6, rhombic (ZnO)16, large rhombic (ZnO)30. (d) rope (ZnO)13, prism (ZnO)22, blunted prism
To get more accurate values for the energies calculations were performed for the optimized structures using the 6-31G(d,p) basis set. In table 1 the lattice energies for the smallest cluster in some of the series are tabulated for comparison of the two basis sets used. It is clear that the 6-31G(d,p) basis set gives larger lattice energies, and they are therefore farther from de
reference lattice energy for the bulk ZnO.
Structure Lattice energy*10-3 (kJ/mol) Lattice energy*10-3 (kJ/mol) 6-31G(d,p) Rod (ZnO)6 4.3436 4.5044 Elliptic (ZnO)10 4.3828 4.5413 Rope (ZnO)13 4.3994 4.5556 3flat (ZnO)14 4.4025 4.5357 Rhombic (ZnO)16 4.4125 4.5684 4flat (ZnO)18 4.4113 4.5664 5flat (ZnO)22 4.4185 4.5711 Prism (ZnO)22 4.4273 4.5811 Snowflake (ZnO)24 4.4360 4.5903
Table 1. Lattice energies calculated with the double zeta and 6-31G(d,p) basis sets.
4.1.3 Electronic structure
The electronic structure of nanostructured ZnO was studied by DFT calculations to obtain the density of states, from which the HOMO-LUMO band gap and the effective band gap. In figure 11 through 15 the results of some of the DOS calculations are displayed. In figure 16 the band gap is plotted against the number of layers in the structure. Most structures show band gaps that do not change much with an increasing number of added layers. The triangular structures exhibit a pronounced decrease in the width of the band gap with increasing particle size. The rhombic structures have a fluctuating width of the band gap that is seen as a zigzag pattern in the plot. Upon closer examination this pattern seems to arise from two curves that might depend on different properties discussed below. It is possible that for larger rhombic structures than the ones examined in this project, the size will approach a point where one property dominates the band gap. In figures 11 through 13, which show the DOS for different series of clusters, you can see that there is no clear correlation between band gap and cluster size within the range studied. In figure 14 and 15 pictures of the HOMO and LUMO are displayed next to the corresponding band in the DOS plot. The correlation between band gap and dipole moment is illustrated in table 2. From figure 14 and 15, and table 2 you can see that the clusters with a large resulting dipole moment within the particle, also exhibit a smaller band gap than does the particles with a smaller dipole moment. Therefore you can come to the conclusion that the width of the band gap is more dependent on the resulting dipole moment than the particle size. The larger the dipole moment gets, the smaller the band gap is.
Structure lμl Band gap (eV) 3flat (ZnO)14 45,8 5,918 3flat (ZnO)21 7266,8 5,375 3flat (ZnO)28 35,7 5,756 3flat (ZnO)35 4648,5 5,709 3flat (ZnO)42 12,2 5,745 Rhombic (ZnO)16 61 5,872 Rhombic (ZnO)24 16525 4,061 Rhombic (ZnO)32 24,1 5,406 Rhombic (ZnO)40 14998,5 4,731 Rhombic (ZnO)48 11,4 5,159 Rope (ZnO)13 168,3 5,813 Rope (ZnO)26 8723,3 5,216 Rope (ZnO)39 21059,8 4,247 Prism (ZnO)22 662,6 5,922 Prism (ZnO)44 11350 5,123 Prism (ZnO)66 32059,5 3,805 Prism (ZnO)88 55173,8 2,845
Figure 15. DOS plots for the rope (top) and prism (bottom) series of clusters. MOs corresponding to the valence
0 1 2 3 4 5 6 7 0 2 4 6 8 10 Number of layers B a n d g a p ( e V ) Rod Elliptic Rope 3Flat 4Flat Rhombic 5flat Prism Snowflake Large rhombic Large prism Blunted prism Large snowflake
Figure 16. Band gap plotted against the number of layers in the clusters.
