Đây là một bài báo khoa học về dây nano silic trong lĩnh vực nghiên cứu công nghệ nano dành cho những người nghiên cứu sâu về vật lý và khoa học vật liệu.Tài liệu có thể dùng tham khảo cho sinh viên các nghành vật lý và công nghệ có đam mê về khoa học
Trang 1Effects of simultaneous doping with boron and phosphorous on the
structural, electronic and optical properties of silicon nanostructures
F Ioria, S Ossicinib,
a
CNR-INFM-S 3
and Dipartimento di Fisica, Universita’ di Modena e Reggio Emilia, via Campi 213/A, I-41100 Modena, Italy
b CNR-INFM-S 3 and Dipartimento di Scienze e Metodi dell’Ingegneria, Universita’ di Modena e Reggio Emilia, via Amendola 2 Padiglione Morselli, I-42100 Reggio Emilia, Italy
a r t i c l e i n f o
Available online 14 August 2008
PACS:
73.22.f
71.15.m
78.55.m
78.20.e
Keywords:
Silicon nanocrystals
Silicon nanowires
Multidoping
Formation energy
Optical properties
Electronic structures
Doping
a b s t r a c t
We show, by means of ab-initio calculations, that by properly controlling the doping a significant modification of both the absorption and the emission of light of silicon nanocrystals can be achieved
We have considered impurities, boron and phosphorous (codoping), located at different substitutional sites of silicon nanocrystals with size ranging from 1.1 to 1.8 nm in diameter We have found that the codoped nanocrystals have the lowest impurity formation energies when the two impurities occupy nearest neighbour sites near the surface In addition, such systems present band-edge states localized
on the impurities giving rise to a red-shift of the absorption thresholds with respect to that of undoped nanocrystals Our detailed theoretical analysis shows that the creation of an electron–hole pair due to light absorption determines a geometry distortion that in turn results in a Stokes shift between absorption and emission spectra In order to give a deeper insight in this effect, in one case, we have calculated the absorption and emission spectra going beyond the single-particle approach showing the important role played by many-body effects Moreover, we also investigate how the properties of the codoped nanoclusters are influenced by the insertion of more impurities (multidoping) Finally, we have studied the effect of B and P codoping on the electronic and optical properties of Si nanowires, thus investigating the role of dimensionality The entire set of results we have collected in this work give a strong indication that with the doping it is possible to tune the optical properties of silicon nanostructures
&2008 Elsevier B.V All rights reserved
1 Introduction and computational methods
During the last decade, several breakthroughs have boosted
the hopes that silicon (Si) could be used as an optical active
material when it is nanostructured[1,2] The basic idea is to take
advantage of the reduced dimensionality of the nanocrystalline
phase (1–5 nm in size) where quantum confinement, band folding
and surface effects play a crucial role[3–6] Indeed, it has been
found that Si nanocrystals (Si-nc) band-gap moves to the visible
region with decreasing size, moreover, optical gain has been
demonstrated [7,8] Nevertheless, Si-nc still have a memory of
the indirect band-gap of the bulk phase This drawback can
be circumvented by introducing isoelectronic impurities or by the
simultaneous doping with n- and p-type impurities In this last
case, it has been established that a codoped (B and P) Si-nc shows
always a higher photoluminescence intensity than a single-doped
(B or P) Si-nc and than a pure undoped Si-nc [9] Besides the
codoped samples did not exhibit structures related to
momentum-conserving phonons suggesting that, in this case, the quasi-direct optical transitions are predominant[9–11]
From theoretical point of view, a handful number of first-principle studies have been devoted to quantum confinement effects in single-doped Si-nc[12–16] The outcomes point out that the ionization energy for the Si-nc is virtually size independent that the impurity formation energy (FE) is greater for smaller nanocrystals and that impurity segregation strongly affects the conductance properties of the nanostructures In these last years,
we have performed several theoretical studies that also consider the simultaneous doping of Si-nc with n- and p-type impurities
[17–25] showing that the codoped Si-nc undergo a minor structural distortion around the impurities and that the formation energies are always smaller than those for the corresponding single-doped cases Moreover, we have found that the band-gap
of the codoped Si-nc is reduced with respect to the gap of the pure ones showing the possibility of an impurity-based engineering of the optical properties of Si-nc Here, we report on a comprehen-sive investigation of the structural, electronic and optical proper-ties of B and P simultaneously doped Si-nc and Si nanowires using ab-initio density functional theory Our results are obtained in a plane-wave pseudopotential DFT scheme, using the ESPRESSO package[26] Full relaxation with respect to the atomic positions
Contents lists available atScienceDirect
journal homepage:www.elsevier.com/locate/physe
Physica E
1386-9477/$ - see front matter & 2008 Elsevier B.V All rights reserved.
