Self-passivation reduces the Fermi level pinning in the metal-semiconductor contacts

Domain: physics
Published: 2025-11-27
Editorial outcome: major_revision

Abstract
The metal-induced gap states (MIGS) are commonly believed to cause the strong Fermi level pinning (FLP) in the metal-semiconductor contacts. Here, we reveal that the dangling-bond-induced surface states play a crucial role, even comparable with MIGS. The first-principles calculations show that metal-germanium (Ge) and metal-silicon (Si) contacts should possess a similar FLP strength if they adopt an identical interface bonding configuration: the reconstructed bonding configuration renders Si and Ge having pinning factors of 0.16 and 0.11, respectively, and the ideal non-reconstructed bonding configuration gives them pinning factors of 0.05 and 0, respectively. We illustrate that Si favors the reconstructed bonding configuration, and Ge favors the ideal non-reconstructed bonding configuration after metal deposition. The self-passivation of the dangling bonds reduces the interface gap states to give a much weaker FLP in the metal-Si contacts than in the metal-Ge contacts. We also demonstrate that the full passivation of the interface dangling bonds can further increase the pinning factor to 0.5 by further reducing the interface gap states. These findings shed light on alleviating the FLP to lower the contact resistance for Si and emerging materials towards advanced semiconductor technology.

Introduction
With the continued scaling of silicon (Si) complementary metal-oxide-semiconductor (CMOS) technology, the influence of source/drain contact resistance on the performance of metal-oxide-semiconductor field-effect transistors (MOSFETs) has been increasingly significant due to a smaller contact area and is now becoming a major bottleneck for advanced transistor performance scaling1,2. The International Roadmap for Device and Systems (IRDS 2022)3 sets a target for Si contact resistance below 10−9 Ω cm2, a goal that is challenging yet attainable. The challenge is primarily due to the strong Fermi level pinning (FLP) effect that causes a finite Schottky barrier height (SBH) ΦB,n to form at the metal–Si interface. Meanwhile, the continued dimensional scaling of Si transistors also substantially degrades the channel mobility, which poses another great challenge and underscores the urgency to explore high-mobility channel materials, such as germanium (Ge)4, to sustain Moore’s Law. Although Ge possesses superior carrier mobility, as it has the highest hole mobility among all semiconductors, with electron mobility approximately three times higher than in Si4, the pronounced FLP effect at the metal–Ge interfaces5 prevents it from replacing Si for developing advanced low-power transistors. Two-dimensional (2D) semiconductors as channel materials could enable transistors with sub-10 nm gate length while maintaining sufficiently small subthreshold swing and leakage current with body thickness down to one atomic layer, but also suffer from poor source and drain contacts with a considerably large SBH due to the FLP effect6–9. The strength of the FLP for a given semiconductor is usually characterized by a pinning factor S10:

S = dΦB,n / dϕM, (1)

where ϕM is the work function (WF) of the metal in contact. Experiments show that n-type Si has a pinning factor of S = 0.1611,12, whereas n-type Ge possesses S = 0.025,13,14, the strongest FLP among semiconductors, manifesting the Fermi level firmly pinned at about 0.05 eV above the valence band maximum (VBM) and yielding a large constant n-type SBH (0.57 ± 0.07 eV) for the metal–Ge interface, irrespective of the metal in contact15. Given the similarities in both crystal structures and electronic properties between Si and Ge, it is particularly interesting to note that Ge has much stronger pinning than Si, which makes Ge unlikely to replace Si for NMOS channel5,16.

The FLP effect is well recognized as arising from an interface dipole caused by charge redistribution at the metal–semiconductor (MS) interface due to the metal-induced gap states (MIGS), which originate from the penetration of metal Bloch wave functions into the semiconductor band gap17,18. The occupation of the MIGS by electrons from the metal generates charges on the semiconductor surface, accompanied by induced opposing charges with the same amount on the metal surface. This charge redistribution establishes an interface dipole across the MS interface, resulting in a deviation of the metal Fermi level from its anticipated position as predicted by the Schottky–Mott rule19,20 and the pinning of the Fermi level towards a specific energy level, which is usually named the charge-neutrality level (CNL)18,21,22. Based on the electrical double-layer model, the pinning factor S can be expressed as follows:

S = 1 / (1 + e2δit Dit / εit), (2)

where Dit, δit, and εit are the density of interface gap states per unit area, effective distance away from the interface (associated with the decay length of interface states), and effective dielectric constant at the interface region, respectively23. It is straightforward to learn that a higher density of interface gap states Dit gives rise to a smaller S and thus a stronger FLP effect23. The MIGS model also relates the Dit and δit to the magnitude of band gap Eg for a semiconductor11,24, suggesting that Ge with a narrower band gap should exhibit a stronger FLP effect than Si due to higher density and larger decay length of MIGS11. The alleviation of the strong FLP by inserting an ultrathin dielectric insulator layer into the interface between metal and semiconductor (Si and Ge) has further proved the MIGS model, regarding that it can reduce the penetration of MIGS from the metal into the semiconductor13,15,25,26. However, the MIGS model has recently been questioned by both theoretical and experimental observations that show interface structure can strongly modify the SBH and FLP27,28, which are unlikely to be explained in the context of the MIGS model since it regards FLP as purely an intrinsic property of the bulk semiconductor as it relies solely on bulk band gap or dielectric constant without considering the role of the specific structure of the interface. Therefore, the microscopic mechanisms underlying the strong FLP in the MS interfaces remain ambiguous. It prompts us to reconsider whether the difference in the FLP strength between Ge and Si originates from their difference in interfacial bonding structures instead of intrinsic MIGS to explore more feasible ways to overcome the contact resistance challenge for advanced semiconductor technology nodes.

In this work, by performing the first-principles calculations, we show that both Si and Ge have a similar FLP strength if they adopt the same interface bonding structure in contact with metals. Specifically, if a p(2×2) dimer reconstruction interface bonding configuration is adopted, the predicted pining factor S = 0.16 is in excellent agreement with the well-established experimental data of S = 0.16 for n-type metal–Si(001) interfaces11,12. However, this interface bonding configuration also results in metal–Ge (001) interfaces having a pinning factor S = 0.11 that is much larger than the experimental data S = 0.025,13,14. Interestingly, the ideal c(1×1) non-reconstructed interface bonding structure reduces the pinning factor of Ge to S = 0 to reproduce the experimental data well, but it gives rise to the pinning factor of Si dropping to S = 0.05. We show that the self-passivation of the interfacial Si dangling bonds renders the p(2×2) dimer reconstruction to have a smaller density of interface states and, thus, a larger S and a weaker FLP in comparison with the c(1×1) non-reconstructed interface bonding structure. We further illustrate that metal–Si (001) interfaces prefer the p(2×2) dimer reconstruction as expected29,30, but the metal–Ge (001) interfaces prefer the c(1×1) non-reconstructed structure because it gains much less energy from the dimer reconstruction due to a longer bond length. We also demonstrate that we can alleviate the FLP by increasing the pinning factor S to near 0.5 by fully passivating the interface dangling bonds with, e.g., hydrogen atoms for both Si and Ge. Note that the residual effect hindering the approach to the Schottky–Mott limit S = 1 should arise from the MIGS, which is commonly considered as the major factor for FLP. These findings shed light on overcoming the contact resistance for advanced technology nodes and new materials for future transistors.

Results
Schottky barrier height comparison of metal–Si and metal–Ge

It is well documented that the topmost-layer atoms of the clean Si (001) and Ge (001) surfaces will undergo pairing spontaneously, yielding reconstructions in c(2×1), c(4×2), p(2×2), or p(4×1) configurations30,31. The p(2×2) dimer reconstruction surface has the lowest energy at low temperatures32 and arises from the non-reconstructed ideal c(1×1) surface by pairing the topmost-layer atoms along the [110] direction to form alternating buckled asymmetric dimers: one atom of the dimers displaces away from the surface (dimer-up atom), while the other moves inward (dimer-down atom)33,34. Therefore, we calculate the SBHs of the metal–Si and metal–Ge interfaces by considering metal deposition on the CMOS-compatible Si(001) and Ge(001) substrates, which are both in either p(2×2) dimer reconstruction or ideal non-reconstructed c(1×1) surface.

Figure 1 shows the first-principles calculated SBHs against the metal WF with both considered surface configurations, in comparison with the well-established experimental data5,11–14,35–37. For the p(2×2) dimer reconstruction surface, one can see from Fig. 1a that the first-principles calculated SBHs of the metal–Si(001) interfaces are in reasonable agreement with the experimental measurements, considering experimental data exhibiting a large scatter, but it is not true for the metal–Ge(001) interfaces. By fitting the theoretically predicted SBHs as a linear function of metal WF, we obtain a pinning factor S = 0.16, same as the experimentally reported value S = 0.16 for the metal–Si (001) interfaces11,12. The only exception is a slightly vertical shift (<0.1 eV) in energy between two fitted curves, which may arise from the first-principles calculation uncertainties38–40, e.g., the difference of the predicted electron affinity of bulk semiconductors from the experimental data. Fortunately, these uncertainties do not affect our conclusions, which are based on the slope of the SBHs (see Supplementary Table 2 for detailed SBHs). However, for the metal–Ge(001) interfaces with the same p(2×2) dimer reconstruction, the predicted pinning factor S = 0.11 is unexpectedly large (Fig. 1c), which is only 0.05 smaller than that of the metal–Si interfaces and thus is too large to account for the strong FLP (S = 0.02) observed experimentally in the metal–Ge contacts5,13,14. Interestingly, as we change the interface configuration from the p(2×2) dimer reconstruction to the ideal c(1×1) non-reconstructed structure, the first-principles calculations reproduce the experimentally measured pinning factor of the metal–Ge contacts by substantially reducing the predicted pinning factor from S = 0.11 to S = 0 (Fig. 1d). However, the ideal c(1×1) non-reconstructed structure also reduces the pinning factor of the metal–Si interfaces to S = 0.05 (Fig. 1b), indicating that such an interface configuration artificially leads to FLP in Si comparable to that in Ge.

Consequently, we show that the interface atomic bonding configuration plays a crucial role in determining the FLP strength since metal–Ge and metal–Si interfaces have similar FLP strength if they adopt an identical interface configuration. It implies that the metal–Si contacts prefer a reconstruction interface with a weaker FLP (S = 0.16)11,12, and the metal–Ge contacts prefer an ideal non-reconstructed interface with a stronger FLP (S = 0.02)5,13,14. This finding is strikingly in contrast with the common wisdom according to the MIGS models13,17,18, which suggest the FLP strength to be an intrinsic property of bulk semiconductor without the need to consider the detailed atom arrangements at the interface13,18. Evidence has been accumulated that metal deposition may destroy the reconstructed surface structure of the substrate41,42, although both clean Si(001) and Ge (001) surfaces are predicted theoretically30,32 and observed experimentally43 to be stabilized in the p(2×2) dimer reconstruction32. For instance, experiments have shown that Ba adsorption on the (001) Ge surface results in a change from the reconstructed surface to a c(1×1) non-reconstructed surface44. It is worth noting that the small discrepancy between our first-principles calculations and experimental data may arise from the admixture of the c(1×1) non-reconstructed configuration and dimer reconstruction configuration in reality, as well as the limitations of the first-principles calculations.

The role of two types of interface gap states in the FLP effect

We begin by revealing the microscopic mechanism responsible for the effect of interface atomic bonding configurations on the FLP strength before addressing why metal–Si contacts prefer a reconstruction interface but metal–Ge contacts prefer a non-reconstructed interface. To do so, we take Ag as a prototypical metal using an Ag–Ge supercell containing 9 Ag atomic layers and 13 Ge atomic layers in the [001]-direction, as shown in Supplementary Fig. 2, to examine the metal–Ge (001) interface band structure by projecting the electronic states of the Ag–Ge (001) interface onto the topmost Ge layer. The projected density of states (PDOS) is more critical since the density of interface gap states Dit governs the pinning factor S according to Eq. (2).

