study on n-type doping with phosphorous in diamond by means of density functional theory
TRANSCRIPT
Study on n-type doping with phosphorous in diamond by means ofdensity functional theory
Ying Dai a,b,*, Shenghao Han a,b, Baibiao Huang b, Dadi Dai c
a School of Physics and Microelectronics, Shandong University, Jinan 250100, People’s Republic of Chinab The State Key Laboratory of Crystal Material, Shandong University, Jinan 250100, People’s Republic of China
c Department of Chemistry, North Carolina State University, Raleigh, NC 27695-8204, USA
Received 10 June 2002; received in revised form 15 August 2002; accepted 10 October 2002
Abstract
To investigate the n-type doping with phosphorous (P) in diamond, the electronic structure of a series of diamond clusters has
been calculated by means of density functional theory method. From the results, we have found some of interesting properties of P
doping. Firstly, the n-type doping behavior with P in diamond is very similar to that in silicon. Secondly, the donor level induced by
P is shallower for the larger cluster than for the smaller cluster. Lastly, the phosphorous-dangling-bond complex is one of the factors
defining the donor level position if dangling bonds (DBs) exist in samples. These findings may well explain some of experimental
data of n-type materials doped with P.
# 2002 Elsevier Science B.V. All rights reserved.
Keywords: Diamond; Doping effects; Electronic states; DFT
1. Introduction
Diamond is a promising semiconductor material for
many electronic and biomedical applications. Intrinsic
and p-type material with good quality are already
available. However, many efforts to produce diamond
or diamond-like carbon thin films with high n-type
conductivity have been unsuccessful [1�/8]. Although
part of the prior work [2,3,5,8] demonstrated that n-type
doping of diamond could produce shallow donor levels
close to the conduction band, the room temperature
conductivities are still too low for the application of
these materials in conventional electronic devices [2�/5].
Very little is known about the n-type doping of diamond
whereas the p-type doping of diamond has been well
understood. Therefore, to understand the origin of the
n-type doping inefficiency and to find a good n-type
dopant have become of a key factor in the investigation
of diamond semiconductor devices. P is regarded as a
potential n-type dopant in diamond, but its high
formation energy [9] leads to a small solubility, which
makes the P doping by thermal or grown diffusions
ineffective [10]. Ion implantation may be a reliable way
to dope diamond with P. However, it was found that the
P atoms were not electrically activated though half of
them are located on substitutional sites by implantation
[11]. The present paper demonstrates that in ideal
hydrogenated cluster of diamond, the n-type doping
with P in a substitutional site produces a shallower
donor level for the large cluster than for the small
cluster. The present work also shows that the dangling
bonds (DBs) on the surface strongly affect the n-type
doping efficiency of P, indicating that the low electrical
activation of P n-type doping in diamond should be
associated with the interaction between the P donor
center and the DBs. In addition, we point out that the
efficiency of the P n-type doping of diamond could be
improved by reducing the number of remaining DBs
after hydrogenation in samples with fluorination if it
could be realized.
* Corresponding author. Tel.: �/86-531-8060182; fax: �/86-531-
8367032.
E-mail address: [email protected] (Y. Dai).
Materials Science and Engineering B99 (2003) 531�/535
www.elsevier.com/locate/mseb
0921-5107/02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 1 - 5 1 0 7 ( 0 2 ) 0 0 5 4 9 - 4
2. Computational details
The Kohn�/Sham DFT approach is employed and the
Amsterdam Density Functional (ADF2.3) program isused [12]. The 2s, 2p orbital of C, 3s, 3p orbital of P and
1s orbital of H are considered as valence shells, while 1s
orbital of C and 1s, 2s, 2p orbital of P are frozen in the
core. The triple-z Slater type orbital plus polarization
functions are employed in the calculations. The VWN
[13]�/Be88 [14]�/Perdew86 [15] is selected as the ex-
change-correlation functional. The relative error of
numerical integration in our calculations is 10�6.We have carried out DFT calculations on three
groups of eleven clusters. (a) The basic cluster C47H60
is constructed as follows: one C atom locates at the
center, surrounded by four nearest, 12 second-nearest,
12 third-nearest, 6 fourth-nearest and 12 fifth nearest
neighbor carbon atoms, takes on Td symmetry, and
coheres with 60 H atoms that terminate the boundary
DBs. (b) C29H36 is constructed as (a) but without thefourth and fifth nearest neighbor C atoms and the
boundary DBs are terminated by 36 H atoms. (c) C17H36
is the same as (b) but without the third-nearest C atoms
and with 36 H atoms terminating the boundary DBs .