Corresponding author.
E-mail address: ossicini@unimore.it (S Ossicini).
Trang 2is performed for all systems All the DFT calculations are
performed within the generalized gradient approximation
using Vanderbilt ultrasoft pseudopotentials [27] for both the
determination of the structural and electronic properties and
norm-conserving pseudopotential within the local density
approximation (LDA) at the relaxed geometry to evaluate the
optical properties All the considered Si nanostructures are
embedded in large supercells in order to prevent interactions
between the periodic replicas A careful analysis has been
performed in order to test the convergence of the structural and
electronic properties with respect to both the supercell side and
plane-wave basis set cut-off
2 Doped Si nanocrystals
2.1 Single-doped Si nanocrystals
We resume, here, the effects of size and shape of Si-nc on the
incorporation of group-III (B and Al), group-IV (C and Ge) and
group-V (N and P) impurities Single-doping has been investigated
both in spherical and faceted-like Si-nc[13,16] The spherical Si-nc
are built taking all the bulk Si atoms contained within a sphere of
a given radius and terminating the surface dangling bonds with H;
whereas the faceted Si-nc are resulting from a shell-by-shell
construction procedure, which starts from a central atom and
adds shells of atoms successively We consider spherical Si-nc
with radius ranging from 0.52 nm (Si29H36) to 1.12 nm (Si293H172)
and the impurity is located in a substitutional site As for
impurities in bulk Si, Jahn–Teller distortions occur in the
neighbourhood of the impurity sites and the bond lengths show
a dependence with respect to size and shape of the Si-nc Starting
from the SinHmnanocluster[28], the FE for the neutral X impurity
can be defined as the energy needed to insert the X atom
with chemical potential mX within the cluster after removing
a Si atom (transferred to the chemical reservoir, assumed to be
bulk Si)[29]
EF¼EðSin1XHmÞ EðSinHmÞ þmSimX (1)
where E is the total energy of the system,mSithe total energy per
atom of bulk Si,mHthe total energy per atom of the impurity The
results show that for smaller Si-nc a larger energy is needed for
the formation of the impurity We have also calculated how the FE
changes as a function of the impurity position within the Si-nc
[13](seeFig 1) For the B neutral impurity in the large Si146BH100
cluster, we have moved the impurity from the cluster centre
towards the surface along different paths still considering
substitutional sites It comes out that as far as the internal core
is concerned, variations not higher than 0.06 eV are found On the
contrary, an energy drop between 0.25 and 0.35 eV is found as
the B impurity is moved to the Si layer just below the surface
This is explained by considering that such positions are the only
ones which allow a significant atomic relaxation around the
impurity, because in the other cases the surrounding Si cage
is quite stable Thus, as the B atom is moved towards the surface
the FE decreases, making the subsurface positions more stable
The situation is different for the P atom[16]
Concerning the electronic properties, the acceptor (group-III)
and donor (group-V) levels become deeper as the Si-nc become
smaller and their level positions are influenced by the position
of the impurity site Significant changes on the onset of the
absorption spectra are present due to the doping Moreover, the
radiative lifetimes are sensibly influenced by the shape, especially
for the small Si-nc, whereas these influences disappear when the
size of the nanoparticles increase
2.2 B and P codoped Si nanocrystals
Since Fujii et al.[9]have shown that B and P impurities occupy substitutional sites of the Si-nc, we always locate the B and P impurity atoms substitutionally in the Si layer just below the nanocrystal surface, since we have previously demonstrated[22]
(in accordance with other theoretical predictions [31] and experimental outcomes[32]that in the case of codoping, these are the most stable positions Initially, we consider impurities located at the largest possible distance on opposite sides of the Si-nc of different size, and then we explore different configuration
by varying the distance between the dopants
2.2.1 Structural properties and formations energies First we fix out attention on the structural changes induced by the impurities, comparing the B and P codoped cases with the single-doped ones (for the structure of a codoped Si-nc seeFig 2)
If we compare the impurity-Si bond lengths with those of the corresponding Si atoms in the pure Si-nc, it is clear that some significant relaxation occurs around the impurities The amount
of the relaxation around the impurity is directly related to the
Fig 1 Formation energies for neutral impurities as a function of the impurity position in the nc (b) The impurity is moved along two different paths toward the surface, as shown in (a) The lines are guides for eyes.
