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: daiy60@sdu.edu.cn (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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