PHYSICAL REVIEW B 108, 235201 (2023)

How does hydrogen transform into shallow donors in silicon?
Akira Kiyoi
11,*

and Takahide Umeda2

Advanced Technology R&D Center, Mitsubishi Electric Corporation, Amagasaki 661-8661, Japan
2
University of Tsukuba, Tsukuba 305-8573, Japan(Received 23 March 2023; accepted 24 October 2023; published 5 December 2023)

We conducted electron paramagnetic resonance (EPR) and cyclotron resonance studies on hydrogen-relateddonors (HDs) in silicon, whose origins have remained unclear for 50 years. In floating-zone silicon substrates
irradiated with 2-MeV protons, followed by optimized annealing at 400 ◦ C and 500 ◦ C, we identified three
original EPR spectral signals originating from HDs, labeled the MT1, MT2, and MT3 centers. The three centers
exhibited a tetragonal symmetry around the 100 axis and were classified into two types of HDs: a HD witha lower thermal stability and a normal single-donor nature/positive-U nature (MT1), and a HD with a higher
thermal stability and a double-donor nature/negative-U nature (MT2 and MT3). Most importantly, the MT2
center revealed 29 Si hyperfine interactions closely resembling the B3 EPR center with a tetragonal symmetry,
which has been identified as a tetrainterstitial cluster, I4 . Contrarily, we could not resolve any 1 H hyperfine
interactions for the three MT centers. According to the experimental results, an atomistic model was proposed
for the HDs based on the I4 center weakly coupled with hydrogen atom(s). We deduce that different numbersof incorporated hydrogen atoms and/or different types of hydrogen bonding to I4 generated the two types ofHDs. These findings are the first step in understanding how hydrogen works as a donor in Si and offer important
insights into the use of proton-irradiation doping processes in device applications.
DOI: 10.1103/PhysRevB.108.235201

I. INTRODUCTION

Hydrogen is a chemically active element that interacts withcrystalline lattices as well as defects and impurities in a variety
of materials. Such interactions can modify the electrical andoptical properties of materials, particularly Si. As shown in
Fig. 1, hydrogen in Si is typically found in three forms: (a)mobile, (b) bound, and (c) shallow donors, which have been
intensively studied by several experimental and theoreticalworks since the early 1980s [1–9].
The most fundamental configuration of hydrogen in Si isisolated atomic hydrogen [Fig. 1(a)] [5–9]. Previous studies
have revealed that H+ is stable at bond-center (BC) sites witha large relaxation of its neighboring Si atoms, and H− is stable
at tetrahedral interstitial sites. Theoretical studies have proposed three different charge states of hydrogen [10,11], whereH+ and H− have the lowest energies in p-type and n-type Si,
respectively, and H0 is unstable at any Fermi level position;
this means that the isolated H atom in Si has a negative-U
nature [12].
Isolated hydrogen is highly mobile; therefore, it will bondwith other hydrogen atoms to form Hn aggregates even atroom temperature. The smallest Hn involves two hydrogenatoms (H2 [11] and H2∗ [13]), which have been predicted
theoretically and observed using Raman [14] and infraredabsorption spectroscopies [15,16].
Hydrogen also interacts with defects, resulting in the deactivation of the electrical activity of these defects [17,18] or*Corresponding author: Kiyoi.Akira@ay.MitsubishiElectric.co.jp

2469-9950/2023/108(23)/235201(11)in the formation of new electrically active centers [19–21][Fig. 1(b)]. Hydrogen-containing defects (e.g., platelets [21]and vacancy-H defects [19]) exhibit a variety of hydrogenbonds, such as Si-H bonds [17–21]. Through the interaction
with hydrogen, the formation of a different deep level has been
investigated in Si devices [20].
Hydrogen can also lead to the formation of shallow-donor
states [hydrogen-related donors (HDs)] [22–25]. This phenomenon has recently given rise to a different doping methodin Si devices [26–29]. HDs form via an unidentified structuralunit that extracts electrons from hydrogens in Si [Fig. 1(c)].
HDs have been observed in neutron [30], electron [31], andproton-irradiation [32–35] experiments when sufficient hydrogen was available in irradiated Si materials. Therefore,
unidentified structural units are phenomenologically considered as radiation-induced defects. The microscopic structuresof HDs have been discussed based on experimental results anddensity functional theory (DFT) calculations. A hydrogenand carbon-incorporated thermal donor [Ci Oi (n)−H] [36–38]
was demonstrated as a model for HDs. HDs were also reported
to be related to intrinsic defects (vacancies and interstitial
silicon and their clusters) [23–25,28,29,32–34].
Besides, the microscopic model of unidentified structural units is missing, and the mechanism of generating thedonor state from hydrogen atoms has also remained unclear
for over half a century. Therefore, understanding HDs remains an important challenge to be addressed in the fieldof fundamental defect physics for modern silicon device
technology.
In this study, we found a “double-donor” nature of theHDs [see Fig. 1(c)] and identified the unidentified structural