Fig 2 Calculated atomic structure of the Si 85 BPH 76 codoped nc B ((magenta), grey) and P (black) impurities have been located at sub-surface position in substitutional sites on opposite sides of the Si-nc.
Trang 3impurity valence, actually, the more significant distortion is found
for the trivalent atom (B) than for the pentavalent one (P) Beside
that, it is interesting to note that in the codoped case the
differences among the four impurity-Si bond lengths are always
smaller with respect to the single-doped case Thus, if carriers in
the Si-nc are perfectly compensated by simultaneous n- and
p-type impurities doping, an almost Tdconfiguration is recovered
in which the four impurity-Si bonds are practically the same
In order to clarify which are the parameters that play an
important role in the determination of the FE, we have performed
a series of total energy calculations considering: (i) single-doped
and codoped nanocrystals, (ii) nanocrystals of different sizes,
(iii) impurities located in different sites and (iv) variable
impurity–impurity distance in a nanocrystal InFig 3,we report
the calculated formation energies of Si35H36(diameter d ¼ 1.10 nm),
Si87H76(d ¼ 1.50 nm) and Si147H100(d ¼ 1.79 nm) nc compared, as
reference, with the single-doped Si-nc FE values
For the codoped case, B and P impurities have been placed as
second neighbours FromFig 3,it is clear that the simultaneous
B- and P-doping strongly reduces (of about 1 eV) the FE with
respect to both B and P single-doped cases and that this reduction
is similar for Si-nc of different sizes Thus, while B or P
single-doping is very costly, the cosingle-doping is much easier and, as a good
approximation, independent of the nanocrystal size The
impor-tant point here is that Si-nc can be more easily, simultaneously
doped than single-doped; this is due to both the charge
compensation and to the minor structural deformation Also the
distance between impurities plays a fundamental role on the
decrease of the FE For each nanocrystal, the FE takes on negative
values below a given distance Moreover, the FE have a minimum
value when the impurities are located at the minimum possible
distance Indeed, the impurity–impurity distance seems to play a
major role with respect to the nanocrystals size, since the FE for
similar impurity configurations are quite independent of the
nanocrystal dimension
2.2.2 Electronic properties
Concerning the electronic properties, in the single-doped
cases, we have already shown that the presence of donor or
acceptor states can considerably lower the energy gap Egof the
undoped Si-nc[13] Actually for single-doped Si-nc, the highest
occupied state (HOMO) level contains only one electron and is strongly localized either on B or P impurity Now, what is important is that the electronic properties of B- and P-codoped Si-nc are qualitatively and quantitatively different from those of either B- or P- single-doped Si-nc The presence of both a n and a p impurity leads to a HOMO level that contains two electron and to
a HOMO-LUMO (lower unoccupied state) gap strongly lowered with respect to that of the corresponding undoped nanocrystals
As an example,Fig 4reports the calculated energy levels atG
point for the Si33BPH36 system at the optimized geometries, where only the levels corresponding to the HOMO, LUMO, HOMO-1 and LUMO+1 states are depicted Calculated square modulus contour plots related to HOMO and LUMO states reveal their localization within the Si-nc, in particular the HOMO state is localized on the B impurity, while the LUMO is localized on the P one[17] The presence of these donor and acceptor states lowers the energy gap from 3.51 eV for the pure cluster to 2.86 eV for the codoped one The possibility of modulating the Si-nc energy gap
Eg, it is evident if we keep the distance between the impurities constant and look at the dependence of Egon the Si-nc size.Fig 5
shows, for three different Si-nc where the impurities are placed as second neighbours, how the undoped Si-nc Egis reduced in the presence of codoping
The same quantum confinement effect trend (i.e larger gap for smaller nanocrystals) is observed for both the undoped and codoped cases The Eg of the codoped Si-nc is shifted towards lower energies with respect to that of the undoped Eg; this shift is stronger for smaller nanocrystals Moreover, our results show that the mutual impurity distance affects not only the FE, but also the electronic structure We observe that, within the same Si-nc,
