Home

SearchCollections

Journals

About

Contact us

My IOPscience

Ground-state splitting of ultrashallow thermal donors with negative central-cell corrections insiliconThis content has been downloaded from IOPscience. Please scroll down to see the full text.
2017 Jpn. J. Appl. Phys. 56 068001(http://iopscience.iop.org/1347-4065/56/6/068001)
View the table of contents for this issue, or go to the journal homepage for more
Download details:
IP Address: 157.118.208.83
This content was downloaded on 19/05/2017 at 00:28
Please note that terms and conditions apply.

You may also be interested in:
Mechanism of formation of ultrashallow thermal donors in carbon-doped oxygen-rich monocrystalline
silicon preannealed to introduce hydrogen
Akito Hara and Teruyoshi Awano
Hydrogen-like Ultrashallow Thermal Donors in Silicon Crystals
Akito Hara
Structural Elements of Ultrashallow Thermal Donors Formed in Silicon Crystals
Akito Hara, Teruyoshi Awano, Yutaka Ohno et al.
Perturbation model for the thermal-donor energy spectrum in silicon
J T Borenstein, J W Corbett, M Herder et al.
Electrically active light-element complexes in silicon crystals grown by cast method
Kuniyuki Sato, Atsushi Ogura and Haruhiko Ono
Oxygen diffusion and precipitation in Czochralski silicon
R C Newman
Oxygen precipitates distributed around random grain boundaries in a cast-grown multicrystalline
silicon crystal
Takumi Uno, Kuniyuki Sato, Atsushi Ogura et al.
Electrically active radiation-induced defects in Cz-Si with low carbon content
V P Markevich, L I Murin, S B Lastovskii et al.

BRIEF NOTEJapanese Journal of Applied Physics 56, 068001 (2017)https://doi.org/10.7567/JJAP.56.068001

Ground-state splitting of ultrashallow thermal donors
with negative central-cell corrections in silicon
Akito Hara and Teruyoshi Awano
Department of Engineering, Tohoku Gakuin University, Tagajo, Miyagi 985-8537, Japan
Received November 23, 2016; accepted March 21, 2017; published online May 17, 2017
Ultrashallow thermal donors (USTDs), which consist of light element impurities such as carbon, hydrogen, and oxygen, have been found inCzochralski silicon (CZ Si) crystals. To the best of our knowledge, these are the shallowest hydrogen-like donors with negative central-cellcorrections in Si. We observed the ground-state splitting of USTDs by far-infrared optical absorption at different temperatures. The upper groundstate levels are approximately 4 meV higher than the ground-state levels. This energy level splitting is also consistent with that obtained by thermal
excitation from the ground state to the upper ground state. This is direct evidence that the wave function of the USTD ground state is made up of alinear combination of conduction band minimums. © 2017 The Japan Society of Applied Physics

Light element impurities in silicon (Si) have been a topic ofinterest in mono- and multi-crystalline Si,1–3) because it has
been reported that complex centers or aggregative defects
composed of light element impurities degrade the yield andreliability of Si large-scale integration (Si-LSI) circuits andsolar cells. Thus, it is very important to clarify the origin andelectron structure of complexes that contain light element
impurities. Many types of donor are found in Si crystals
containing light element impurities such as oxygen, carbon,
and nitrogen. Thermal double donors (TDDs) are the mostwell-known donors and are considered to be made up ofoxygen impurities.4,5) In Si containing both oxygen andnitrogen, nitrogen–oxygen complex donors [D(N,O)s] areformed.6–9) In addition, a new type of shallow donor has beenfound in Si containing oxygen, nitrogen, and carbon.10)
Hydrogen is also an important element in Si-LSI circuits
and solar cells, because various reactive gases includinghydrogen are used in the thin-ﬁlm growth process. Hydrogenis also important in the passivation and activation of impurities and defects. When hydrogen combines with acceptors or donors, the electrical activity of those acceptors anddonors ceases.11,12) Conversely, hydrogen changes electrically neutral impurities and defects into electrically active
centers such as hydrogen-related shallow thermal donors[STD(H)s].13–16) In addition, hydrogen acts as a catalyst andenhances the formation of TDDs.17)
We found ultrashallow thermal donors (USTDs) in carbonrich and hydrogen-doped Czochralski silicon (CZ Si) crystals.10,18) USTDs are donors with a hydrogen-like electron
structure but slightly diﬀerent energy levels, some of which
exhibit negative central-cell corrections.10,18) To the best of
our knowledge, these are the shallowest energy levels among
the previously reported hydrogen-like donors in Si crystals.
Note that USTDs are absent in carbon-lean and hydrogendoped CZ Si, as demonstrated in a previous report.18)
We evaluated the intensity of the far-infrared (far-IR)
optical absorption of USTDs as a function of temperature andobserved new absorption peaks. In this paper, these peaks are
attributed to the excitation of electrons from the upper levelof the ground state to the original 2p0, 2p+−, and 3p+− statesof the USTDs. This is direct evidence that the wave functionof the USTD ground state is made up of a linear combinationof conduction band minimums.
Three types of CZ Si crystal, not intentionally doped withgroup-III and group-V impurities, were used as precursors. The
ﬁrst precursor (precursor 1) was a carbon-doped CZ Si crystal