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PHYSICAL REVIEW B 108, 235201 (2023)

FIG. 1. (a) Mobile (atomic hydrogen and H2 molecules); (b) bound (e.g., Si-H bonds and bond-center form); and (c) shallow-donor state
via an unidentified structural unit that extract conduction electrons from hydrogen atoms. The hydrogen and Si atoms are indicated by light
blue and orange colors, respectively.

units of HDs. Our electron paramagnetic resonance (EPR)
studies identified three types of paramagnetic centers withthe following features: (i) tetragonal symmetry around the100 axis; (ii) one center with negative-U nature, following
an exchange-narrowing signal, and hyperfine (HF) interaction
with 29 Si nuclear spin, similar to that of a B3 EPR center[39]; and (iii) HF interactions with 1 H nuclear spins were
not resolved for all centers. These results afford interesting
insights into the atomic structure of the HDs, enabling us toadvance the proposition of a suitable microscopic model for
HDs based on the I4 center weakly coupled with hydrogenatom(s).
II. EXPERIMENT

Phosphorus (P)-doped (100) FZ-Si with a high resistivityof ∼ 830  cm was used as the substrate. The wafer was irradiated with 2-MeV protons with a total dose of 5 × 1014 cm−2
using a cyclotron particle accelerator. Back surface polishing
was applied to produce thin samples (0.3 × 0.8 × 0.01 cm3 ),which were annealed at 400 ◦ C and 500 ◦ C for 1 h in an
ambient air environment. Surface treatments with diluted hydrogen fluoride and tetramethylammonium hydroxide wereapplied to remove the surface damage layers. Furthermore,
two-point spreading resistance (SR) profiles were obtainedusing a solid-state measurement (SSM-2000) instrument witha bevel angle of 2.5 °.
The EPR and cyclotron resonance (CR) spectra were measured using a Bruker E500 X-band spectrometer with a Bruker
ER4122SHQ cavity and an Oxford instruments ESR900 He
cryostat. We examined the stacked samples (a set of either
14 or 24 slices) in the cavity. The HF interactions in the
EPR spectra were examined using the latter sample set. We
performed EPR measurements both in the dark and underphotoexcitation (100 W halogen cold lamp). With this illumination condition, the photoexcited changes in the EPR and CR
spectra were fully saturated. The EPR and CR measurements
were performed with a 100-kHz magnetic field modulation of
0.1- and 0.5-mT widths, respectively. To check the symmetry
and spectroscopic nature of the observed signals, we examined their angular dependencies by rotating the magnetic field(B) in the (01̄1) plane. The magnetic field angles of 0◦ and90◦ correspond to B//[100] and B//[011], respectively. Thisrotation system is the most conventional one used in previous
EPR studies for silicon.
III. RESULTS
A. Depth profile of HDs

The proton irradiation and subsequent annealing processes induced deep- and shallow-level defects [20–23].
Figure 2 shows the carrier concentration profiles of the protonirradiated FZ-Si after annealing treatments. The depth ofthe projected ion range (R p ) from the incident surface was∼ 44.5 μm, which is in accordance with the stopping andrange of ions in matter (SRIM) simulations [40]. N-type to
p-type conversion occurred in the penetrated layers (extending
from the surface to the R p depth) owing to the irradiationinduced shallow acceptor-type defects. The broad peaks ofthe carrier concentration around the R p depth correspondto the n-type region where shallow HDs were formed because of the interaction between the introduced hydrogen andthe irradiation-induced defects after the annealing treatment.
Consequently, p-n junctions were observed at a depth of
20 µm and near the surface for the samples annealed at 400 ◦ C

FIG. 2. Carrier concentration profiles of FZ-Si irradiated with 2MeV protons and subsequently annealed at 400 ◦ C and 500 ◦ C. The
profiles were obtained from SR measurements. The conversion tocarrier concentration profiles was performed using Thurber’s curve[41]. For the profile of the sample annealed at 400 ◦ C (red), the ntype to p-type converted layer, the layer where HDs were formed,
and the unaffected substrate are indicated.

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FIG. 3. EPR spectra of HDs in proton-irradiated FZ-Si after 400 ◦ C annealing, measured (a) in the dark and (b) under photoexcitation
conditions. All spectrum were measured with a magnetic field parallel to the [100] axis (magnetic field angle = 0◦ ). (c) Angular maps of MT1,
MT2, and MT3 at 9.428 GHz. The magnetic field was parallel to the [100] and [011] axes for 0 ° and 90 °, respectively. The symbols indicate
the experimental data. Solid lines correspond to the simulation data using the spin-Hamiltonian (SH) parameters given in Table II. The angularmap of P donors (included in the base substrate) was also simulated using g = 1.998 50 and 31 P hyperfine-splitting width = 4.195 mT [45].
EPR spectra in proton-irradiated FZ-Si after 500 ◦ C annealing measured (d) in the dark and (e) under photoexcitation.

and 500 ◦ C, respectively. At 58 µm and a deeper range, a basen-doping level was observed. In fact, we detected a weak EPR
signal of shallow P donors in the substrate.
B. EPR signals of HDs