Figure 2a shows that in the c(1×1) non-reconstructed configuration Dirac-cone-like bands cross at the X-point, which, however, is absent in the p(2×2) dimer reconstruction configuration (Fig. 2b). It causes the total density of the interface states near the Fermi level to get reduced by changing the arrangement of the interfacial Ge atoms from the c(1×1) non-reconstructed configuration to the p(2×2) dimer reconstruction. It should account for a larger pinning factor S and weaker FLP strength observed in the p(2×2) dimer reconstruction interface configuration.

To better understand the FLP mechanism, it is necessary to identify these gap states. From the partial charge distribution of these interface gap states in real space, we can distinguish them either as MIGS17,18 or dangling-bond-induced surface states (DBSS)45. Specifically, MIGS originates from the penetration of metal Bloch wave functions into the semiconductor band gap17,18, resulting in charges distributed across the entire metal region and gradually decaying towards the semiconductor side10. Whereas DBSS emerges from the surface dangling bonds owing to the crystal lattice termination at the surface, and thus, its charges localize predominantly in the interface region and decay towards both sides46. Subsequently, we can identify Dirac-cone-like bands crossing at the X-point in the c(1×1) non-reconstructed configuration as DBSS and derived from the rehybridized pxy states of surface Ge atoms (see the partial charge distribution indicated by A in Fig. 2a and will be discussed below)47,48. We can further ensure the identification of the DBSS in Fig. 2a by referring to the surface states of the bare Ge(001) surface (Supplementary Fig. 6), which possesses nearly identical Dirac-cone-like bands in both the energy dispersion and partial charge distributions. It confirms Dirac-cone-like bands arising from the pxy-states of the surface dangling bonds induced by the semiconductor surface termination.

We also identify some interface gap states, e.g., indicated by B in Fig. 2a, arising from MIGS as expected. Figure 3 schematically shows that when changing from the c(1×1) non-reconstructed configuration to the p(2×2) dimer reconstruction configuration, the in-plane dimerization of the Ge surface dangling bonds will shift most pxy orbital states out of the band gap to below the VBM or above the conduction band maximum (CBM), thereby preventing the formation of Dirac-cone-like bands, as shown in Fig. 2b. Specifically, these rehybridized pxy states (such as indicated by C in Fig. 2b) are predominantly localized within the dimer region and resonate with the Ge bulk states, yielding the surface resonance states45,46. On the other hand, the pz-MIGS orbital states show little energy shifts and remain inside the band gap as changing the interface configuration (such as indicated by B and D). Although both DBSS and MIGS contribute to the total density of the interface gap states Dit for FLP effect, the contribution of the MIGS is unlikely to be changed by altering the interface structures due to it is an intrinsic property of bulk semiconductors. It implies that the engineering of these DBSSs, giving rise to the Dirac-cone-like bands composed of pxy states, is mainly responsible for the reduction of the total density of interface gap states Dit near the Fermi level shown in Fig. 2, and thus a smaller interface dipole potential and a weaker FLP strength by changing the c(1×1) non-reconstructed configuration to the p(2×2) dimer reconstruction interface configuration. This variation is also observed in other Ge–metal interfaces and Si–metal interfaces (see Supplementary Fig. 4), with moderated differences arising from perturbations induced by different metals. Nonetheless, the overall trend of a decrease in the pxy DOS, attributed to the disappearance of the Dirac-cone-like band due to in-plane dimer reconstruction, remains a general phenomenon.

Microscopic mechanism governing interface states evolution

We now turn to explain the formation and change of DBSS in terms of atomic orbitals, using schematic diagrams as shown in Fig. 3. The ideal c(1×1) non-reconstructed (001) surface results from cleaving along the (001) plane of the cubic unit cell of the diamond structure, leaving two dangling bonds for each surface atom and one valence electron in each dangling bond. For each surface atom, two sp3 hybrid orbitals from two dangling bonds will rehybridize into one pxy and one spz states. The energy level of the rehybridized pxy state rises from the sp3 level to the atomic level of the outermost p-orbitals (3p in Si and 4p in Ge), and the rehybridized spz state goes down to the average of the outermost s- and p-orbital atomic levels, respectively. Then, the two valence electrons owned by the two dangling bonds in each surface atom transfer to the lower-lying rehybridized spz state to make it fully occupied and leave the higher-lying rehybridized pxy state completely empty, as shown in Fig. 3a. The higher-lying rehybridized pxy states from two adjacent surface atoms will couple together to give rise to the bonding σ and antibonding σ* states by shifting upward and downward in their energy levels. The periodic potential perturbation within the (001) plane further broadens these discrete σ pxy and σ* pxy energy levels into Dirac-cone-like bands for the bare Ge(001) surface (and similarly for the bare Si(001) surface, as shown in Supplementary Figs. 5 and 6)47. In contrast, Supplementary Fig. 5 shows that the energy band of the rehybridized pz surface states exhibits negligible dispersion due to its much weaker coupling between adjacent pz orbitals within the (001) plane.

When two adjacent surface atoms come closer to each other along the [110] direction to form a dimer as a result of the transition from the c(1×1) non-reconstructed structure to the p(2×2) dimer reconstruction, as shown in Fig. 3b, their rehybridized pxy states overlap end to end and develop into the σ bonding and σ* antibonding states, opening energy gap at the X-point for the Dirac-cone-like bands and moving from the central band gap to below the VBM or above the CBM of the bulk semiconductor. At the same time, their low-lying rehybridized spz states overlap to form π bonding and π* antibonding states, but with less energy shift. Note that the surface dimers would further tilt to have an asymmetric dimer structure with one atom up and another atom down, rendering the rehybridized spz state of the dimer-down atom to have more pz character29. The valence electrons that occupy the lower-lying rehybridized spz state in the c(1×1) non-reconstructed structure transfer to the even lower σ and π bonding states, which further lowers the surface energy of the p(2×2) dimer reconstruction and thus explains why both clean Si(001) and Ge(001) surfaces are stabilized in the p(2×2) reconstruction at T = 0 K32. More details are given in Supplementary Fig. 5. The energy shift caused by the dimerization of surface dangling bonds reduces the interface gap states to alleviate the FLP effect in the p(2×2) dimer reconstruction configuration, yielding a self-passivation effect of the surface dangling bonds.

The energy gain from the p(2×2) dimer reconstruction on the (001) surface is governed by the energy level separation between the bonding and antibonding states of the dimer, which is inversely proportional to the square of the dimer bond length49 or the lattice constant of bulk semiconductors. Because the lattice constant of Ge is 4.3% larger than that of Si, energy gain from the dimer reconstruction on the Ge(001) surface is less than that on the Si(001) surface, as shown schematically in Fig. 3b. This argument is supported by the reduced surface reconstruction energy, which shows that the dimer formation energy is 1.24 eV per dimer for Ge and 1.77 eV per dimer for Si according to our first-principles calculations. Thus, the p(2×2) dimer reconstruction is expected to be less stable in Ge than in Si, consistent with previous studies29,50,51. Specifically, weaker dimer bonding on the reconstructed Ge(001) surface has been confirmed by measurements of the dimer bond length and bonding strength29, manifesting that dimer bonds in Ge exhibit nearly single-bond character, while those in Si exhibit partial double-bond character. Subsequently, on the Ge(001) surface, metal deposition is more likely to perturb the σ bonding state, shifting it above the π* anti-bonding state (see Fig. 3b and Supplementary Fig. 5e–h). This energy level reversal would result in no energy gain from dimerization, potentially causing the Ge(001) surface to revert to the ideal c(1×1) non-reconstructed configuration. To further explore this behavior, we perform ab initio molecular dynamics simulations at 300 K to investigate the evolution of the interface atomic structure. The result in Supplementary Fig. 7 show that the fluctuations in the dimer bond lengths at the p(2×2) dimer reconstruction Ag–Ge(001) interface gradually increase over time, indicating a progressive weakening of the dimer bonds, whereas it remains relatively stable over time in the Ag–Si (001) interface. Although the simulation timescale is limited to ~7000 fs (~7 ps) and only captures the initial stages of bond fluctuation after the structure is allowed to relax at 300 K, the pronounced differences suggest that Ge dimers in the metal–Ge(001) interfaces are less stable compared to Si dimers in the metal–Si (001) interfaces. Therefore, both thermodynamic and kinetic results confirm that metal–Si interfaces favor the p(2×2) interface reconstruction, while the metal–Ge interfaces tend toward the c(1×1) non-reconstructed structure.

To broaden the scope of our study, we also extend our investigation to diamond (C), another group IV semiconductor with an ultrawide bandgap of Eg = 5.4 eV. Both theoretical calculations (see Supplementary Note 2) and experimental measurements show that a large pinning factor of S ~ 0.3552,53 arises from the self-passivation effect by the reconstruction in the C (001) surface, since diamond bond length is 34% shorter than Si bond length and thus the C(001) surface is better-preserved in dimer reconstruction after metal deposition29,50. Otherwise, our first-principles results show that the metal–C (001) interfaces have a much smaller pinning factor of S ~ 0.14 using the c(1×1) non-reconstructed configuration (see Supplementary Fig. 9 and Supplementary Table 3). We note that from Ge, Si, to C, the first-principles calculations predicted pinning factor S increases from 0.0 to 0.05 to 0.14 using the c(1×1) non-reconstructed configuration, and increases from 0.11 to 0.16 to 0.31 using the p(2×2) dimer reconstruction. Such an increase is inversely proportional to the magnitude of the band gap, which is because the density of interface gap states Dit given in Eq. (2) is inversely proportional to Eg.

The full passivation of the dangling bonds

We have illustrated that the dimerization-induced self-passivation of the surface dangling bonds is a key factor in reducing the interface gap states to alleviate the FLP in metal–Si interfaces relative to metal–Ge interfaces. Considering the surface dangling bonds have not yet been fully passivated even in the p(2×2) interface reconstruction, as shown in Fig. 2b, we postulate that we can further alleviate the FLP by improving the passivation of the surface dangling bonds using, e.g., hydrogen (H) atoms, which have been successfully used to shift all surface states out from the band gap on bare Si and Ge surfaces54,55. To validate this postulation, we terminate each surface dangling bond by a H atom using a bond length of 1.51 Å for the Si–H bond and 1.56 Å for the Ge–H bond, a configuration found to be stable by Northrup56. Figure 4a shows that the H-passivation increases the pinning factor S from 0.16 to 0.5 for the metal–Si interfaces, accompanied by a reduction in the interface gap states, as shown in Supplementary Fig. 8. This is also true for the metal–Ge interfaces as the pinning factor S increased from 0.11 to 0.45, as shown in Fig. 4b. Consequently, we have explicitly demonstrated the critical role of the DBSS on the FLP in MS interfaces. Considering the pinning factor increases up to 0.5 for the metal–Si interfaces by eliminating almost all the interface gap states arising from the dangling bonds, the residual effect hindering the approach of the Schottky–Mott limit S = 1 should arise from MIGS, which is commonly regarded as the prime factor for FLP.

Note that although S = 0.5 is still far from the Schottky–Mott limit S = 1, it enables us to have a better SBH tunability to overcome the challenge of contact resistance in advanced technology nodes2. For instance, after full dangling bonds passivation, we can now use the low-work-function metals (e.g., Ti, Ta, Mg, Ag, Cu, as shown in Fig. 4) to achieve near-zero N-SBH for n-type Si and Ge, minimizing contact resistance. Optimizing both non-metallic atom passivation for DBSS elimination and compatible low-work-function metals is key for future high-performance, CMOS-compatible transistors.

Methods
We constructed (001)-oriented metal–Si(Ge) interface comprising 13 atomic layers of Si (Ge) and 9 layers of metals. We considered c(1×1) non-reconstructed and the p(2×2) dimer reconstruction configuration, as well as the 2×1 monohydride H-passivated surface; the preferred interface bonding structures of each type of interface are provided in Supplementary Figs. 1 and 2. We kept the lateral lattice parameters of Si (Ge) slabs fixed to their calculated equilibrium bulk constants, and rotated metal lattices and applied lateral strain to match the lattice parameters of Si (Ge) slabs. The corresponding strained-metal work functions used in the analysis were recalculated (see Supplementary Table 1 and Supplementary Note 1).