with [C] = (2.0–2.3) × 1017 cm−3 and [O] = (1.5–1.6) × 1018
cm−3 (Old American Society for Testing and Materials).
The second precursor (precursor 2) was [C] = (2.5–2.7) ×
1017 cm−3 and [O] = (1.5–1.6) × 1018 cm−3. The carbon-doped
CZ Si crystal of these two precursors was grown frommolten Si doped with carbon powder. The third precursor(precursor 3) was a CZ Si crystal with a low carbon content,i.e., [C] < 1 × 1016 cm−3 and [O] = 1.6 × 1018 cm−3.
Hydrogen doping was performed by preannealing the Si
crystals at 1300 °C for 60 min in wet oxygen, and thenfollowed by quenching at room temperature after retrieving
them from the furnace. We refer to CZ Si prepared in thismanner as hydrogen-doped Si. This hydrogen doping method
is a variant process proposed by Martynov et al.15)
The samples used had a thickness of 2.0 mm. Far-IR
optical absorption measurements were performed at beamline
6B (resolution: 0.5 cm−1) using a ﬂowing cryostat at the
UVSOR facility of the Institute for Molecular Science. We
used ﬁve samples for far-IR absorption. Samples a and b
were prepared from hydrogen-doped precursors 1 and 2,
respectively, after annealing at 480 °C for 40 h. Samples cand d were prepared from hydrogen-doped precursor 1 after
annealing at 480 °C for 20 and 10 h, respectively. Our
previous research reported that concentrations of USTDs
increase with increasing annealing duration up to 40 h.18)
Thus, the concentration of USTDs in samples a and b are thehighest and that of USTDs in sample c is higher than thatof sample d. Sample e was prepared from hydrogen-doped
precursor 3 after annealing at 480 °C for 40 h.
Figure 1 shows the temperature dependences of the
USTDs and STD(H)s at diﬀerent measurement temperatures
formed in sample a. The intensities of the obtained spectra
decrease as the temperature increases to up to 70 K. Thisbehavior is expected because the donors have shallow energy
levels. The eﬀective mass theory (EMT) predicts the donor
ground-state energy in Si to be 31.27 meV.19) However, weobserved two main peaks for the USTD ground state (USTDs
1 and 3) at 27.90 and 28.65 meV below the conduction band
minimum, indicating a negative central-cell correction for the
USTDs as shown in Fig. 2.10,18,19)
We observed new broad peaks, labeled A, B, and C in
Fig. 1, as the temperature was increased to a higher range(20–50 K), despite the decreases in USTD and STD(H) intensities.20) The same results were obtained for samples b, c, andd. Since samples a and b include approximately the sameamounts of carbon and oxygen, they showed nearly the same

068001-1© 2017 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 56, 068001 (2017)
2.8

USTD-3 2P0
USTD-1

2.6

2P+-

A. Hara and T. Awano

STD(H)

60 K

2.2

50 K

2.0

A

1.8

B

45 K

C

40 K

1.6
35 K

1.4

2P0

2P+-

3P+STD(H)
2P0

2P+-

3P+-

A
B
㻝㻜㻜

㻝㻡㻜

㻞㻜㻜

㻞㻡㻜

㻟㻜㻜

25 K

1.0

0.1

21 K

0.8

ln[Trans(T)/Trans(15 K)]

