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) \({\Phi }_{{{{\rm{B}}}},{{{\rm{n}}}}}\) 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 effect6,7,8,9. The strength of the FLP for a given semiconductor is usually characterized by a pinning factor S10:

$$S=\frac{{{d}{\Phi }_{{{{\rm{B}}}},{{{\rm{n}}}}}}}{{{{d}}{\phi }_{{{{\rm{M}}}}}}},$$
(1)

where \({\phi }_{{{{\rm{M}}}}}\) 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:

$$S={\left(1+\frac{{e}^{2}{\delta }_{{{{\rm{it}}}}}{D}_{{{{\rm{it}}}}}}{{\varepsilon }_{{{{\rm{it}}}}}}\right)}^{-1}$$
(2)

where \({D}_{{{{\rm{it}}}}}\), \({\delta }_{{{{\rm{it}}}}}\), and \({\varepsilon }_{{{{\rm{it}}}}}\) 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 \({D}_{{{{\rm{it}}}}}\) gives rise to a smaller S and thus a stronger FLP effect23. The MIGS model also relates the \({D}_{{{{\rm{it}}}}}\) and \({\delta }_{{{{\rm{it}}}}}\) 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 data5,11,12,13,14,35,36,37. 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 uncertainties38,39,40, 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.

Fig. 1: First-principles calculated n-type Schottky barrier heights (N-SBH) of metal–semiconductor contacts.
figure 1

Metal–Si (001) interfaces in a p(2 × 2) dimer reconstruction interface configuration and b c(1 × 1) non-reconstructed interface configuration. Metal–Ge (001) interfaces in c p(2 × 2) dimer reconstruction interface configuration and d c(1 × 1) non-reconstructed interface configuration. Gray squares with error bars (representing standard deviation) show the experimental data5,11,12,13,14,35,36,37.

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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 on the topmost Ge layer. The projected density of states (PDOS) is more critical since the density of interface gap states \({D}_{{{{\rm{it}}}}}\) 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.

Fig. 2: First-principles calculated interface band structures of the metal–Ge (001) interfaces.
figure 2

The Ag–Ge (001) interface electronic states are projected onto the first layer of Ge atoms (left panel) and the projected density of states (PDOS) of all Ge layers (middle panel) for a c(1 × 1) non-reconstructed interface configuration and b p(2 × 2) dimer reconstruction interface configuration, respectively. The light-blue shadow represents the bulk band projected to the (001) surface Brillouin zone; the gray lines denote the interface band structure, and the colored dots represent Ge atomic orbitals with dot size accounting for the relative amplitude. In the PDOS plots, the insets magnify the vicinity of the Fermi level. Partial charge distributions correspond one-to-one to the typical interface states circled in the band structures. Orange and green spheres denote Ge and Ag atoms, respectively.

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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 \({p}_{{xy}}\) 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 \({p}_{{xy}}\)-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 \({p}_{{xy}}\) orbital states out of the bandgap 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 \({p}_{{xy}}\) 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 \({p}_{z}\)-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 \({D}_{{{{\rm{it}}}}}\) 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 \({p}_{{xy}}\) states, is mainly responsible for the reduction of the total density of interface gap states \({D}_{{{{\rm{it}}}}}\) 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 moderate differences arising from perturbations induced by different metals. Nonetheless, the overall trend of a decrease in the \({p}_{{xy}}\) DOS, attributed to the disappearance of the Dirac-cone-like band due to in-plane dimer reconstruction, remains a general phenomenon.

Fig. 3: Schematic diagram illustrating the coupling and the corresponding energy level shift of the dangling-bond-induced surface states.
figure 3

a The process of cleavage along the (001) plane in bulk Si or Ge, and the rehybridization of the \(s{p}^{3}\) states of the dangling bonds into \({p}_{{xy}}\) and \({{sp}}_{z}\) states, which will couple together to form new dangling-bond-induced surface states. b The coupling of adjacent (001) surface atomic orbitals in the [110] direction resulting from the dimerization in the p(2 × 2) dimer reconstruction configuration on the Si (001) and Ge (001) bare surfaces before metal deposition. Here, \(d\) and \(V\) represent the distance between two dimer atoms and the energy level shift caused by various types of orbital coupling.