Figure 3 shows the low-temperature EPR spectra of the
proton-irradiated Si after annealing at 400 ◦ C. Owing to thestrong dielectric loss of the free carriers, the spectra were
only measurable below 25 K. In the EPR spectra [Figs. 3(a)and 3(b)], three new EPR signals related to the HDs wereobserved; hereafter, “MT1,” “MT2,” and “MT3.” The MT1(electron spin, S = 1/2) signal appeared in the dark (thermal equilibrium), whereas the MT2 and MT3 (both S = 1/2)
signals were only observable under photoexcitation at low
temperatures (< 15 K). Their angular maps [Fig. 3(c)] formed
different patterns compared to those of previously reported
EPR centers [42]. We assume that MT2 and MT3 belong to thesame defect because MT3 was observed as the averaged signalof MT2. Therefore, the EPR signals related to the HDs could
be classified into two different types of dark and photoexcited
centers (MT1 and MT2/3, respectively).
For the sample annealed at 500 ◦ C [Figs. 3(d) and 3(e)],only MT2 and MT3 were observed with weaker intensities
than those of the 400 ◦ C sample. The total spin concentrationsof the MT1, MT2, and MT3 centers are listed in Table I. For
both the samples annealed at 400 ◦ C and 500 ◦ C, the total spin
concentrations agree well with the total HD concentrations

within the experimental errors. Thus, we conclude that theobserved EPR centers arise from the HDs. Thus far, twotypes of HDs have been reported: one (described as “HD1”)
was found to decay at 380–440 ◦ C and the other (“HD2”) at
500–540 ◦ C [34,43,44]. Therefore, we assign that the MT1
center corresponds to HD1 with a lower thermal stability,
and the MT2/3 centers are another HD with a higher thermal
stability (HD2).
The angular maps [Fig. 3(c)] of the EPR centers reveal
the nature of HDs. The solid lines were fitted using the gtensor in Table II. The MT1 center was similar to the conduction electron resonance (g = 1.998 75) but was weakly
anisotropic; e.g., the MT1 signal weakly split into double
peaks when B was set to 0◦ [Figs. 3(a) and 3(b)]. This weakanisotropy is shown in Fig. 4: MT1 splits into double peaks
with a 1:2 ratio for 0◦ or B//[100], it sharpens the mostfor 54.75◦ or B//[111], and finally it broadens slightly for90◦ or B//[011]. Such features can be reproduced exactly by
assuming a tetragonal symmetry (100 axial symmetry) with
g// = 1.999 70 and g⊥ = 1.998 75 for this center. Furthermore, the determined g tensor can completely fit the observed
angular dependence of MT1 [see Fig. 3(c)]. The conductionelectron-like g value of MT1 indicates that MT1 is a typeof shallow-donor electron weakly coupled with a tetragonalsymmetrical point defect.
Contrarily, the MT2 center was found to be strongly
anisotropic with the same tetragonal symmetry. The
corresponding g tensor was given by g// = 2.019 38 and g⊥ =235201-3

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PHYSICAL REVIEW B 108, 235201 (2023)

TABLE I. Concentrations of the hydrogen-related donors and EPR centers (MT1 and MT2/3) in proton-irradiated FZ-Si after annealing at
400 ◦ C and 500 ◦ C. The donor concentration was calculated by integrating the carrier concentrations shown in Fig. 2. The spin concentration
was calculated from an EPR spectrum measured under photoexcitation at 10 K with a magnetic field parallel to the [100] axis. The intensity
ratio of MT3 and MT2, “MT3/MT2,” was calculated from areas of absorption EPR signals (integrated signals).
Annealing

Donor concentration

temperature(cm−2 )

400 ◦ C500 ◦ C

Spin concentration (spins/cm2 )Total

3.86 × 10
0.79 × 1012
12

MT1

3.15 × 10
0.68 × 1012

1.30 × 10
undetectable

12

1.994 90. This strong anisotropy implies a large structural
distortion in this center along the 100 axis and may berelated to its higher thermal stability. The tetragonal symmetry
is known for only a few point defects in Si [42]; e.g., the B3
center, identified as the I4 (+) center in Si [39], as noted inTable II.
MT3 was always observed together with MT2 and was
detected exactly at the center of two split peaks of MT2
for all angles [Fig. 3(c)]. Therefore, we attribute this signal
to an exchange-narrowing signal of the MT2 center. This is
supported by the fact that, unlike MT2, MT3 exhibited asingle Lorentzian-like peak without any HF structures (seeSec. III D). Feher et al. reported similar findings for Si,
demonstrating the exchange-narrowing interaction of shallow
P donors with 1 × 1018 cm−3 or higher concentrations when
the average distance of P donors was 10 nm [45]. For
HD concentrations (peak values = 8 × 1015 cm−3 for 400 ◦ C

FIG. 4. Angular dependence of the MT1 spectra with tetragonal
symmetry. The spectral simulations based on tetragonal symmetry(blue lines) fully reproduced the observed characteristic of the MT1
spectra.

