Japanese Journal of Applied
Physics

REGULAR PAPER

Electrical properties and conduction mechanismsof heavily B+-ion-implanted type IIa diamond:
effects of temperatures during the ion implantationand postannealing upon electrical conduction
To cite this article: Yuhei Seki et al 2020 Jpn. J. Appl. Phys. 59 021003

Recent citations- Extremely high-efficient activation of
acceptor boron introduced by ion
implantation at room temperature withvarious doping concentrations in epitaxiallysynthesized diamond films by chemical
vapor deposition
Yuhei Seki et al- Schottky barrier diodes fabricated on highpurity type-IIa CVD diamond substrates
using an all-ion-implantation process
Seiya Shigematsu et alView the article online for updates and enhancements.

This content was downloaded from IP address 153.156.47.237 on 29/07/2021 at 02:36

REGULAR PAPER

Japanese Journal of Applied Physics 59, 021003 (2020)
https://doi.org/10.35848/1347-4065/ab699c

Electrical properties and conduction mechanisms of heavily B+-ion-implanted typeIIa diamond: effects of temperatures during the ion implantation andpostannealing upon electrical conduction
Yuhei Seki, Yasushi Hoshino*, and Jyoji Nakata
Department of Mathematics and Physics, Kanagawa University, 2946, Tsuchiya, Hiratsuka, Kanagawa 259-1293, Japan*

E-mail: yhoshino@kanagawa-u.ac.jp

Received December 13, 2019; accepted January 9, 2020; published online February 7, 2020
We investigated the electrical properties and conduction mechanism of heavily B+-implanted type IIa diamond with respect to the implantation andpostannealing temperatures. The B atoms were shallowly implanted with a flat concentration of 3.5 × 1019 cm−3 at RT and 900 °C; these samples
were finally annealed at 1150 °C, 1300 °C and 1450 °C. We consequently confirmed p-type conductivity and typical ionization energy of acceptor B
in a wide measured temperature range. The doping efficiency progressed remarkably well and attained 78% and the Hall mobility at RT was
realized to be 108 cm2V−1s−1 for the RT-implanted sample followed by annealing at 1300 °C. On the other hand, hot B+ implantation at 900 °C
slightly degraded the electrical properties. The higher-temperature annealing at 1450 °C after B+ ion implantation promoted hopping conduction
fairly well at a lower measured temperature range below around RT. We systematically investigated the hopping conduction mechanism based ontheoretical relations. © 2020 The Japan Society of Applied Physics

1. Introduction

Effective impurity doping into single-crystalline diamondsubstrates has been a crucial subject in the application ofhigh-power and high-frequency electronic devices.1–3)
Impurity doping has usually been performed in the synthesis
process of diamond ﬁlm by chemical vapor deposition(CVD).4–7) It is well known that impurity doping by ion
implantation is quite superior to that in epitaxial growth interms of the merits of short process time, large doping areaand low ﬁnancial cost. In addition, one can easily introduce
any dopants in the desired area and depth with an accurate
concentration; therefore, it is a common tool for fabricating
Si- and GaAs-based semiconductor devices. In the case of
diamond semiconductor fabrication, impurity doping by ion
implantation has not been practically accomplished, in spiteof research in this regard for several decades.8–18)
According to previous studies, the substrate quality andtemperatures during ion implantation and postannealing are
regarded as signiﬁcantly important parameters for the ﬁnal
electronic properties of diamond semiconductor. Concerning
the substrate temperature during B+ ion implantation for theformation of p-type semiconductor, various temperaturesfrom −196 °C to 400 °C have been investigated so far.
Prins performed impurity doping by ion implantation at−196 °C followed by rapid thermal annealing.8–11) UzanSaguy et al. and Fontaine et al. then developed the doping
process and obtained a small doping efﬁciency of 2% at
most.12,14) In the case of RT implantation, Vogel et al. carriedout B δ-doping by 2 MeV B+ ion implantation followed byannealing at higher than 1500 °C. The doping efﬁciency wasslightly improved to 30% for the sample with a ﬂuence of1014 cm−2. Tsubouchi et al. recently performed B+ ion
implantation with B concentrations of 1018–1021 cm−3 at
400 °C followed by 1450 °C and 1600 °C annealing. In theheavily B+-implanted sample with 5 × 1019 cm−3, the doping
efﬁciency was only 9%.
In the aspect of application to high-power and highfrequency devices, the establishment of the fabrication
process of low-resistance layer with highly controlled
p- and n-type conductivity using ion implantation is theinevitable issue. In the previous letter, we reported theprogress of the electrical properties for type IIa diamondsubstrates doped by B+ ion implantation at RT followedby relatively low-temperature annealing at 1150 °C and1300 °C.19) In the present study, we have further investigatedthe dependence of electrical properties of B+-implanted typeIIa diamond substrates on the implantation temperatures andpostannealing temperatures. Finally, we have comprehensively clariﬁed the mechanisms of hopping conduction,
especially those appearing in the high-temperature postannealing samples, based on the theoretical relations. We also
qualitatively referred to the reasons such excellent electricalproperties can be obtained.
2. Experimental