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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 \(s{p}^{3}\) hybrid orbitals from two dangling bonds will rehybridize into one \({p}_{{xy}}\) and one \({{sp}}_{z}\) states. The energy level of the rehybridized \({p}_{{xy}}\) state rises from the \(s{p}^{3}\) level to the atomic level of the outermost p-orbitals (3p in Si and 4p in Ge), and the rehybridized \({{sp}}_{z}\) 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 \({{sp}}_{z}\) state to make it fully occupied and leave the higher-lying rehybridized \({p}_{{xy}}\) state completely empty, as shown in Fig. 3a. The higher-lying rehybridized \({p}_{{xy}}\) 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 \({\sigma }_{{p}_{{xy}}}\) and \({\sigma }_{{p}_{{xy}}}^{*}\) 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 \({p}_{z}\) surface states exhibits negligible dispersion due to its much weaker coupling between adjacent \({p}_{z}\) 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 \({p}_{{xy}}\) 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, respectively. At the same time, their low-lying rehybridized \({sp}_{z}\) 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 \({sp}_{z}\) state of the dimer-down atom to have more \({p}_{z}\) character29. The valence electrons that occupy the lower-lying rehybridized \({sp}_{z}\) 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 shows 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 bandgap, which is because the density of interface gap states \({D}_{{{{\rm{it}}}}}\) 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.

Fig. 4: First-principles calculated n-type Schottky barrier heights (N-SBH) after the complete passivation of the surface dangling bonds by hydrogen atoms.
figure 4

a, b Metal–Si interfaces and metal–Ge interfaces. For comparison, the gray dots represent the predicted values in the ideal c(1 × 1) non-reconstructed and the p(2 × 2) dimer reconstruction configurations, as shown in Fig. 1.

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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.

Discussion

In addition to passivating the surface dangling bonds, there is another way to have the DBSS out of the middle bandgap to alleviate the FLP. Different from the covalent group IV semiconductors such as diamond, Si, and Ge, where DBSS with an unpaired electron is formed near the middle of the band gap, as shown in the bottom panel of Fig. 5b, the DBSS in ionic group II–VI semiconductors are near the CBM or VBM46. Because the CBM in strong ionic semiconductors is mainly made of the unoccupied orbitals of the cation and the VBM is mainly made of the occupied orbitals of the anion; therefore, the energy levels of DBSS, which are either the non-bonding states of the cation or the non-bonding states of the anion, are formed near the CBM or VBM, allowing the dangling bonds to act as shallow defects (the top panel of Fig. 5b). The density of DBSS in the middle bandgap is reduced as increasing the ionicity. Our calculated density of states for these dangling bonds (see Fig. 5c) in bare surfaces confirms this trend: for ZnO and SrO, DBSS vanishes within the band gap, and for GaAs and BAs, the DBSS appears but is reduced compared with that in Si and C. This reduction in DBSS for highly ionic materials directly correlates with the much larger pinning factor S observed for II–VI compounds, such as ZnO (Eg = 3.44 eV, S ~ 0.57) and SrO (Eg = 5.79 eV, S ~ 0.93) compared with covalent group IV covalent semiconductors, particularly diamond (Eg = 5.4 eV, S ~ 0.35), despite their comparable Eg, as shown by the literature-reported S in Fig. 5a11,36,52,53,57,58.

Fig. 5: Pinning factor S and its relationship with the dangling bonds.
figure 5

a The pinning factor S of various semiconductors11,36,52,53,57,58, with an inset at the upper-left corner indicating the electronegativity values of different elements75. b Schematic illustration of the band gap formation mechanisms in ionic and covalent semiconductors and the typical energy positions of dangling-bond-induced surface states. c The density of states projected onto the surface layer for bare, unreconstructed, nonpolar surfaces of ZnO, SrO, GaAs, BAs, C, and Si, where the light-blue shaded regions indicate the band gap.

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Thus, we have established a preliminary framework to generalize the role of DBSS in FLP across a broader range of materials. Nevertheless, more in-depth studies are necessary to fully validate and extend this mechanism in future research. We note that, in highly ionic group II–VI semiconductors, the effect of the surface reconstruction process and even the surface itself is relatively minor, as these are weak perturbations compared with the strong Coulomb forces. As a result, the surface reconstruction has a limited impact on the electronic structure46,59. In contrast, in more covalent semiconductors, the FLP is strongly affected not only by MIGS but also by DBSS, and thus the influence of self-passivation on the pinning strength is more pronounced as previously discussed. Overall, these findings point to a stepwise design principle for interface engineering to alleviate FLP by selectively modifying DBSS, including (1) self-passivation, such as in-plane dimerization, which shifts DBSS away from the mid-gap; (2) extrinsic full passivation through strong bonding with non-metallic atoms, which further reduces DBSS within the gap; and (3) fundamental suppression of DBSS formation by increasing the material’s ionicity.