The bond length of C�/C and C�/H adopted are 1.54 A
and 1.00 A, respectively, in the calculations.
3. Results and discussion
In order to investigate the effect of size on the donorlevel position with respect to the bottom of conduction
band, we have studied the electronic structure of the
following group of clusters [Fig. 1 (1)�/(3)]: (1)
C16P1H36, the same as cluster (c) with the center C
atom substituted by P, (2) C28P1H36, the same as cluster
(b) but with the center C atom substituted by P, and (3)
C46P1H60, the same as cluster (a) but with P substituting
the center C atom (the change of C�/P bond length has
little effect on the discussion for the donor behaviors).
The bottom of conduction band EC is defined as the
lowest energy level with zero electron occupation and
the top of valence band EV is defined as the highest
energy level with full occupation. Fig. 1 shows that P
atom introduces a donor EP level in the gap below the
bottom of the conduction band of the clusters. The
energy differences DEP�/EP�/EC of the three clusters
are 0.785 eV, 0.343 eV and 0.210 eV, respectively, in turn
with increasing cluster size. This demonstrates that the
larger the cluster, the smaller the energy difference DEP.
Therefore, it is reasonable to deduce that, if P atom is
located at substitutional sites the activation energy EF�/
EC will be smaller for larger clusters or bulk diamond
than that of the smaller cluster used. The Fermi level EF
is defined as the energy at which the Mulliken popula-
tion is one for the single electron approximation.
Experiments have shown that almost half of the P
implanted was found to locate at substitutional sites
[11], so that P should be a good n-type dopant for larger
clusters or bulk diamond due to its small activation
energy, according to our above theoretical results. It is
noted that our calculated donor level is consistent with
that theoretically estimated based on the band structure
analysis of diamond and on the results of molecular
quantum dynamics techniques applied to atomic con-
Fig. 1. Electronic structure of clusters (1) C16P1H36, (2) C28P1H36, (3) C46P1H60 and (4) Si46P1H60. Dot line represents donor level. EC: the bottom of
conduction band. EV: the top of valence band.
Y. Dai et al. / Materials Science and Engineering B99 (2003) 531�/535532
figurations of an impurity that is surrounded by carbon
atoms in ‘supercells’ containing up to 64 atoms [9].
Because the calculated energy difference DEP of the
cluster C46P1H60, 0.210 eV, is in good agreement with
0.2 eV reported by reference [9], we employed C46P1H60
as a basic simulated cluster to discuss the doping
property. Since it is well known that P is a good donor
dopant (the ionization energy is 0.044eV) in silicon, we
have studied the electronic structure of cluster (4)
Si46P1H60 that has similar structure of C46P1H60, as
given in Fig. 1 (4). By comparing the energy difference in
diamond (DEP�/0.210 eV) and that in silicon (DEP�/
0.175 eV), we found that P could be a donor dopant for
ideal fully hydrogenated diamond as good as P for
silicon. However, implantation experiment results
showed that the P atoms are not electrically activated
though half of the P atoms locate on substitutional sites
by implantation [11]. We explain this contradiction as
follows.
