IC/2007/101
Available at: http://publications.ictp.it
United Nations Educational, Scientific and Cultural Organization
and
International Atomic Energy Agency
THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS
STRUCTURAL AND ELECTRONIC PROPERTIES
OF BULK YN AND OF THE YN/ScN SUPERLATTICE
Youcef Cherchab
Centre Universitaire de Béchar, Département d’Electrotechnique,
B.P. 417, Rue de Kanadissa, 08000 Bechar, Algeria,
Bouhalouane Amrani
Laboratoire de Traitement de Surface et Sciences des Matériaux, Département de Physique,
Faculté des Sciences, Université des Sciences et de la Technologie d’Oran (U.S.T.O.),
Oran 31000, Algeria,
Nadir Sekkal*
Département de Physique-Chimie, Ecole Normale Supérieure de l’Enseignement Technique,
B.P. 1523, El M’Naouer, 31000 Oran, Algeria,
Physia-Laboratory, B.P. 47 (RP), 22000 Sidi Bel Abbès, Algeria,
Université de Sidi Bel Abbès, 22000, Sidi Bel Abbès, Algeria†
and
The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy,
Mohamed Ghezali and Khadija Talbi
Centre Universitaire de Béchar, Département d’Electrotechnique,
B.P. 417, Rue de Kanadissa, 08000 Bechar, Algeria.
MIRAMARE – TRIESTE
September 2007
*
†
Corresponding author. [email protected]; [email protected]
On leave of absence from.
Abstract
The structural and electronic properties of YN are investigated using two different first
principles methods, the full potential linear augmented plane waves (FPLAPW) method and a recent
version of the first principles full potential linear muffin-tin orbitals method (FPLMTO) which enables
an accurate treatment of the interstitial regions. Our calculations show that the ground state
configuration of YN is the rocksalt (B1) structure and that it is a semiconductor. We have also
investigated the A3 hexagonal structure which is nearly five-times coordinated and found it more
stable than the previous wurtzite phase. So we confirm the presence of another local minimum, but in
this A3 phase and not in the wurtzite (B4). Nevertheless, the transition from rocksalt (B1) to CsCl
(B2) structure is found to be possible at high pressure. The zinc blende structure (B3) has also been
investigated and is found to have a large and direct fundamental gap. The resemblances between YN
and ScN and their small lattice mismatch led us to perform predictive investigations on
rocksalt/rocksalt ScN/YN heterostructure superlattices. The latter shows interesting features: these
systems constituted from indirect bandgap bulk materials are found to have a direct bandgap
suggesting that the reason is probably the zone folding phenomena which is suspected to be at the
origin of a similar effect observed in the popular Si/SiGe systems. To our knowledge, rocksalt/rocksalt
superlattice systems have not received particular attention before.
1
1
Introduction
Due to their interesting properties, the transition metal nitrides like ScN, YN and LaN are actually attracting
more attention [1,2]. The ScN is undoubtedly the most studied of them. Recently, it seems that it has been
definitively confirmed as a semiconductor [3]. The latter is found to have a rocksalt (B1) structure which can
transform to the CsCl (B2) phase under high pressure [3,4] and it presents also an additional local minimum in
the wurtzite structure (B4) with a total energy 0.39 eV/unit cell higher [3]. However, Farrer et al [5] have shown
that the nearly five-times coordinated A3 hexagonal structure, that has recently been found in MgO [6], is more
stable than the wurtzite structure (B4).
Recent investigations on YN [7] have shown that the latter has many similarities with ScN. It crystallizes in the
rocksalt (B1) phase and has a second local minimum in the wurtzite structure (B4) with total energy 0.28 eV/unit
cell higher and it is expected to transform to the CsCl (B2) phase under high pressure. Another interesting
finding is that in the B1 phase, it is a semiconductor with a lattice constant of 4.877 Å [7] which is close to that
of ScN which is between 4.54 Å [3] and 4.651 Å [4] giving small lattice mismatches of 7.16 % and 4.80 %
respectively with ScN. These low values enable us to suppose the fabrication of YN/ScN superlattices from their
rocksalt (B1) phase to be possible.