18 K

0.6

15 K

0.4
0.2
0.0
50

100

150

200

250

300

Wavenumber (cm-1)

Fig. 1. (Color online) Temperature dependence of the transmittances of
USTDs and STD(H)s. Several new broad peaks are generated as thetemperature increases, labeled A, B, and C in red.
This
work

Theory0

USTD-1

USTD-3

Li

P

As

Sb

3p+2p+-

-5.0
-10.0

-0.1
-0.2
-0.3
-0.4

-20.0

1S

-25.0

1S

-30.0
1S

1S

A
E+T

E
T

E
T

-40.0
-45.0
-50.0
-55.0

A
18 K
21 K
25 K
30 K
35 K
40 K
45 K
50 K

B

80 90 100 110 120 130 140 150 160 170 180 190 200

Fig. 3. (Color online) (a) Temperature dependence of the absorptionof the new broad peaks. The vertical axis is ln[Trans(T )=Trans(15 K)](T in Kelvin), where Trans(T) represents the transmittance at the temperature
T K. (b) Magniﬁed image of spectra A and B.

2p0

-15.0

-35.0

(b)

0.0

-0.5

Energy (meV)

USTD-3
USTD-1

18 K
21 K
25 K
30 K
35 K
40 K
45 K
50 K

㻡㻜

30 K

1.2

(a)

ln[Trans(T)/Trans(15 K)]

70 K

2.4

Transmittance

2.2
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6

3P+-

E
T
A

A
A

Fig. 2. Energy level of hydrogen-like donors in Si.10,18,19)

intensity of new broad peaks. Sample c showed new broad
peaks, the intensities of which are lower than those of samples
a and b, but higher than that of sample d. Sample d showed
new broad peaks, but their intensities were very low. These
results indicate that the intensity of new broad peaks correlateswith that of USTDs.
The wavenumber diﬀerences of 42 cm−1 between A and B,
and 30 cm−1 between B and C are consistent with the EMT
predictions. Their spectral intensities are also consistent
with EMT predictions. Thus, peaks A, B, and C represent the
1s–2p0, 1s–2p+−, and 1s–3p+− transitions of hydrogen-like
donor, respectively. On the basis of the EMT, the groundstate energy of a new hydrogen-like donor is estimated to be
24.4 meV below the conduction band minimum, i.e., approximately 3.5 and 4.3 meV less than the ground-state energies of
USTDs 1 and 3, respectively, as shown in Fig. 2.
The temperature dependence of the new hydrogen-like
donor in Fig. 1 indicates the occurrence of a certain thermal
activation process. To evaluate the relationship between theabsorption coeﬃcient of the new hydrogen-like donor and thetemperature, we analyzed the temperature dependence of theabsorption coeﬃcient for samples a, b, c, and d. We assumed
that the absorption coeﬃcient of the new hydrogen-like donor
at 15 K, which is the lowest temperature in this experiment, iszero to simplify the analyses. This absorption coeﬃcient is

proportional to N0 × exp(−ΔE=kBT), where ΔE, N0, and kB are
the activation energies for occupying the new hydrogenlike donor state, the total population, and the Boltzmann constant, respectively. Figure 3(a) shows a plot of ln[Trans(T)=Trans(15 K)] at various temperature T values for sample a (inunits of Kelvin), where Trans(T) represents the transmittanceat T K. Figure 3(b) shows a magniﬁed image around spectral
peaks A and B. Because we assumed the absorption coeﬃcientof the new hydrogen-like donor at 15 K to be zero, the verticalvalues correlate with the absorption coeﬃcient at T K.
Figure 4 shows plots of the variation in the intensity ofpeak B as a function of 1=T for samples a, b, and c. The
vertical axis expresses ln{−ln[Trans(T )=Trans(15 K)]}. It wasvery diﬃcult for sample d to determine the variation in temperature owing to the small peak of the new hydrogen-like
donor. The gradient of the plots is −ΔE=kB, implying ΔE =4 meV. This magnitude is reasonable because we observed
the new hydrogen-like donor with a thermal energy of kBT(T = 20–40 K) at 2–4 meV. The reduction in absorption
coeﬃcient above 40 K is attributed to the excitation ofelectrons in the conduction band.
The linewidth of the new hydrogen-like donor is very large
compared with those of the USTDs and STD(H)s. A carefulobservation of peak A in Fig. 3(b) reveals at least two peaks,
as shown by small arrows. Thus, one reason for the large
linewidth is the overlap of at least two signals. Anothermechanism is expected to be caused by coupling withphonons and the local vibrational mode of impurities.
The above measurement was repeated to verify theexistence or absence of the new peaks in sample e, yielding
the results shown in Fig. 5. There are no peaks apart fromthose corresponding to the STD(H)s. We therefore conclude
that the new hydrogen-like donor observed in this study is
not related to the STD(H)s.