It is well known that the key factor determining the
doping effect on the conductivity of a semiconductor is
the gap-states induced by defects and useless impurities
in the materials. Experiments show that some defects
related to DBs remain on the hydrogenated diamond
surface, or in the grain-boundary [16]. The EPR signal
in chemical vapor deposition (CVD) diamond also
reveals the presence of DBs associated with H atoms
[6]. Practically such defects cannot be eliminated in
general hydrogenation processes [17,18]. The existential
defect in an ideal hydrogenated undoped cluster of
diamond with ideal C47 core is only DB. In order to
investigate the nature of gap-states induced by DB, we
calculated the electronic structure of the second group
clusters as following: (5) C47H60; (6) C47H59D1, the same
as (5) but with one DB replacing one H atom; (7)
C46P1H60; (8) C46P1H59D1, the same as (7) but one H is
replaced by a DB; (9) C46P1H58D2, the same as (7) but
two H atoms are replaced by two DBs; (10)
C46P1H56D4, the same as (7) but with four H atoms
replaced by four DBs. The results are given in Fig. 2
(5)�/(10). Obviously, no state appears in the gap for the
ideal hydrogenated diamond cluster (5) C47H60, which
indicates diamond should be an insulator. In cluster (6)
C47H59D1, a DB induces a deep level that lies below the
middle of the gap, which is unfavorable for n-type
doping. In cluster (7) C46P1H60, the energy difference
DEP is 0.210 eV, which shows that P in a substitutional
site is a shallow donor dopant. In cluster (8)
C46P1D1H59, a relatively deep level with two-electron
occupation appears below EC. Similarly, in clusters (9)
C46P1D2H58 and (10) C46P1D4H56, two deep levels with
totally three electrons occupied and four energy levels
with totally five electrons occupied appear below the
middle of the gap. The activation energy increases when
more DBs are introduced. We attribute this to the
passivation of the doping activity of P by DBs. By
analyzing Mulliken charge population in the gap states
(see Fig. 2), we find that there is interaction between P
and DBs. As a result, a P�/DBs complex instead of
dopant-isolated center is formed, leading to a group of
deeper gap states. The more the DBs are, the deeper the
group of the gap states locates. That is, DBs may
increase the activation energy of the clusters. Therefore,
the interaction between P and DBs may result in the
formation of the complexes and leads to that P atoms
are low electrically activated when the number of DBs
Fig. 2. Electronic structure of clusters (5) C47H60, (6) C47H59D1, (7) C46P1H60, (8) C46P1H59D1, (9) C46P1H58D2, and (10) C46P1H58D4. The numbers
in parenthesis on the gap state levels are the electron Mulliken populations.
Y. Dai et al. / Materials Science and Engineering B99 (2003) 531�/535 533
increases. In other words, the P�/DBs complexes is one
of the factors that determine the activation energy EF�/
EC
As there are some DB-related defects on the surfaceor in the grain boundary of samples commonly hydro-
genated diamond [16�/18], it is reasonable to believe that
the existence of some DBs in the samples may be one of
the possible inefficiency factors of n-type doping in
diamond. Therefore, to reduce the number of DBs as
much as possible is one of the methods to improve the n-
type doping efficiency. In order to evaluate this method
theoretically, we have examined the electronic structureof the third group clusters as following (Fig. 3): (11)
C46(P1D2)H58; (12) C46(PDF)1H58, the same as (11) but
with substituting one of the DBs by fluorine (F); and
(13) C46(P1F2)H58, the same as (11) but the two DBs are
replaced by two F. Fig. 3 (12) shows that the formation
of one C�/F bond makes the donor level clearly
shallower than that of (11). Similarly, in (13) only a P-
related much shallow relatively donor level with oneelectron occupation appears below EC, and the energy
difference DEP is only 0.158 eV because the two DBs are
saturated by two F atoms. It is concluded that fluorina-
tion can improve the efficiency of n-type doping with P
if it could be practically realized in experiments.
4. Conclusions
By having investigated the effect of DBs on P n-typedoping in hydrogenated diamond, we find that P may be
a good donor dopant if the diamond is ideally hydro-
genated without defects and useless impurities. In
experiments, one of the reasons for the difficulty of
making the diamond n-type doping is the existence of
DBs in the surface or on the grain boundary of
commonly used samples and their interaction with thedapants. One possible way to improve the P n-type
doping efficiency of the hydrogenated diamond is
fluorination to eliminate the remaining DBs on the
surface. The discussions in the paper relate only to the
relative values of donor levels, the cluster size, in
principle, does not affect the nature of the conclusions.
Acknowledgements
The financial support from the ministry of science and
technology of China (973, 001CB610504). The calcula-tions performed in the computer of the network center
of Chinese science academy during the time of the first
author as a visiting scholar of State Key Lab in Peking
University, and Origin 2100 workstation of Physics
department, Shandong University.
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