Type IIa diamond substrates of standard grade with a typicalsize of 3 × 3 mm2 synthesized by the CVD method werepurchased from Element Six Ltd. These samples weremechanically polished in advance at Syntek Co. Ltd. The
average surface roughness was evaluated by atomic force
microscope to be less than 0.03 nm. The atomically ﬂatsamples were then treated with a typical wet chemicalcleaning process for diamond: dipping in H2SO4 and HNO3
solution followed by diluted NH3 and H2O2 solution. The
samples were immediately introduced into a vacuum
chamber for B+ ion implantation, whose base pressure wasachieved below 10−5 Pa. The accelerated 11B+ ions witheight different energies from 5–60 keV were implanted into
the substrates to obtain a ﬂat concentration from the surface
to the ∼130 nm depth. The B+ ions were implanted at thesubstrate temperatures of 900 °C or RT to investigate thedependence of doping efﬁciency on the temperatures during
the implantation. The total ﬂuence of B+ ion was
4.6 × 1014 cm−2, and the ﬂuence for each energy wasestimated by TRIM simulation in advance.20) The concentration and thickness at the plateau region were estimated bysecondary ion mass spectroscopy (SIMS) after all electricalproperties were measured. Samples were then covered with athin SiO2 cap layer ∼100 nm thick by RF sputtering toprevent the surface graphitization during the subsequent
high-temperature annealing. We ﬁnally annealed the samples

021003-1© 2020 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 59, 021003 (2020)
Table I.
Temperature(implant.)

RT

900 °CY. Seki et al.
Electrical properties obtained by Hall effect measurements.

Temperature(postanneal)

NB(cm−3)

NA(cm−3)

ND(cm−3)K (%)(ND/NA)

Deff (%)(NA/NB)

μmax(cm2/Vs)

EA(eV)1150 °C
1300 °C
1450 °C
1150 °C
1300 °C
1450 °C

3.6 × 1019
3.3 × 1019——
3.5 × 1019—

2.8 × 1019
1.7 × 1019—
>1.0 × 1019
1.3 × 1019—

4.7 × 1018
2.9 × 1018—
4.8 × 1018
4.2 × 1018
—

18.5
19.5
∼17.0
47.0
36.5
∼20.0

78
52
—
—
37
—

90
108
39
71
61
19

0.335
0.302
∼0.25
0.375
0.305
∼0.21

in a quartz furnace in Ar ambient. After the annealing, thedeposited SiO2 layer was completely removed by wet HF
treatment and the electrical properties were then measured.
We adopted the postannealing temperatures of 1150 °C,
1300 °C and 1450 °C, and carried out the electrical measurements for the samples postannealed at each temperature. The
preparation processes are brieﬂy listed in Table I.
The electrical measurements of resistivity and Hall effectbased on the van der Pauw method were carried out by
Resitest 8300 Hall effect apparatus from Toyo Corp. Ohmicelectrodes consisting of Au/Pt/Ti multilayers with a diameterof 0.5 mm were then formed near the four corners of thesubstrates by magnetron sputtering at a substrate temperatureof 550 °C followed by 800 °C annealing in high vacuum. The
electrical properties of speciﬁc resistance, carrier concentration and Hall mobility were measured at sample temperaturesfrom 77–1073 K, though reliable experimental data wereobtained above 173 K due to a lack of sufﬁcient electricalactivation at such low temperatures.
3. Results and discussion
3.1. Electrical properties in the band conduction
regionFigure 1 shows the concentration proﬁle of 11B atoms
implanted in type IIa diamond substrates at 900 °C or RT
followed by thermal annealing measured with SIMS. The
relative sensitivity of secondary ion intensity was calibrated
by a well-quantiﬁed B-doped diamond in advance. The
sputtering rate was determined by the crater depth after
SIMS measurement. Black, red, and green curves indicate thedepth proﬁle for the samples as implanted at RT and thenpostannealed at 1150 °C and 1300 °C, respectively. The blue
curve shows the depth proﬁle for the 900 °C-implanted
sample followed by 1300 °C annealing. The depth proﬁle forthe as-implanted sample was fairly broad near the tail edge ofthe doped layer. This fact is probably attributed to the ionchanneling effect during the B+ implantation because theimplantation was performed with low energies from
5–60 keV along almost the normal axis to the substratesurface. After the annealing at high temperatures, the interface became abrupt and a ﬂat B concentration of∼3.5 × 1019 cm−3 was observed from the surface to∼130 nm depth. The thickness of the doped layer wasdetermined from the full width at half-maximum concentration. The concentrations of intrinsically incorporated N and H
atoms were estimated to be less than 2 × 1016 and2 × 1017 cm−3, respectively, by the same SIMS measurement.
Figure 2 shows the carrier concentration (a) and Hall
mobility (b) as a function of reciprocal and absolutetemperatures, respectively, obtained by Hall effect measurement for the 900 °C-implanted samples followed by 1150 °C,
1300 °C and 1450 °C annealing. The circles denote theresults obtained by Hall effect measurement: closed circles
indicate the points appearing in p-type conduction and open
circles are undeterminable points of carrier type. The solidlines indicate the theoretically calculated carrier concentration shown below. It is well known that the temperaturedependent hole concentration (p) can be theoretically formalized by the charge neutrality condition and Fermi–Dirac
distribution function, and thus given by the following relation
with three parameters of NA, ND and EA:

Fig. 1. (Color online) Depth proﬁle of implanted 11B at 900 °C and RT followed by thermal annealing measured by SIMS. Black, red, and green curvesindicate the obtained depth proﬁle of 11B for the as-implanted sample at RT, and postannealed samples at 1150 °C and 1300 °C, respectively. Blue curve shows
the proﬁle for the 900 °C-implanted sample followed by 1300 °C annealing.

021003-2© 2020 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 59, 021003 (2020)

Y. Seki et al.

(a)p (K , EA) =(b)

Fig. 2. (Color online) Carrier concentration (a) and Hall mobility (b) as afunction of temperature obtained by Hall effect measurement for the 900 °Cimplanted samples followed by annealing at 1150 °C (black), 1300 °C (red)and 1450 °C (green). Closed circles show the points appearing in p-typeconductivity and open circles are undeterminable points of conduction type.

p ( p + N D)
2 ⎛ 2pm*k B T ⎞=⎜⎟⎠NA - ND - p
g (T ) ⎝
h2

3 2

⎛ E ⎞
exp ⎜ - A ⎟.
⎝ kB T ⎠(1 )Here, NA and ND are acceptor and donor concentration,
respectively; EA is the activation energy of the acceptor. g(T)and m* are, respectively, the degeneracy factor and effective
hole mass, while these values varied relatively among
previous reports. Collins et al. and Fontaine proposed therelations of degeneracy factor; monotonically varying from 4
at low temperatures to 6 at high temperatures.21,22) We thus
adopted the temperature-dependent degeneracy factor g(T)suggested by Collins et al. as follows:⎛ D ⎞g (T ) = 4 + 2 exp ⎜ ⎟.
⎝ kB T ⎠(2 )Here, Δ is a spin–orbit coupling of diamond with a small
split width of Δ = 6 meV. Concerning the effective holemass of diamond, it is relatively scattered around unity, andis not precisely deﬁned. In the previous reports on theanalysis of electrical properties, the effective hole massfrom 0.7–1.0 was usually used. We then adopted the mostcommonly referred value of 0.8m0 in the present
analysis.12,14,16)
In accordance with Eq. (1), it is found that the carrier
concentration does not depend on NA at enough lowtemperature region, except for the hopping region. Holeconcentration at such temperatures can be therefore approximated to be a famous relation of,⎛ E ⎞⎞NV ⎛⎜ 1- 1⎟ exp ⎜ - A ⎟.
⎝⎠⎝ kB T ⎠g (T ) K(3 )Here, NV is the effective density of states. The parameters ofactivation energy (EA) and compensation ratio (K = ND NA )are directly related to the gradient and offset in the semi-log
plot, respectively, indicating that three ﬁtting parameters canbe reduced to two parameters of EA and K. We ﬁrst best-ﬁtted
the hole concentration by assuming K, and EA at theintermediate temperature region from 300–700 K.
It can be clearly seen in Fig. 2(a) that the carrier
concentrations for the 900 °C-implanted samples followedby 1150 °C or 1300 °C annealing were exponentially increased as a function of reciprocal temperature, except forlower temperatures than RT. For the 1450 °C-annealed
sample, hopping conduction was dominated below 573 K.
We cannot quantitatively discuss the details of temperaturedependent carrier concentrations for the 1450 °C-postannealed sample due to the high contribution of hopping
conduction; therefore, we here focus on the properties of
the 1150 °C- and 1300 °C-postannealed samples. The details
with regard to hopping conduction will be discussed later.
In accordance with Eq. (3), the compensation ratio of the1150 °C, 1300 °C and 1450 °C-postannealed samples were
determined to be 47.0%, 36.5% and 20.0%, respectively,
though these were relatively high ratio. The activationenergies for the 1150 °C- and 1300 °C-annealed samples
were estimated to be 0.375 and 0.305 eV, respectively. The
estimated activation energies almost correspond to theacceptor level of substitutional B atom in diamond. The ptype conductivity was conﬁrmed from 250–1073 K for the1150 °C-postannealed sample, and was entirely observed attemperatures from 173–1073 K after the 1300 °C annealing.
It is found that the temperature dependence of hole concentration was signiﬁcantly decreased below RT, and thetendency was more remarkable in the 1300 °C-postannealed
sample. It is suggested that the electrical conduction was
dominated by the hopping process in place of band conduction, which will be discussed later in accordance with thetemperature-dependent speciﬁc resistance.
As can be seen in Fig. 2(b), the Hall mobility took the
maximum value of 61 and 71 cm2V−1s−1 around RT for the1150 °C- and 1300 °C-postannealed samples, respectively.
The Hall mobility followed the typical temperature dependence of T−3/2 at a comparatively higher temperature region
than RT. It is indicated that the carrier scattering mechanism
is governed by acoustic phonons above RT. The signiﬁcantdecrement of Hall mobility at low temperatures is probably
due to the change of conduction mechanism from band
conduction to hopping process.
Figure 3 shows the carrier concentration (a) and Hall
mobility (b) for the samples B-implanted at RT followed byannealing at 1150 °C, 1300 °C and 1450 °C. The compensation ratio was signiﬁcantly decreased to less than 20.0% for
the 1150 °C (black), 1300 °C (red) and 1450 °C (green)
postannealed samples compared to the 900 °C-implanted
samples followed by annealing at the same temperatures.
By best-ﬁtting the observed hole concentration using Eq. (3),the ionization energy for the 1150 °C-postannealed sample
was estimated to be 0.335 eV, and was slightly decreased to021003-3© 2020 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 59, 021003 (2020)

