We have investigated the relationship between the Ag concentration and the pn-junction depth in the Mg2Si pn-junction photodiodes fabricated by thermal diffusion of the Ag acceptor. The Ag concentration profiles and pn-junction depths in the samples annealed between 400 and 550 °C were studied by secondary ion mass spectroscopy and electron beam-induced current (EBIC) images. We observed two kinds of lattice diffusions of substitutional and interstitial Ag atoms with two different diffusion coefficients, of which activation energies were ∼0.97 and 0.75 eV, respectively. The depth of pn-junction observed by EBIC images increased with annealing temperature and annealing time. On the other hand, the average Ag concentration did not depend on the annealing time but depended on the annealing temperature. These results indicate that the average Ag concentration and pn-junction depth in Mg2Si photodiodes can be controlled by annealing temperature and annealing time, respectively. This study would contribute to the development of Mg2Si pn-junction photodiodes.

Photodetectors in short wavelength infrared (SWIR, 0.9–2.5 μm) region are attracting attention as one of the key devices for application in night vision systems, automated vehicle operations, and biological monitoring systems.1 Pure Si as a conventional infrared photodetector is not suitable for this SWIR region due to the bandgap limitation (1.12 eV). Therefore, narrow-gap bulk semiconductors, such as InGaAs, Ge, InAs, and HgCdTe, have been explored for a long time.2 Among them, magnesium half silicide, Mg2Si, having an anti-CaF2 structure, has been expected to be an Si-based infrared photodetector that operates in the SWIR region3–11 because it has an indirect energy gap, Eg = 0.61 eV,12,13 and its Eg is varied between 0.57 and 0.36 eV by allowing with Mg2Ge and Mg2Sn, respectively.14–18 

Previously, we have studied the crystal growth of bulk Mg2Si19–21 and first reported a photoresponse from the Mg2Si pn-junction photodiode (PD) fabricated by conventional thermal diffusion,3–8,11 where Ag atoms as acceptors were diffused into n-type single crystalline Mg2Si substrates (carrier concentration ∼1015 cm−3).3–5 We also demonstrated the improvement in photosensitivity by fabricating a planar structure with a ring electrode and a mesa-structure with a ring electrode using Mg2Si pn-junction PD.5,6

In the doping process for the fabrication of the Mg2Si pn-junction photodiode, we have used thermal diffusion because this process can dope impurities easily compared to ion implantation.22–29 However, it is difficult for this process to control diffusion depth and impurity concentration. In fact, the photosensitivity of Mg2Si pn-junction PD has been limited by a large pn-junction depth due to the high diffusivity of Ag atoms in Mg2Si.30 We also reported that the pn-junction depth observed by electron beam induced current (EBIC) images and the voltage constant (VC) techniques was lowered by short-time (30 s and 1 min) annealing between 400 and 480 °C.7 However, the mechanism of thermal diffusion of Ag atoms in Mg2Si has not been elucidated. To control the junction depth and impurity concentration for further improvement in photosensitivity, a detailed analysis of Ag diffusion in Mg2Si is required.

In this study, we investigated the relationship between the Ag concentration profile and the pn-junction depth in Mg2Si pn-junction photodiodes and elucidated the mechanism of thermal diffusion of Ag atoms in Mg2Si.

N-type (6.0 × 1015 cm−3) Mg2Si single crystals with a diameter of 18 mm were fabricated by the melt-growth method using a BN-coated PBN crucible.13,31 Mg2Si (111) substrates with a size of 3 × 3 × 1 mm3 were cut out from the Mg2Si bulk ingot. Both surfaces of the wafers were lapped and polished using diamond abrasives to adjust their thickness. After that, they were polished like a mirror face using anhydrous fumed silica (Akasel A/S).