To calculate the molecular orbital energies the double-zeta basis set was used. This kind of basis set yields shorter calculation times, but also less accuracy in the calculated energies, especially for the unoccupied molecular orbital, which gives rise to an error in the HOMO-LUMO band gap.
To give more accurate results the 6-31G(d,p) basis set was used for calculation of the
electronic structure for some of the smaller clusters. The result of this comparison is tabulated in table 3. The band gap calculated with the 6-31G(d,p) basis set is much smaller, and more closely resemble the reference value of 3.37 eV for bulk ZnO. The band gap of zinc oxide clusters of the studied sizes are generally larger than for the bulk. This may be the result of lacking accuracy in the B3LYP functional.
Structure Band gap (eV) DZ Band gap (eV) 6-31G(d,p)
Rod (ZnO)6 5.635 3.465
Elliptic (ZnO)10 5.770 3.532
Rope (ZnO)13 5.813 3.433
4.2 Functionalized ZnO
The functionalization of zinc oxide surfaces were studied by DFT and analyzed by DOS calculations. The properties and structure of hydroxylated ZnO clusters were studied by the adsorption of water molecules onto the bare zinc oxide surface. Then the adsorption of MPTHS on the bare and hydroxylated zinc oxide surfaces followed.
4.2.1 Structure
Figure 17 and 18 show the geometry optimized adsorptions. The hydroxylation of the surface with water yields a network of dissociated water molecules, hydrogen bonded to each other. The water does not seem to have any prominent effect on the ZnO lattice. The adsorption of MPTHS on the other hand appears to disrupt the lattice structure. For the adsorption of MPTHS to 0001 surface of rod (ZnO)6
Figure 17. Adsorption of water on the optimized ZnO clusters. (a) Adsorption of one molecule of water on the
10-10 surface of rod (ZnO)
, with the hydrogen on the other side of the cluster, the lattice looks like it reverts to the bulk structure.
6. (b) Adsorption of six molecules of water on the 10-10 surface of rod (ZnO)6. (c)
Adsorption of eight molecules of water on the 10-10 surface of elliptic (ZnO)20. (d) Adsorption of sixteen
molecules of water on the 10-10 surface of elliptic (ZnO)
Figure 18. Adsorption of MPTMS on the (e) water covered 10-10 surface of elliptic (ZnO)
20.
20, (f) 10-10 surface
of rod (ZnO)6, (g) 0001surface of rod (ZnO)6, (h) 10-10 surface of rod (ZnO)9, (i) 10-10 surface of elliptic
(ZnO)20, (j) 0001 surface of rod (ZnO)6 with hydrogen moved to the opposite surface, (k) 0001 surface of rod
a b c d
e f g h
4.2.2 Adsorption energies
Adsorption energies were calculated by subtracting the energy of the bare particle and the number of free molecules of the adsorbate multiplied by the energy of one particle of the adsorbate, from the energy of the particle with the adsorbate on the surface after adsorption.
E
ads= - (E
cluster + adsorbate– E
cluster– n*E
adsorbateAdsorption
)
For the adsorption reactions where MPTHS was adsorbed on a hydroxylated surface of a particle, the adsorption energy was calculated using the energy of the hydroxylated particle rather than the energy of the bare particle. These energies are summarized in table 3 below.
Adsorption energy (kJ/mol)
(a) Rod (ZnO)6 and 1 H2O 182.5
(b) Rod (ZnO)6 and 6 H2O 1086.7
(c) Elliptic (ZnO)20 and 8 H2O 1385.2
(d) Elliptic (ZnO)20 and 16 H2O 2687.3
(e) Elliptic (ZnO)20 , MPTHS and 8 H2O 177.7
(i) Elliptic (ZnO)20 and MPTHS 393.2
(f) Rod (ZnO)6 and MPTHS on 10-10 surface 327.1 (j) Rod (ZnO)6 and MPTHS on 0001 surface,
hydrogen at bottom
361.1 (k) Rod (ZnO)6 and MPTHS on 0001 surface,
hydrogen on top
373.9 (g) Rod (ZnO)6 and MPTHS on 0001 surface 391.3 (h) Rod (ZnO)12 and MPTHS on 10-10 surface
(hydrogen bond)
234.3 (l) Rod (ZnO)12 and MPTHS on 10-10 surface 299.4
Table 3. Adsorption energies for adsorption of water and MPTHS on ZnO.