Y. Seki et al.

(a)

(b)

Fig. 3. (Color online) Carrier concentration (a) and Hall mobility (b) as afunction of temperature obtained by Hall effect measurement for the RTimplanted samples followed by annealing at 1150 °C (black), 1300 °C (red)and 1450 °C (green). Closed circles show the points appearing in p-typeconductivity and open circles are undeterminable points of conduction type.

acceptor B concentration. It can be found in Fig. 4 that theHall mobility observed in this study is comparable to the bestvalue expected in the B-doped diamond with the same B
concentration.23–30) The compensation ratio of less than
20.0% was independent of the postannealing temperature
for the RT-implanted samples, though the ratio was signiﬁcantly smaller than that for the 900 °C-implanted sample, as
shown in Fig. 2. This fact presumably shows that the highertemperature implantation is likely to enhance the diffusionand prevent the recombination of generated Frenkel pairs
during hot ion implantation, and residual defects are probably
developed to irreducible secondary defects. Consequently,
we strongly suggest that B-ion implantation as a doping
method should be performed at low temperatures such as RT
rather than higher temperatures. After determining the parameters of K and EA, we performed the curve ﬁtting of carrier
concentration at higher temperature region (>700 K) by
using Eq. (1); eventually determining NA value, independently.
Figures 5 and 6 show the obtained carrier concentrations as
a function of reciprocal temperature calculated by Eq. (1) for
the 900 °C- and RT-implanted samples, respectively. The
theoretical values depicted by solid curves were calculated byassuming various NA. Here, K and EA are the adopted values
just determined in the above analysis shown in Figs. 2(a) and
3(a). We can thus uniquely determine the acceptor concentration from the temperature dependence of the hole concentration by iteratively ﬁtting the theoretically calculated
values. In the case of the 900 °C-implanted sample followedby 1150 °C annealing, as shown in Fig. 5(a), the carrier

0.302 eV after 1300 °C annealing. The carrier type entirely
showed p-type conductivity for both samples at the reliabletemperature region from 173–1073 K. The Hall mobility
depicted in Fig. 3(b) shows the typical relation of T−3/2
above RT and took the maximum of 108 cm2 V−1 s−1 at RT
for the 1300 °C-postannealed sample. Figure 4 shows thepreviously reported Hall mobilities of diamond B-doped in
the CVD process and our present value as a function ofFig. 4. (Color online) Hall mobilities around RT as a function of acceptor
B concentration for previously reported B-doped diamonds by the CVD
process as well as our present ones doped by ion implantation at RT and
900 °C.

Fig. 5. (Color online) Experimental and simulated carrier concentrations as
a function of reciprocal temperature for the 900 °C-implanted samples
followed by subsequent annealing at 1150 °C (a) and 1300 °C (b). Solid
curves indicate the theoretical values calculated by assuming various NA.

021003-4© 2020 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 59, 021003 (2020)

Y. Seki et al.

Fig. 6. (Color online) Experimental and simulated carrier concentrations as
a function of reciprocal temperature for the RT-implanted samples followedby subsequent annealing at 1150 °C (a) and 1300 °C (b). Solid curvesindicate the theoretical values calculated by assuming various NA.