12

MT2, MT3

MT3/MT2

1.85 × 10
0.68 × 1012

0.69
0.66

12

and 1 × 1015 cm−3 for 500 ◦ C; see Fig. 2), their averageseparations are estimated to be 50 and 100 nm, respectively,
appearing to be much larger than the spatial extent of any
shallow donors with exchange-narrowing interactions in Si.
Nevertheless, MT3 was detectable in both samples and evenwith a similar intensity ratio (MT3/MT2 = 0.66–0.69; see
Table I).Therefore, we strongly suggest that the formationof close pairs of HD2 is favorable, resulting in the all-timecoexistence of the MT2 and MT3 signals.
C. Cyclotron resonance of conduction-band electrons

Comparing the EPR results with CR spectroscopic results
described in this section, we further reveal a double-donor
nature of the HDs. Figures 5(a) and 5(b) compare the CR
spectra in the dark and under photoexcitation, where theconduction-band electrons (CEs) are observable in a very
low field range. As far as the CR spectra are concerned, the400 ◦ C and 500 ◦ C samples were very similar with a slightfluctuation in their temperature dependencies. Below 25 K,
we found two broad peaks related to CR [Fig. 5(c)]. We also
found a tetragonal symmetry of CEs in association with the
100-oriented ellipsoidal six-valleys of the conduction-band
minima in Si [Fig. 5(d)] [46]. The solid lines indicate thesimulation data obtained using the known electron effective
mass m∗ and the electron rest mass m0 for Si (longitudinal andtransverse effective masses, ml∗ = 0.98m0 and mt∗ = 0.19m0 ,respectively [46]). Note that the tetragonal symmetry of theCEs is independent of the tetragonal symmetry of the HDs
because the former is always found for any conventional
donors such as the P donor (cubic symmetry). The relationshipbetween HDs and CEs can be examined using the CR signals.
At 15 K (and higher temperatures), the CR signal was
clearly detectable in the dark [Fig. 5(a)] in both samples(400 ◦ C sample: HD1 and HD2; 500 ◦ C sample: only HD2).
This indicates that the CEs are emitted from HD2s at 15 K,
and HD2 should be stabilized into an empty state (S = 0).
Previously, in low-temperature CV measurements, freeze-out
behaviors of HD1 and HD2 were found to obey activationenergies of 70–80 meV and 30–40 meV, respectively [34].
Judging from such data, we consider that the HD1s werefrozen at 15 K, resulting in the formation of a singly occupied
state of the MT1 EPR center. The observed situations and theirinterpretations are listed in Table III.
When the temperature was decreased to 10 K, the CR
signal completely disappeared [Fig. 5(a)], indicating that the
CEs were converted into their frozen states with the HDs.
Nevertheless, HD2 did not show its EPR signal and kept an
S = 0 state. Namely, each HD2 received double electrons and235201-4

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TABLE II. SH parameters of the EPR centers of the HDs, MT1, MT2, and MT3. The conditions indicate the typical observation conditions
for each center, under which the SH parameters were determined. For each center, SH was defined as H = μB B · g · S + i Ii · Ai · S [39],where μB is the Bohr magneton, B is the external magnetic field, g is the g tensor, S is the spin operator, Ii is the 29 Si nuclear spin operator(i is its suffix), and Ai is the HF tensor for each nuclear spin. Only the MT2 center revealed resolved 29 Si HF structures that resembled thoseof the B3 (I4 ) center [39]. N is the number of Si atoms included in the first to third shells [39]. Within tetragonal symmetry, the symmetry axesof g and Ai (principal g// and A// axes) are given by a 100 axis.
CenterSpin(condition)

S

Symmetry

MT1 (dark and photo, 10 K)
MT2 (photo, 10 K)

1/2
1/2

tetragonal
tetragonal

MT3 (photo, 10 K)
B3 (40 K)

1/2
1/2

29

g tensor (g)
g//

g⊥

Shell

1.999 70 1.998 75
2.019 38 1.994 90

Si HF tensor (Ai )Reference

N A// (mT) A⊥ (mT)defect model

not observed
first
2
0.93
second 12
0.32
tetragonal
2.019 38 1.994 90
not observed
2
1.36
tetragonal (D2d ) 2.015 90 2.005 10 firstsecond 4
0.54
third 80.29

froze into a doubly occupied state (S = 0). Therefore, we
consider HD2 as a double donor; HD2 always favors either
a doubly occupied state or an empty state. Thus, HD2 hasa negative-U nature. Under photoexcitation, HD2 captures aphotoexcited carrier, generating a self-trapped carrier with aHD2, which is EPR-active as the MT2/3 EPR signal. Suchbehaviors resemble those of thermal double donors (the NL10
EPR center) in Si [47,48].
Contrarily, HD1 is regarded as a normal positive-U donorsuch as the P donor; a frozen state is EPR-active (MT1 EPR

0.4
0.2
0.76
0.5
0.2

HD1
HD2
HD2 with exchange interaction
Ref. [39] tetrainterstitial Si(I4 ) in p-type Si

signal) in the dark. The MT1 EPR signal decreased in thedark below 15 K [Fig. 3(a)] as the MT1 center was converted
into its doubly occupied state (S = 0). We speculate that partof the CEs was used to generate doubly occupied states ofHD1s. Under photoexcitation where the CR signal recovers[Fig. 5(b)], the HD1s become EPR-active again by capturinga photoexcited carrier.
One may wonder why the sum of the MT1, MT2, and MT3
spin densities is approximately equal to the total concentrationof HDs (Table I), although each HD2 emitted two electrons.