On studying the adsorption energies in table 3 you can come to the conclusions that it is more energetically favorable for MPTHS to adsorb to the 0001 surface of rod (ZnO)6
4.2.3 Electronic structure
rather than the 10-10 surface, and that the adsorption of MPTHS to a hydroxylated surface is less favorable than adsorption to the bare ZnO surface. This may be due to that the main bonding type between the hydroxyl groups on the surface and those on MPTHS is hydrogen bonding. The report [4] by Petoral et al. suggested that there may be a mechanism of dehydration upon adsorption of MPTMS.
DOS plots of the adsorption calculations shown in figures 19 and 20, tell us that the band gap does not change upon adsorption. This is because the HOMO and LUMO of MPTHS lie within the conduction and valence bands for zinc oxide.
Figure 19. DOS plot for (a) bare and (b) functionalized rod (ZnO)6. In (a), the blue line represents the
contribution from zinc and the red line represents the contribution from oxygen in ZnO. In (b), the blue line represents the contribution from ZnO and the red line represents the contribution from MPTHS.
5. Conclusions
5.1 Optimization of bare ZnO particles
From the DFT calculations on bare ZnO clusters of different size and shape, information about the stability and band gap of the particles, and also the structure of the lattice and molecular orbitals were derived.
The optimized clusters loose their bulk structure in favor of a more compact structure, with shorter bond lengths. Surface oxygen protrudes from the surface more than zinc and therefore has a greater chance to interact with the medium surrounding the particle.The flat particles with more than two rings exhibit a loss of the wurtzite structure and instead form a more compressed structure in parts of the cluster.
Calculations show that lattice energies increase with particle size, and when the particle approaches infinite size the values become close to that of the reference bulk lattice energy. There seems to be no clear correlation between band gap and cluster size, but the band gap appear to be affected by large dipole moments within the particle, in such a way that a large dipole moment decreases the band gap. Band gaps for the nanoparticles studied by DFT are larger than that of bulk zinc oxide.
5.2 Functionalization with MPTMS
Energy optimization for MPTMS adsorbed onto bare and hydroxylated ZnO surfaces give information about the adsorption energies. DOS calculations for the adsorbent on the surface show the effect on the band gap of the particle.
A comparison of the adsorption energies for MPTMS on bare (ZnO)6 show that adsorption to the 0001 surface is more energetically favorable than adsorption to the 10-10 surface. Also, the adsorption to bare zinc oxide surfaces appear to be more favorable than adsorption to hydroxylated surfaces. On this account however, more studies regarding the reaction mechanisms are needed to come to a full conclusion.
6. References
[1] David R. Lide, CRC Handbook of Chemistry and Physics, 88th Edition, Taylor and Francis Group LLC 2008
[2] C. Klingshirn, The Luminescence of ZnO under high One- and Two-Quantum Excitation, Phys. Status Solidi B, 1975, vol. 71, pp. 547–556.
[3] R. Yakimova, G. Steinhoff, R.M. Petoral Jr. , C. Vahlberg, V.Khranovskyy, G.R. Yazdi, K. Uvdal, A. Lloyd Spetz (2006) Novel material concepts of transducers for chemical and biosensors. Biosensors and Bioelectronics 22, 2780-2785
[4] R.M. Petoral Jr. , G.R. Yazdi, A. Lloyd Spetz, R. Yakimova, and K. Uvdal (2007)
Organosilane-functionalized wide band gap semiconductor surfaces. Applied Physics Letters 90, 223904
[5] M. J. Frisch et al. , GAUSSIAN03, Gaussian inc. , Wallingford, CT, 2004. [6] A. D Becke, J. Chem. Phys. 98 (1993) 5648.
[7] Y. Bouteiller, C. Mijoule, M. Nizam, J. C. Barthelat, J. P. Daudey, M. Pelissier, B. Silvi, Mol. Phys. 65 (1988) 295.