concentration did not signiﬁcantly depend on NA due to highcompensation ratio of 50%. We could not therefore precisely
determine the adequate NA value from these data. For the1300 °C-postannealed sample [Fig. 5(b)], the acceptor concentration was estimated to be ∼1.3 × 1019 cm−3. The
doping efﬁciency (Deff = NA/NB), deﬁned by the ratio of
NA to implanted B concentration (NB) evaluated by SIMS,
was estimated to be 36%, which is about four times higher
than the previously reported efﬁciency for heavily B-doped
diamond with almost the same density.16,17) In the case of the
RT implantation shown in Fig. 6, the estimated acceptor anddonor concentrations were respectively 2.8 × 1019 and4.7 × 1018 cm−3, suggesting that the Deff was greatly enhanced to 78%, which is 8.7 and 5.2 times higher than theprevious results for similar doping concentration reported
by Tsubouchi et al. and Vogel et al., respectively. Bothacceptor and donor concentrations slightly decreased to
1.7 × 1019 cm−3 and 2.9 × 1018 cm−3, respectively, and thedoping efﬁciency was eventually estimated to be ∼50% for
the 1300 °C-postannealed sample. The electrical parameters
obtained by Hall effect measurement are summarized inTable I. Based on the fact that the compensation ratio for the
RT-implanted sample did not signiﬁcantly change, highertemperature annealing decreases both substitutional B atoms
and donor-like center concentrations. The reasons the electrical properties were signiﬁcantly improved are not yet
evident through the present experiments; however, thequality improvement of diamond substrates during several
decades is thought to be one of the reasons for obtaining

excellent electrical properties. The decrement of numbers of
intrinsically incorporated impurities and introduced primary
defects such as vacancies and interstitials formed during
synthesis processes is also supposed to decrease secondary
defect formation such as dislocations, stacking faults or
defect complexes during implantation and postannealing
processes. Defect-free diamond substrates therefore undoubtedly decrease the diffusion of defects and impurities during
implantation and postannealing, resulting in the lower
processing temperature and eventually the excellent electricalproperties.31–33) We would like to emphasize that in Si device
fabrication processes, the optimum processing temperature
decreases with the great improvement of substrate quality of
crystalline Si wafer.
Figure 7 shows speciﬁc resistance (σ−1) for the 900 °Cimplanted (a) and RT-implanted (b) samples followed by
1150 °C (black), 1300 °C (red) and 1450 °C (green) annealing. The solid curves show the theoretically calculated
resistivity in accordance with the following formalism. The
dashed line (EA = 0.1 eV) in the ﬁgure is guide for the eye.
The temperature-dependent resistivity was found to besigniﬁcantly changed around RT (∼300 K): there are two
activation energies at higher (>RT) and lower (<RT)
temperature regions. This suggests that the hopping conduction has been dominant below RT. The temperature at which
the electrical conduction mechanism changes from band to
hopping largely depends on the postannealing temperature.
3.2. Dominant conduction mechanisms
Next, we quantitatively introduce the analytical procedure of
speciﬁc resistance shown with solid curves in Fig. 7. Figure 8
schematically shows the impurity band diagram of B acceptor
levels for B-doped diamond in accordance with the following
relations as a function of NA. The electric conductivity σ for
impurity-doped semiconductors is generally described bythree conductive elements of σ1, σ2 and σ3. The substantial
conductivity σ can be expressed by the summation of thesecomponents.
s = s1 + s2 + s3,(4 )s1 = epm ,

(5 )

⎛  ⎞
s2 = s02 · exp ⎜ - 2 ⎟ ,⎝ kB T ⎠

(6 )

⎛  ⎞
⎛ T ⎞ns3 = s NNH· exp ⎜ - 3 ⎟ + sVRH
· exp ⎜ - 0 ⎟ .
03
03
⎝ T⎠
⎝ kB T ⎠(7 )In the case of p-type semiconductors, the σ1 conduction isderived from the ionization of holes from the neutral acceptor
level to the valence band. The activation energy corresponds
to the ionization energy of a single isolated acceptor. For
relatively heavily doped semiconductors, the impurity levels
are signiﬁcantly broadened due to the overlap of acceptor
wave functions, resulting in the formation of narrow impurity
bands. The impurity band widths of ground and excited states
thus depend on the doped impurity concentration. The σ2
conduction is derived from holes excited from the neutral
impurity band (A0) to the positively charged band (A+), as
shown in Fig. 8, and appears under speciﬁc conditions withlow compensation ratio (K < 0.2) at high impurity

021003-5© 2020 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 59, 021003 (2020)

Y. Seki et al.

(a)

(b)

Fig. 7. (Color online) Sheet and speciﬁc resistance for the B-implanted samples at 900 °C and RT followed by 1150 °C (black dots), 1300 °C (red dots) and
1450 °C (green dots) annealing. Solid curves show the theoretical results based on the inverse of Eq. (4). The dashed line (EA = 0.1 eV) in the ﬁgure is guidefor the eye.

where ò3 corresponds to the energy barrier between
neighboring energy states.37) At enough low temperatures,
the NNH regime is eventually altered to the VRH[µexp (-(T0 T )n ].38)
It is well known that the highest and lowest energy level ofneutral B acceptor band (E1()) with respect to valence band
maximum can be written as,34,39)
E1() =  0  g

Fig. 8. (Color online) Impurity band diagram of B acceptor levels doped
into diamond as a function of NA.