Photodiodes of Mg2Si with pn-junction were fabricated on the n-type (111) Mg2Si substrate by rapid thermal diffusion. Patterned Ag-metal source and Au-capping layer were deposited on the substrate by evaporation through a metal mask, and then, the deposited sample was annealed in an Ar atmosphere using a rapid anneal furnace (MIRA 3000, ULVAC). The diffusion temperature and time were varied from 400 to 550 °C and from 30 s to 10 min, respectively, to make various pn-junction depth samples.

The Ag diffusion profile was evaluated by secondary ion mass spectroscopy (SIMS). Because the Ag diffusion depth is in order of μm, it is difficult to measure the whole range at once. Thus, SIMS measurement was performed in each region after the substrates were polished obliquely by tilting them to 3°. Therefore, the depth profiles were determined by multiplying the length of measurement direction with sin θ (θ = 3°). The Ag concentrations were determined by a calibration curve using the data of uniformly doped bulk samples with the relationship between Ag/Mg ratios obtained by SIMS measurement and Ag concentrations determined by inductively coupled plasma mass spectrometry (ICP-MS) (Fig. S1). The depth of the junction interface was observed on the cross section of the samples by EBIC and VC techniques using HITACHI SU8200.

The Ag concentration in pn-junction samples was measured by SIMS analysis. Figure 1 shows the Ag concentration profiles of samples annealed between 400 and 550 °C for 10 min, where the Ag concentration was determined using the calibration curve measured on Ag-doped Mg2Si bulk standard crystals. The Ag concentration increased especially near the surface as the annealing temperature increased, indicating that larger amounts of Ag atoms were introduced into Mg2Si from the surface by higher-temperature annealing. Each profile annealed above 450 °C had a clear kink, which would be a characteristic sign of a two-stream diffusion. These two-stream diffusion profiles can be observed in the case of high solubility and slow interstitial diffusivity, where the diffusion of interstitial and substitutional species does not interact significantly.32 Based on the two-stream diffusion mechanism, the concentration of diffused element, C(w, t), can be expressed by two independent atomic diffusion equations containing the complementary error function as follows:
Cw,t=NS+NI=CSerfcw2DSt+CIerfcw2DIt,
(1)
where the subscripts S and I indicate the substitutional and interstitial Ag atoms, NS and NI are the Ag concentrations, CS and CI are the equilibrium concentrations, DS and DI are the diffusion coefficients, and w and t are the depth from surface and annealing time, respectively. Figure 2 shows the fitted examples of Ag concentration profiles at 400–550 °C using Eq. (1), where the fitting parameters are CS, CI, DS, and DI. The fitted lines (red dashed lines) of samples annealed at 450–550 °C are in good agreement with experimental data. Meanwhile, because the data of the sample annealed at 400 °C could not be fitted with two-stream diffusion, it was fitted with only interstitial Ag atoms corresponding to CS = 0 in Eq. (1). The obtained fitting parameters are shown in Table I. The values of CS were much higher than those of CI, while those of DS were much lower than those of DI. The ratio of CS/CI and DI/DS was 5–22 and 31–38, respectively. These results indicate that above 450 °C, Ag impurity diffuses both substitutional and interstitial sites in Mg2Si without significant interaction between Ag substitution and Ag interstitial. Imai et al. calculated the excess formation energy of Ag impurity at interstitial occupancy (AgI), Mg substitution (AgMg), and Si substitution (AgSi) in Mg2Si crystal lattice and predicted similar excess formation energy in those three sites of occupancy: +0.721 eV for AgSi, +0.722 eV for AgI, and +0.733 eV for AgMg.33 Their prediction supports our experimental result because the similar excess formation energy for Ag impurity will permit those three sites of occupancy.
FIG. 1.

SIMS profiles of Ag concentration in Mg2Si after thermal annealing at 400–550 °C. The dashed lines represent the fitted ones (NS + NI) with Eq. (1).

FIG. 1.

SIMS profiles of Ag concentration in Mg2Si after thermal annealing at 400–550 °C. The dashed lines represent the fitted ones (NS + NI) with Eq. (1).