068001-2© 2017 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 56, 068001 (2017)

A. Hara and T. Awano

ln{-ln[Trans(T)/Trans(15 K)]}

0.0

Sample aSample b-0.5

Sample c

-1.0
4 meV

-1.5
-2.0

4 meV

-2.5
-3.0
0

0.01

0.02

0.03

0.04

0.05

0.06

1 / T (K-1)

Fig. 4. (Color online) Temperature dependence of the absorption
coeﬃcient of the new broad peaks for samples a, b, and c. The vertical axis isln{−ln[Trans(T )=Trans(15 K)]} (T in Kelvin). The gradient of this curve
reﬂects the thermal activation energy.
0.8
20 K

ln[Trans(T)/Trans(10 K)]

0.6

30 K
40 K

0.4

STD(H)

50 K
2P0

0.2

2P+-

3P+-

0.0
-0.2
-0.4
-0.6
㻡㻜

㻝㻜㻜

㻝㻡㻜
㻞㻜㻜
Wavenumber (cm-1)

㻞㻡㻜

㻟㻜㻜

Fig. 5. (Color online) Temperature dependence of the transmittanceobserved in carbon-lean hydrogen-doped CZ Si sample e. The vertical axis isln[Trans(T)=Trans(10 K)] (T in Kelvin), where Trans(T) indicates thetransmittance at the temperature T K.

We propose the following model to explain the origin of the
new hydrogen-like donor. This donor is associated with theexcitation of electrons from the upper level of the ground state
to the original 2p0, 2p+−, and 3p+− states of the USTDs, arisingfrom the level splitting of the ground state rather than from thegeneration of new types of donor. This model explains why
the intensity of the new hydrogen-like donor correlates wellwith that of USTDs. In addition, this model explains thethermal excitation energy of 4 meV, which is required togenerate a new hydrogen-like donor, because the opticalenergy-level splitting between the upper level of the groundstate and the ground state is approximately 4 meV. This model
also explains why the new hydrogen-like donor produces two
peaks. The spacing of the two peaks of A, indicated by thearrows in Fig. 3(b), is approximately 6 cm−1, consistent withthat of the two main peaks, USTDs 1 and 3, of the USTDs.
The ground-state splitting indicates that the wave functionof the USTD ground state is made up of a linear combinationof wave functions from the conduction band minimum. It is
well known that the ground state of a group-V donor with Td
symmetry is split into three states, A, E, and T, because of
the potential ﬁeld around the donor.21) The energy splitting
between ground state A and upper ground states T and E isalso shown in Fig. 2 for many types of donor in Si. In caseswith P, Sb, and As impurities, the A-state is very deep compared with that of the EMT, and the energy diﬀerence between
the ground state A and upper ground states E and T is about 10
to 20 meV.19,21) However, the USTD ground state displays anegative central-cell correction, and the energy diﬀerence
between the upper ground state and the ground state is only
4 meV. Moreover, electron-spin resonance (ESR) measurement has shown a single sharp line with nearly isotropic
and absent of hyperﬁne interactions of 13C (nuclear spin =
1=2).22) It indicates a low electron density at the core site.
We would like to propose that the USTD symmetry must be
lower than Td. We previously proposed the following modelfor the formation of USTDs.18) First, STD(H)s are generated
rapidly. Then, interstitial carbon atoms, generated by the kickout of substitutional carbon by self-interstitial Si, combinewith STD(H) core sites. STD(H)s have been shown to display
C2v symmetry,15,16) and therefore, carbon incorporation into
the STD(H) core structure should lead to a symmetry lower
than C2v. However, other spectroscopic measurement techniques are required to identify the symmetry of USTDs.
In summary, the ground-state splitting of USTDs wasobserved by far-IR optical absorption at diﬀerent temperatures. To the best our knowledge, this is the ﬁrst observationof ground-state level splitting in a hydrogen-like donor with anegative central-cell correction in Si. The upper ground-statelevel is approximately 4 meV higher than the ground-statelevel. This energy level is also consistent with the results
obtained by thermal excitation from the ground state to theupper level of the ground state. This is direct evidence that
the USTD ground state is made up of a linear combination ofwave functions from conduction band minimums.
Acknowledgments This study was partly conducted under the Joint
Studies Program of the Institute for Molecular Science and JSPS KAKENHI
Grant Number (C) 16K06311.