The main purpose of this work is to investigate the structural and the electronic properties of YN. The YN/ScN
superlattice systems are also addressed. The paper is organized as follows: The methods utilized are presented in
section 2 and the results for the bulk YN are discussed in section 3. The superlattice case is investigated in
section 4, then conclusions are summarized in section 5.
2
Details of calculation
For reasons of comparison, the structural and electronic properties of YN were calculated using two all-electron,
full potential electronic LDA –based techniques [8,9]; the Savrasov version of the full potential linear muffin-tin
orbitals (FPLMTO) method [10] as implemented in the lmtART code [11] and the full potential linear
augmented plane wave (FPLAPW) method [12,13] as implemented in the WIEN2k code [14]. The exchange and
correlation effects are described in the framework of both LDA (local density approximation) and GGA96
(generalized gradient approximation) within the parameterization of Perdew et al [15,16]. In both methods, the
unit cell is divided into non overlapping muffin-tin spheres (MTS) of radius RMTS and an interstitial region, the
Kohn-Sham wave functions being expressed in spherical harmonics within spheres. Both techniques include the
contributions of all electrons explicitly, without the use of pseudopotentials, and do not impose any particular
shape on the density or potential.
Table 1: Parameters used in the FPLMTO calculations. NPLW is the number of plane waves used in the
interstitial regions, Ecut is the cut-off energy in Rydbergs, RMTS is in atomic units and K-Point represents the
number of special K –points in the irreductibe BZ involved in the calculations.
parameters
NaCl (B1)
LDA
6
lmax
NPLW (s) 136
NPLW (p) 228
NPLW (d) 386
Total NPLW 2974
RMTS (Y) 2.56
RMTS (N) 1.931
Ecut (s)
11.7
Ecut (p)
17.1
Ecut (d)
24.9
17
K-Point
CsCl (B2)
Wurtzite (B4)
Zinc blende(B3)
Hexagonal (A3)
GGA
6
136
180
338
6566
2.65
1.919
11.3
15.1
22.7
LDA
6
92
170
256
3070
2.648
1.939
11.3
15.5
22.5
GGA
6
92
170
256
7152
2.737
2.003
10.5
14.5
21.1
LDA
6
180
338
560
5064
2.401
1.811
13.3
20.0
27.9
GGA
6
180
306
536
9984
2.482
1.797
12.9
17.4
25.9
LDA
6
402
650
1146
14844
2.385
1.799
13.4
18.9
27.8
GGA
6
324
602
1082
28144
2.537
1.837
11.5
16.5
24.3
LDA
6
314
528
962
11882
2.479
1.87
12.2
17.7
25.7
GGA
6
314
528
962
23496
2.56
1.854
12.1
17.6
25.6
17
21
21
23
23
41
41
22
22
2
Table2: Parameters used in the FPLAPW calculations. NPLW is the number of plane waves used in the
interstitial regions. N-Dist, NN-Dist, NNN-Dist and NNNN-Dist specify the first, second, third and fourth
nearest-neighbour distances respectively in atomic units. RMTS is in atomic units and K-Point represents the
number of special K –points in the irreductibe BZ involved in the calculations.