We performed density-functional theory (DFT) calculations using the PWmat plane-wave package71 with norm-conserving pseudopotentials (NCPP). The plane-wave cutoff energies were 50 Ry for electronic structure calculation and 70 Ry for structure relaxations. Geometries were optimized using the PBE functional. To mitigate the band gap underestimation in DFT calculation, we employed the HSE06 hybrid functional72,73 for band gap corrections. In bulk HSE calculations, we used a 10×10×10 Monkhorst–Pack grid and adjusted the mixing coefficient a to reproduce experimental band gaps (For Si, when a = 0.25, Eg = 1.17 eV and for Ge, when a = 0.18, Eg = 0.67 eV). For supercell calculations, considering the computational cost of HSE functional calculation, we used a 4×4×1 k-point grid in the self-consistent calculations, 10×10×1 k-point grid in the non-self-consistent calculations for density of states analysis. Band structures were obtained with a denser sampling along high-symmetry paths, as shown in Supplementary Fig. 3.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This paper provides a thorough and innovative analysis of the impact of source/drain contact resistance on MOSFET performance, particularly focusing on the Fermi level pinning (FLP) effect at the metal-semiconductor interface. The authors use first-principles calculations to demonstrate that Si and Ge exhibit similar FLP strengths when adopting the same interfacial bonding structure, challenging traditional models like MIGS. Overall, the study is methodologically sound, offers new insights into the role of interface structure in FLP, and has strong academic and practical relevance, making it a valuable contribution to the field. I recommend accepting the paper after major revisions.\n1.The first-principles calculations show discrepancies between the predicted and experimentally observed pinning factors for metal-Ge interfaces, especially when using the p(2×2) dimer reconstruction. How do the authors account for these discrepancies in their theoretical model, and what are the potential factors that could explain the difference between theoretical predictions and experimental observations for metal-Ge contacts?\n2.The study identifies two types of interface gap states: metal-induced gap states (MIGS) and dangling-bond-induced surface states (DBSS). How do the authors assess the relative contributions of MIGS and DBSS to the overall FLP effect at the metal-Ge interface, and how might this influence device performance?\n3.In the section \"The microscopic mechanism of different Fermi level pinning strengths,\" the calculations suggest a shift in the behavior of pxy orbital states due to surface dimerization in the p(2×2) reconstruction. Could the authors elaborate on how these findings might influence the design of future metal-semiconductor interfaces, particularly in terms of interface passivation strategies?\n4.The authors suggest that hydrogen passivation of dangling bonds significantly reduces interface gap states. How might the effectiveness of hydrogen passivation compare with other passivation techniques.\n5.In the molecular dynamics simulations, the fluctuations in the dimer bond lengths were observed at the Ag/Ge interface. Can the authors provide more details on the timescale of these fluctuations and how they might influence the long-term stability of the interface?\n6.How can the insights from this study guide the selection of materials for future high-performance transistors, particularly when considering metal-Si and metal-Ge interface compatibility?", "reviewer_2": "The electronic structures of the c(1×1) and p(2×2) surfaces on Si(100) and Ge(100), as well as the interfacial electronic structures formed with various metals, were evaluated using first-principles calculations, and this type of systematic study has not been reported. Although this study may not have a significant impact, it is fundamentally valuable.\nOn the other hand, some key conclusions in this paper appear to involve logical leaps. The authors evaluate the validity of the interface structural models based on the FLP strength (S factor), comparing it with experimentally reported correlations between a metal’s work function and the Schottky barrier height (SBH), as shown in Fig. 1. They then make two main conclusions:\n1. Due to the quantitative similarity between experimental (Refs. 5, 11, 12, 14, 15) and calculated S factors, the metal/semiconductor interface structures are likely to be p(2×2) for Si(100) and c(1×1) for Ge(100).\n2. Consequently, the dominant origin of strong FLP at these interfaces is attributed to interface states of bond structures.\nHowever, carefully considering the experimental results reported so far, it is not straightforward to conclude that FLP in Si(100) and Ge(100) is primarily governed by p(2×2) or c(1×1) structures, which serve as the basis for conclusions 1 and 2.\nMetal/Ge(100) interfaces:\n- In Reference 5, the Ge(100) surface before metal deposition exhibits (2×1) surface reconstruction.\n- In References 14 and 15, the Ge(100) surface undergoes HF cleaning before metal deposition. In this study, the Ge surface may be hydrogen-terminated, which is reported to weaken FLP in this work.\n- Another study (Ref. 16) reports an S factor of 0.17 for germanide metal/Ge(100) interfaces, which exceeds the calculated value of 0.11 for p(2×2) in this study. Additionally, Bi exhibits behavior that deviates from strong FLP trends.\nMetal/Si(100) interfaces:\n- In both References 11 and 12, the metal/Si interface is formed on the Si(111) surface.\nGiven that (1) the calculation results in this study may not accurately represent the interface structure in Ge, (2) germanide and Bi may exhibit different characteristics at the Ge(100) interface, and (3) the experimental conditions for the Si interface differ from the assumptions in this study, it is difficult to strongly support the conclusions (1 and 2) presented in this paper.", "reviewer_3": "The study proposes that interface states induced by dangling bonds, in addition to MIGS, play a significant role in Fermi level pinning. It demonstrates that metal-Si and metal-Ge contacts exhibit different Fermi level pinning (FLP) strengths due to their preferred bonding configurations. Hydrogen passivation of dangling bonds reduces interface gap states and significantly weakens FLP, providing a potential strategy for lowering contact resistance in advanced semiconductor technologies. However, while these results and analyses are quite interesting, they do not yet meet the level of innovation and scope required for Nature Communications due to the following concerns:\n1) The paper introduces the novel concept of dangling bond-induced interface states. However, a deeper analysis of the role of dangling bonds is needed to fully substantiate the novelty of this study.\n2) The Fermi level pinning is still relatively high. The authors suggest that, given the importance of dangling bonds, complete passivation can significantly alleviate Fermi level pinning and reduce contact resistance. However, after complete passivation, the pinning factor only improves to 0.5, which is insufficient. The authors should explore other techniques or provide additional methods to further reduce Fermi level pinning.\n3) The study only considers two specific cases, Si and Ge, raising questions about the generalizability to other materials with different surface reconstruction mechanisms. A more comprehensive investigation is needed to strengthen the conclusions drawn here.\n4) Both MIGS and dangling bond-induced interface states play critical roles in metal-semiconductor contacts. The relationship between these states in determining FLP strength should be further discussed to help readers better understand the underlying mechanism.\n5) The authors identify Dirac-cone-like bands crossing at the X-point in the c(1×1) non-reconstructed configuration as dangling bond states (DBSS). However, the rationale for this identification is not sufficiently justified, and further evidence is needed.\n6) The authors present the interface band structure of the Ag-Ge interface in Fig. 2. It remains unclear whether this mechanism is applicable to other metals, and further exploration is needed."}, "author_response": "Comment #1: The first-principles calculations show discrepancies between the predicted and\nexperimentally observed pinning factors for metal-Ge interfaces, especially when using the p(2\n×2) dimer reconstruction. How do the authors account for these discrepancies in their theoretical\nmodel, and what are the potential factors that could explain the difference between theoretical\npredictions and experimental observations for metal-Ge contacts?\nAuthor Response: The large discrepancy in pinning factors S between experimental observations\n(S = 0.02) and our first-principles calculations (S = 0.11) using the p(2×2) dimer reconstruction\nconfiguration is mainly caused by the distinct interface structures because we have revealed that\nmetal-Ge (100) interfaces favor the c(1×1) non-reconstructed configuration in experimental\nmeasurements. If we change the interface structure of the metal-Ge (100) interfaces to the c(1×1)\nnon-reconstructed configuration, our theoretically predicted S reduces to 0, which is in excellent\nagreement with experimental data of S=0.02. The dimerization of the surface Ge dangling bonds\nshifts partial interface states derived from p orbitals out of the bandgap to below the VBM or above\nxy\nthe CBM in the p(2×2) dimer reconstruction configuration and thus reduces the interface gap states,\nwhich in turn alleviates the Fermi level pinning (FLP) and thus increases pinning factor S from 0 to\n0.11. We call this effect self-passivation. From this understanding, we then propose that we can\nfurther alleviate FLP to increase S by fully passivating the Ge surface dangling bonds. Indeed, we\nshow that the hydrogen passivation of the Ge surface dangling bonds raises the pinning factor S to\n0.45 for the metal-Ge (100) interfaces. Considering the pinning factor increases up to 0.45 by\neliminating almost all the interface gap states arising from the dangling bonds, the residual effect\nhindering the approaching of the Schottky-Mott limit S =1 should arise from MIGS, which is\ncommonly regarded as the prime factor for FLP.\nInterestingly, such a discrepancy in pinning factors S also exists in metal-Si (100) interfaces when\nwe adopt a different c(1×1) non-reconstructed configuration in our calculations from the\nexperimentally favored p(2×2) dimer reconstruction configuration. We show that in both metal-Si\n(100) and metal-Ge (100) interfaces, the c(1×1) non-reconstructed configuration gives rise to an\nextremely strong FLP with very small S (0.05 for the former and 0.0 for the latter). The p(2×2)\ndimer reconstruction configuration raises S to 0.16 and 0.11, respectively, resulting from a\nremarkable reduction of interface gap states by self-passivation due to the dimerization of surface\ndangling bonds. We note that both Si (100) and Ge (100) bare surfaces (without metal in contact)\nundergo a reconstruction spontaneously to lower the surface energy, which has been widely\nobserved in experiments [e.g., Phys. Rev. B 51, 14504 (1995); Phys. Rev. B 32, 2344 (1985)].\nHowever, it is also well documented that metal deposition may destroy the reconstructed surface\nstructure of the Si or Ge substrate [Phys. Rev. B 66, 155339 (2002); Phys. Rev. B 70, 085312 (2004)].\nWe illustrate that the energy gained from the dimerization of surface dangling bonds is much larger\nin the Si(100) surface than that in the Ge(100) surface, since it is inversely proportional to the square\nof the bond length and Si bond length is 4.3% larger than Ge bond length. Therefore, the dimers in\nthe Ge(100) surface are more likely to be broken with respect to the Si(100) surface due to less\nenergy gained from dimerization in the surface reconstruction. Subsequently, we can safely draw\n1\nthe conclusion that in experimental measurements, real metal-Ge (100) interfaces favor the c(1×1)\nnon-reconstructed surface, and real metal-Si(100) interfaces favor the p(2×2) dimer reconstruction\nsurface.\nBesides the large discrepancy caused by different interface configurations, we also note that in Fig.\n1(d), the calculated pinning factor (S = 0) adopted the c(1×1) non-reconstructed configuration is\nstill slightly smaller than the experimental one (S = 0.02) for metal-Ge(100) interfaces, which we\ndid not give a detailed explanation in our original manuscript. In addition to the accuracy of the\nfirst-principles calculations, another potential reason is that the actual metal-Ge interfaces may not\nnecessarily be strictly the c(1×1) non-reconstructed configuration, as they may sustain a part of\nunresolved dimers after metal deposition, which will make the S factor slightly larger.\nWe have now added the following text in the revised manuscript to make these points stand out\nmore clearly in the Results section, page 7.\n“It is worth noting that the small discrepancy between our first-principles calculations and\nexperimental data may arise from the admixture of the c(1×1) non-reconstructed configuration and\ndimer reconstruction configuration in reality as well as the limitations of the first-principles\ncalculations.”