concentration near Mott transition. The σ3 conduction is
known as the intraband hopping process, derived fromhopping theory, which will be discussed later [Eq. (17)].34)
The ﬁrst and second terms in Eq. (7) are related to the nearest
neighbor hopping (NNH) and variable range hopping (VRH),
respectively. Here, To and n are the speciﬁc parameters of
VRH conduction, which can be referred in the previous
reports.34–36) With decreasing temperatures, σ1 or σ2 conductions are changed to the NNH regime [µexp (- 3 kB T )],

e2
.
kR

(8 )

Here, the  0 and κ indicate the ionization energy of a single
isolated acceptor and dielectric constant of diamond, known
to be  0 = 0.37 eV for acceptor B and κ = 5.7, respectively.
R is deﬁned as the nearest neighbor distance of acceptors,(3 4pNA )1 3 and γ is around unity.40) In this case of
NA = 1019 cm−3, ò1, corresponding to E1(-), is to be∼0.3 eV. The A0 band width Ω1 is thus written as,
2e 2 ⎛ 3 ⎞ 3
W1 =
⎜
⎟ .
k ⎝ 4pNA ⎠1(9 )According to Mycielski et al., the energy level of ò2, which
is not clearly deﬁned, is simply described to be,39,41)⎛ e2 ⎞
 2 »  0 - 3 ⎜ ⎟ NA1 3.
⎝k⎠

(10)

In the case of NA = 1019 cm−3, ò2 can be estimated to be∼0.20 eV. More recently, Baskin et al. proposed the σ2021003-6© 2020 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 59, 021003 (2020)

Y. Seki et al.

conduction mechanism based on delocalized A0 and A+
bands:42) 2 = ( 0 -  +) - c - 3 .
(11)2Here,  + and c are the energy levels of the excited state (A+)
and the mobility edge in the A+ band, respectively. The
mobility edge can be estimated from the overlap integral of
acceptor wave functions. The meaningful excitation contributing to electrical conduction is holes excited above c;consequently, ò2 is smaller than the average energy gap(U =  0 -  +) between A0 and A+ bands.43)
Shklovskii et al. proposed the activation energy ò3 as,⎛ e2 ⎞
 3 = 0.99 ⎜ ⎟ NA1 3 (1 - 0.3K1 4) ,
⎝k⎠

(12)

⎛
⎞
1
 0⎟ ,~ 0.054 eV ⎜for NA = 1019 cm-3, 1 ⎝
⎠
K

(13)

E3() =  0 

3
,
2

(14)

for low compensation limit.44,45) The band width (Ω3)
involving the σ3 conduction will be,W3   3.

(15)

The energy width (Ω3) of σ3 conduction should be smaller
than that of Ω1; typically one third of Ω1.
As shown in Fig. 7, the observed activation energy below
RT was less than 0.1 eV, indicating that the electricalconduction below RT was probably governed by σ3 hopping
conduction. According to Massarani et al.,34) the transition
probability (P) of hole hopping from an occupied site to anunoccupied site can be expressed as the following relation:⎛w ⎞P = nph · exp ⎜ - 2aR ⎟,⎝kB T ⎠(16)

where νph = 4 × 1013 Hz corresponds to the maximum
phonon frequency, R is a distance between neighboring
hopping sites deﬁned as (3 4pNA )1 3, and α−1 is a localization length of an acceptor wave function; to be 2m* 0  .
w is the energy difference between neighboring hoppingsites, corresponding to ò3. If 2αR is relatively larger than
w/kBT, the conduction is preferably governed by the hopping
process between the nearest neighbor sites. On the other
hand, hopping to a far site with small energy difference will
preferentially take place in the case of 2aR < w kB T
(VRH). Under the present condition, 2αR is relatively larger
than w/kBT near RT, even if we assume the maximum valueof w ∼ Ω3. It is indicated that the dominant contribution ofhole transport is mainly attributed to the NNH regime. This isconsistent with the previous reports.28,46) In accordance with
Einstein’s relation, hopping conductivity σ3 is ﬁnally expressed as,s3 =⎛3e2 nphw ⎞· exp ⎜ - 2aR ⎟,⎝4pf wR
kB T ⎠(17)

where f is a coordination number of acceptors in diamondlattice, typically adopted as 6 in the previous reports.33,34)
We eventually ﬁt the experimentally obtained speciﬁc
resistance shown in Fig. 7 by the theoretical relations (σ−1)

Table II.
Temperature(implant.)
RT
900 °C

Obtained parameters for hopping conduction.

