Optimization parameter settings of germanium

The unit cell structure of germanium is a cubic crystal system, and the space group is Fd-3M with a side length of 5.65 Å. First-principles calculations were performed using density functional theory (DFT) with CASTEP in Materials Studio. The generalized gradient approximation (GGA) was employed as an independent exchange-correlation function with a noncanonical conservation pseudopotential (nom conservation). For structural optimization, the k point was 4 × 4 × 4, the truncation energy was 400 eV, and the energy convergence accuracy was 1.0 × 10⁶ eV/atom^{[29, 31, 32]}.

The side length of the germanium cell is relaxed to 5.59 Å after geometry optimization. The valence band maximum (VBM) and conduction band minimum (CBM) are located at the γ point and R point with indirect band gap semiconductors. The bandgap width is 0.661 eV, which is similar to the 0.67 eV of the theoretical data^[23].

Passivation model of different termination groups

The Ge cell structure is derived from a diamond structure. The optimized Ge supercell was expanded in the (100) direction and cut off to avoid the influence of periodicity. A vacuum layer of 10 Å was added to the cell with a supercell side length (d + 10 Å) in the a-axis direction with nine germanium atoms. The passivation groups were attached to the Ge atoms with broken bonds. The atoms with a vacant outermost electron structure were connected to -H atoms, and 12 passivation atoms or groups formed bonds with the germanium atoms. Two types of germanium atoms have dangling bonds: the first one is in the middle and forms a bond with one atom or group; it is named Ge1. The second type is in the corner and bonds with two atoms or groups; it is named Ge2. After the passivation model structure was established, GGA was selected as the independent exchange-correlation function with no conservation. The k point was 4 × 1 × 1, the truncation energy was 650 eV, and the energy convergence accuracy was 1.0 × 10⁵ eV/atom^{[29, 32]}.

Passivation film preparation and MOS device characterization

A P-type germanium substrate with a <100> crystal orientation was selected, and its resistance was approximately 5-40 Ω. First, the substrate was rinsed with an ultrasonic cleaner consisting of ethanol, acetone, and deionized water for 15 min. A cylindrical magnetron sputtering source was connected to an RF power generator using a matcher. Before film deposition, the pressure of the vacuum chamber was pumped below 3.0 × 10^-4 Pa.

Physical characterization of the thin GeO_xN_y passivation layer was performed using electrical characteristics, scanning electron microscopy (SEM), and X-ray photoelectron spectroscopy (XPS). The electrical characteristics and surface-state density of the GeO_xN_y passivation layer were measured using a Keithley 4200A-SCS instrument at room temperature. SEM was performed using a Zeiss Merlin Compact Field Emission Scanning Electron microscope to analysis the passivation layer thickness and uniformity. XPS was performed utilizing a Thermo 250XI with monochromatic X-ray using the Al Kα line.

Band structure and density of states of Ge passivation (-H, -OH, -NH₂)

The ball-and-stick models of Ge with -H, -OH, and -NH₂ group passivation are shown in Figs. 1(a), 1(b), and 1(c), respectively. The energy location of 0 eV in the figures of band structure and DOS represents the position of the Fermi level. The bandgaps of Ge-H, Ge-OH, and Ge-NH₂ are 4.06, 2.20, and 1.87 eV, respectively. The Ge-H structure has a direct band gap, whereas the Ge-OH and Ge-NH₂ structures have both indirect band gaps. The band structure and DOS of the different atoms or groups were analyzed to determine the rationality of the passivation. The low surface leakage current was confirmed by the moderate bandgap and low D_it near the Fermi level.