1) F. Shimura, Semiconductor Silicon Crystal Technology (Academic Press,
San Diego, CA, 1988).
2) C. Peng, H. Zhang, M. Stavola, V. Yelundur, A. Rohatgi, L. Carnel, M.
Seacrist, and J. Kalejs, J. Appl. Phys. 109, 053517 (2011).
3) H. Zhang, M. Stavola, and M. Seacrist, J. Appl. Phys. 114, 093707 (2013).
4) P. Wagner and J. Hage, Appl. Phys. A 49, 123 (1989).
5) J. Michel, J. R. Niklas, and J.-M. Spaeth, Phys. Rev. B 40, 1732 (1989).
6) M. Suezawa, K. Sumino, H. Harada, and T. Abe, Jpn. J. Appl. Phys. 25,
L859 (1986).
7) M. Suezawa, K. Sumino, H. Harada, and T. Abe, Jpn. J. Appl. Phys. 27, 62(1988).
8) A. Hara, T. Fukuda, T. Miyabo, and I. Hirai, Jpn. J. Appl. Phys. 28, 142(1989).
9) H. Ch. Alt and H. E. Wagner, Physica B 407, 2985 (2012).
10) A. Hara, T. Awano, Y. Ohno, and I. Yonenaga, Jpn. J. Appl. Phys. 49,050203 (2010).
11) Hydrogen in Semiconductor, ed. J. I. Pankove and N. M. Johnson(Academic Press, New York, 1991) Semiconductors and Semimetals,
Vol. 34.
12) J. Pearton, W. Corbett, and M. Stavola, Hydrogen in Crystalline
Semiconductors (Springer, New York, 1992).
13) R. E. Pritchard, M. J. Ashwin, J. H. Tucker, R. C. Newman, E. C.
Lightowlers, T. Gregorkiewicz, I. S. Zevenbergen, C. A. J. Ammerlaan, R.
Falster, and M. J. Binns, Semicond. Sci. Technol. 12, 1404 (1997).
14) R. C. Newman, M. J. Ashwin, R. E. Pritchard, and J. H. Tucker, Phys.
Status Solidi B 210, 519 (1998).
15) Yu. V. Martynov, T. Gregorkiewicz, and C. A. J. Ammerlaan, Phys. Rev.
Lett. 74, 2030 (1995).
16) A. Hara, Jpn. J. Appl. Phys. 46, 463 (2007).
17) A. R. Brown, M. Claybourn, R. Murray, P. S. Nandhra, R. C. Newman, andJ. H. Tucker, Semicond. Sci. Technol. 3, 591 (1988).
18) A. Hara and T. Awano, Jpn. J. Appl. Phys. 54, 101302 (2015).
19) R. A. Faulkner, Phys. Rev. 184, 713 (1969).
20) A. Hara and T. Awano, 2015 UVSOR Activity Rep., 2016, p. 78.
21) W. Kohn, in Solid State Physics, ed. F. Seitz and D. Turnbull (Academic
Press, New York, 1957) Vol. 5, p. 257.
22) A. Hara, Jpn. J. Appl. Phys. 34, 3418 (1995).

068001-3© 2017 The Japan Society of Applied Physics