Close modal
FIG. 2.

Each SIMS profile of samples annealed at (a) 550, (b) 500, (c) 480, (d) 450, and (e) 400 °C. The red dashed lines represent the fitted ones (NS + NI) with Eq. (1). The blue dashed lines and green chain lines represent NS and NI extracted from Eq. (1) corresponding to the profile of substitutional and interstitial Ag atoms.

FIG. 2.

Each SIMS profile of samples annealed at (a) 550, (b) 500, (c) 480, (d) 450, and (e) 400 °C. The red dashed lines represent the fitted ones (NS + NI) with Eq. (1). The blue dashed lines and green chain lines represent NS and NI extracted from Eq. (1) corresponding to the profile of substitutional and interstitial Ag atoms.

Close modal
TABLE I.

Fitting parameters (CS, DS, CI, and DI) in Eq. (1) for Ag concentration profiles of the samples annealed at 400–550 °C.

Temperature T (°C)CS (cm−3)DS (cm2/s)CI (cm−3)DI (cm2/s)
550 7.4 × 1018 6.5 × 10−9 3.3 × 1017 2.0 × 10−7 
500 3.8 × 1018 2.8 × 10−9 2.6 × 1017 1.0 × 10−7 
480 2.6 × 1018 1.8 × 10−9 2.6 × 1017 6.5 × 10−8 
450 1.2 × 1018 9.9 × 10−10 2.3 × 1017 3.8 × 10−8 
400 ⋯ ⋯ 2.3 × 1017 2.0 × 10−8 
Temperature T (°C)CS (cm−3)DS (cm2/s)CI (cm−3)DI (cm2/s)
550 7.4 × 1018 6.5 × 10−9 3.3 × 1017 2.0 × 10−7 
500 3.8 × 1018 2.8 × 10−9 2.6 × 1017 1.0 × 10−7 
480 2.6 × 1018 1.8 × 10−9 2.6 × 1017 6.5 × 10−8 
450 1.2 × 1018 9.9 × 10−10 2.3 × 1017 3.8 × 10−8 
400 ⋯ ⋯ 2.3 × 1017 2.0 × 10−8 
The Arrhenius plots of these fitted diffusion coefficients (DS and DI) determined from the Ag concentration profiles are shown in Fig. 3. To evaluate the activation energy for the diffusion of Ag atoms, the obtained DS and DI were fitted with the following equation:
DS,IT=D0S,IexpEDS,IkT,
(2)
where D0S,I represents the extrapolated value at infinity temperature, EDS,I represents the activation energy, and k is the Boltzmann constant. Both fitted lines (solid lines) are in good agreement with the plotted diffusion coefficient. The obtained fitting parameters are shown in Table II. The EDS of 0.97 eV was larger than the EDI of 0.75 eV. This suggests that more thermal energy is required to diffuse substitutional Ag atoms than interstitial ones. It should be noted that the EDS of Ag atoms in Mg2Si was much smaller than that of dopants in other semiconductors, such as 3.69 and 3.70 eV for P and B atoms in Si, respectively.32 This activation energy is due to the lower atomic density of Mg2Si than that of Si. This small value makes it difficult to form a shallow pn-junction depth in Mg2Si. The more detailed physical mechanism of Ag diffusion is going to be discussed by obtaining additional experiments in the future.
FIG. 3.

Arrhenius plots of the diffusion coefficients for substitutional (DS) and interstitial (DI) Ag atoms in Mg2Si. The blue circles and green diamonds represent DS and DI, respectively. The solid lines represent the fitted ones with Eq. (2).

FIG. 3.

Arrhenius plots of the diffusion coefficients for substitutional (DS) and interstitial (DI) Ag atoms in Mg2Si. The blue circles and green diamonds represent DS and DI, respectively. The solid lines represent the fitted ones with Eq. (2).