\nComment #2: The study identifies two types of interface gap states: metal-induced gap\nstates (MIGS) and dangling-bond-induced surface states (DBSS). How do the authors\nassess the relative contributions of MIGS and DBSS to the overall FLP effect at the metal-\nGe interface, and how might this influence device performance?\nAuthor Response: In this work, we have demonstrated that the pinning factor S is increased from\n0.0 (0.05) to 0.11 (0.16) by changing the interface structure from c(1×1) non-reconstructed\nconfiguration to p(2×2) dimer reconstructed configuration for metal-Ge(100) (metal-Si(100))\ninterfaces. On the other hand, MIGS is an intrinsic property of semiconductors, and its contribution\nto Fermi level pinning by reducing the pinning factor S cannot be changed by modifying the metal-\nsemiconductor interface structures. Thus, the increase in S should be exclusively caused by the\nreduction of the DBSS interface gap states due to the self-passivation of the interface dangling bonds\nduring dimerization. We also show that we can further increase the pinning factor S to 0.45 (0.5) by\nfully passivating the dangling bonds to eliminate all DBSS using one hydrogen atom for each\ndangling bond. Considering the pinning factor only increases to 0.45 by almost eliminating the\ninterface gap states arising from the dangling bonds, the residual effect hindering the approaching\nof the Schottky-Mott limit S = 1 should arise from the MIGS. Therefore, we evaluate the\ncontributions of DBSS and MIGS to the overall FLP effect to be roughly equal.\nThis understanding offers a new way to overcome the challenge of contact resistance issues for both\nSi transistors and Ge transistors. Based on the common thought that the strong FLP in Ge and Si\narises entirely from MIGS, an approach of inserting an ultrathin insulator oxide layer into the metal-\nsemiconductor interface has been developed to alleviate the FLP by pushing the MIGS away from\nthe semiconductor interface. However, the experimentally obtained contact resistance is still orders\n2\nof magnitude higher than the theoretical prediction for the ultrathin inserting oxide layer approach\ndue to the inappropriate band alignment, which may introduce an additional tunneling layer by\ninserting such an ultrathin wide bandgap oxide layer [Appl. Phys. Lett. 101, 042108 (2012);\nElectronics 11, 2419 (2022)]. Furthermore, such an approach also adds complexity for the\ncompatibility with the gate-all-around field effect transistor (GAAFET) technology. The finding of\nDBSS contributing almost equally to FLP as MIGS in metal-Ge and metal-Si interfaces sheds new\nlight on why metal-Ge interfaces have much stronger FLP than metal-Si interfaces and offers new\nmethods to alleviate the FLP by passivating the interface dangling bonds. It remarkably broadens\nour choice of metals and passivating ligands to achieve a zero Schottky barrier height (SBH) for\nboth metal-Si(100) and metal-Ge(100) interfaces, which will substantially improve the device\nperformance of Si transistors and even overcome the limits of integration of high mobility Ge\ntransistors.\nTo make it clearer, we have revised the manuscript to more explicitly highlight the estimated\ncontributions of MIGS and DBSS and the implications of this finding for device performance in the\nDiscussion section, page 18:\n“Since MIGS is an intrinsic property of semiconductors and its contribution to S cannot be altered\nby hydrogen-passivation, we can roughly suppose that the increase of S from near 0 to around 0.5\nby hydrogen passivation for both Si and Ge is due to the elimination of DBSSs, while the remaining\nfactor to hinder the approach of the Schottky-Mott limit S = 1 is due to residual MIGS. This finding\noffers new ways to improve device performance, particularly for Ge transistors, by alleviating FLP\nstrength. For instance, after modulating the interface atomic structure configuration, the large\ncontribution of DBSS to FLP strength can be reduced without increasing the tunneling resistance\nand adding complexity to the next generation gate-all-around field effect transistor (GAAFET)\ntechnology; these two factors are usually suffered by the state-of-the-art approach of inserting an\nultrathin insulator oxide layer into the metal-semiconductor interface to alleviate the FLP 15,78.”\nComment #3: In the section “The microscopic mechanism of different Fermi level pinning\nstrengths”, the calculations suggest a shift in the behavior of pxy orbital states due to surface\ndimerization in the p(2×2) reconstruction. Could the authors elaborate on how these findings\nmight influence the design of future metal-semiconductor interfaces, particularly in terms of\ninterface passivation strategies?\nAuthor Response: The FLP effect is well recognized as arising from an interface dipole caused by\ncharge redistribution at the metal-semiconductor (MS) interface due to the interface states inside the\nsemiconductor bandgap. We can reduce the interface dipole to alleviate the FLP strength by either\neliminating the interface states or shifting these interface states out of the bandgap to lower the\ncharge redistribution. The former way is manifesting in the approach of inserting an ultrathin\ninsulator oxide layer into the metal-semiconductor interface to alleviate the FLP by pushing the\nMIGS away from the semiconductor interface. The latter way to alleviate the FLP is achieved by\npassivating interface dangling bonds, which does not eliminate the states but shifts their energy.\nWe show that changing the interface structure from the c(1×1) non-reconstructed configuration to the\n3\np(2×2) dimer reconstruction, the dimerization of the surface dangling bonds shifts the 𝑝 orbital\n𝑥𝑦\nstates out of the bandgap, which reduces the density of the interface gap states to partially alleviate\nthe FLP by increasing S from 0.0 to 0.11 for metal-Ge (100) interfaces and increasing S from 0.05\nto 0.16 for metal-Si (100) interfaces. We call this effect self-passivation.\nLearn from the self-passivation, we also propose that we can further enhance S by fully passivating\nthe surface dangling bonds. Indeed, we show that using one hydrogen atom for each dangling bond\nof Ge surface raises the pinning factor S to 0.5 for the metal-Si interfaces and to 0.45 for the metal-\nGe interfaces. Considering the pinning factor only increases to 0.45 by almost eliminating the\ninterface gap states arising from the dangling bonds, the residual effect hindering the approaching\nof the Schottky-Mott limit S =1 should arise from the MIGS. More importantly, we show that metals\nwith lower work functions, such as Mg, Ag, Cu, Ta, and Ti, can achieve near-zero SBH for both n-\ntype Si and Ge (as shown in Fig. 4) to meet the requirement of low contact resistivity for future\nhigh-performance transistors. Specifically, this approach overcomes the challenge of large\nsource/drain contact resistance for using high mobility Ge to replace Si for further high-performance\ntransistors.\nWe have discussed the influence of self-passivation for interface design learned from the shift in the\nbehavior of p orbital states in the Discussion section, page 18:\nxy\n“Crucially, the design principle governing hydrogen passivation, which achieves DBSS elimination\nthrough strong σ-bonding, also extends to other non-metallic atoms. Halogen (e.g., Cl) and\nchalcogen (e.g., S) atoms have also been reported to be capable of strongly binding to Si and Ge\ndangling bonds in experiment 79,80, and should also show notable passivation effectiveness.”\nAdditionally, our new results reveal an alternative method to shift DBSS out of the mid-gap region\nand thereby alleviate the FLP: increase the material’s ionicity. We found that greater ionicity in a\nsemiconductor can fundamentally influence the formation process of DBSS itself. Please refer to\nour response to Reviewer#3 comment#17, for the complete additional results. Here we present only\nthe design principle we have developed for alleviating FLP by selectively moving DBSS out of the\nband gap, as discussed in the Discussion section, page 16-17:\n“Overall, these findings point to a stepwise design principle for interface engineering to alleviate\nFLP by selectively modifying DBSS, including (1) self-passivation, such as in-plane dimerization,\nwhich shifts DBSS away from the mid-gap; (2) extrinsic full-passivation through strong bonding\nwith non-metallic atoms, further reducing DBSS within the gap; and (3) fundamental suppression\nof DBSS formation by increasing the material’s ionicity.”\nComment #4: The authors suggest that hydrogen passivation of dangling bonds significantly\nreduces interface gap states. How might the effectiveness of hydrogen passivation compare with\nother passivation techniques?\nAuthor Response: We agree with the reviewer that hydrogen is only one of the passivation ligands\nthat could be used for passivating Si and Ge dangling bonds. In this work, we take hydrogen as an\nexample to demonstrate the concept to alleviate the FLP by controlling the passivation of interface\n4\ndangling bonds. Actually, we have also investigated other passivation techniques and compared their\neffectiveness. We found that halogen (e.g., Cl) and chalcogen (e.g., S) atoms can effectively bond\nto the sp - and p - dangling bonds on Si and Ge surfaces, demonstrating the effectiveness for\nz xy\npassivating dangling bonds as reported in some experiments [Appl. Surf. Sci. 462, 8-17 (2018), Proc.\nIEEE PVSC 47, 1167–1170 (2020)]. Nonetheless, achieving a robust passivation demands not only\nthe capability to eliminate the DBSS but also operational stability [Jpn. J. Appl. Phys. 51 (2012), J.\nAppl. Phys. 98, 023503 (2015), Solid State Phenom. 134, 33–36 (2007)], which is influenced by\nthermodynamic and kinetic factors under varied preparation conditions [Appl. Phys. Rev. 1, 011304\n(2014)]. Considering this, we find that halogen and chalcogen atoms show better passivation\neffectiveness than hydrogen atoms, as the latter often suffer from instability issue in Ge and Si\nsurfaces [J. Appl. Phys. 98, 023503 (2015); Solid State Phenomena 134, 33 (2007); J. Chem. Phys\n102, 7222-7228 (1995)]. Beyond such direct-atom passivation, organic molecular layers have also\nbeen explored, although their passivation effectiveness tends to be limited by weaker bonding\ninteractions at the dangling bonds and the potential instability problem [Langmuir 20, 1539–1542\n(2004), J. Phys. Chem. B 109, 11263–11272 (2005)]. Alternatively, inserting an insulator layer may\noffer relatively better chemical robustness [Appl. Phys. Lett. 100 (2012)], yet often at the cost of\nincreased tunneling resistance [Electronics 11, 2419 (2022), Appl. Phys. Lett. 101, 042108 (2012)]\nand less versatile passivation of all DBSS sites [Phys. Rev. B 94, 035421 (2016)].\nWe have expanded our discussion on other passivation techniques in the revised manuscript in the\nDiscussion section, page 18:\n“Crucially, the design principle governing hydrogen passivation, which achieves DBSS elimination\nthrough strong σ-bonding, also extends to other non-metallic atoms. Halogen (e.g., Cl) and\nchalcogen (e.g., S) atoms have also been reported to be capable of strongly binding to Si and Ge\ndangling bonds in experiment 79,80, and should also show notable passivation effectiveness. From a\ndevice integration perspective, at typical CMOS processing temperature (>400 ℃), hydrogen\npassivation is thermally unstable on both Si and Ge 81,82, whereas Cl and S passivation provide\nmuch better stability and effective interface states suppression 79, which might be better choices for\nDBSS passivation. Therefore, balancing DBSS passivation, interface stability, and minimal impact\non electrical transport remains a key challenge for future interface engineering studies.”\nComment #5: In the molecular dynamics simulations, the fluctuations in the dimer bond lengths\nwere observed at the Ag/Ge interface. Can the authors provide more details on the timescale of\nthese fluctuations and how they might influence the long-term stability of the interface?\nA uthor Response: In our original manuscript, the timescale of our MD simulation under 300K was\nle ss than 103 fs (1 ps). This timescale covers only the very initial stage of bond fluctuation processes\nand is unlikely to fully capture the long-term interfacial dynamic behavior in real devices since it\ntypically spans microseconds to even seconds under real operating conditions.\nTo further substantiate our previous observations and exclude the possibility of non-physical\nartifacts such as numerical noise causing spurious instantaneous fluctuations, we have extended our\n5\nsimulation time from 400 fs to 7000 fs (see Fig. SM-7) to assess whether the observed trends in\ndimer bond length fluctuations persist over a longer timescale. The results indeed reveal more\npronounced differences in dimer bond length fluctuations. For the Ag-Si interface, although certain\ndimers exhibit significant bond-length fluctuations in the early stage, the system eventually\nstabilizes over longer simulation times, demonstrating the inherent robustness of the metal-Si\ninterface structure. Whereas the Ag-Ge interface exhibits sustained and amplified bond-length\nfluctuations over the whole simulation timescale. This behavior highlights a progressive weakening\nand pronounced instability of the Ge interface under extended simulation times.