Eg decreases almost linearly with the increase of the impurity distance[22] In principle, it is possible to tune Egas a function of both the Si-nc size and the impurity–impurity distance It is easy
to predict that for Si-nc larger than those considered here it would
be possible by codoping to obtain a Egeven smaller than that of bulk Si Playing with both the nanocrystal size and the distance between the impurities, may open new interesting routes for optoelectronic applications
2.2.3 Absorption and emission spectra Now, we discuss the results for the absorption and emission spectra The Si-nc excitation has been studied considering the excited state as the electronic configuration in which the HOMO contains a hole h, while the LUMO contains the corresponding electron e, thus simulating the creation of an electron–hole pair
[30] Initially the system is in its ground state and the electronic excitation occurs with the atomic positions fixed in this config-uration After the excitation, due to the change in the charge density, relaxation occurs until the atoms reach a new minimum energy due to the presence of the e–h pair The new atomic positions modify the electronic spectrum, implying that the levels involved in the emission process change This model assumes that the relaxation under excitation is faster than the e–h recombination The difference between the absorption and emission energies due to the different atomic positions represents the nanocrystal Stokes shift (SS) The calculations have been performed for two Si-nc of different sizes taking, in the larger Si-nc, the impurities located at different distances As shown in
Table 1, both the absorption and emission HOMO–LUMO energies are affected by these two parameters With regard to the first parameter, we note that the SS strongly depends on the size showing a strong decrease on increasing the diameter of the Si-nc This is due to the fact that for larger nanocrystals the excitation determines a minor distortion of the geometry Concerning the second parameter, we see that the SS tends to slightly increase
Si:B
-0.25
0
0.25
0.5
0.75
1
1.25
1.5
Fig 3 Formation energy for single-doped and codoped Si-nc In the codoped
nanocrystals, the impurities are placed as second neighbours in the first
subsurface shell (see text) (Green) Triangles are related to Si 35 H 36 , (blue)
diamonds to Si 87 H 76 and (red) circles to Si 147 H 100 based nanocrystals The lines
Trang 4with B–P distance, although this effect is small if compared with
the lowering due to the increase of the Si-nc dimensions The
comparison between these results and the ones previously
obtained for undoped clusters (0.92 eV for the Si35H36-nc [28]
and 0.22 eV for the Si87H76-nc[30]confirm that the SS is mainly
determined by the Si-nc size, but that nevertheless it depends
slightly on the presence of the impurities and also on their mutual
distance
Looking at the single-particle optical spectra inFig 6,we note that the HOMO-LUMO transition in Si85BPH76 (1.75 eV, bottom panel) is almost dark when the two impurities are far apart and becomes instead allowed (2.32 eV, top panel) when their distance decreases
The emission ((red) dashed lines inFig 6) spectra is red-shifted with respect to the absorption ((black) solid lines inFig 6) This shift is a consequence of the geometry relaxation in the excited
Fig 4 Calculated energy levels atGpoint for the Si 33 BPH 36 -nc Alignment has been performed locating at the same energy the fully occupied levels with the same type of localization.
Radius (Å)
1.8
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
Undoped Codoped
5.5 6 6.5
Fig 5 Comparison between E g of the undoped ((black) triangles) and the codoped
((red) circles) Si-nc as a function of the Si-nc radius Impurities are located in the
first shell below the surface, as second neighbours The lines are a guide for the
eye.
Table 1
Absorption and emission energy gaps (and their difference, 5th row) calculated as
HOMO-LUMO differences in the ground and the excited relaxed geometries
configuration, respectively
Si 33 BPH 36 Si 85 BPH 76
D BP (A˚) 3.56 2.00 10.60
The results are obtained within the DFT single-particle approach d is the
nanocrystal diameter, D BP is the distance between impurities, andDthe calculated
Stokes shift between absorption and emission energy gaps.