parameters
lmax
RMT KMAX
Total NPLW
RMTS (Y)
RMTS (N)
N-Dist
NN-Dist
NNN-Dist
NNNN-Dist
K –points
NaCl (B1)
LDA
10
8
272
2.56
1.931
4.5632
6.453
7.904
9.126
47
GGA
10
8
286
2.65
1.9
4.6487
6.574
8.052
9.297
47
CsCl (B2)
LDA
10
8
246
2.648
1.939
4.8
5.542
7.838
9.19
56
GGA
10
8
260
2.737
2.18
4.928
5.686
8.041
9.429
56
Zinc blende(B3)
LDA
10
8
602
2.401
1.8
4.252
6.944
8.143
9.82
73
GGA
10
8
632
2.482
1.797
4.332
7.074
8.295
10.004
73
Wurtzite (B4)
LDA
10
8
2243
2.385
1.799
4.206
4.261
6.623
6.784
60
GGA
10
8
2341
2.487
1.8
4.296
4.325
6.762
6.911
60
Hexagonal (A3)
LDA
10
8
1091
2.47
1.87
4.342
4.545
6.286
7.286
80
GGA
10
8
1149
2.56
1.854
4.431
4.631
6.409
7.674
80
At the reverse of the previous LMTO methods, the present one treats the interstitial regions on the same footing
with the MTS regions. The non overlapping MTS potential is expanded in spherical harmonics inside the spheres
and Fourier transformed in the interstitial regions [10]. In the FPLAPW method, the interstitial regions do not
represent a problem since the relative Kohn-Sham wave functions are expressed in plane waves. In the interstitial
regions, the wave functions are expanded in plane waves with RMT KMAX fixed to 8 (RMT is the smallest atomic
sphere radius in the unit cell and KMAX is the maximum modulus for the reciprocal lattice vector). In the muffintin spheres of radius RMTS, the l-expansion of the non-spherical potential and charge density was carried out up
to lmax=10. Notice that the RMTS of the same atomic specie can vary with different phases since the full
potential is utilized and which ensures the no dependency of calculations on the RMTS. The details of the
calculations are listed in Table 1 for FPLMTO and in Table 2 for FPLAPW.
3
Results for the bulk YN
First, we have calculated the equilibrium lattice parameters within both FPLMTO and FPLAPW methods in both
LDA and GGA96 frameworks using the habitual minimization procedure. The total energy was calculated for
different values of the lattice constant, and the equilibrium corresponds to the lowest value of the total energy.
We have investigated the rocksalt (B1), the CsCl (B2), the zinc blende (B3), the wurtzite (B4) and also the A3
hexagonal phase which is nearly five-times coordinated [6] and which has been confirmed by Farrer et al [5] to
be stable for ScN. The latter belongs to the hc class of hexagonal phases. Its primitive lattice vectors of the direct
(
)
(
)
Bravais lattice are ax= 1/ 2,− 3 / 2,0 a0, ay= 1/ 2, 3 / 2,0 a0 and az=c0. a0 and c0 being the two different lattice
parameters, c0/a0 being the axial ratio. The primitive unit cell contains two Y atoms at r1=0 and r2=(2/3,1/3,
c0/2.a0) a0, and two N atoms at r3=(0, 0, u. c0/a0) a0 and r4=(2/3,1/3, c0(u+1/2)/a0) a0, u being the internal
parameter (dimensionless).
In Fig. 1, and for each method, we show the minimization curves for the four phases. Volume and energy are per
single formula unit. Our calculations show that the ground state configuration is the rocksalt (B1) structure.
Nevertheless, depending on the pressure, the CsCl phase (B2) can be formed because the curves corresponding
to B1 and B2 cross each other. The difference between the minima of the B1 and B4 phases is found to be small
in the GGA96+FPLAPW so that we expect the wurtzite (B4) to be a metastable phase for YN. The difference
between the minima of B1 and B4 structures are found to be 0.68 eV/unit cell for LDA+FPLMTO, 0.39 eV/unit
cell for GGA96+FPLMTO, 0.47 eV/unit cell for LDA+FPLAPW and 0.27 eV/unit cell for GGA96+FPLAPW.
These results show serious differences while the last result obtained with GGA96+ FPLAPW agrees well with
those of Ref [7] in which the same method has been utilized. The A3 structure is found to be more stable than B4
for YN and occupies a second minimum in energy after rocksalt. The same result has been found in ScN [5].
Using these minimization curves, the equilibrium volume, the equilibrium lattice constant, the bulk modulus B
and its derivative have been calculated by fitting to the Murnaghan equation of state [17]. Results are
summarized in Table 3. To determine the most stable structure at finite pressure and temperature, we have used
the enthalphy H=E+PV. The latter was calculated for both B1 and B2 and from their curve crossing, we obtain
the pressure of this phase transition. The results are summarized in Table 4. Our FPLMTO results for transition
pressures are different from Ref [7] while those obtained with FPLAPW are comparable, especially when the
same method of the above reference, i.e. FPLAPW+GGA96 is used. Small differences between our
FPLAPW+GGA96 calculation and those of Mancera et al [7] are due to a different K points sampling.