\nAlthough such an extended timescale is still rather short compared to the timescale required to\ncapture real device phenomena, our results clearly highlight the inherent difference in the stability\nof Si-metal and Ge-metal interfaces. These findings suggest that the observed stability differences\nare intrinsic to the systems and will likely become more pronounced over longer timescales.\nSpecifically, the Ge dimer bonds are far more susceptible to continued fluctuation and eventual\ndestabilization than their Si counterparts, raising challenges for maintaining the long-term stability\nof Ge-based interface systems.\nWe have now added the following text to the Results section, page 13:\n“Although the simulation timescale is limited to approximately 7000 fs (~7 ps) and only captures\nthe initial stages of bond fluctuation after the structure allowed to relax at 300 K, the pronounced\ndifferences suggest that Ge dimers in the metal-Ge (001) interfaces are less stable compared to Si\ndimers in the metal-Si (001) interfaces.”\nFig. SM-7. Time evolution of the dimer bond lengths under molecular dynamics\nsimulations at 300K. Simulations were performed with a supercell expansion to a p(4×2)\nsurface structure, where each unit cell contains four dimers in both (a) Ag-Si (001) interface\nand (b) Ag-Ge (001) interface. The higher dashed lines indicate the equilibrium distances at 0K\nbetween adjacent surface atoms along the [110] direction in the non-reconstructed configuration,\nwhile the lower dashed lines represent the equilibrium dimer bond lengths at 0K in the\nreconstructed configuration.\nhigh-performance transistors, particularly when considering metal-Si and metal-Ge interface\ncompatibility?\nAuthor Response: In this work, we uncover the reason why Ge has a much stronger FLP effect\nthan Si: metal-Ge interfaces are stabilized in the c(1×1) non-reconstructed configuration rather than\nin the reconstructed configuration seen in the metal-Si interfaces. We show that the pinning factor\nS in the metal-Si interfaces will also drop to 0.05 if we use the same non-reconstructed configuration\nas in the metal-Ge interfaces. We illustrate that the larger S in the reconstructed configuration arises\nfrom the reduction of the DBSS interface gap states by the self-passivation of the interface dangling\nbonds due to their dimerization. We can further increase the pinning factor S to 0.5 for the metal-Si\ninterfaces and to 0.45 for the metal-Ge interfaces by fully passivating the dangling bonds to\neliminate all DBSS, e.g., using one hydrogen atom for each dangling bond. Subsequently, metals\nwith lower work functions, such as Mg, Ag, Cu, Ta, and Ti, can achieve a near-zero SBH for both\nn-type Si and Ge (as shown in Fig. 4) to meet the requirement of low contact resistivity for future\nhigh-performance transistors. Specifically, this approach overcomes the challenge of large\nsource/drain contact resistance for using high mobility Ge to replace Si for further high-performance\ntransistors.\nWe have expanded our discussion on the selection of materials compatible with modern Si CMOS\ntechnology in the Results section, page 14:\n“Note that although S = 0.5 is still way from the Schottky-Mott limit S =1, it enables us to have a\nsubstantial SBH tunability to overcome the challenge of contact resistance in advanced technology\nnodes 2. For instance, after full dangling bonds passivation, we can now use the low-work-function\nmetals (e.g., Ti, Ta, Mg, Ag, Cu, as shown in Fig. 4) to achieve near-zero Schottky barrier heights\nfor n-type Si and Ge, minimizing contact resistance. Optimizing both non-metallic atom passivation\nfor DBSS elimination and compatible low-work-function metals is key for future high-performance,\nCMOS-compatible transistors.”\nBesides, we have added discussion about compatibility with Si CMOS technology in the Discussion\nsection, page 18:\n“From a device integration perspective, at typical CMOS processing temperature (>400 ℃),\nhydrogen passivation is thermally unstable on both Si and Ge 81,82, whereas Cl and S passivation\nprovide much better stability and effective interface states suppression 79, which might be better\nchoices for DBSS passivation. Therefore, balancing DBSS passivation, interface stability, and\nminimal impact on electrical transport remains a key challenge for future interface engineering\nstudies.”\nComment #7: The electronic structures of the c(1×1) and p(2×2) surfaces on Si(100) and\nGe(100), as well as the interfacial electronic structures formed with various metals, were\nevaluated using first-principles calculations, and this type of systematic study has not been\nreported. Although this study may not have a significant impact, it is fundamentally valuable.\nAuthor Response: Thank you for your appreciation of our work. To address the helpful comments\nraised by the reviewer, we have highlighted the impact of our work more clearly in the revised\nmanuscript.\nComment #8: On the other hand, some key conclusions in this paper appear to involve logical\nleaps. The authors evaluate the validity of the interface structural models based on the FLP\nstrength (S factor), comparing it with experimentally reported correlations between a metal’s\nwork function and the Schottky barrier height (SBH), as shown in Fig. 1. They then make two\nmain conclusions:\n1. Due to the quantitative similarity between experimental (Refs. 5, 11, 12, 14, 15) and\ncalculated S factors, the metal/semiconductor interface structures are likely to be p(2×2) for\nSi(100) and c(1×1) for Ge(100).\n2. Consequently, the dominant origin of strong FLP at these interfaces is attributed to interface\nstates of bond structures.\nHowever, carefully considering the experimental results reported so far, it is not straightforward\nto conclude that FLP in Si(100) and Ge(100) is primarily governed by p(2×2) or c(1×1)\nstructures, which serve as the basis for conclusions 1 and 2.\nAuthor Response: In this work, we show that if both metal-Si and metal-Ge interfaces adopt the\nsame interface structure, they will have similar pinning factors. Specifically, the p(2×2) dimer\nreconstructed configuration gives rise to the metal-Si and metal-Ge interfaces having pinning factors\nof 0.16 and 0.11, respectively. On the other hand, the c(1×1) non-reconstructed configuration gives\nrise to the metal-Si and metal-Ge interfaces having pinning factors of 0.05 and 0.0, respectively.\nThe predicted pinning factor S = 0.16 is in excellent agreement with experimental data for the metal-\nSi interfaces if they adopt the p(2×2) dimer reconstructed configuration. The predicted pinning\nfactor S = 0 is in excellent agreement with experimental data of S = 0.02 for the metal-Ge interfaces\nif they adopt the c(1×1) non-reconstructed configuration. Considering MIGS is an intrinsic property\nof semiconductors, and its contribution to Fermi level pinning cannot be changed by modifying the\nmetal-semiconductor interface structures, we demonstrate that the larger S in the reconstructed\nconfiguration arises from the reduction of the DBSS interface gap states by the self-passivation of\nthe interface dangling bonds due to their dimerization. We also illustrate that the Ge (100) interface\ngains less energy than the Si (100) interface from the interface reconstruction due to a longer bond\nlength and thus is more likely to be restored to the c(1×1) non-reconstructed configuration by metal\ndeposition. Consequently, we conclude that the reason why Ge has a much stronger FLP effect than\nSi is due to metal-Ge interfaces being stabilized in the c(1×1) non-reconstructed configuration rather\n8\nthan in the reconstructed configuration as in the metal-Si interfaces.\nFurthermore, we also show that we can further increase the pinning factor S to 0.45 for Ge (0.5 for\nSi) by fully passivating the dangling bonds to eliminate all DBSS using one hydrogen atom for each\ndangling bond. Considering the pinning factor only increases to 0.45 by almost eliminating the\ninterface gap states arising from the dangling bonds, the residual effect hindering the approaching\nof the Schottky-Mott limit S = 1 should arise from the MIGS. Therefore, we evaluate the\ncontributions of both DBSS and MIGS to the overall FLP effect to be important.\nSubsequently, we disagree respectfully with the reviewer that we do not conclude that FLP in Si\n(100) and Ge (100) is primarily governed by p(2×2) or c(1×1) structures. We also must stress that\nthe reviewer correctly summarized our first conclusion, but not our second conclusion, because we\nconclude that the strong FLP at these interfaces arises equally from both DBSS and MIGS rather\nthan from DBSS (interface states of bond structures) alone.\nIn response to the following comments, we will explicitly address the reviewer’s concerns about the\ndifference between experimental data and our theoretical prediction.\nComment #9: Metal/Ge(100) interfaces:\n- In Reference 5, the Ge(100) surface before metal deposition exhibits (2×1) surface\nreconstruction.\nAuthor Response: We agree with the reviewer that experiments such as Ref. 5 [Appl. Phys. Lett.\n89, 252110 (2006)] observed the bare Ge(100) surface to be in the p(2×1) surface reconstruction,\nsame as the bare Si(100) surface. We illustrate that the (100) surfaces will gain energy by such\nreconstruction, but the Ge(100) surface gains much less energy than the Si(100) surface due to a\n4.3% longer bond length. It implies that the reconstructed surface structure in the Ge(100) surface\nis more prone to damage and recover to the c(1×1) non-reconstructed configuration during metal\ndeposition. It has also been confirmed by both thermodynamic and kinetic results presented in our\nResults section by performing a comparison between the metal-Si(100) and metal-Ge(100)\ninterfaces. Several studies have also reported that metal deposition will cause damage to the\nreconstructed Ge surface. For instance, extensive research has observed that the adsorption of metal\natoms on top of the Ge (100) surface could break the Ge dimers [ Phys. Rev. B 66, 155339 (2002);\nPhys. Rev. B 70 (2004); Mater. Sci. Semicond. Process. 9, 701-705 (2006)]. Studies have also shown\nthat both the c(1×1) non-reconstructed configuration and the dimerization reconstruction\nconfiguration coexist on the Ge(100) surface during the initial stage of metal deposition [Phys. Rev.\nB 66, 155339 (2002); Surf Sci. 596, 126 (2005)]. In real devices, experimental characterizations\noften struggle to directly observe the entire atomic configuration of intimate MS interfaces.\nTechniques such as TEM or XPS typically focus on regions close to the surface or provide data\nlimited to cross-sectional cuts, making it challenging to infer complete interface structures across\nthe entire surface plane. Consequently, the exact bonding configuration of the MS interface is often\nambiguous since metastable interface configurations may form, and this is why we not only consider\n9\ndimerization configuration p(2×2), as observed in experiments before metal deposition (Ref. 5), but\nalso consider c(1×1) non-reconstructed configuration when building the interface models.\nComment #10: Metal/Ge(100) interfaces:\n- In References 14 and 15, the Ge(100) surface undergoes HF cleaning before metal deposition.\nIn this study, the Ge surface may be hydrogen-terminated, which is reported to weaken FLP in\nthis work.\nAuthor Response: We agree with the reviewer that, in Refs. 14 and 15, the Ge(100) surface\nundergoes HF cleaning before metal deposition, implying that those measured metal-Ge(100)\ninterfaces may have already been passivated by hydrogen. However, many studies have shown that\nHF treatment does not necessarily produce a stable hydrogen passivation layer on the Ge surface\n[e.g., J. Appl. Phys. 98, 023503 (2015); Solid State Phenomena 134, 33 (2007); J. Chem. Phys 102,\n7222-7228 (1995)]. Particularly, it has been observed that the HF-treated Ge surfaces tend to have\na lower hydrogen coverage (less stability) than another surface hydrogenation method using atomic\nhydrogen generated by thermal decomposition of H under the ultra-high vacuum (UHV) conditions\n2\n[J. Vac. Sci. Technol. A 7, 2104-2109 (1989); Riedel, D. and Sordes, Delphine, et al. in 2016\nProceedings of the International Workshop on Atomic Wires]. This is because solution-based\npassivation techniques usually suffer from relatively poor thermal stability compared to other\npassivation techniques [Appl. Surf. Sci. 462, 8 (2018)]. Furthermore, the sustained hydrogen\npassivation of the Ge surface treated by the HF solution will also be damaged by the metallization\nprocess [Jpn. J. Appl. Phys. 42, 4650-4654 (2003); Solid State Commun. 151, 1641-1644 (2011)].\nTherefore, experimental results in Refs. 14 and 15 show that the S factor for the HF-treated metal-\nGe(100) interfaces remains close to zero, indicating that HF treatment on the Ge surface does not\nprovide a good passivation for the surface dangling bonds. However, our calculated results, shown\nin Fig. 4, with an increase of the pinning factor S to nearly 0.45, are based on the assumption of a\n100% passivation of interface Ge dangling bonds by hydrogen atoms.