Temperature(postanneal)

Activation energyò3 (eV)

Localization length
α−1 (cm)

1300 °C
1450 °C
1300 °C
1450 °C

0.070
0.025
0.070
0.015

5.0 × 10−8>8.5 × 10−8
5.7 × 10−8>9.0 × 10−8

using Eqs. (5) and (17) with only two ﬁtting parameters of
the localization length α−1 and activation energy w. Here, theparameters of μ and p in Eq. (5) were referred fromexperimentally determined values by Hall effect measurements discussed in Figs. 2 and 3. The best-ﬁt curves andobtained parameters are shown in Fig. 7 and Table II for the1300 °C- and 1450 °C-postannealed samples. The activationenergy ò3 and localization length for 1300 °C-annealed
samples were estimated to be 0.070 eV and 5–6 × 10−8 cm,
respectively. The observed ò3 corresponds to the theoretically
predicted value for NNH conduction [Eq. (13)], and theobtained α−1 took the value close to the effective Bohrradius, but was somewhat larger. After 1450 °C annealing,
the resistivity and activation energy were signiﬁcantly
decreased. The localization length was increased to be at least
8.5 × 10−8 and 9.0 × 10−8 cm for each sample; however, thevalue could not be uniquely determined, due to the lack of
accurate NA in the Hall measurements. The increase of thelocalization length in the higher-temperature annealing stage
clearly shows the enhancement of the overlap of impurity
wave functions. This increment of the localization length
induces connection of the percolation channels of conductionin the impurity bands, resulting in the appearance of hopping
conduction. It is because extremely high-temperature annealing promotes the diffusion and recombination of createddefects, which causes the formation of new products such asgraphite-like or disordered microstructures.31–33)
Consequently, effective B doping should be performed by
low-temperature implantation at around RT followed byannealing at relatively low temperatures from 1150 °C–
1300 °C. Effective B doping is probably related to the
diffusion and recombination of created defects during ion
implantation and postannealing.47–50)
4. Conclusions

The electrical properties of heavily B-doped diamond formedby ion implantation were comprehensively investigated fromthe viewpoints of temperatures in B+ ion implantation andpostannealing. We compared the electrical properties forshallowly and ﬂatly B+ ion-implanted type IIa diamondsubstrates at 900 °C and RT, with a ﬂat concentration of
3.5 × 1019 cm−3. These samples were subsequently annealed
at 1150 °C, 1300 °C and 1450 °C after ion implantation. The
electrical properties of the compensation ratio and doping
efﬁciency for the 900 °C-implanted samples were not
sufﬁciently improved even by high-temperature annealing.
On the other hand, the B implantation at RT followed bypostannealing at 1150 °C and 1300 °C realized the excellent
properties of doping efﬁciency (78%), Hall mobility(108 cm2V−1s−1) and resistivity for the RT-implanted
sample. We conﬁrmed p-type conductivity and typicalionization energy of acceptor B atoms at a wide temperature

021003-7© 2020 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 59, 021003 (2020)

Y. Seki et al.

range from 173–1073 K for both samples. The accomplishment of effective B doping at lower-temperature processes isprobably realized by the decrement of intrinsically incorporated defects in substrates when they are synthesized. Thisdecrement of primary defects effectively reduced new defectcreations during the ion implantation and postannealingstages.
Acknowledgments

We gratefully acknowledge Prof. Mizuno and Mr. Saito for
their support in setting up the experiments and for theirvarious suggestions. This study was partly supported by
grant-aid from the Research Institute for Integrated Science,
Kanagawa University (Grant No. RIIS201702).

1) C. E. Nebel and J. Ristein, Semiconductors and Semimetals (Elsevier,
Amsterdam, 2003) 76.
2) A. Paoletti and A. Tucciarone, Proceedings of the International School ofPhysics “Enrico Fermi” (IOS Press, Bologna, 1997) 135, The Physics of
Diamond.
3) L. Pan and E. Kania, Diamond: Electrical Properties and Applications(Kluwer, Boston, MA, 1995).
4) J.-P. Lagrange, A. Deneuville, and E. Gheeraert, Carbon 37, 807 (1999).
5) R. F. Mamin and T. Inushima, Phys. Rev. B 63, 033201 (2001).
6) J. Pernot, P. N. Volpe, F. Omnés, P. Muret, V. Mortet, K. Haenen, andT. Teraji, Phys. Rev. B 63, 033201 (2010).
7) M. Aono, O. Maida, and T. Ito, Diamond Relat. Mater. 20, 1357 (2011).
8) J. F. Prins, Phys. Rev. B 38, 5576 (1988).
9) J. F. Prins, Appl. Phys. Lett. 76, 2095 (2000).
10) J. F. Prins, Diamond Relat. Mater. 11, 612 (2002).
11) J. F. Prins, Semicond. Sci. Technol. 18, S27 (2003).
12) C. Uzan-Saguy, R. Kalish, R. Walker, D. N. Jamieson, and S. Prawer,
Diamond Relat. Mater. 7, 1429 (1998).
13) T. Vogel, J. Meijer, and A. Zaitsev, Diamond Relat. Mater. 13, 1822 (2004).
14) F. Fontaine, C. Uzan-Saguy, B. Philosoph, and R. Kalish, Appl. Phys. Lett.
68, 2264 (1996).
15) N. Tsubouchi, M. Ogura, Y. Horino, and H. Okushi, Appl. Phys. Lett. 89,
012101 (2006).
16) N. Tsubouchi and M. Ogura, Jpn. J. Appl. Phys. 47, 7047 (2008).
17) N. Tsubouchi, M. Ogura, N. Mizuochi, and H. Watanabe, Diamond Relat.
Mater. 18, 128 (2009).
18) K. Ueda and M. Kasu, Diamond Relat. Mater. 17, 502 (2008).
19) Y. Seki, Y. Hoshino, and J. Nakata, Appl. Phys. Lett. 115, 072103 (2019).
20) J. F. Ziegler, J. P. Biersack, and U. Littmark, The Stopping and Range ofIons in Solids (Pergamon, Oxford, 1985).