3
The energy variations are quadratic with the volume. The pressure induces changes in both volume and energy
following the relation:
⎡
V (P ) = V 0 ⎢ 1 + B
⎣
'
P ⎤
B ⎥⎦
−1
B
'
where B is the bulk modulus for a zero pressure. Table 4
summarizes the results for the volume reduction which occurs after the B1 to B2 transition. It is about 18% for
LDA+FPLMTO, 12.9% for GGA96+FPLMTO, 8.9% for LDA+FPLAPW and 9.4% for GGA96+FPLAPW. The
last GGA96+ FPLAPW result agrees well with those of Ref [7]. Similar transitions from B1 to B2 have been
observed experimentally and predicted theoretically by other works [18,19].
Fig. 2 shows the band structure of YN in the equilibrium rocksalt (B1) phase for the equilibrium volume
obtained within the four methods (LDA + FPLMTO, GGA96 + FPLMTO, LDA + FPLAPW and GGA96 +
FPLAPW ). The 4p state is treated adequately as a valence state and is taken into account for the calculation of
the self energy. There are three main regions. The lower region in energy is constituted from valence bands due
essentially to Y 4p states, while the second region higher in energy is originated from the N 2s orbital. The third
region, the higher in energy is moderately dispersive and is characterized by a p-d hybridisation.
All the employed methods lead to band structure results for YN that agree well with Ref [7] and show that it is
quite similar to the band structure of ScN [3]. In summary, we obtain a small indirect fundamental gap since the
top of the valence band (VB) is at Γ and the bottom of the conduction band at X. Its magnitude is found to be
about ~0.2eV in the FPLAPW+ GGA96 approach so that YN is probably a semiconductor like ScN. We have to
remember that LDA is known to underestimate bandgaps in semiconductors. Stampfl et al [22] who used a
screen exchange (SX) LDA [23] found that YN was a semiconductor with an indirect gap of ~0.85 eV.
Table 3: The structural parameters of YN in the four phases (V0 is the equilibrium volume, a0 the lattice
constant, B the bulk modulus and B’ is its pressure derivative). V0 is taken equal to a3/4 for both zinc blende and
NaCl phases, a3 for the CsCl phase and 1/2.[a2.c.(3/4)½] for the two hexagonal phases for which the volume per
unit formula is taken into account.
YN / PHASE
FPLAPW
LDA
FPLAPW
GGA96
FPLMTO
LDA
FPLMTO
GGA96
OTHER WORKS
NaCl (B1)
V0(Å3)
a0(Å)
B(GPa)
B’
29.89a
28.29617
30.04517
26.98647
4.837
4.9348
4.7614
170.56
3.82412
144.7
3.72011
186.97
3.66986
25.22344
2.9327
164.99
4.57815
27.248
3.009
132.15
4.06
22.13748
2.80786
172.8
4.1423
24.33032
2.9016
151.1
3.80587
27.27a
3.01 3.002c
136a 149.083c
4.11a4.135c
35.08501
5.19669
121
3.74965
37.10226
5.294
107.07
3.60269
34.48978
5.157
131.347
3.3218
35.93987
5.2385629
109.24
2.99744
36.74a
5.28a
110a
4.39a
34.85463
3.703
1.5852
124.0784
3.92272
0.3875
36.87647
3.7806
1.576
110.355
3.70
0.3834
34.77765
3.6774
1.615
138.8695
3.28285
0.385
36.73702
3.7718
1.602
124.8832
3.19048
0.386
36.93
3.78a
1.58a
115a
3.73a
0.375
32.9979
3.98
1.2085
139.955
4.15299
0.5
35.0053
4.061
1.207
120.48
3.80498
0.5
32.98566
3.9935
1.196
157.405
3.37256
0.5
34.6202
4.0449
1.196
142.2530
3.44153
0.5
-------------------
28.42954
4.8448 4.93a 4.877b 4.915c 4.85d
4.77e
a
c
d
153.0768
157 154.377 163 204e
3.20258
3.50a 3.06c 4.77e
CsCl (B2)
V0(Å3)
a0(Å)
B(GPa)
B’
Zinc Blende (B3)
V0(Å3)
a0(Å)
B(GPa)
B’
a
Wurtzite (B4)
V0(Å3)
a0(Å)
c0\a0
B(GPa)
B’
u
Hexagonal (A3)
V0(Å3)
a0(Å)
c0\a0
B(GPa)
B’
u
a
Reference 7
Reference 20
c
Reference 21
b
4
d
e
Reference 22 using FPLAPW+GGA 92.