FIG. 5. CR spectra of the 400 ◦ C sample measured (a) in the dark and (b) under photoexcitation. (c) Temperature dependence of the CR
signal examined at a lower microwave power (but decreased CR signal intensities). (d) Angular map of the CR signal which is excellently
fitted with the known effective masses of conduction-band electrons in Si [46]. Cyclotron resonant field (position) is calculated by m∗ m0 /2π eν,where m∗ is the electron effective mass, m0 is the electron rest mass, e is the electron charge, and ν is the microwave frequency [46]. The angulardependence of the cyclotron resonant field was calculated using Eq. (38) in Ref. [46].
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TABLE III. Comparison between EPR and CR results. The statuses of HD1, HD2, and conduction-band electrons (CEs) are explained.
Signal (origin)

Dark, 15 K

Dark, below 15 K

MT1 (HD1)

Detected
HD1 stays in asingle-occupied state (S = 1/2).

MT2/3 (HD2)

Not detected
HD2 emits double electrons tothe conduction band and stays
in an empty state (S = 0).

CR (CE)

Detected
CEs are emitted from HD2s.

Decreased
Part of HD1 receives an electron andis converted into a double-occupied
state (S = 0).
Not detected
HD2 receives double electrons andis stabilized to a double-occupied
state (S = 0). Part of HD2 remains inan empty state.
Not detected
CEs return to HD2s and partly to
HD1s.

To satisfy the above equality, we have to assume the chargetransfer between the HD2s; i.e., one HD2 moves its electron toanother HD2, resulting in a pair of an empty state and a doubly
occupied state of two HD2s. This behavior is expected for anegative-U center. Then, only the doubly occupied state of an
HD2 emits two electrons. The close pair is favorable for HD2,
because of the all-time presence of the exchange-narrowing
MT3 signal. Therefore, it is reasonable to expect the chargetransfer between HD2s.
D. Hyperfine interactions of HDs

Assuming that an HD comprises an intrinsic defect andhydrogen atom(s), we can expect HF interactions of 29 Si
nuclear spin(s) (nuclear spin I = 1/2, natural abundance =4.7%) and 1 H nuclear spin(s) (I = 1/2, natural abundance =99.9%). 1 H HF interactions are easily detectable owing to adoublet HF splitting in EPR spectrum; however, such a splitting was never found in the MT1, MT2, and MT3 centers. The
incorporation of hydrogen into HDs has been evidenced byinfrared-absorption experiments with a deuterium substitution[30,32]. We can therefore conclude that the 1 H HF splitting
widths should be significantly smaller than the observed EPR
signal width ( 0.2 mT). 1 H HF splitting is reduced becauseof two factors: the spatial separation of an unpaired-electron
wave function from 1 H nuclear spin(s), and the widely spreading wave function of the donor electron that significantly
weakens any HF interactions [48].
The core structure of the HDs can be revealed via their29
Si HF interactions. In Fig. 6(a), we find a 29 Si doublet HF
structure in the low-field-side MT2 signal (0.93 mT splitting;black arrows). Additionally, this signal is the superposition of
three peaks caused by another 29 Si HF splitting (red arrows).
Contrarily, MT1 and MT3 do not reveal any HF structures, as
indicated by Figs. 6(a) and 6(b) and by other EPR data.
The 29 Si HF doublet structures of the low-field-side MT2
signal can be well fitted by the “first shell” (two equivalent
Si atoms) and the “second shell” (12 equivalent Si atoms)of 29 Si HF structures [see Fig. 7(a)].These HF doublets became unclear in the high-field-side MT2 signal, however,they apparently convoluted 29 Si HF structures as simulated inFig. 7(b). By rotating the magnetic field in the (01̄1) plane, we
found that these 29 Si HF doublets show a tetragonal symmetry

Photoexcitation
Detected
HD1 captures a photoexcited
carrier.
Detected
HD2 captures a photoexcited
carrier, and a self-trapped carrier
generates MT2/3 signals.
Detected
Photoexcited CEs are generated.

