Effects of simultaneous doping with boron and phosphorous on the structural, electronic and optical properties of silicon nanostructures

Effects of simultaneous doping with boron and phosphorous on the
structural, electronic and optical properties of silicon nanostructures
F. Iori
a
, S. Ossicini
b,
Ã
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
article info
Available online 14 August 2008
PACS:
73.22.Àf
71 .1 5.Àm
78.55.Àm
78.20.Àe
Keywords:
Silicon nanocrystals
Silicon nanowires
Multidoping
Formation energy
Optical properties
Electronic structures
Doping
abstract

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 impur ities, 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 indicati on 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
ARTICLE IN P RESS
Contents lists available at ScienceDirect

journal h omepage: www.elsevier.com/locate/physe
Physica E
1386-9477/$ - see front matter & 2008 Elsevier B.V. All rights reserved.
doi:10.1016/j.physe.2008.08.010
Ã
Corresponding author.
E-mail address: (S. Ossicini).
Physica E 41 (2009) 939–946
is 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 (Si
29
H
36
) to 1.12 nm (Si
293
H
172
)
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 Si
n
H
m
nanocluster [28], the FE for the neutral X impurity
can be defined as the energy needed to insert the X atom
with chemical potential
m
X
within the cluster after removing
a Si atom (transferred to the chemical reservoir, assumed to be
bulk Si) [29]
E
F
¼ EðSi
nÀ1

XH
m
ÞÀEðSi
n
H
m
Þþ
m
Si
À
m
X
(1)
where E is the total energy of the system,
m
Si
the total energy per
atom of bulk Si,
m
H
the 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] (see Fig. 1). For the B neutral impurity in the large Si
146
BH
100
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 see Fig. 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
ARTICLE IN PRESS
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.
F. Iori, S. Ossicini / Physica E 41 (2009) 939–946940
impurity 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 T
d
configuration 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. In Fig. 3, we report
the calculated formation energies of Si
35
H
36
(diameter d ¼ 1.10 nm),
Si
87
H
76
(d ¼ 1.50 nm) and Si
147
H
100
(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. From Fig. 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 codoping 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 E
g
of 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. 4 reports the calculated energy levels at
G
point for the Si
33
BPH
36
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
E
g
, it is evident if we keep the distance between the impurities
constant and look at the dependence of E
g
on 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 E
g
is 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 E
g
of the codoped Si-nc is shifted towards
lower energies with respect to that of the undoped E
g
; 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,

E
g
decreases almost linearly with the increase of the impurity
distance [22]. In principle, it is possible to tune E
g
as 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 E
g
even 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
ARTICLE IN P RESS
Si:B
-0.25
0
0.25
0.5
0.75
1
1.25
1.5
Formation Energy (eV)
Si:B:P Si:P
Si
87
H
76
clusters
Si
35
H

36
clusters
Si
147
H
100
clusters
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
are a guide for eyes.
F. Iori, S. Ossicini / Physica E 41 (2009) 939–946 941
with 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 Si
35

H
36
-nc [28]
and 0.22 eV for the Si
87
H
76
-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 in Fig. 6, we note
that the HOMO-LUMO transition in Si
85
BPH
76
(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 in Fig. 6) spectra is red-shifted
with respect to the absorption ((black) solid lines in Fig. 6). This
shift is a consequence of the geometry relaxation in the excited
ARTICLE IN PRESS
Fig. 4. Calculated energy levels at G point 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.

5 7 7.5 8 8.5 9 9.5
Radius (Å)
1.8
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
Energy Gap (eV)
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 (nm) 1.10 1.50 1.50
D
BP
(A
˚
) 3.56 2.00 10.60
Abs. (eV) 2.77 2.32 1.75
Ems. (eV) 1.78 2.20 1.36
D (eV) 0.99 0.12 0.39
The results are obtained within the DFT single-particle approach. d is the
nanocrystal diameter, D
BP
is the distance between impurities, and D the calculated
Stokes shift between absorption and emission energy gaps.
1 1.5 2 2.5
Energy(eV)
ε
2
(ω) (arb.units)
1 1.5 2 2.5
Ener
gy
(eV)
0
ε
2

(ω) (arb.units)
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.
F. Iori, S. Ossicini / Physica E 41 (2009) 939–946942
state 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 Si
35
BPH
36
-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 by Fig. 8, which gives the real-space probability distribu-
tion |
C

exc
(r
e
, r
h
)|
2
, for the bound exciton as a function of the
electron position r
e
, when the hole is fixed in a given r
h
position. 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.
From Table 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
E
b
. 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 E
b

$1 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
ARTICLE IN P RESS
ε
2
(ω) (arb.units)
1 1.5 2 2.5 3 3.5 4 4.5
Energy (eV)
ε
2
(ω) (arb.units)
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
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:
absorption (dashed line) and emission (solid line) many-body spectra of Si
33
BPH
36.
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.
F. Iori, S. Ossicini / Physica E 41 (2009) 939–946 943
excitonic peak is evident at about 2.75 eV (see Fig. 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. 9 shows how the FE of a large Si
147
H
100
-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 Si
145
BPH
100
-nc, Si
143
BBPPH
100
-nc and Si

141
BBBPPPH
100
-nc
(not showed in the figure) show a FE of À0.32, À0.42 and
À0.97 eV, respectively.
Next, we investigate how the electronic levels are influenced
by adding one or t w o mor e impurities to the c odoped Si
145
BPH
100
-nc.
We consider the Si
145
BPH
100
-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
Si
144
BBPH
100
(with an excess of B: 2 B atoms and 1 P) or the
Si
144
BPPH
100
-nc (with an excess of P: 1 B and 2 P) and finally,
adding simultaneously two B and two P atoms, we obtain the

Si
143
BBPPH
100
-nc.
Looking at the electronic structure in Fig. 10, the two Si-nc with
3 impurities present a similar behaviour to those corresponding to
B or P single-doped Si-nc (Si
146
BH
100
-nc, or Si
146
PH
100
-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 Si
144
BBPH
100
-nc
with respect to 2.08 eV for the B single-doped case (Si
146
BH
100
),
and 0.15 eV for the Si

144
BPPH
100
-nc, with respect to 0.13 eV for the
P single-doped case (Si
146
PH
100
), respectively. Besides, another
time, when the impurities are compensated, as in the case of the
Si
143
BBPPH
100
-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 E
g
of the codoped Si
145
BPH
100
-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
ARTICLE IN PRESS
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
D (eV) 1.01 1.15 1.15
D is 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 the G point 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,
locating at the same energy, the fully occupied levels with the same type of localization.
F. Iori, S. Ossicini / Physica E 41 (2009) 939–946944
on 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 [110] 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 at
G
, 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 À0.15, À0.60 and
À0.64 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
ARTICLE IN P RESS
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
-0.05
1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4
Impurity distance (Å)
Formation Energy (eV)
1
3
B
2
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
guide for the eye.
Fig. 12. DFT-GGA direct band-gap calculated at G point 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.
F. Iori, S. Ossicini / Physica E 41 (2009) 939–946 945
is 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 the
G
point,
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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