Reference 22 using FPLAPW+LDA.
Table 4: The transition pressures PT from rocksalt (B1) to CsCl (B2) structure.
YN
PT(GPa)
VB1(Å3)
VB2(Å3)
∆V(Å3)
a
b
FPLMTO
LDA
≈54.74
22.12
18.08
4.03
FPLMTO
GGA96
≈77.44
21.0449
18.3096
2.73
FPLAPW
LDA
121.98
20.048
18.26
1.788
FPLAPW
GGA96
≈131.84
20.1877
18.2852
1.9
Other work
138a 136.39a
20.0 a 20.07 b
18.3 a 18.15b
Reference 7
Reference 21
Fig. 3 shows the band structure of YN in the equilibrium CsCl (B2) phase for the equilibrium volume obtained
within the four methods (LDA + FPLMTO, GGA96 + FPLMTO, LDA + FPLAPW and GGA96 + FPLAPW). In
this phase, we have obtained broadening bands and we observe some mixing between the valence and the
conduction bands. These results indicate a semi metallic behaviour. We found increasing p-d hybridization
compared to the NaCl structure indicating that there is more interaction between Y and N atoms.
There are two key concepts that govern the response of the YN in different volumes (i) changes in nearestneighbor bondlengths as they affect overlaps and bandwidths and (ii) changes in symmetry as they affect p-d
hybridization and the band repulsion. In fact, during compression, the B1 sixfold-coordinated cubic NaCl
structure changes to the eightfold-coordinated cubic CsCl structure. Consequently, we obtain a transition from
semiconductor to semi metallic behaviour, where the symmetry enables the hybridization of N 2p and Y dderived bands, which pushes the anion 2p states upwards, an effect previously noted in both binary [24] and
ternary [25] semiconductors.
In Figs. 4 and 5, we show the band structure of YN in the zinc blende and wurtzite phases respectively for their
respective equilibrium volumes obtained within the same four previous methods. The results are similar for both
phases B3 and B4. They exhibit an indirect bandgap with values close to 2 eV (W→Γ, M →Γ) respectively.
Also observed is great p-d hybridization especially for B4 meaning an increasing interaction between Y d and N
p states. Therefore, the bonding of this material in the zinc blende and the wurtzite has a more ionic-like
character than in both NaCl and CsCl structures.
On the other hand, even if YN cannot have a phase transition to B3 phase, it can be combined with, for example,
materials like the zinc blende (Ga,Al,In)As arsenides or (Ga,Al,In)N nitrides to form semiconducting ternary
alloys with probably wide bandgaps. The problem is less severe for the B4 phase which has a minimization
curve close to that of the A3 phase but is expected to be a metastable because of the presence of the second
minimum.
The A3 (meta)stable phase is found to have a semiconducting indirect bandgap with the top of the valence band
(VB) located at Γ and the bottom of the conduction band (CB) at K (Fig. 6). The location of the CB minimum at
K results from the change in the reciprocal space location for this phase. Each atom in YN is linked to five other
atoms of different specie, three in the basal plane (short bonds) and two other ones below and above the c–plane
(slightly longer). It results that A3 is nonpolar with 24 symmetry elements including inversion (P63/mmc point
group). Going from NaCl to A3 and then to the wurtzite structure we have the change in the coordination
number from six to five then to four and, on the other hand, it increases the c/a ratio from 1 to 1.2 to about 1.581.61 so that the VB splitting decreases while the gap increases.