Close modal
TABLE II.

Fitting parameters (D0 and ED) in Eq. (2) for Arrhenius plots of the diffusion coefficients for substitutional and interstitial Ag atoms.

SpeciesD0 (cm2/s)ED (eV)
Ag-substitutional 5.7 × 10−3 0.97 
Ag-interstitial 7.0 × 10−3 0.75 
SpeciesD0 (cm2/s)ED (eV)
Ag-substitutional 5.7 × 10−3 0.97 
Ag-interstitial 7.0 × 10−3 0.75 

The interfaces of the pn-junction were observed by cross-sectional EBIC images as shown in Fig. 4. The contrast change in the interface is observed at the position represented by the arrows. In Figs. 4(a)4(c), the interface lies at about 15, 55, and 95 µm from the surface for samples annealed at 400, 450, and 480 °C for 10 min, respectively. The junction depth clearly increases with the annealing temperature. Figures 4(d)4(f) show the samples of short-time annealing at 400, 450, and 480 °C, respectively, where the junction depth decreased by short-time annealing. The pn-junction depth observed by EBIC images was summarized as a function of annealing time in Fig. 5(a). It was found that the pn-junction depth can be controlled with annealing temperature and annealing time. However, the carrier concentration in p-Mg2Si can also be varied under annealing conditions. Thus, we discuss the relationship between the activation rate or Ag concentration and annealing conditions in the below paragraphs.

FIG. 4.

Cross-sectional EBIC images of samples annealed at (a) 400 °C, 10 min, (b) 450 °C, 10 min, (c) 480 °C, 10 min, (d) 400 °C, 30 s, (e) 450 °C, 1 min, and (f) 480 °C, 1 min. The arrows represent the interfaces of the pn-junction.

FIG. 4.

Cross-sectional EBIC images of samples annealed at (a) 400 °C, 10 min, (b) 450 °C, 10 min, (c) 480 °C, 10 min, (d) 400 °C, 30 s, (e) 450 °C, 1 min, and (f) 480 °C, 1 min. The arrows represent the interfaces of the pn-junction.

Close modal
FIG. 5.

(a) Annealing time dependences of the pn-junction depth observed by EBIC images for samples annealed at 400, 450, and 480 °C. The dashed lines in (a) are eye guides. The fitting lines of SIMS profiles with Eq. (1) for samples annealed at (b) 400 °C, (c) 450 °C, and (d) 480 °C. The arrows in (b) and (c) represent the pn-junction depth observed by EBIC images. The dashed lines in (b)–(d) indicate the Ag concentration at the pn-junction depth.

FIG. 5.

(a) Annealing time dependences of the pn-junction depth observed by EBIC images for samples annealed at 400, 450, and 480 °C. The dashed lines in (a) are eye guides. The fitting lines of SIMS profiles with Eq. (1) for samples annealed at (b) 400 °C, (c) 450 °C, and (d) 480 °C. The arrows in (b) and (c) represent the pn-junction depth observed by EBIC images. The dashed lines in (b)–(d) indicate the Ag concentration at the pn-junction depth.

Close modal

Figures 5(b)5(d) show the fitting lines for Ag concentration profiles of samples annealed at 400, 450, and 480 °C, respectively. The arrows represent the pn-junction depth observed by EBIC images. The Ag concentration at the pn-junction depth was almost the same values for each annealing temperature, represented by the dashed lines. This Ag concentration slightly decreased with annealing temperature. Here, we hypothesized that pn-junction arises at the same concentration of holes generated by Ag acceptors as the intrinsic carrier concentration of Mg2Si substrates (6.0 × 1015 cm−3). Based on this hypothesis, holes of 6 × 1015 cm−3 were generated from Ag acceptors of 1 × 1017 cm−3 for the sample annealed at 450 °C, corresponding to an activation rate of 6%. Similarly, the activation rate for the samples annealed at 400 and 480 °C was calculated to be 5% and 8%, respectively. This result indicates that the activation rate at pn-junction increased with annealing temperature. Meanwhile, considering that the Ag concentration at the pn-junction depth was not changed by annealing time, the activation rate was also not changed. Because these activated acceptors at pn-junction were diffused as interstitial Ag atoms, the activation rate of substitutional Ag atoms in the shallow region would be higher than that of the interstitial Ag atoms from the analysis of diffusion coefficients.