21) A. T. Collins and A. W. S. Williams, J. Phys. C 4, 1789 (1971).
22) F. Fontaine, J. Appl. Phys. 85, 1409 (1999).
23) P.-N. Volpe, J. Pernot, P. Muret, and F. Omnés, Appl. Phys. Lett. 94,
092102 (2009).
24) M. Gabrysch, S. Majdi, A. Hallén, M. Linnarsson, A. Schöner, D. Twitchen,
and J. Isberg, Phys. Stat. Sol. (a) 205, 2190 (2008).
25) K. Tsukioka and H. Okushi, Jpn. J. Appl. Phys. 45, 8571 (2006).
26) V. Mortet, M. Daenen, T. Teraji, A. Lazea, V. Vorlicek, J. D’Haen,
K. Haenen, and M. D’Olieslaeger, Diamond Relat. Mater. 17, 1330 (2008).
27) T. Teraji, H. Wada, M. Yamamoto, K. Arima, and T. Ito, Diamond Relat.
Mater. 15, 602 (2006).
28) M. Werner, R. Locher, W. Kohly, D. S. Holmes, S. Klose, and H. J. Fecht,
Diamond Relat. Mater. 6, 308 (1997).
29) M. Werner, R. Job, A. Zaitzev, W. R. Fahrner, W. Seifert, C. Johnston, and
P. R. Chalker, Phys. Stat. Sol. (a) 154, 385 (1996).
30) T. H. Borst and O. Weis, Phys. Stat. Sol. (a) 154, 423 (1996).
31) S. Ogawa, T. Yamada, S. Ishizduka, A. Yoshigoe, M. Hasegawa,
Y. Teraoka, and Y. Takakuwa, Jpn. J. Appl. Phys. 51, 11PF02 (2012).
32) N. Tokuda, M. Fukui, T. Makino, D. Takeuchi, S. Yamasaki, andT. Inokuma, Jpn. J. Appl. Phys. 52, 110121 (2013).
33) T. Matsumoto, H. Kato, N. Tokuda, Y. Makino, M. Ogura, D. Takeuchi,
H. Okushi, and S. Yamasaki, Phys. Status Solidi 8, 137 (2014).
34) B. Massarani, J. C. Bourgoin, and R. M. Chrenko, Phys. Rev. B 17, 1758
(1978).
35) N. F. Mott and E. A. Davies, Electronic Processes in Non-Crystalline
Materials (Clarendon, Oxford, 1971).
36) A. L. Efros and B. I. Shklovskii, J. Phys. C 8, L49 (1975).
37) B. I. Shklovskii and A. L. Efros, Electronic Properties of Doped
Semiconductors (Springer, Berlin, 1984).
38) H. Liu, A. Pourret, and P. Guyot-Sionnest, ACS Nano 4, 5211 (2010).
39) J. Mycielski, Phys. Rev. 123, 99 (1961).
40) G. L. Peason and J. Bardeen, Phys. Rev. 75, 865 (1949).
41) F. H. Pollak, Phys. Rev. 138, A618 (1965).
42) E. Baskin, A. Reznik, D. Saada, J. Adler, and R. Kalish, Phys. Rev. B 64,
224110 (2001).
43) E. Gheeraert, S. Koizumi, T. Teraji, H. Kanda, and M. Nesládek, Phys.
Status Solidi (a) 174, 39 (1999).
44) B. I. Shklovskii, A. L. Efros, and I. Y. Yanehef, JETP Lett. 14, 233 (1971).
45) B. I. Shklovskii, A. L. Efros, and I. Y. Yanehef, Phys. Status Solidi (b) 50,
45 (1972).
46) J.-P. Lagrange, A. Deneuville, and E. Gheeraeri, Diamond Relat. Mater. 7,1390 (1998).
47) G. Davies, S. C. Lawson, A. T. Collins, A. Mainwood, and S. J. Sharp, Phys.
Rev. B 46, 13157 (1992).
48) A. Allers, A. T. Collins, and J. Hiscock, Diamond Relat. Mater. 7, 228(1998).
49) J. Bernholc, A. Antonelli, T. M. Del Sole, Y. Bar-Yam, and S. T. Pantelides,
Phys. Rev. Lett. 61, 2689 (1988).
50) A. Mainwood, F. P. Larkins, and A. M. Stoneham, Solid-state Electron 21,
1431 (1978).

021003-8© 2020 The Japan Society of Applied Physics