4 The YN/ScN superlattice
The investigated structure consists of an ideal quantum well superlattice SL(2,2) made of a periodical sequence
(with period D=9.5628 Å) of two monolayers of YN atoms and two other monolayers of ScN atoms (a
monolayer contains two atoms, one anion and one cation). To our knowledge, rocksalt/rocksalt superlattice
systems have not received particular attention before. In Fig. 7, we show the direct lattice of a (001) growth axis
SL(1,1) made up of an alternation of one monolayer of YN and another one of ScN. The SL(2,2) has a tetragonal
symmetry. The link between the bulk and the SL direct lattices is shown in the figure.
The reciprocal lattice of the (001) growth axis SL(m=2, n=2) can be represented in a unified manner for all
values of m and n which represent the number of YN and ScN monolayers respectively, m+n being even (Fig. 8).
In the case of a (001) SL(1,1), the high symmetry points B and Y are identical to R and X respectively. For the
SL(2,2) calculation, we have supposed the lattice constant to be the mean value of that of 4.8448 Å YN (Table 3:
FPLMTO+GGA96) and that of ScN (4.718 Å) which was calculated back by us with the same method, it is a
little bit different from that of Ref [4] which has used Vosko parametrization without GGA.
As in the bulk parent materials, the electronic structure (Fig. 9) shows three main regions in the valence band but
now with added contribution of orbitals of the different species of ScN. We notice essentially in the upper
5
valence bands a significant contribution of the Sc 3d orbital which leads to an increasing p-d hybridization. In
the case of a (001) growth axis superlattice, as its period increases, the superlattice Brillouin zone decreases and
the bulk bands need to be folded to quarters, this is the case of SL(2, 2). We also observe that both the top of the
VB and the bottom of the CB are at Γ. We have then a fundamental direct bandgap close to zero (~0.1eV). This
is an interesting feature: these systems constituted from indirect bandgap bulk materials are found to have a
direct bandgap suggesting that the reason is probably the zone folding phenomena which is suspected to be at the
origin of a similar effect observed in the popular Si/SiGe systems. This result shows that this hypothetic system
may be a good candidate for optoelectronic applications.
5
Conclusion
In conclusion, we have studied the structural and electronic properties of YN using both FP-LMTO and FPLAPW methods, within both GGA96 and LDA approximations. The two methods were used for comparison in
all steps of our work. The main conclusions can be summarized as follows:
i) The rock salt is the ground state configuration.
ii) YN is lattice matched to ScN in the rock salt phase
iii) The A3 structure is found to be stable in YN and occupies a second minimum. We confirm in this paper that
the A3 phase has a total energy lower than wurtzite by 0.12eV and the axial ratio increases by 34 % as much as
when going from A3 to wurtzite structures. This result is comparable to what was found for ScN in Ref [5] and
not in the wurtzite phase as predicted in Ref [7]. However, the differences between the B4 and A3 phases are not
severe for the present YN compound.
iv) Our calculations show the possibility of a phase transformation from B1(rock salt) phase to B2 (caesium
chloride).
v) The band structures of B1 phase YN calculated within different methods show an indirect nonzero bandgap
(Γ→Χ) so that we can conclude that YN is a semiconductor like ScN.
vi) The inhabitual rocksalt/rocksalt superlattice YN/ScN system has been investigated. It consists of an ideal
quantum well superlattice SL(2,2) made of a periodical sequence (with period D = 9.5628 Å) of two monolayers
of YN atoms and two other monolayers of ScN atoms. We have found that the ScN/YN SL(2,2) has a direct
fundamental bandgap at Γ despite the fact that its bulk parent materials have both an indirect bandgap. This is
probably due to the zone folding effect and resembles to what is observed in the popular Si/SiGe systems. This
result suggests that these systems be candidates for further optoelectronic applications.
