In spite of large concentrations of phosphorus being incorporated into diamond, the material often remains insulating. It is argued that this occurs through the formation of phosphorus-vacancy complexes which are deep acceptors and compensate any donor. The complex is analyzed using a first principles cluster method. In the ionized state, the defect is diamagnetic and cannot give rise to any internal optical transitions although broad band donor-acceptor transitions are expected - and observed - in material co-doped with nitrogen.
There has been a considerable amount of work carried out on
incorporating phosphorus in diamond with the aim of making a shallow
donor defect. However, almost all studies have succeeded in making
highly resistive material despite substitutional P (P 
) being
expected to behave as a donor [1, 2, 3].
Electron paramagnetic resonance (EPR) provides some evidence for
P [4], and a second P defect is found in P doped diamond
grown by the high pressure method [5]. The latter defect is
trigonal with very little spin density at the P nucleus.
P has also been incorporated into chemical vapur deposition grown
(CVD) diamond by adding PH 
to the gas phase [6, 7].
Nitrogen apparently increases the incorporation of P within the films
yielding concentrations as high as 3 
cm 
(as
measured via SIMS). In spite of these large concentrations, the films
were highly resistive. Photoluminescence (PL) experiments revealed
broad intense bands around 1.7 eV which increased with [P]. These
were assigned to donor-acceptor pair recombination although the
identities of the defects are not known. Significantly, no sharp
optical lines due to P or the vacancy were detected.
Success at making conducting, n-type diamond has been achieved through a cold implantation of P ions followed by rapid thermal annealing [8]. It may be that this process rapidly removed vacancies resulting from the implantation.
CVD diamond usually contains a high concentration, up to 
cm of vacancies [9]. The lack
of an optical signal due to vacancies in the P rich material suggests
that they are bound up with P in some form. Now, impurity-vacancy
complexes are important optical centers in diamond. The best
understood is the N-V center whose electronic structure is easily
understood in terms of the ideal neutral
vacancy [10, 11, 12]. This has the electronic
configuration 
. In the N-V defect, where a C atom
bordering the vacancy is replaced by N, the 
level is split into
an 
-level lying below an e-doublet. For (N-V) 
, the
e-level contains two electrons in an S=1 state [13]. The
partial occupancy of the e level permits 
optical
transitions which are assigned to the 1.945 eV optical center for
[N-V] [14, 15] and 2.156 eV for neutral
N-V [16, 13].
It might be thought that the P-V defect would be similar to N-V. In
that case we would expect it to act as an acceptor, with spin 1 in the
ionized state, and to possess a sharp luminescence line arising from
the internal transition. However, we shall show
below that this is not the case and [P-V] has spin S=0 and no
internal optical transitions are possible. However, P-V does act as a
deep acceptor and compensates substitutional P and N. This would
explain the insulating properties of P-rich diamond, the lack of
P-related sharp luminescent bands, as well as the presence of broad
donor-acceptor optical bands.
We have carried out spin-polarized, ab initio calculations on
P-V complexes using the AIMPRO [17] code. We used 86 atom
clusters, C 
H 
, having trigonal symmetry from which two C
atoms were removed and a P atom added. This generates a P-V pair.
The basis used is similar to recent investigations on N-V and Si-V
centers [13]. Previously [3], we have investigated
substitutional phosphorus finding it to be an on-site defect with a
localized vibrational mode around 380 cm 
.
In the first case the P atom was placed as far away from the vacancy and the surface as possible. The structure was relaxed in the neutral charge state. Then the P atom was moved to border the vacancy and the cluster re-relaxed. The energy in this case was lower by 1.5 eV than the case where P was separated from the vacancy. This shows that substitutional P is unstable in the presence of vacancies and readily forms the P-V complex.
In the P-V complex, the P atom did not remain at its lattice site but
drifted away until it lay mid-way between two lattice sites. This
structure is quite distinct from N-V but is similar to the
split-vacancy Si-V complex [13]. Fig. 1 shows the inner core
of the relaxed 86 atom cluster showing its 
symmetry. The six
P-C lengths are 2.00 Å. The reason for the stability of the
split-vacancy is partially connected with the large atomic size of P
although Ge-V does not appear to assume the same structure. Fig. 2
shows the spin-polarized Kohn-Sham energy levels of the P-V defect in
the vicinity of the band gap, together with those of a similar sized
cluster without any defects. These reveal a mid-gap 
-level
(even) containing three electrons and an 
-level just
above the valence band top, resulting in an effective spin of S=1/2.
The position of this mid-gap level is qualitatively similar to that
found in the Si-V defect and thus the defect would be expected to trap
electrons arising from say substitutional N or indeed P. Thus the P-V
defect acts as a deep acceptor. However, the levels
are then filled and the defect must be diamagnetic and no internal
optical transitions are possible.
When the Fermi-level is low, such as for example when the material is
Irradiated or the absence of substitutional N, then a neutral P-V
defect would be formed having S=1/2. The wave-functions of the
gap levels are combinations of 
orbitals on the six C
atoms surrounding P and possess very little amplitude on P itself as
shown in Fig. 3. The trigonal symmetry of the defect and the fact
that the spin density is very low on P suggests that this defect might
be the EPR center investigated in Ref. [5].
Although no internal optical transitions are possible for the ionized
defect, neutral pairs of N 
and (P-V) defects could luminesce
and be the source of the broad band donor-acceptor recombination band
observed in Ref. [7]. The luminescence energy would then be:
With the N donor level and the P-V acceptor level (Fig. 2) at
eV and 
eV respectively, then for r about
5 Å, this transition would be around 1.5 eV, close to the observed
value.
In conclusion, the calculations suggest a strong binding energy of P
with vacancies. In the P-V center, the P atom lies mid-way between
two vacancies. The center has symmetry with spin
S=1/2 in the neutral charge state, and there is little
spin-density on the P atom consistent with EPR experiments. The
defect acts as a deep acceptor and together with N would explain the
pronounced broad PL bands seen around 1.7 eV in P-doped diamond. The
defect could also compensate remaining substitutional P atoms. This
would explain the difficulties in making phosphorus electrically
active in diamond.
present address: Department of Physics, University of
Exeter, Exeter, EX4 4QL, UK.