Figures 6(a)6(c) show the integrated Ag concentration in the depth direction calculated from Figs. 5(a)5(c), respectively. The integrated Ag concentrations of all samples were sufficiently saturated at ∼100 µm. The saturated values are almost corresponding to the dose amounts of Ag atoms into Mg2Si substrates. It was found that the dose amounts increased as the annealing temperature or annealing time increased. Here, the average Ag concentrations Cave of Ag-doped Mg2Si were calculated with the following equation:
Cave=Cint/djunc,
(3)
where Cint is the integrated Ag concentration at the pn-junction depth and djunc is the pn-junction depth. The calculated Cave values as a function of annealing time are shown in Fig. 6(d). The Cave values did not depend on the annealing time but depended on the annealing temperature. From the discussion about activation rate in the previous paragraph, the activation rates also increased as the annealing temperature increased. Therefore, the average carrier concentration would more largely depend on the annealing temperature. Considering that the pn-junction depth was increased with annealing time [Fig. 5(a)], only the pn-junction depth can be varied with annealing time while maintaining the average Ag concentration.
FIG. 6.

Integrated Ag concentration for the samples annealed at (a) 400, (b) 450, and (c) 480 °C. (d) Average Ag concentration calculated with Eq. (3). The dashed lines in (d) are eye-guides.

FIG. 6.

Integrated Ag concentration for the samples annealed at (a) 400, (b) 450, and (c) 480 °C. (d) Average Ag concentration calculated with Eq. (3). The dashed lines in (d) are eye-guides.

Close modal

These results indicate that the average Ag concentration and pn-junction depth in Mg2Si photodiodes can be controlled by annealing temperature and time, respectively. Therefore, we can design Mg2Si pn-junction photodiodes by optimizing these annealing conditions. Because forming a shallower junction with a certain level of doping is important to improve the photosensitivity of the diode, short period-annealing is an ideal method.

We investigated the Ag concentration profiles and pn-junction depths in Mg2Si pn-junction photodiodes formed by thermal annealing between 400 and 550 °C. We observed two kinds of lattice diffusions of substitutional and interstitial Ag atoms and determined two different diffusion coefficients with activation energies of ∼0.97 and 0.75 eV, respectively. The depth of pn-junction observed by EBIC images increased with annealing temperature and annealing time. The activation rate at the pn-junction depth also increased with the annealing temperature. The calculated average Ag concentration did not depend on the annealing time but depended on the annealing temperature. Therefore, the average Ag concentration and pn-junction depth in Mg2Si photodiodes can be controlled by annealing temperature and time, respectively. This study would contribute to the development of Mg2Si pn-junction photodiodes.

See the supplementary material for the calibration curve for SIMS measurement.

This work was supported by Grants-in-Aid for Scientific Research (B) under Grant Nos. 17H03228 and 23H01440 from JSPS KAKENHI, Japan, and the Adaptable and Seamless Technology Transfer Program (A-STEP) under Grant Nos. JPMJTR21RB and JPMJTR22R3 from the Japan Science and Technology Agency (JST). We would like to thank Dr. F. Esaka of Japan Atomic Energy Agency (JAEA) for the contribution to SIMS measurement and graduate students in the laboratory, N. Hori, T. Akiyama, Y. Onizawa, and T. Ootsubo, for their contributions to the experiments in this study.

The authors have no conflicts to disclose.

S. Sakane: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). H. Udono: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Supplementary Material