\nComment #11: Metal/Ge(100) interfaces:\n- Another study (Ref. 16) reports an S factor of 0.17 for germanide metal/Ge(100) interfaces,\nwhich exceeds the calculated value of 0.11 for p(2×2) in this study. Additionally, Bi exhibits\nbehavior that deviates from strong FLP trends.\nAuthor Response: Since we conclude that the strong FLP at the metal-Ge(100) and metal-Si(100)\ninterfaces arises equally from both DBSS and MIGS rather than from DBSS (interface states of\nbond structures) alone, which is misunderstood by the reviewer, we agree with Ref. 16 and the\nrelated study [Appl. Phys. Express 9, 081201 (2016)] that the reported S factor of 0.17 for germanide\nmetal/Ge(100) interfaces, which exceeds the calculated value of 0.11 for p(2×2) in this study, may\narise from reduced MIGS. We also agree with Ref. 16 and another related study [AIP Advances 9\n(2019)] that the reported Bi exhibiting behavior that deviates from strong FLP trends may also arise\nfrom a reduction of MIGS.\nchanges indicated in blue font to the Discussion section, page 17:\n“However, it should also be emphasized that we do not disprove the significance of MIGS on the\nFLP in Ge and Si, although we attribute their different FLP to their different interface bonding\nconfiguration. The pinning factor S is consistently predicted to be slightly larger (within 0.05) in Si\nthan that in Ge for the same configurations, as shown in Fig. 1, indicating the effect of MIGS on\nFLP since Si has a larger band gap than Ge and, thus, a smaller density of MIGS. This is consistent\nwith studies from Nishimura et al., where they find another effective method of using metals with\nlow free-electron density such as Bi or germanide to substantially reduce MIGS thus alleviating\nFLP [Electronics 11, 2419 (2022); Appl. Phys. Express 9, 081201 (2016); AIP Advances 9 (2019)]”\nComment #12: Metal/Si(100) interfaces:\n- In both References 11 and 12, the metal/Si interface is formed on the Si(111) surface.\nAuthor Response: We really appreciate the reviewer for pointing out this important issue to us.\nSince the experimental data sets cited in review articles Ref. 11 and 12 have been widely adopted\nas a benchmark for studying metal-Si contacts, we naturally considered them as the Si (100) surfaces.\nUpon examining Ref. 11, we confirm that the experimental data reported in this work indeed\ncorrespond to metal/Si(111) interfaces. Regarding Ref. 12, we further investigated the origin of the\ndata used in this work. Reference 12 compiled data from even earlier studies ([Appl. Phys. Letters 4,\n91 (1964); Ann. N. Y. Acad. Sci. 101, 697 (1963); Phys. Rev. 127, 2006 (1962); Phys. Rev. 134,\nA713 (1964); Phys. Rev. Letters 10, 471 (1963); J. Appl. Phys. 34, 3061 (1963)], ranging from 1960\nto 1965), and those original data also correspond to measurements on Si(111) surfaces.\nTo rigorously validate our conclusions, we have now replaced the experimental data from that cited\nin Refs. 11 and 12 to more recently experimental measurements using the Si(100) interfaces [Appl.\nPhys. Express 13, 031003 (2020); Zeitschrift für Naturforschung A 59a, 795-798 (2004)]. The S\nfactors directly reported in these two references are 0.16 and 0.162, respectively. We have\nreproduced their results of N-SBH and the pinning factor S (see below), which are also excellent\nagreement with our predicted value of S = 0.16 for metal-Si (100) interfaces.\nadopted from the above two references in the revised manuscript in the Results section, page 6.\nFig. 1. First-principles method calculated n-type Schottky barrier height (N-SBH) of metal-\nsemiconductor contacts with non-reconstructed and reconstruction interface configurations.\na, b Metal-Si (001) interfaces in (a) p(2×2) dimer reconstruction interface configuration, and (b)\nc(1×1) non-reconstructed interface configuration. c, d Metal-Ge (001) interfaces in (c) p(2×2) dimer\nreconstruction interface configuration, and (d) c(1×1) non-reconstructed interface configuration.\nGrey squares with error bars represent the experimental data.\nComment #13: Given that (1) the calculation results in this study may not accurately represent\nthe interface structure in Ge, (2) germanide and Bi may exhibit different characteristics at the\nGe(100) interface, and (3) the experimental conditions for the Si interface differ from the\nassumptions in this study, it is difficult to strongly support the conclusions (1 and 2) presented\nin this paper.\nAuthor Response: In the above responses, (1) we have addressed that the gained energy from the\nreconstruction of the Ge (100) surface is so small that will be destroyed to back to non-reconstructed\nconfiguration after metal deposition; (2) since our conclusion is that MIGS and DBSS equally\ncontribute to the FLP strength for both metal-Si (100) and metal-Ge (100) interfaces rather than\nDBSS alone, our conclusion is also aligned with literature for the special cases of germanide and Bi\nbased on the reduction of MIGS; (3) we have demonstrated the change of the experimental data sets\nfrom Si(111) interfaces to Si (100) interfaces does not alter our original conclusion. Therefore, these\n12\nvaluable comments raised by the reviewer all support our original conclusions and considerably\nstrengthen our case.\nComment #14: The study proposes that interface states induced by dangling bonds, in addition\nto MIGS, play a significant role in Fermi level pinning. It demonstrates that metal-Si and metal-\nGe contacts exhibit different Fermi level pinning (FLP) strengths due to their preferred bonding\nconfigurations. Hydrogen passivation of dangling bonds reduces interface gap states and\nsignificantly weakens FLP, providing a potential strategy for lowering contact resistance in\nadvanced semiconductor technologies. However, while these results and analyses are quite\ninteresting, they do not yet meet the level of innovation and scope required for Nature\nCommunications due to the following concerns:\nAuthor Response: We appreciate the reviewer’s interest in our results and analyses. In response to\nthe reviewer’s concerns regarding the innovation and scope of our study, we have carried out\nextensive additional work to address the following concerns. Since receiving the reviewer’s report,\nwe have conducted further calculations to address all the concerns. These results all support our\noriginal conclusions and considerably strengthen our case.\nComment #15: The paper introduces the novel concept of dangling bond-induced interface\nstates. However, a deeper analysis of the role of dangling bonds is needed to fully substantiate\nthe novelty of this study.\nAuthor Response: In this work, we show that if both metal-Si and metal-Ge interfaces adopt the\nsame interface structure, they will have similar pinning factors. Specifically, the p(2×2) dimer\nreconstructed configuration gives rise to the metal-Si and metal-Ge interfaces having pinning factors\nof 0.16 and 0.11, respectively. On the other hand, the c(1×1) non-reconstructed configuration gives\nrise to the metal-Si and metal-Ge interfaces having pinning factors of 0.05 and 0, respectively. The\npredicted pinning factor S = 0.16 is in excellent agreement with experimental data for the metal-Si\ninterfaces if they adopt the p(2×2) dimer reconstructed configuration. The predicted pinning factor\nS=0 is in excellent agreement with experimental data of S = 0.02 for the metal-Ge interfaces if they\nadopt the c(1×1) non-reconstructed configuration. Considering MIGS is an intrinsic property of\nsemiconductors, and its contribution to Fermi level pinning cannot be easily changed by modifying\nthe metal-semiconductor interface structures, we demonstrate that the larger S in the reconstructed\nconfiguration arises from the reduction of the DBSS interface gap states by the self-passivation of\nthe interface dangling bonds due to their dimerization. We also illustrate that the Ge (100) interface\ngains less energy than the Si(100) interface from the interface reconstruction due to a longer bond\nlength and thus is more likely to be restored to the c(1×1) non-reconstructed configuration by metal\ndeposition. Consequently, we conclude that the reason why Ge has a much stronger FLP effect than\nSi is due to metal-Ge interfaces being stabilized in the c(1×1) non-reconstructed configuration rather\nthan in the reconstructed configuration as in the metal-Si interfaces.\nFurthermore, we also show that we can further increase the pinning factor S to 0.45 for Ge (0.5 for\nSi) by fully passivating the dangling bonds to eliminate all DBSS using one hydrogen atom for each\ndangling bond. Considering the pinning factor only increases to 0.45 by almost eliminating the\n14\ninterface gap states arising from the dangling bonds, the residual effect hindering the approach of\nthe Schottky-Mott limit S = 1 should arise from the MIGS. Therefore, we evaluate the contributions\nof both DBSS and MIGS to the overall FLP effect to be important.\nSubsequently, metals with lower work functions, such as Mg, Ag, Cu, Ta, and Ti, can achieve a near-\nzero SBH for both n-type Si and Ge (as shown in Fig. 4) to meet the requirement of low contact\nresistivity for future high-performance transistors. Specifically, this approach overcomes the\nchallenge of large source/drain contact resistance for using high mobility Ge to replace Si for further\nhigh-performance transistors.\nTherefore, we demonstrate the critical role of dangling bonds in determining the Fermi level pinning\nstrength. More importantly, this understanding offers a new way to overcome the challenge of\ncontact resistance issues for both Si transistors and Ge transistors. Based on the common thought\nthat the strong FLP in Ge and Si arises entirely from MIGS, an approach of inserting an ultrathin\ninsulator oxide layer into the metal-semiconductor interface has been developed to alleviate the FLP\nby pushing the MIGS away from the semiconductor interface. However, the experimentally\nobtained contact resistance is still orders of magnitude higher than the theoretical prediction for the\nultrathin inserting oxide layer approach due to the inappropriate band alignment, which may\nintroduce an additional tunneling layer by inserting such an ultrathin wide bandgap oxide layer\n[Appl. Phys. Lett. 101, 042108 (2012); Electronics 11, 2419 (2022)]. Furthermore, such an approach\nalso adds complexity for the compatibility with the gate-all-around field effect transistor (GAAFET)\ntechnology. The finding of DBSS contributing almost equally to FLP as MIGS in metal-Ge and\nmetal-Si interfaces sheds new light on why metal-Ge interfaces have much stronger FLP than metal-\nSi interfaces and offers new methods to alleviate the FLP by passivating the interface dangling bonds.\nIt remarkably broadens our choice of metals and passivating ligands to achieve a zero Schottky\nbarrier height (SBH) for both metal-Si(100) and metal-Ge(100) interfaces, which will substantially\nimprove the device performance of Si transistors and even overcome the limits of integration of\nhigh mobility Ge transistors.\nComment #16: The Fermi level pinning is still relatively high. The authors suggest that, given\nthe importance of dangling bonds, complete passivation can significantly alleviate Fermi level\npinning and reduce contact resistance. However, after complete passivation, the pinning factor\nonly improves to 0.5, which is insufficient. The authors should explore other techniques or\nprovide additional methods to further reduce Fermi level pinning.\nResponse: We note that even with complete DBSS passivation, the increase in the pinning factor S\nremains limited to ~ 0.5 due to persistent MIGS. Previous strategies for mitigating FLP in Si or Ge\nsystems, such as inserting insulating interlayers (aiming to alleviate MIGS) achieved a maximum S\n~ 0.3 [J. Appl. Phys. 105, 023702 (2009); Electronics 11, 2419 (2022)]. Besides, these methods\ninherently introduce tunneling resistance, because if they want to achieve a significant alleviation\nof MIGS, at least 1~2nm thickness is needed [Appl. Phys. Lett. 101, 042108 (2012); Electronics 11,\n2419 (2022)]. In contrast, our approach can increase the pinning factor S to 0.45 for Ge (0.5 for Si)\nby fully passivating the dangling bonds to eliminate all DBSS without significant associated large\n15\ntunnel resistance because we only intend to modify the first one layer of semiconductor,\ndemonstrating substantial progress. Importantly, since the contact resistance R and Schottky\nc\nbarrier height Φ follow the exponential relationship, increasing S to 0.5 enables a dramatic\nB,n\nreduction in R by a factor of ~e12 ~105 if Φ can be reduced to 0.05 eV. Given that typical\nc B,n\ncontact resistivity for n-Ge and n-Si are in the range of 10-6 ~ 10-4 Ω·cm2, achieving a near-zero n-\nSBH with metals of lower work functions, such as Mg, Ag, Cu, Ta, and Ti (as shown in Fig. 4),\nwould allow both n-type Si and Ge to meet the requirement of IRDS target of < 10-9 Ω·cm2. Thus,\nthis approach overcomes the challenge of large source/drain contact resistance for using high\nmobility Ge to replace Si for further high-performance transistors.