[8] W. J. Hehre, R. Ditchfield, J. A. Pople, J. Chem. Phys. 56 (1972) 2257.
[9] Lijuan Li, Mingwen Zhau, Xuejuan Zhang, Zhonghua Zhu, Feng Li, Jiling Li, Chen Song, Xiangdog Liu, and Yueyuan Xia. (2008) Theoretical Insight into Faceted ZnS Nanowires and Nanotubes from Potential and First-Principles Calculations. J. Phys. Chem. C 2008, 112, 3509-3514
[10] Baolin Wang, Shigeru Nagase, Jijun Zhao and Guanghou Wang (2007) Structural growth sequences and electronic properties of (ZnO)(n) (n=2-18). J. Phys. Chem. C 2007, 111, 4956-4963
[11] Xiao Shen, Mark R. Pederson, Jin-Cheng Zheng, James W. Davenport, James T.
Muckerman, Philip B. Allen (2006) Electronic Structure of ZnO nanowire. eprint arXiv:cond-mat/0610002
[12] H. J. Xiang, Jinlong Yang, J. G. Hou, Qingshi Zhu (2006) Piezoelectricity in ZnO nanowires: A first-principles study. Applied Physics Letters 89 (2006) 223111
[13] Zeng YJ, Ye ZZ, Lu YF, et al. (2007) Investigation on ultraviolet photoconductivity in p-type ZnO thin films. Chemical Physics Letters 441 (2007) 115-118
[16] MOLEKEL 4.0, P. Flükiger, H.P. Lüthi, S. Portmann, J. Weber, Swiss National Supercomputing Centre CSCS, Manno (Switzerland), 2000.
7. Acknowledgments
I would like to thank my supervisor Lars Ojamäe for his help, guidance and devotion during this project.
And I also would like to thank Annika Lenz and Maria Lundquist for all their help and support.
8. Appendix
For particle growth in tree directions the particle were approximated to be spherical and the energy of that particle is
E = C
1* A + C
2* V (1)
where C1 and C2 are constants, A is the area of the surface and V is the volume of the sphere.
V = 4πr
3/
3 = δ * n (2)
A = 4πr
2= C
3* r
2(3)
δ is the volume occupied by one molecule of ZnO and n is the number of ZnO in the lattice. From equation 2 follows that
n = C
4* r
3(4)
r = n
1/3* C
4’ (5)
V = C
4’’ * r
3
(6)
When equations (3), (6) and (5) are put into equation (1) and this expression is divided by n we get an equation for the lattice energy
E / n = C
1’ / n
1/3+ C
2’ (7)
From equation (7) the conclusion is drawn that the lattice energy E / n is directly proportional to 1 / n 1/3.
For growth in two directions the particle is approximated to be a circular area with δ being the area occupied by one molecule of ZnO, and the energy expression is
E = C
1* L + C
2* A (8)
where L is the circumference.A = πr
2= δ * n
(9)
L = 2
πr
= C
3* r
(10)
Equation (9) and (10) give the expressions of n and rn = C
4* r
2
(11)
r = n
1/2* C
4’ (12)
that when put into equation (8) give the expression for the relationship between E and n.
E / n = C
1’ / n
1/2+ C
2’ (13)
Equation (13) shows that the lattice energy E / n is directly proportional to 1 / n 1/2 for expansion of a particle in two directions.
The expansion of a particle in one direction requires the assumption that the particle is represented by a strait line, and that δ is the length of one molecule of ZnO. The expression for the energy of such a particle would be
E = C
1+ C
2* L (14)
L is the length of the particle and is described byL = n * δ (15)
Equation (14) is rearranged into equation (16) and divided by n to give rise to equation (17).
E = C
1+ C
2’ * n (16)
E / n = C
1/ n + C
2’ (17)
From equation (17) we see that for particle growth in one direction, the lattice energy is proportional to 1 / n.
Equation (7), (13) and (17) give the incentive to make the plots in figure 10.