Energy(eV)
ε2
Energy(eV) 0
ε2
Excitedgeometry Groundgeometry
Groundgeometry Excitedgeometry
Fig 6 Single-particle imaginary part of the dielectric function for the codoped
Si 85 BPH 76 -nc in the ground ((black) solid line) and in the excited ((red) dashed line) geometries B and P atoms are at the smallest possible distance (2.00 A˚, top panel) or at the largest possible distance (10.60 A˚, bottom panel) for this nanocrystal A Gaussian broadening of 0.1 eV has been applied.
Trang 5state due to the excess energy necessary for promoting an electron
in the LUMO level The dependence of the emission spectra both
on the nanocrystals size and on the impurities positions reveals
once more the possibility of tuning the optical response of Si-nc
3 Many-body results
In order to give a complete description, within the many-body
framework, of the codoped Si-nc response to an optical excitation,
we consider both the self-energy corrections by means of the GW
method[33]to obtain the quasiparticle energies and the excitonic
effects through the solution of the Bethe-Salpeter equation (BSE)
[34] The effect of local fields is also included, to take into account
the inhomogeneity of the systems To carry out emission spectra
calculations, we have used the excited state geometry and
the ground state electronic configuration, as already described
The choice of studying the small Si35BPH36-nc is due to the
fact that the GW-BSE calculations, necessary to obtain the
many-body optical spectra, are very computing demanding Thus, the
electron–hole interaction is considered here also in the emission
geometry[22]
Fig 7 (right panel) shows the calculated absorption and
emission spectra fully including the many-body effects
The e–h interaction yields significant variations with respect to
the single-particle spectra (shown in the left panel), with an
important transfer of the oscillator strength to the low-energy
side Moreover, in the emission spectrum, the rich structure of
states characterized, in the low-energy side, by the presence of
excitons with largely different oscillator strengths, determines
excitonic gaps well below the optical absorption onset Thus, the
calculated emission spectrum results to be red-shifted to lower
energy with respect to the absorption one This energy difference
between emission and absorption, the SS, can be lead back to
the relaxation of the Si-nc after the excitation process The new
important features that appear in the emission many-body
spectra are related to the presence of both B and P impurities as
showed byFig 8, which gives the real-space probability
distribu-tion |Cexc(re, rh)|2, for the bound exciton as a function of the electron position re, when the hole is fixed in a given rhposition In this case, the hole is fixed on the boron atom and we see that the bound exciton is mainly localized around the phosphorous atom FromTable 2,it can be seen that the single-particle DFT results strongly underestimate the absorption and emission edge with respect to the GW+BSE calculation, in which the excitonic effect are taken exactly into account This means that, in this case, the cancellation between GW gap opening (which gives the electronic gap) and BSE gap shrinking (which originates the excitonic gap) is only partial[35]
The difference between the GW electronic gap and the GW+BSE optical excitonic gap gives the exciton binding energy
Eb We note the presence of exciton binding energies as big as 2.2 eV, which are very large if compared with bulk Si (15 meV) or with carbon nanotubes [36,37] where Eb1 eV, but similar to those calculated for undoped Si-nc[38]of similar size and for Si and Ge small nanowires[39,40]
It is interesting to note that the HOMO-LUMO transition in the emission spectrum at 2.20 eV is almost dark, while an important
ε2
Energy (eV)
ε2
Energy (eV)
Fig 7 Single-particle imaginary part of the dielectric function for the codoped Si 33 BPH 36 -nc in the ground (dashed line) and excited (solid line) geometries Right panel:
Fig 8 Excitonic wave function of Si 33 BPH 36 (atom colors as in Fig 1) The gray isosurface represents the probability distribution of the electron, with the hole fixed on the B impurity.
