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

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

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

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

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

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,

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

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.

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

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

$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

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

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

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

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

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

[25] F. Iori, et al., Superlattices Microstructures (2008), doi:10.1016/j.spmi.
2007.09.002.
[26] S. Baroni, et al., / />[27] D. Vanderbilt, Phys. Rev. B 41 (1990) R7892.
[28] E. Degoli, et al., Phys. Rev. B 69 (2004) 155411.
[29] S.B. Zhang, J.E. Northrup, Phys. Rev. Lett. 67 (1991) 2339.
[30] A. Puzder, et al., J. Am. Chem. Soc. 125 (2003) 2786.
[31] L. Colombi Ciacchi, M.C. Payne, Phys. Rev. Lett. 95 (2005) 196101.
[32] E. Garrone, et al., Adv. Mater. 17 (2005) 528.
[33] EXC Code, V. Olevano, /S.
[34] We have used the non selfconsistent G
0
W
0
approach within the RPA plasmon
pole approximation. We use a planewave-frequency space code.
[35] C. Delerue, et al., Phys. Rev. Lett. 84 (2000) 2457.
[36] C.D. Spataru, et al., Phys. Rev. Lett. 92 (2004) 077402.
[37] E. Chang, et al., Phys. Rev. Lett. 92 (2004) 196401.
[38] E. Luppi, et al., Phys. Rev. B 75 (2007) 033303.
[39] M. Bruno, et al., Phys. Rev. B 72 (2005) 153310.
[40] M. Bruno, et al., Phys. Rev. Lett. 98 (2007) 036807.
[41] Y. Cui, et al., Nano Lett. 3 (2003) 149.
[42] Y. Cui, C. Lieber, Science 291 (2001) 851.
[43] Y. Cui, et al., Science 293 (2001) 1289.
[44] Y. Cui, et al., J. Phys. Chem. B 104 (2000) 5213.
[45] D. Ma, Appl. Phys. Lett. 79 (2001) 2468.
[46] F. Buda, et al., Phys. Rev. Lett. 69 (1992) 01272.
[47] A.J. Read, et al., Phys. Rev. Lett. 69 (1992) 01232.
[48] S. Ossicini, et al., Thin Solid Films 297 (1997) 154.
[49] R. Kagimura, et al., Phys. Rev. Lett. 95 (2005) 115502.