Acknowledgments One of the authors, N. Sekkal thanks the Center of Theoretical and Applied Physics
(CTAPS) of Irbid in Jordan and the Abdus Salam International Centre for Theoretical Physics, Trieste, Italy for
support and hospitality in 2005 and 2007 where parts of this work have been done. He also thanks M. Poropat
and V. Kravtsov for the help provided before and during his stay at ICTP and S.Y. Savrasov for his help and his
Mindlab software freely available for research. He would also like to thank Mr. K. Sekkal for his valuable help
in the English writing of the paper. This work has been supported by CTAPS of Jordan, ICTP in Trieste, ENSET
of Oran (Algeria) and by the Algerian National Research Projects CNEPRU under number J 3116/02/05/04, J
3116/03/51/05 and D05520060007.
6
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7
Fig 1b
Fig 1a
-93568
a
-93458
-93460
-93574
-93464
-93466
-93576
-93578
-93468
-93580
-93470
-93582
-93472
-93584
10
20
30
40
% (YN-B1)
% (YN-B2)
% (YN-B3)
% (YN-B4)
% (YN-A3)
-93572
Energy(eV)
Energy(eV)
-93462
b
-93570
% (YN-B1)
% (YN-B2)
% (YN-B3)
% (YN-B4)
% (YN-A3)
50
10
60
20
c
-93577
-93579
Energy(eV)
Energy(eV)
-93468
-93469
-93581
-93582
-93583
-93471
-93584
-93472
-93585
30
35
40
45
50
15
55
d
-93580
-93470
25
% (YN-B1)
% (YN-B2)
% (YN-B3)
% (YN-B4)
% (YN-A3)
-93578
-93467
20
60
Fig 1d
% (YN-B1)
% (YN-B2)
% (YN-B3)
% (YN-B4)
% (YN-A3)
15
50
-93576
-93464
-93466
40
Volume(A )
Fig 1c
-93465
30
3
3
Volume(A )
20
25
30
35
40
45
50
55
3
3
Volume(A )
Volume(A )
Fig. 1: Calculated total energy versus relative volume for YN within (a) LDA and FPLMTO, (b) GGA96 and
FPLMTO, (c) LDA and FPLAPW and (d) GGA96 and FPLAPW.
8
Fig 2b
a
EF
Energy(eV)
Energy(eV)
Fig 2a
10
8
6
4
2
0
-2
-4
-6
-8
-10
-12
-14
-16
-18
-20
-22
-24
W
L
Γ
X
K
W
b
EF
W
Γ
L
X
K
W
Fig 2d
Fig 2c
10
10
8
6
4
2
0
-2
-4
-6
-8
-10
-12
-14
-16
-18
-20
-22
-24
c
d
8
6
4
2
EF
EF
0
-2
-4
Energy(eV)
Energy(eV)
10
8
6
4
2
0
-2
-4
-6
-8
-10
-12
-14
-16
-18
-20
-22
-24
-6
-8
-10
-12
-14
-16
-18
-20
-22
-24
W
L
Γ
Χ
W
Κ
W
L
Γ
X
W
K
Fig. 2: The band structure of YN in the equilibrium rocksalt (B1) phase for the equilibrium volume. (a) LDA
and FPLMTO, (b) GGA96 and FPLMTO, (c) LDA and FPLAPW and (d) GGA96 and FPLAPW.
9
a
EF
Energy(eV)
Energy(eV)
Fig 3a
10
8
6
4
2
0
-2
-4
-6
-8
-10
-12
-14
-16
-18
-20
-22
-24
Γ
X
Γ
M
c
EF
R
Γ
EF
Γ
X
Γ
M
Fig 3d
Fig 3c
10
8
6
4
2
0
-2
-4
-6
-8
-10
-12
-14
-16
-18
-20
-22
-24
b
R
Energy(eV)
Energy(eV)
R
Fig 3b
10
8
6
4
2
0
-2
-4
-6
-8
-10
-12
-14
-16
-18
-20
-22
-24
X
M
Γ
10
8
6
4
2
0
-2
-4
-6
-8
-10
-12
-14
-16
-18
-20
-22
-24
d
EF
R
Γ
X
M
Γ
Fig. 3: The band structure of YN in the CsCl (B2) phase for the equilibrium volume. (a) LDA and FPLMTO,
(b) GGA96 and FPLMTO, (c) LDA and FPLAPW and (d) GGA96 and FPLAPW.