Trang 6excitonic peak is evident at about 2.75 eV (seeFig 7), red-shifted
with respect to the first absorption peak
4 Multidoping
In this section, we will study how the FE and the electronic
properties of the Si-nc are influenced by the insertion of more and
more impurities We call this insertion of several impurities
multidoping.Fig 9shows how the FE of a large Si147H100-nc varies
as function of the impurity numbers We note that the presence of
an odd number of dopants (1 or 3) already brings the FE to higher values Instead, the presence of an even, compensated number
of B and P impurities strongly lowers the FE that drop down
to a negative value, indicating that as in the case of simple codoping, multidoping is much easier to realize when one has the same number of donor and acceptor dopant atoms In fact the Si145BPH100-nc, Si143BBPPH100-nc and Si141BBBPPPH100-nc (not showed in the figure) show a FE of 0.32, 0.42 and
0.97 eV, respectively
Next, we investigate how the electronic levels are influenced
by adding one or two more impurities to the codoped Si145BPH100-nc
We consider the Si145BPH100-nc where the starting B and P pair is located in a particular site, which is the more stable configuration Thus we add first one single impurity in order to obtain either the
Si144BBPH100 (with an excess of B: 2 B atoms and 1 P) or the
Si144BPPH100-nc (with an excess of P: 1 B and 2 P) and finally, adding simultaneously two B and two P atoms, we obtain the
Si143BBPPH100-nc
Looking at the electronic structure inFig 10, the two Si-nc with
3 impurities present a similar behaviour to those corresponding to
B or P single-doped Si-nc (Si146BH100-nc, or Si146PH100-nc) Every new dopant inserted gives raise to a new impurity level, which is half occupied Thus looking at the figure, we see that the HOMO-LUMO energy difference for the nanoclusters with an odd number
of impurity atoms are very similar: 2.02 eV for the Si144BBPH100-nc with respect to 2.08 eV for the B single-doped case (Si146BH100), and 0.15 eV for the Si144BPPH100-nc, with respect to 0.13 eV for the
P single-doped case (Si146PH100), respectively Besides, another time, when the impurities are compensated, as in the case of the
Si143BBPPH100-nc Si, the system becomes a semiconductor, now the HOMO contains again two electrons, and the value of the energy gap (1.97 eV) is an intermediate one between the two corresponding extrema Eg of the codoped Si145BPH100-nc with impurities located at different distance (2.03 eV for impurities closer to each other and 1.59 eV for impurities at the opposite side
of the Si-nc)
The single-particle absorption spectra reflect the results for the electronic properties For what concern all the compensated codoped Si-nc, we observe a shift of the absorption onset toward lower energy on increasing the distance between impurities It is worth pointing out that when impurities are at a larger distance, the transition intensities near the band edges become weaker due
to small oscillator strengths When, instead, impurities are closer
to each other due to the strong localization of HOMO and LUMO
Table 2
Absorption and Emission energies calculated as HOMO-LUMO energy difference
within the singleparticle DFT, the many-body GW and the GW+BSE approaches
Si 33 BPH 36 DFT GW GW+BSE
Abs (eV) 2.80 5.52 3.35
Ems (eV) 1.79 4.37 2.20
Dis the calculated Stokes shift between absorption and emission energy gaps.
Fig 9 Formation energies for single, codoped and multidoped Si 147 H 100 based
nanocrystals.
Fig 10 Calculated energy levels at theGpoint for the Si 145 BPH 100 -nc, the Si 144 BBPH 100 -nc, the Si 144 BPPH 100 -nc and the Si 143 BBPPH 100 -nc Alignment has been performed,
Trang 7on the impurity sites, the transitions near the band edge are more
intense
5 Codoped silicon nanowires
Among one-dimensional semiconducting nanostructures,
silicon nanowires (Si-nw) have attracted in the last years an
increasing interest since it has been shown that they are, together
with carbon nanotubes, potential candidates to build up future
nanoelectronic and nanophotonic devices[41–43] In fact, they
offer the advantage to be compatible with the existing
silicon-based microelectronics Moreover, the possibility to tailor their
electronic properties by changing thickness, orientation, surface
morphology and doping is another important point in their favour
[44,45] Obtain a systematic relation between structure, surface
morphology and electronic properties is from an experimental
point of view, a very difficult task For this reason, theoretical/
computational investigations, based on reliable ab-initio DFT
approaches, can be of great help to the experimentalists to grow
Si-nw suitable for a particular application Several ab-initio
studies on Si-nw are present in the literature They are mainly
concentrated on H-passivated or pristine Si-nw and demonstrate
the dependence of the energy band-gap from the wire diameter
and from the surface morphology[4,40,46–51]
Instead, few investigations have been dedicated to the
influence of the electronic and transport properties from doping
[52,53] In particular, due to the application in electronic devices,
the main efforts have been devoted to the study of B and P