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 DBSS 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 experiment60. The metal deposition is conducted at room temperature without post-thermal annealing 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 atoms61, 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.

We also note that both Nishimura et al.13 and Kuzmin et al.62 found that the modification of the atomic arrangement by altering the surface condition hardly changes the FLP strength or the pinning position and thus concluded that FLP of metal–Ge contacts is an intrinsic property and rises from MIGS. We must stress that their results are due to poor surface treatments, which may not effectively reduce the DBSS, considering Kuzmin’s photoemission measurements showed little changes in the total surface component of core-level spectra by changing surface treatments62. However, it should also be emphasized that we do not disprove the significance of MIGS on the FLP in Ge and Si, although we attribute their different FLP to their different interface bonding configuration. The pinning factor S is consistently predicted to be slightly larger (within 0.05) in Si than that in Ge for the same configurations, as shown in Fig. 1, indicating the effect of MIGS on FLP since Si has a larger band gap than Ge and, thus, a smaller density of MIGS. This is consistent with studies from Nishimura et al., where they find another effective method of using metals with low free-electron density, such as Bi or germanide, to reduce MIGS, thus alleviating FLP14,26,63. Besides, inserting an ultrathin insulator layer between the metal and the semiconductor has also been explored to alleviate the FLP by reducing the MIGS via suppressing the wave function tailing of the metal into the band gap of the semiconductor16. The ultrathin insulator insertion approach has been demonstrated to increase the pinning factor S of the metal–Si and metal–Ge contacts up to 0.2464 and 0.326,65, respectively. The residual FLP should be due to the effect of DBSS.

Since MIGS is an intrinsic property of semiconductors and its contribution to S cannot be altered by H-passivation, we can roughly suppose that the increase of S from near 0 to around 0.5 by hydrogen passivation for both Si and Ge is due to the elimination of DBSS, while the remaining factor to hinder the approach of the Schottky–Mott limit S = 1 is due to residual MIGS. This finding offers ways to improve device performance, particularly for Ge transistors, by alleviating FLP strength. For instance, after modulating the interface atomic structure configuration, the large contribution of DBSS to FLP strength can be reduced without increasing the tunneling resistance or adding complexity to advanced gate-all-around field effect transistor (GAAFET) technology; these two factors are usually suffered by the approach of inserting an ultrathin insulator oxide layer into the MS interface to alleviate the FLP26,66. Crucially, the design principle governing hydrogen passivation, which achieves DBSS elimination through strong σ-bonding, also extends to other non-metallic atoms. Halogen (e.g., Cl) and chalcogen (e.g., S) atoms have also been reported to be capable of strongly binding to Si and Ge dangling bonds in experiment67,68, and should also show notable passivation effectiveness. From a device integration perspective, at typical CMOS processing temperature (>400 °C), hydrogen passivation is thermally unstable on both Si and Ge69,70, whereas Cl and S passivation provide much better stability and effective interface states suppression67, which might be better choices for DBSS passivation. Therefore, balancing DBSS passivation, interface stability, and minimal impact on electrical transport remains a key challenge for future interface engineering studies.

In summary, we have revealed that the self-passivation of the interface dangling bonds is a primary factor in governing the different FLP strengths between the metal–Si and metal–Ge contacts since the former prefers the p(2 × 2) dimer reconstruction interface and the latter prefers the c(1 × 1) non-reconstructed interface structure. We have also demonstrated that utilizing hydrogen atoms to passivate the surface dangling bonds completely can further increase the pinning factor S to 0.5, and the residual FLP should arise from the commonly suggested MIGS11,13. Thus, we shed light on lowering contact resistance for advanced technology nodes via modulating the FLP strength by passivating the interface bonding bonds without the need for an ultrathin dielectric layer16,35, thereby avoiding the associated increase in tunneling resistance26,66.

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.