10
Fig4b
a
EF
Energy(eV)
Energy(eV)
Fig4a
10
8
6
4
2
0
-2
-4
-6
-8
-10
-12
-14
-16
-18
-20
-22
-24
W
Γ
L
X
W
K
b
EF
W
L
Γ
X
W
K
Fig4d
Fig4c
10
10
8
c
d
8
6
6
4
4
EF
2
0
2
0
-2
-2
-4
-6
-4
Energy(eV)
Energy(eV)
10
8
6
4
2
0
-2
-4
-6
-8
-10
-12
-14
-16
-18
-20
-22
-24
-8
-10
EF
-6
-8
-10
-12
-12
-14
-16
-14
-18
-18
-20
-22
-20
-22
-16
W
L
Γ
X
W
W K
L
Γ
X
W K
Fig. 4: The band structure of YN in the ZincBlende (B3) phase for the equilibrium volume. (a) LDA and
FPLMTO, (b) GGA96 and FPLMTO, (c) LDA and FPLAPW and (d) GGA96 and FPLAPW.
11
Fig5a
Fig5b
a
10
5
5
EF
-5
-10
-5
-10
-15
-15
-20
-20
Γ
EF
0
Energy(eV)
Energy(eV)
0
-25
b
10
M
K
Γ
-25
A
Γ
M
Γ
A
Fig5d
Fig5c
c
10
d
10
5
5
EF
0
EF
0
Energy(eV)
Energy(eV)
K
-5
-10
-5
-10
-15
-15
-20
-20
Γ
M
K
Γ
A
Γ
Μ
Κ
Γ
Α
Fig. 5: The band structure of YN in the wurtzite (B4) phase for the equilibrium volume. (a) LDA and FPLMTO,
(b) GGA96 and FPLMTO, (c) LDA and FPLAPW and (d) GGA96 and FPLAPW.
12
Fig6b
a
EF
Energy(eV)
Energy(eV)
Fig6a
10
8
6
4
2
0
-2
-4
-6
-8
-10
-12
-14
-16
-18
-20
-22
-24
Γ
M
Γ
K
10
8
6
4
2
0
-2
-4
-6
-8
-10
-12
-14
-16
-18
-20
-22
-24
b
EF
Γ
A
M
EF
Energy(eV)
Energy(eV)
c
Γ
M
K
Γ
A
Fig6d
Fig6c
12
10
8
6
4
2
0
-2
-4
-6
-8
-10
-12
-14
-16
-18
-20
-22
K
Γ
A
12
10
8
6
4
2
0
-2
-4
-6
-8
-10
-12
-14
-16
-18
-20
-22
d
EF
Γ
M
K
Γ
A
Fig. 6: The band structure of YN in the A3 phase for the equilibrium volume. (a) LDA and FPLMTO, (b)
GGA96 and FPLMTO, (c) LDA and FPLAPW and (d) GGA96 and FPLAPW.
13
Y
N
XSL
ZSL
aSL
YSL
j
i
k
Fig. 7: The direct zones of both bulk semiconductor and a (001) growth axis SL(1,1). i, j and k are the cartesian
unitary vectors. Dots represent nodes containing two atoms of the same specie. aSL is the lattice constants of the
superlattice.
Kx
R
X
A
M
Kz
Z
Γ
B
Y
Ky
Fig. 8 : The Brillouin zone of the (001) growth axis SL(1,1) superlattices.
14
Fig 9
2.0
1.5
1.0
Energy(eV)
0.5
EF
0.0
-0.5
-1.0
-1.5
-2.0
Γ
X
M
Γ Z
R
A
Z
Fig. 9: The band structure of YN/ScN SL(2,2) superlattice calculated within FPLMTO+GGA96, both bulks
being in the rocksalt (B1) phase.
15