\nTo address the practical significance of achieving S = 0.5 and highlight future research direction,\nwe have now added the following text to the Results section, page 14:\n“Note that although S = 0.5 is still way from the Schottky-Mott limit S =1, it enables us to have a\nsubstantial SBH tunability to overcome the challenge of contact resistance in advanced technology\nnodes 2. For instance, after full dangling bonds passivation, we can now use the low-work-function\nmetals (e.g., Ti, Ta, Mg, Ag, Cu, as shown in Fig. 4) to achieve near-zero Schottky barrier heights\nfor n-type Si and Ge, minimizing contact resistance. Optimizing both non-metallic atom passivation\nfor DBSS elimination and compatible low-work-function metals is key for future high-performance,\nCMOS-compatible transistors.”\nWe have also added sentences to the Discussion section, page 18:\n“This finding offers new ways to improve device performance, particularly for Ge transistors, by\nalleviating FLP strength. For instance, after modulating the interface atomic structure\nconfiguration, the large contribution of DBSS to FLP strength can be reduced without increasing\nthe tunneling resistance and adding complexity to the next generation gate-all-around field effect\ntransistor (GAAFET) technology; these two factors are usually suffered by the state-of-the-art\napproach of inserting an ultrathin insulator oxide layer into the metal-semiconductor interface to\nalleviate the FLP 15,78”\nComment #17: The study only considers two specific cases, Si and Ge, raising questions about\nthe generalizability to other materials with different surface reconstruction mechanisms. A more\ncomprehensive investigation is needed to strengthen the conclusions drawn here.\nAuthor Response: We appreciate the reviewer’s insightful comment regarding the generalizability\nof our conclusions beyond the specific cases of Si and Ge. We have now extended our investigation\nbeyond Si and Ge to newly include not only group IV diamond but also group III-V and group Ⅱ-\nⅥ materials to demonstrate the generalizability of our conclusions.\nFirstly, to extend the study within group IV semiconductors, we have also analyzed the metal-\ndiamond (001) interfaces. Our first-principles results show that the dimer-reconstructed surface\nexhibits a significantly higher pinning factor S (~0.31) than the non-reconstructed one (~0.14). This\nbehavior is similar to our results of Ge and Si, indicating that self-passivation decreases the total\n16\ndensity of states near the Fermi level and thus weakens FLP. Notably, the S value of calculated\ndimer-reconstruction structure closely matches the experimental result (S~0.35), indicating that\ndiamond (001) shares the same structural preference as Si (100). Thus, we conclude that the FLP\nstrength in group IV semiconductors is strongly affected not only by MIGS but also by the interface\nbonding configuration. The results have been added in the Results section, page 13-14:\n“To generalize our conclusion, we also extend our investigation to diamond, another group IV\nsemiconductor with an ultrawide bandgap of Eg = 5.4 eV. Both theoretical calculations and\nexperimental measurements show that large pinning factor of S~0.35 62-65 arises from the self-\npassivation effect by the reconstruction in the diamond (001) surface, since diamond bond length is\n34% shorter than Si bond length and thus the diamond (001) surface is better-preserved in dimer\nreconstruction after metal deposition 29,60. Otherwise, our first-principles results show that the\nmetal-diamond (001) interfaces have a much smaller pinning factor of S~0.14 using the c(1×1) non-\nreconstructed configuration (see Fig. SM-9 and calculation details in the Supplementary). We note\nthat from Ge, Si, to C, the first-principles calculations predicted pinning factor S increases from 0.0,\nthrough 0.05 to 0.14 using the c(1×1) non-reconstructed configuration, and increases from 0.11,\nthrough 0.16 to 0.31 using the p(2×2) dimer reconstruction. Such increase is inversely proportional\nto the magnitude of bandgap, which is because the density of interface gap states 𝐷 given in Eq.\n𝑖𝑡\n(2) is inversely proportional to Eg.”\nFig. SM-9. Calculated n-type Schottky barrier height (N-SBH) of metal-diamond (001)\ninterfaces under different configurations. The inset depicts the schematic atomic structures of\nnon-reconstructed and reconstruction configurations, respectively.\nMore importantly, we have analyzed the relationship between the pinning factor S and the density\nand distribution of their dangling-bond-induced gap states (DBSS) across boarder range of materials,\nincluding not only group IV semiconductors but also group III-V and group Ⅱ-Ⅵ materials. Our\nresults show that the intrinsic ionicity plays a decisive role in the formation of DBSS and,\nconsequently, Fermi level pinning (FLP). Moreover, we find that DBSS is particularly crucial for\nFLP in more covalent semiconductors, where the influence of self-passivation surface\nreconstructions on the pinning strength becomes more pronounced. While this broader analysis\nextends the scope of our investigation, we emphasize that Si and Ge remain the primary focus of\nthis study. This is because Si CMOS technology continues to dominate modern semiconductor\ndevices, and Ge is fully compatible with Si CMOS processes, making both materials highly relevant\n17\nfor practical applications. These considerations define the central focus of our study. Nevertheless,\nto broaden the perspective and potentially inspire further investigation in this field, we provide a\npreliminary summary of our extended results in the Discussion section, page 15-17. There, we\npropose a general framework describing the relationship between interface configurations, dangling\nbonds, and Fermi level pinning, and we outline a design principle for controlling FLP by regulating\nthe DBSS:\n“ In addition to passivating the surface dangling bonds, there is another way to have the DBSS\nout from the middle bandgap to alleviate the FLP. Different from the covalent group IV\nsemiconductors such as C, Si, and Ge, where a dangling bond state with an unpaired electron is\nformed near the middle of the band gap, as shown in the bottom panel of Fig. 5(b), the dangling\nbond states in ionic group II-VI semiconductors are near the CBM or VBM 56,70. Because the CBM\nin strong ionic semiconductors is mainly made of the unoccupied orbitals of the cation and the VBM\nis mainly made of the occupied orbitals of the anion; therefore, the energy levels of DBSS, that are,\neither the non-bonding states of the cation or the non-bonding states of the anion, are formed near\nthe CBM or VBM, allowing the dangling bonds to act as a shallow defects (the top panel of Fig.\n5(b)). The density of DBSS in the middle bandgap is remarkably reduced as increasing the bandgap.\nOur calculated density of states for these dangling bonds (see Fig. 5(c)) in bare surfaces confirms\nthis trend: for ZnO and SrO, DBSS is vanishing within the band gap, and for GaAs and BAs, the\nDBSS appeared but significantly reduced compared with Si and diamond. This reduction in DBSS\nfor highly ionic materials directly correlates with the much larger pinning factor S observed for II–\nVI compounds, such as ZnO (Eg = 3.44 eV, S~0.57) and SrO (Eg = 5.79 eV, S~0.93) compared to\ncovalent group IV covalent semiconductors, particularly diamond (Eg = 5.4 eV, S~0.35), despite\ntheir comparable Eg, as shown by the literature-reported S in Fig. 5(a) 11,46,62-65,71,72.\nFig. 5. Pinning factor S and its relationship with the dangling bonds. (a) The pinning factor S\nof various semiconductors, with an inset at the upper-left corner indicating the electronegativity\nvalues of different elements. (b) Schematic illustration of the bandgap formation mechanisms in\ncovalent (bottom) and ionic (top) semiconductors and the typical energetic position of dangling-\nbonds-induced surface states, which is at the middle band gap in covalent semiconductor and near\nthe CBM or VBM in the ionic semiconductor. (c) The density of states projected onto the surface\nlayer for bare, unreconstructed, nonpolar surfaces of ZnO, SrO, GaAs, BAs, C and Si, where the x-\naxis denotes the energy relative to the valence band maximum Ev, and the light-blue shaded region\nindicates the band gap.\nacross a boarder range of materials. Nevertheless, more in-depth studies are necessary to fully\nvalidate and extend this mechanism in future research. Notably, in highly ionic group II-VI\nsemiconductors, the effect of the surface itself or the reconstruction process is relatively minor, as\nthese are weak perturbations compared to the strong Coulomb forces. As a result, the reconstruction\ndoes not significantly influence the electronic structure 56,73. In contrast, in more covalent\nsemiconductors, the FLP is strongly affected not only by MIGS but also by DBSS, and thus the\ninfluence of self-passivation on the pinning strength is more pronounced as previously discussed.\nOverall, these findings point to a stepwise design principle for interface engineering to alleviate\nFLP by selectively modifying DBSS, including (1) self-passivation, such as in-plane dimerization,\nwhich shifts DBSS away from the mid-gap; (2) extrinsic full-passivation through strong bonding\nwith non-metallic atoms, further reducing DBSS within the gap; and (3) fundamental suppression\nof DBSS formation by increasing the material’s ionicity.”\nComment #18: Both MIGS and dangling bond-induced interface states play critical roles in\nmetal-semiconductor contacts. The relationship between these states in determining FLP\nstrength should be further discussed to help readers better understand the underlying\nmechanism.\nResponse: In this work, we have demonstrated that the pinning factor S is increased from 0.0 (0.05)\nto 0.11 (0.16) by changing the interface structure from c(1×1) non-reconstructed configuration to\np(2×2) dimer reconstructed configuration for metal-Ge(100) (metal-Si(100)) interfaces. On the\nother hand, MIGS is an intrinsic property of semiconductors, and its contribution to Fermi level\npinning by reducing the pinning factor S cannot be changed by modifying the metal-semiconductor\ninterface structures. Thus, the increase in S should be exclusively caused by the reduction of the\nDBSS interface gap states due to the self-passivation of the interface dangling bonds during\ndimerization. We also show that we can further increase the pinning factor S to 0.45 (0.5) by fully\npassivating the dangling bonds to eliminate all DBSS using one hydrogen atom for each dangling\nbond. Considering the pinning factor only increases to 0.45 by almost eliminating the interface gap\nstates arising from the dangling bonds, the residual effect hindering the approaching of the Schottky-\nMott limit S = 1 should arise from the MIGS. Therefore, we evaluate the contributions of DBSS and\nMIGS to the overall FLP effect to be roughly equal.\nIn our Introduction section, we showed that the pinning factor S is governed by the density of gap\nstates 𝐷 , indicating that both MIGS and DBSS collectively contribute to 𝐷 . We further\nit it\ndemonstrated that the total density of states decreases after the suppression of p -DBSS, leading\nxy\nto weakened FLP. This also indicates DBSS and MIGS collaboratively contribute to 𝐷 and\nit\ninterface dipole formation, which both collectively enhance the pinning effect. We have also\nclarified the relationship between DBSS, MIGS, total density of surface states, and FLP in the\nResults section, page 9-10, with changes indicated in blue font:\n“Although both DBSS and MIGS contribute to the total density of the interface gap states 𝐷 for\n𝑖𝑡\nFLP effect, the contribution of the MIGS is unlikely to be changed by altering the interface structures\n19\ndue to it is an intrinsic property of bulk semiconductors. It implies that the engineering of these\nDBSSs, giving rise to the Dirac-cone-like bands composed of 𝑝 states, are mainly responsible\n𝑥𝑦\nfor the reduction of total density of interface gap states 𝐷 near the Fermi level shown in Fig. 2,\n𝑖𝑡\nand thus a smaller interface dipole potential and a weaker FLP strength by changing the c(1×1)\nnon-reconstructed configuration to the p(2×2) dimer reconstruction interface configuration.”\nComment #19: The authors identify Dirac-cone-like bands crossing at the X-point in the c(1×1)\nnon-reconstructed configuration as dangling bond states (DBSS). However, the rationale for this\nidentification is not sufficiently justified, and further evidence is needed.\nResponse: We have added additional real-space partial charge analysis to demonstrate that the\nDirac-cone-like band originates from localized surface states rather than MIGS. To further\nsubstantiate this identification, we have compared the Dirac-cone-like band observed in the Ag-Ge\ninterface with the Dirac-cone-like band observed in the Ge bare surface as shown in Fig. SM-6. The\nsimilarity in both energy dispersion relation and partial charge distribution between these bands\nstrongly supports their shared origin, which is attributed to the surface truncation. Since the Dirac-\ncone-like band in the bare Ge surface (also in the Si bare surface) without metal contact is clearly\nunrelated to metal Bloch wave, this comparison confirms that the Dirac-cone-like band in the Ag-\nGe interface also arises from DBSS rather than MIGS.