single-doped Si-nw, while only one ab-initio study has investigated the B
and P codoping[53] For this reason, in complete analogy with
the Si-nc, we have recently performed a systematic analysis of the
effect of the B and P codoping in Si-nw, concentrating not only on
the structural properties but also on how doping influences the
electronic and optical properties Here, we aim to resume the
main outcome of this work and illustrate specific results only for
one single-doped and codoped H-passivated Si-nw (with a linear
cross section of about 1 nm) grown in the [11 0] direction, while
a more complete discussion will be found elsewhere [54] In
particular, we have considered different positions for the
impurities in the Si-nw; moreover, we have varied the unit cell
in our calculations Augmenting the unit cell, correspond to an
increase of the overall number of atoms within the cell and thus to
a decrease in the dopant concentration
Fig 11 shows how the FE for the B and P codoped Si-nw changes as function of the position of the dopants within the nanowire In the figure, the inset show the single Si-nc unit cell used in this case We note that the minimum is reached when the P atom moves to a surface position Moreover, also in the corresponding case (not shown in the figure) where the P impurity is located in a subsurface position and the B atom is in
a surface site, the FE becomes negative Indeed it is worthwhile to note that in all cases of single-doped Si-nw, the FE shows high positive value (1.13 and 0.66 eV for the single B- and P-doped nanowire, respectively), thus confirming the stabilizing role of compensated doping Concerning the electronic properties, the band structure show a direct energy gap behaviour atG, whose values depends on the impurity position For the positions labelled 1, 2 and 3 in Fig 11, these values are 0.63, 0.08 and 0.97 eV, respectively
If we concentrate on the dependence of the doped Si-nw properties on the dopant concentration, we note first that on augmenting the number of atoms in the cell (thus lowering the dopant concentration), the FE lowers For the smallest unit cell (28 atoms in total) the FE shows a value of 0.41 eV, where using
a two-time (56 atoms), three-time (84 atoms) and fourth-time (112 atoms) larger unit cell brings this value to 0.15, 0.60 and
0.64 eV, respectively This demonstrates that a lowering of the impurity concentration results in a gain of the stability for the nanowire The impurity concentration plays a role also re-garding the electronic properties From Fig 12,we see that the direct band-gap increases as the impurity concentration lowers (the impurities here are located in the position 2 of Fig 11), approaching asymptotically the value of the band-gap of the undoped Si-nw This is another indication of how doping can modify the electronic and optical properties of the Si nanostructures
6 Conclusions
The structural, electronic and optical properties of Si nanos-tructures doped with different numbers of B and P impurities have been studied from first-principles We have considered Si-nc with the impurities located at different distances and in different combinations Besides also doped Si nanowires have been investigated We show, in all systems, that compensated codoping
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
-0.05
Impurity distance (Å)
1
P in 1
B at I shell
P in 3
B at I shell
P in 2
B at I shell
Fig 11 Formation energy for the codoped Si-nw (shown in the inset) as function
of the related position between the two dopants The B impurity is frozen in a
subsurface site, while the P occupies different sites labelled 1, 2 and 3 The lines are
Fig 12 DFT-GGA direct band-gap calculated atGpoint for the codoped Si-nw with respect to the number of atoms in the unit cell A larger number corresponds to a decrease in impurity concentration The dotted line is a guide for the eye The dashed line corresponds to the band-gap for the undoped Si-nw.
Trang 8is always energetically favoured with respect to a not
compen-sated number of B- or P-doping Our results demonstrate that the
codoped nanostructures present valence and conduction
band-edge states which are localized on the two impurities,
respec-tively, and energy band gaps always lower in energy with respect
to that of pure undoped Si nanostructures On going from
nanocrystals to nanowires, the reduced quantum confinement
results in a reduced energy band-gap that is direct at theGpoint,
elucidating the role of dimensionality Indeed the impurity
located band-edge states originate absorption and emission
thresholds in the visible region which are shifted lower in energy
with respect to that of corresponding pure undoped Si structures
The dependence of the optical onset on Si-nc size, impurity
positions, impurity distances and dopants concentration, thus
shows the possibility to tune the optical properties
Acknowledgements
We are grateful to all our co-workers We acknowledge
the support of the MIUR PRIN Italy, of the Galileo Project
Italy-France All the calculations were performed at CINECA-Bologna
(‘‘Iniziativa Calcolo Parallelo del CNR-INFM’’)
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