[Fig. 7(c)]. The determined 29 Si HF parameters are summarized in Table II. The 29 Si HF tensor and the symmetry of
MT2 and the B3 EPR center [39] are similar, although the B3
signal enabled us to deconvolute the second shell (12 atoms)
into two groups (four and eight atoms). Figure 7(d) shows theangular pattern of the B3 center using the spin-Hamiltonian(SH) parameters in Table II, which resembles that of MT2.
In fact, the B3 center was found to be a type of implantation
damage evolving after 300–500 ◦ C postimplantation annealing [39]. This formation behavior exactly coincides withthat of the HDs in the present samples. Therefore, we conclude that the MT2 and MT3 centers (originated from HD2)
were closely related to the B3 (I4 ) centers [39]. Given the

FIG. 6. HF interactions in HD EPR spectra, measured (a) underphotoexcitation and (b) in the dark. In (a), the arrows indicate the 29 Si
HF doublets of MT2. MT3 is a single Lorentzian-like peak without
any HF structures, suggesting that MT3 is an exchange-narrowing
signal. In (b), MT1 (for 0◦ and 90◦ ) does not exhibit any HF structures (see the right half side of MT1 signal). Its left half side is
obscured by weak interference signal(s) probably owing to weak CR
signal(s).

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FIG. 7. 29 Si HF interactions of MT2. (a) Low-field-side and (b) high-field-side MT2 signals simulated by two sets of 29 Si HF doublets (firstshell: orange; second shell: green).29 Si HF splitting in (a) and (b) corresponds to A// and A⊥ components, respectively (see Table II). In (b), we
focused on a spectral simulation using the right half side of MT2, because of the overlapped MT1 signal in the left half side of MT2. Angularmaps of 29 Si HF interactions for (c) the MT2 and (d) the B3 centers. In (c), the symbols (black and gray) are the individual experimental datameasured at 10 K under photoexcitation. The solid lines plot the simulation data using the SH parameters (g and 29 Si HF tensors) shown in
Table II.

similar formation condition and same tetragonal symmetry,we speculate that another HD (HD1) is also a type of B3related center.

IV. DISCUSSION ON MICROSCOPIC HD MODEL

Hydrogen and certain defects were inevitable in the formation of HDs [22–38], and the concentration of HDs increased
linearly with the proton-irradiation dose, independent of the
primary impurities (i.e., carbon and oxygen) concentrations in
Si [43]. Moreover, the annealing kinetics of HDs (observed at
260–500 ◦ C) indicated similarities with that of an interstitial
silicon cluster [44]. Previous results suggest that HDs are

intrinsic defects coupled with hydrogen and correlated withinterstitial silicon [44].
Gorelkinskii et al. [23–25] and Tokmoldin et al. [32,33]
investigated proton-irradiation-induced donors and suggested
that the interstitial Si clusters participate in the donor formation process. Among the interstitial Si clusters, triinterstitial
silicon (I3 ) and tetrainterstitial silicon (I4 ) are known tobe thermally stable in the temperature range 250–500 ◦ C(250–350 ◦ C for I3 , and 300–500 ◦ C for I4 [39,44]), where
the HDs (HD1 and HD2) are just observable. Jones and Carvalho et al. [49–51] demonstrated the trigonal I3 [Fig. 8(a)]and tetragonal I4 models [Fig. 8(b)] using DFT calculations.
Furthermore, the I4 center with D2d symmetry (tetragonal
symmetry with the 100 symmetry axis) was identified to235201-7

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FIG. 8. (a) Trigonal triinterstitial and (b) tetragonal tetrainterstitial Si [49]. The left part of each image shows the perfect Si lattice before
the insertion of the extra interstitial Si atoms. In (a), the I3 center is constructed by placing three interstitial Si atoms at the bond center ofadjacent 111 bonds. In (b), the I4 center is constructed by replacing four neighboring Si atoms on the (100) plane with four 100 split
interstitial pairs; (a)–(c) denote the Si shells described in the text.

be the origin of the B3 EPR center [39,49]. Likewise, theB5 EPR center with C3v symmetry (trigonal symmetry with
111 symmetry axis) was assigned to the I3 center [39,49].
Additionally, the possible donor levels of the I3 and I4 centerswere demonstrated near the valence band edge: Ev + 0.19 eV
for I3 and Ev + 0.29 eV for I4 , i.e., the I3 and I4 centers are
deep donors [51].
A possible scenario in which two types of HDs correspondto the sole I3 - and I4 -based donors could be invoked. However,
the experimentally verified symmetry presented here rules out
the incorporation of the I3 center with C3v symmetry into theHDs. Alternatively, we here propose a model in which bothHDs (HD1 and HD2) are based on the I4 center. The observed
first shell of the 29 Si HF structures arises from two Si atoms,“a,” along a 100 axis, resulting in a strongly anisotropic
tetragonal symmetry of the MT2 center. Twelve Si atoms of
the second shell of the MT2 center are also assignable to Si
atoms “b” and “c” [see Fig. 8(b)].
The difference between HD1 and HD2 may be attributed
to different numbers of incorporated hydrogen atoms and/or
their different bonding to I4 . HD2 likely involves more hydrogen atoms because HD2 forms at a higher temperaturethan HD1. For example, HD1 may be transformed into HD2
by capturing additional hydrogen atom(s) when elevating theannealing temperature from 400 ◦ C to 500 ◦ C. The electronnuclear double resonance (ENDOR) study for weak 1 H HF
interactions remains a future work to verify this speculation.
For MT1 (HD1), we found a conduction-electron-like gvalue and absence of any HF signatures, which is characteristic of a widely delocalized wave function of a donor
electron and in contrast with the MT2/3 (HD2). For MT2/3,
we also imagine a similar delocalized donor state, because
we believe that HD1 and HD2 are the same I4 -based donors.
A self-trapped carrier should be accompanied by a structural
relaxation and a lowered symmetry as compared to the original structure before carriers are trapped. Because the MT2/3
centers are interpreted as a self-trapped carrier with an HD2,
they may enhance their tetragonal symmetry, resulting in theobserved strong g anisotropy, which was stronger than that of
the original I4 center (see Table II). Nevertheless, comparing