\nWe have revised the manuscript to provide a more robust justification for identifying the Dirac-\ncone-like band as DBSS in Results section, page 9, with changes indicated in blue font:\n“We can further ensure the identification of the DBSS in Fig. 2(a) by referring to the surface states\nof the bare Ge (001) surface (supplementary Fig. SM-6 38), which possesses nearly identical Dirac-\ncone-like bands in both the energy dispersion and partial charge distributions. It confirms Dirac-\ncone-like bands arising from the 𝑝 -states of the surface dangling bonds induced by the\n𝑥𝑦\nsemiconductor surface termination.”\nFig. SM-6. Partial charge calculation of the selected states. (a) Band structure and the partial\ncharge density of bare Ge surface. (b) Band structure and the partial charge density of Ag-Ge\n20\ninterface. The orange spheres denote Ge atoms, and the silver spheres denote Ag atoms.\nMoreover, after identifying the common origin of the two Dirac-cone-like bands at the Ag-Ge\ninterface and the Ge bare surface, we have provided further explanations how such surface band\narises from the generation of dangling bonds in the following Results section, page 10-11.\nAdditionally, we have combined previous Fig. 3 and Fig. SM-5 into a new Fig. 3 to more clearly\nillustrate the formation mechanism of DBSS and the associated Dirac-cone-like band:\n“Microscopic mechanism governing interface states evolution\nWe now turn to explain the formation and change of DBSS in terms of atomic orbitals, using\nschematic diagrams as shown in Fig. 3. The ideal c(1×1) non-reconstructed (001) surface results\nfrom cleaving along the (001) plane of the cubic unit cell of the diamond structure, leaving two\ndangling bonds for each surface atom and one valence electron in each dangling bond. For each\nsurface atom, two sp3 hybrid orbitals from two dangling bonds will rehybridize into one 𝑝 and\n𝑥𝑦\none 𝑠𝑝 states. The energy level of the rehybridized 𝑝 state rises from the sp3 level to the atomic\n𝑧 𝑥𝑦\nlevel of the outermost p-orbitals (3p in Si and 4p in Ge), and the rehybridized 𝑠𝑝 state goes down\n𝑧\nto the average of the outermost s- and p-orbital atomic levels, respectively. Then, the two valence\nelectrons owned by the two dangling bonds in each surface atom transfer to the lower-lying\nrehybridized 𝑠𝑝 state to make it fully occupied and leave the higher-lying rehybridized 𝑝 state\n𝑧 𝑥𝑦\ncompletely empty, as shown in Fig. 3(a). The higher-lying rehybridized 𝑝 states from two\n𝑥𝑦\nadjacent surface atoms will couple together to give rise to the bonding 𝜎 and antibonding 𝜎∗\nstates by shifting upward and downward in their energy levels. The periodic potential perturbation\nwithin the (001) plane further broadens these discrete 𝜎 and 𝜎∗ energy levels into Dirac-\n𝑝𝑥𝑦 𝑝𝑥𝑦\ncone-like bands for the bare Ge (001) surface (and similarly for the bare Si (001) surface, as\nshown in Fig. SM-5 and Fig. SM-6) 57 . In contrast, Fig. SM-5 shows that the energy band of the\nrehybridized 𝑝 surface states exhibit negligible dispersion due to its much weaker coupling\n𝑧\nbetween adjacent 𝑝 orbitals within the (001) plane.”\n𝑧\nthe dangling bonds induced surface states. (a) The process of cleave along the (001) plane in bulk\nSi or Ge, and the rehybridization of the 𝑠𝑝 states of the dangling bonds into 𝑝 and 𝑠𝑝 states,\n3 𝑥𝑦 𝑧\nwhich will couple together to form new dangling-bonds-induced surface states. 𝜑 and 𝜑\n𝑝𝑥𝑦 𝑠𝑝𝑧\nrepresent the rehybridized wave functions from original 𝑠𝑝 orbitals. (b) The coupling of adjacent\n3\n(001) surface atomic orbitals in the [110] direction resulting from the dimerization in the p(2×2)\ndimer reconstruction configuration on the Si (001) and Ge (001) bares surfaces before metal\ndeposition on it. Note an asymmetric dimer structure causes the rehybridized 𝑠𝑝 and 𝑝 states of\n𝑧 𝑧\nthe dimer-down shift up relative to that of the dimer-up 29. Here, 𝑑 and 𝑉 represents the distance\nof two dimer atoms and the energy level shift caused by various types of orbital-coupling.\nComment #20: The authors present the interface band structure of the Ag-Ge interface in Fig.\n2. It remains unclear whether this mechanism is applicable to other metals, and further\nexploration is needed.\nResponse: We have extended our analysis to include the metal contacts with a small work function\n(Mg) and a large work function (Au) for both Ge and Si. The band structure results are shown in\nFig. SM-4, which demonstrates that the band structure changes are similar to those observed\npreviously for both Ge and Si. Although slight differences in the band structure arise due to different\nperturbations of different metals on the DBSS, the overall decrease in density of p states is a\nxy\nconsistent trend. We have also added a sentence to address this in the Results section, page 10:\n“This variation is also observed in other Ge-metal interface and Si-metal interface (see Fig. SM-4),\nwith moderate differences arising from perturbations induced by different metals. Nonetheless, the\noverall trend of a decrease in the 𝑝 DOS, attributed to the disappearance of the Dirac-cone-like\n𝑥𝑦\nband due to in-plane dimer-reconstruction, remains a general phenomenon.”\n22\nand metal-Si interface. The metal-Ge(Si) slab band structures are projected onto the first\nlayer of Ge(Si) atoms and the density of states (PDOS) are projected onto all Si layers for (a)\nc(1×1) non-reconstructed interface configuration and (b) p(2×2) dimer reconstruction\ninterface configuration, respectively. In the left panels, the light-blue shadow represents the\nbulk band structure projected to the (100) surface BZ; the gray lines denote the interface band\nstructure, and the colored dots represent Ge(Si) atomic orbitals with dot size accounting for\nthe relative amplitude. The insets zoom the PDOS near the Fermi level.\n24"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have addressed all my concerns, I recommend this paper to be accepted by Nature Communications now.", "reviewer_2": "The authors have revised the manuscript in accordance with the reviewers' comments.\nThis paper suggests that the difference in the strength of Fermi-level pinning (FLP) at metal/Si(100) and metal/Ge(100) interfaces may be attributed not only to metal-induced gap states (MIGS), but also to differences in the dangling bond structures (surface reconstructions) at the interfaces.\nAs a future direction of this research, it would be appreciated if the authors could also consider the following concern.\nIt is well known that even at low temperatures below 100oC, deposition of metals such as Au on Si or Ge often leads to the breaking of back bonds of the interfacial semiconductor atoms, causing semiconductor atoms to segregate onto the metal surface.\n[A. Hiraki, Surf. Sci. Rep. 3, 357 (1984).]\nThis phenomenon may also be relevant to the experimental results on FLP in Si and Ge cited in the manuscript. Therefore, it is strongly encouraged that the authors examine the consistency between this phenomenon and the interfacial structures (reconstructions) discussed as a key difference between Si and Ge in the present work."}, "author_response": "Reviewer #1 comments and author response\nComment #1: The authors have addressed all my concerns, I recommend this paper to be accepted by Nature Communications now.\nAuthor Response: Thank you.\nReviewer #2 comments and author response\nComment #2: The authors have revised the manuscript in accordance with the reviewers' comments.\nThis paper suggests that the difference in the strength of Fermi-level pinning (FLP) at metal/Si(100) and metal/Ge(100) interfaces may be attributed not only to metal-induced gap states (MIGS), but also to differences in the dangling bond structures (surface reconstructions) at the interfaces.\nAs a future direction of this research, it would be appreciated if the authors could also consider the following concern.\nIt is well known that even at low temperatures below 100 ℃, deposition of metals such as Au on Si or Ge often leads to the breaking of back bonds of the interfacial semiconductor atoms, causing semiconductor atoms to segregate onto the metal surface.\n[A. Hiraki, Surf. Sci. Rep. 3, 357 (1984).]\nThis phenomenon may also be relevant to the experimental results on FLP in Si and Ge cited in the manuscript. Therefore, it is strongly encouraged that the authors examine the consistency between this phenomenon and the interfacial structures (reconstructions) discussed as a key difference between Si and Ge in the present work.\nAuthor Response: We appreciate the reviewer for bringing this interesting point to our attention. We agree with the reviewer that the breaking of the back bonds of the interfacial semiconductor atoms may provide a chance for metal atoms to fill the vacancies of these semiconductor atoms left, yielding the intermixing between metal atoms and semiconductor atoms crossing the interface. We have shown in the manuscript that the metal layer on top of the semiconductor surface cannot effectively passivate the dangling bonds of the interfacial semiconductor atoms because the valence electrons from metal atoms are delocalized to form a collective “sea” of electrons. On the other hand, isolated metal atoms may be able to passivate the dangling bonds to reduce the dangling-bond-induced surface state and thus alleviate the FLP. Even if they can effectively passivate the dangling bonds to reduce interface states, their effect on the pinning factor S is proportional to the percentage of the passivated bonds, which has been demonstrated in a very recent experiment [J. Zhao et al., Semicond. Sci. Technol. 40\n1\n(2025)]. The temperature (room temperature without post-thermal annealing) for metal deposition in the experiments quoted in our manuscript is much lower than the temperature in Ref. [A. Hiraki, Surf. Sci. Rep. 3, 357 (1984)], implying that only a small fraction of metal atoms diffuse into the semiconductor layer across the interface to substitute the semiconductor atoms, and thus their effect on the pinning factor S is negligible. Therefore, the direct comparison between our first-principles calculations for an ideal interface and experimental data is justified.\nAccording to our understanding, metal atoms have been used to passivate the semiconductor dangling bonds to weaker Fermi level pinning by fully diffusing metal atoms into the semiconductor layer to create uniform, intermixed rare-earth silicides as contacts since the early 1960s [S.-L. Zhang and M. Östling, Crit. Rev. Solid State Mater. Sci. 28, 1 (2003).]. Such silicides have become promising solutions to achieve the required ultralow metal-semiconductor contact resistance for advanced CMOS technology nodes [Yu, H. et al, MRS Advances 7, 1369-1379 (2022); Yu, H. et al., IEEE Trans. Electron Devices 64, 500-506 (2017)]. At present, several different explanations have been proposed in the literature for why silicides/germanides can reduce the Schottky barrier or contact resistance. One view is that, compared to elemental metals, silicides/germanides possess a lower density of free electrons, which reduces the density of MIGS at the interface and thereby weakens FLP [T. Nishimura, Electronics 11, 2419 (2022); T. Nishimura et al., Appl. Phys. Express 9, 081201 (2016)]. A second view is that the Si(Ge) atomic fraction in silicides(germanides) effectively modulates or screens the metal work function, which manifests as an apparent FLP phenomenon [A. Hiraki, Surf. Sci. Rep. 3, 357 (1983); T. Nabatame et al., IEDM Technical Digest. IEEE International Electron Devices Meeting, 2004]. A third view is that dangling bonds on the metallic silicide/germanide side introduce new pinning positions; these new pinning positions shift with the metal atomic energy levels, so the ultimate Fermi level position is influenced by metal-side surface states [L. Lin et al., Appl. Phys. Lett. 101, 052110 (2012); Z. Zhang et al., J. Phys. Chem. C 124, 19698−19703 (2020)]. To prove our postulation of passivation of dangling bonds by metal atoms is out of the scope of this manuscript, we are currently working on it.\nAccordingly, we have now added the following text to the Discussion section (page 16-17):\n“We have shown that the metal layer on top of the semiconductor surface cannot effectively passivate the dangling bonds of the interfacial semiconductor atoms because the valence electrons from metal atoms are delocalized to form a collective “sea” of electrons. On the other hand, isolated metal atoms may be able to passivate the dangling bonds to reduce the dangling-bond-induced surface state and thus alleviate the FLP. Even if they can effectively passivate the dangling bonds to reduce interface states, their effect on the pinning factor S is proportional to the percentage of the passivated bonds, which has been demonstrated in a very recent experiment 71. The metal deposition is conducted at room temperature without post-thermal\n2\nannealing in the experiments quoted in this work, implying that only a small fraction of metal atoms diffuses into the semiconductor layer across the interface to substitute the semiconductor atoms 72, and thus their effect on the pinning factor S is negligible. Therefore, the direct comparison between our first-principles calculations for an ideal interface and experimental data is justified.”"}, {"round": 3, "reviewer_comments": {"reviewer_2": "Thank you for addressing the comment by adding the discussion.\nI recommend that the manuscript be published in this journal.", "reviewer_3": "The authors addressed my concerns and current manuscript is ready to accept."}, "author_response": ""}]

Decision letter