Fig. 1Full-screen View

(Color online) Ball-and-stick models and the corresponding band structures of (a) -H, (b) -OH, and (c) -NH₂ termination groups, represented by H atoms (white balls), O atoms (red balls), and N atoms (blue balls), respectively

To understand whether the interface state density was influenced by the different passivation atoms or groups, the total density of states (TDOS) and partial density of states (PDOS) of the passivation system were analyzed. The DOS was analyzed to identify the passivation atoms or group interactions with the Ge atoms. The atomic interactions and chemical bonds were explored to analyze the DOS. Figure 2(a) shows the TDOS with the Ge-H, Ge-OH, and Ge-NH₂ terminations. The TDOS of the Ge-OH group near the Fermi level is the smallest, whereas that of the Ge-H group is the largest. Figures 2(b), 2(c), and 2(d) show the PDOS of Ge-H, Ge-OH, and Ge-NH₂, respectively. As shown in Fig. 2(b), the DOS near the VBM is mainly contributed by the 4 p orbital of the Ge atom, and the contributions of Ge1 and Ge2 are similar. The DOS near the CBM is mainly contributed by the 4 s and 4 p orbitals of the Ge atom, and the contribution of the 4 p orbital is slightly greater than that of the 4 s orbital. As shown in Figs. 2(c) and 2(d), the DOS near the VBM is mainly contributed by the 2 p orbital of the O and N atoms, which is related to the electronegativity of these atoms being greater than that of the H atoms. The Ge2 atoms in the Ge-OH and Ge-NH₂ structures are shifted to the left in the valence band compared to those in the Ge-H structure. In the structure of the Ge-OH passivation, the 2 p orbital of the O atom has more interactions with the 4 p orbital of the Ge atom. For the Ge-NH₂ passivation system, the 4 p orbital of Ge1 interacts more with the 2 p orbital of N, and the 4 s orbital of Ge2 interacts more with the Ge1 atom. Among the three systems, the -OH passivation group with a moderate bandgap width and small DOS should be selected.

Fig. 2Full-screen View

(Color online) (a) -H, -OH, and -NH₂ terminations of the total density of states (TDOS), and partial density of states (PDOS) of the (b) -H, (c) -OH, and (d) -NH₂ terminations

Band structure of Ge-O_xN_y passivation

With the exception of Ge-O₂N₂, which has a direct bandgap with the VBM and CBM located at the K-point of γ, the other passivation structures show indirect bandgap characteristics. The VBM of Ge-O₂N and Ge-ON₂ are located at the Q-Z point in the K space. The VBM of Ge-ON and Ge-O₃N are located at the γ point. The CBM of Ge-ON and Ge-O₃N are located at the γ point, whereas the CBM of Ge-O₂N and Ge-ON₂ are located at the F and Q-Z points. The bandgap widths of -ON, - O₂N, -O₃N, -ON₂, and -O₂N₂ are 1.81, 0.919, 0.615, 1.568, and 1.124 eV, respectively. The VBM of Ge-ON and Ge-ON₃ are located at the Q-Z point in the K space. The CBM and VBM of Ge-O₂N are located at the F and γ points, and the VBM and CBM of -ON₂ are located at γ and Q-Z points. The increase in the number of either O or N atoms can affect the bandgap width, which may lead to the generation of other energy levels, and the O atom has a greater role in reducing the bandgap width (Fig. 3).

Fig. 3Full-screen View

(Color online) Ball-and-stick models and the corresponding band structures of (a) Ge-ON, (b) Ge-O₂N, (c) Ge-O₃N, (d) Ge ON₂, and (e) Ge-O₂N₂ termination groups

DOS of Ge-O_xN_y passivation

The interface state is influenced by different nitride and oxygen atom ratios, which were researched by analyzing the DOS of the five systems. Figure 4 shows the TDOS diagrams of the five passivation groups with different N/O ratios. The highest TDOS near the Fermi level is for Ge-ON, whereas the lowest TDOS near the Fermi level is for Ge-O₃N. To further analyze the optimal N/O atomic ratios of the passivation groups in the PDOS diagram, the Ge atoms in the different passivation environments were named Ge1 and Ge2 based on the previous definition. The other passivated atoms were named AX-B (where A represents the passivated atom, X indicates the number of passivation atoms, and B denotes the directly connected atom).

Fig. 4Full-screen View

(Color online) TDOS of nitrogen oxides of germanium

The two Ge PDOS conditions are shown in Fig. 5. Overall, the contributions of the 4 s and 4 p orbitals in the vicinity of the VBM (−5 to 0 eV) are very weak for both Ge1 and Ge2 atoms. The contribution of the 4 p orbital is slightly larger than that of the 4 s orbital. Both the Ge1 and Ge2 atoms contribute more to the PDOS in the CBM. The contributions of 4 s and 4 p orbitals near the vicinity of the CBM are equivalent, with the exception of Ge-O₃N. For the PDOS of Ge1 atoms, the introduction of O atoms causes a DOS in the left direction, and the same situation occurs for the PDOS of Ge2 atoms. N atoms also cause a PDOS shift toward the left for Ge1 atoms, but this is not obvious for Ge2 atoms. This finding indicates that N atoms have a large influence on less-bonded Ge atoms, and that O atoms have the same influence on unbonded Ge atoms.