the 29 Si HF interactions between MT2 and B3, we confirm
that the HD electron is more delocalized than the I4 center.
Using Table II, a wave-function density of an unpaired electron, η2 , at the first shell (Si atoms a) [39] can be estimated:η2 = 4.8% per Si atom (3s orbital 0.4% + 3p orbital 4.4%)
for MT2, which is decreased from η2 = 5.6% per Si atom for
the B3 (I4 ) center.
Based on the I4 model, the MT2 center (HD2) consistsof three types of Si atoms [a to c in Fig. 9(a)] and a 4.8%
wave-function density of unpaired electrons at each Si atoma. However, the 1 H HF interactions were completely hidden
within the signal width (0.2 mT) in the EPR results.
Herein, we discuss the possible hydrogen site in the structure of HDs and reason(s) of the absence of a resolved 1 H HF
interactions. In Si, only a few cases in which 1 H HF interactions have been clearly detected are known [see Figs. 9(b)and 9(c)]. Figure 9(b) shows an interstitial form of a hydrogenatom, HBC (the AA9 EPR center), which was also produced
by proton irradiation but at 77 K with a much heavier dose
(1015 cm−2 ) than that of the present study [2]. This center
showed a strongly anisotropic 1 H HF splitting of 0.22 to 1.1
mT [2]. If such a bond-centered hydrogen was formed near
Si atoms a or b of HD2 [Fig. 9(a)], we could have detected1
H HF splitting. The neutral V + H center [Fig. 9(c)] showsan anisotropic 1 H HF splitting of 0.11 to 0.30 mT [19]. Thisanisotropic HF interaction arises from a dipolar interaction
between an electron spin and a 1 H nuclear spin that are
separated by 0.28 nm in a monovacancy [19]. As this HF
splitting is also within the experimentally detectable range,
Si-H bonds for Si atoms a or b may be ruled out. Namely,
Si atoms c may be the most probable site for the Si-H formor bond-centered hydrogen incorporation. We also speculatethat the Si-H bond formation at Si atoms c may destabilize
the structure of the I4 center. Therefore, a hydrogen interstitial
form or an intercalation form seems to be the most acceptable,
as the core of HDs (I4 ) is surrounded by a relatively large“cage” formed by eight Si atoms c. When such forms are
introduced somewhere in Si atoms c, their 1 H HF interactions
may be significantly weakened. In Table IV, we further check

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HOW DOES HYDROGEN TRANSFORM INTO SHALLOW …

PHYSICAL REVIEW B 108, 235201 (2023)

FIG. 9. Hydrogen interactions of paramagnetic centers in Si. The hydrogen and Si atoms are indicated by light blue and blue colors,
respectively. (a) Possible site for hydrogen incorporation in HDs. Three areas for H incorporations are indicated by blue, green, and red, whichcorrespond to equivalent Si atoms a, b, and c, respectively. The red area and surrounding cage formed by the Si atoms are the most probablesite for the hydrogen incorporation. 1 H HF interactions have been detected in Si in (b) a bond-centered hydrogen atom (AA9 center, S = 1/2
with trigonal or C3v symmetry) [2], (c) a monovacancy coupled with a hydrogen atom (S = 1/2 with monoclinic-I symmetry) [19]. In (c),monovacancy is depicted by a dotted circle.
1

H HF interactions quantitatively. First, assuming an effective
mass (EM) donor (typically P in silicon) centered at the Siatom a in Fig. 9(a), its wave function yields isotropic 1 H HF
splitting as shown by Aisotropic in Table IV, when a 1 H nuclear
spin is located at each position, respectively. All the estimatedvalues (1.7–2.2 mT) are within an easily detectable range inthe present EPR experiments. Therefore, we suggest that HDs
have rather different wave function from the EM donors. For
example, we infer that its wave function is not spherical andmay have a node in the vicinity of the hydrogen location. We
also calculated the dipolar interactions of a 1 H nuclear spin,
Adipole . Judging from this calculation, we conclude again thatthe c site or inside the cage are only possible candidates forthe location of hydrogen.
At present, the exact position of hydrogen atoms and howhydrogen atoms create shallow-donor levels of I4 + Hn is notclear (n is unknown). This should be studied in the future, e.g.,
via ENDOR measurements and first-principles calculations
based on the I4 -based donor.
Last, HDs are industrially useful for n-doping in Si devices.
The present study revealed a fundamental limit of their thermal stability to 550 ◦ C, which is the anneal-out temperatureof the I4 center [39,44].