Fig. 5Full-screen View

(Color online) PDOS of nitrogen oxides of germanium: (a) Ge1 PDOS and (b) Ge2 PDOS

Different O/N ratios have distinct effects on the DOS of these systems. The effects of O and N atoms on the DOS warrant further study. Figure 6 shows the PDOS diagrams of the O atoms in different environments. The O atoms significantly contribute to the DOS of the valence band, which is provided by the 2 p orbital. When a Ge2 atom is passivated by an O atom, the DOS in the valence band shifts to the left as the number of O atoms increases. Combined with the previous analysis for Ge atoms, O atoms cause the entire DOS to move toward the left. As shown in the PDOS diagram of the N atom in Fig. 7, N atoms directly connected to Ge atoms contribute slightly to the conduction band, with the exception of Ge-O₂N₂ passivation. The DOS near the VBM of the N atoms connected to the Ge atoms is almost unaffected by the number of O or N atoms in the systems. The N atoms that are connected to the O atoms in the Ge-O₂N₂ system have an effect similar to that of the Ge atoms. However, we discovered that such an anomaly appeared in the structure of O₂N₂. We speculate that the electronegativity of the N atom is strong, and the adjacent N-Ge bond is weak when the N-N bond is formed.

Fig. 6Full-screen View

(Color online) O PDOS of nitrogen oxides of germanium: (a) -ON, -O₂N, -O₃N, and (b) -O₃N, -O₂N, -O₂N₂

Fig. 7Full-screen View

(Color online) N PDOS of nitrogen oxides of germanium: (a) -ON, -O₂N, -O₃N, and (b) -ON₂, -O₂N₂

When connected to the Ge1 atom, an increase in the number of N atoms causes the DOS to shift to the left. However, the DOS of the O atoms directly connected to the N atoms is very small, indicating that the 2 p orbital of the O atoms does not interact strongly with the 2 p orbital of N (N-O₃N). The same result occurs in Ge-ON, where the Ge atom is directly passivated by the O atom, showing the similarity of this structure to -OH passivation. Instead, the O and N atoms passivated the Ge as a whole. Although the Ge-O₃N structure has the lowest DOS, its band gap width is only 0.615 eV, near the 0.67 eV of Ge itself. Therefore, the best passivation effect of the Ge-ON₂ group is obtained with a gap width of 1.568 eV, and its DOS is similar to that of Ge-O₃N.

For the germanium passivation calculation, Houssa et al. determined that there are few defects at the Ge/GeO₂ interface using first principles^[33]. Under ideal conditions, the interfacial state density is only 10¹¹ cm^-2 eV^-1, which is even lower than the detection limit of electron spin resonance (ESR). Saito et al. calculated that the Ge/GeO₂ interface is more flexible than the Si/SiO₂ interface^[34]. Atomic Ge emissions can be inhibited during the oxidation process to change the electrical properties of the Ge/GeO₂ interface. The germanium detector was passivated by applying appropriate oxygen-nitrogen ratios to reduce the interface state density and surface leakage current. Based on the number of Ge and passivation atoms obtained from our calculations, the optimal chemical dose ratio for surface passivation is Ge₂ON₂.

Interface state density at -O_xN_y passivation

All passivation layers were prepared in a 2:1 nitrogen-oxygen mixed atmosphere on a <100> germanium single crystal. The RF power was chosen to be 60-80 W. The prepared oxygen-nitrogen passivation layer film was amorphous and crystalline, with a mixture of various germanium-nitrogen oxides. Figures 8(a), (b), and (c) show the XPS spectra of the Ge 3 d, N 1 s, and O 1 s energy levels, respectively. The ratio of the peak area to the sensitivity factor was calculated, which showed that the Ge:N:O atomic ratio of the passivation film was close to 2:1:2^[35]. The peak values corresponding to the binding energy of GeO₂, GeON, and Ge₃N₄ were 33.2, 32.2, and 32.1 eV^{[36, 37]}, respectively.