V. SUMMARY

We studied hydrogen-related donors (HDs) in Si, which areimportant defects for device applications and for an importantunresolved issue in semiconductor science: how hydrogen
behaves as a donor. We reported EPR signals (MT1, MT2,
and MT3) in proton-irradiated FZ-Si annealed at 400 ◦ C and500 ◦ C. Through a direct comparison of concentrations measured using SR profiling and EPR spectroscopy, the threesignals were attributed to the HDs: MT1 to HD1 with lower
thermal stability and MT2/3 to HD2 with higher thermal
stability. Based on the full angular dependency of the MT1
EPR signal, its g tensor showed a conduction-electron-likeg value but tetragonal symmetry around the 100 axis; no
HF interaction was observed with any nuclear spins. HD1
behaved as a normal shallow donor, similar to the P donor.
Contrarily, HD2 revealed a double-donor behavior (negativeU behavior). The MT2/3 EPR signals of HD2 were only
detectable under photoexcitation as a self-trapped carrier withan HD2. MT2 presented a strongly anisotropic g tensor with atetragonal symmetry around the 100 axis. MT3 was considered as an exchange-narrowing signal of MT2. For HD2, wedemonstrated the preferential formation of close pairs and thepreferential charge transfer in the pairs. We could not find 1 H

TABLE IV. Estimated hyperfine coupling constants between an EM donor electron and a hydrogen nuclear spin. The distance R correspondto the separation between the Si atom a and expected hydrogen sites in the unrelaxed I4 structure shown in Fig. 9(a). The calculation proceduresare described in the Appendix.

1

Position of
H nuclear spin

Distance R(nm)

Aisotropic(mT)

Adipole(mT)

Si atom a site
Si atom b site
Si atom c site
Center in the cage

0
0.23
0.34
0.36

10.4
2.2
1.6
1.7

0.2
0.1
0.1

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Remarks
first neighboring site
second neighboring site

AKIRA KIYOI AND TAKAHIDE UMEDA

PHYSICAL REVIEW B 108, 235201 (2023)

HF interactions in every EPR center and hence concluded that
their 1 H HF interactions should be much smaller than 0.2 mT(signal widths). For MT2, the 29 Si HF interactions were successfully detected and assigned to the first (two Si atoms) andsecond shells (12 Si atoms) of the I4 (tetrainterstitial cluster)
center. Originally, the B3 EPR center has been identified as
the I4 center [39]. This center was considered an implantation
damage center that grew after annealing at temperatures of
300–500 ◦ C [39], similar to the case of the present study, andexhibited characteristic 29 Si HF interactions similar to thoseof MT2. Therefore, we proposed a microscopic model for an
unidentified structural unit to be I4 or the B3 center. Namely,
the HDs consist of an I4 core + hydrogen atom(s). Further
studies to verify the incorporation of hydrogen into the HDs
are underway using techniques such as ENDOR spectroscopy
and first-principles calculations.
ACKNOWLEDGMENTS

A.K. is grateful to J. Ito (SHI-ATEX Co., Ltd) and S.
Takemoto (Melco Semiconductor Engineering Corp.) for theirassistance with the proton-irradiation experiments and spreading resistance profiling measurements, respectively.

of EM donors (As, P, and Sb in silicon) was given in Eq. (42):8πμB μN g gN η |F (r)|2 ,3
where r is the distance from the origin of the wave function,
μB is the Bohr magneton, μN is the nuclear magneton, g is
the electron g factor, gN is the nuclear g factor, η is a constant(they used the value η = 178 reported in Ref. [53]), and F (r)is the envelop function (1s-hydrgogenlike wave function) ofan EM shallow donor, which is approximated following thedual-exponentials function given in Eq. (48) of Ref. [52],Aiso (r) =F (r) = 0.850 (π 153 )

−1/2

−1/2

e−r/15 Å + 0.211 (π 53 )e−r/5 Å .

Considering that the experimentally established isotropic
hyperfine interaction of the P donor is APiso (r = 0) =4.195 mT in silicon, we calculated the strength of isotropic
hyperfine coupling of H atom separated with the distance R
from an EM shallow donor,P
AH
iso (R) = Aiso (0)|F (R)|2 gN (1 H atom).
|F (0)|2 gN (31 P atom)

In Table IV, we estimated the isotropic and dipolar hyperfine interactions using the following theories. According toRef. [52], the following isotropic hyperfine interaction Aiso (r)We also calculated the strength of the dipolar hyperfine
interaction, Adipole (r), within the point-dipole approximation,according to Ref. [54],μ0 μB μN g gN,
Adipole =4π
h R3
where we used 2.79 and 1.13 for the nuclear g factor of H andP atoms and 2.0 for the electron g factor, respectively.

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