Fig. 8Full-screen View

(Color online) Al/Ge₂ON₂/Ge MOS structural characteristics: XPS spectra of the (a) Ge 3 d, (b) N 1 s, and (c) O 1 s energy levels of the Ge₂ON₂ film; (d) I-V characteristic, and (e) C-V characteristic

To extract information regarding the interface state density, the I-V and C-V characteristics of the Al/Ge₂ON₂/Ge MOS structure passivated with germanium nitrogen oxides at room temperature are shown in Fig. 8(d) and 8(e). A higher D_it affected the passivation results for a low leakage current and threshold. The IV characteristics in the scanning range of −1.5 to 1.5 V and the capacitance characteristics from −1 to 1 V of the GeO_xN_y passivation layer with a thickness of 20 nm are analyzed.

It is difficult to determine the dielectric constant of a passivated film owing to its amorphous state, which makes it difficult to determine the capacitance of the oxide layer. In the $\frac{\text{1}}{c} \left({\text{pF}}^{\text{-1}}\right)$ vs. $\sqrt{\frac{\text{d}}{\text{d}{V}_{\text{G}}}\frac{1}{c^2}} \left({\text{V}}^{-\frac{1}{2}}{\text{pF}}^{-1}\right)$ curves shown in Fig. 9(a), the x-intercept of the fitted curve could be recognized as an oxide layer capacitance of 8.9 × 10^-9 F. The D_it calculation using the Terman method is shown in Eq. (1)^{[38, 39]}: $D_{\text{it}}\text{=}\frac{C_{\text{OX}}}{q^{\text{2}}}\left(\frac{\text{d}{V}_{\text{G}}}{{\text{dφ}}_{\text{s}}}\text{-1}\right)\text{-}\frac{C_{\text{s}}}{q^{\text{2}}}\text{=}\frac{C_{\text{OX}}}{q^{\text{2}}}\frac{\text{dΔ}{V}_{\text{G}}}{{\text{dφ}}_{\text{s}}}$ (1) where C_OX and C_s are the oxide layer and semiconductor capacitance, respectively, q is the electron charge size (1.6 × 10^-19 C), ΔV_G represents the difference between the C-V characteristics measured in the experiment and ideal curve, and φ_s represents the surface potential. The Terman method has many approximations and the calculation of the doping concentration and oxidation capacitance leads to an overestimation of D_it^[40]. The distribution of D_it with the energy levels is given by Eq. (2)^[41]: $E_{\text{c}}\text{-}{E}_{\text{T}}\text{=}q{\text{φ}}_{\text{s}}\text{+}\left(E_{\text{c}}\text{-}{E}_{\text{F}}\right)$ (2) where E_c is the conduction band of the semiconductor, E_F is the Fermi level, and E_T is the trap energy at the interface. The interface energy level distribution near the band energy level (E_c) ranges approximately from E_c − 0.29 to E_c − 0.31 eV.

Fig. 9Full-screen View

(a) Cox fitting curve and (b) density of interfacial states at different energy level positions

Figure 9(b) shows an average interface state density of 8.4 × 10¹¹ cm^-2 eV^-1, which indicates that it is feasible to passivate the HPGe detector by magnetron sputtering GeO_xN_y at room temperature for a lower D_it. D_it is uniformly distributed at this energy level, indicating that the amorphous states do not have obvious interface defects. The low surface defects are confirmed by the low D_it, and the low surface leakage current is caused by the low defects at the Ge₂ON₂/Ge interface. In addition, some abnormal D_it values deviate significantly from the average, which is attributed to the presence of amorphous GeO_xN_y at the interface. This finding is consistent with previous simulation results: as the number of nitrogen and oxygen atoms increases, more dangling bonds of germanium are formed, and the interface state density is further reduced. Germanium nitrogen oxide passivation of the reported HPGe detector achieved low leakage (~pA) and good performance^{[30, 42, 43]}. The interface state density and leakage current at low temperatures should be investigated in future studies.