Resistivity scaling of porous MoP narrow lines

Integrated circuits (ICs) in microelectronics contain miles of nanoscale metal interconnects that connect logic and memory components on a chip to transmit signals, forming an essential part of back-end-of-line (BEOL) in ICs.¹ Copper (Cu) has been the dominant material for interconnects since the early 2000s due to its low resistivity and low cost.² However, as the size of the IC components continues to downscale, Cu loses its desirable properties, especially as the interconnect size approaches Cu’s electron mean free path (40 nm at room temperature).³ Due to the extensive electron scattering at surfaces and grain boundaries of narrow Cu interconnects,⁴ the resistivity of Cu interconnects starts to increase rapidly beyond the 7 nm technology node,⁵ causing up to 35% of signal delays and increased power consumption.⁶ Therefore, new materials are needed to overcome the challenges in interconnect technology.

Topological semimetals (TSMs) are promising materials for interconnects because of their defect-tolerant and backscatter-forbidden topologically protected surface states.^7–9 Owing to the large surface-to-volume ratio at very small dimensions, electron conduction from topologically protected surface states may dominate over that from bulk states in nanoscale TSMs, which will result in an unconventional decreasing resistivity with decreasing dimensions. For example, Weyl semimetal NbAs have been shown experimentally to have a factor of 10 lower resistivity as nanobelts (⁠$∼3μΩ⋅cm$⁠) than as bulk crystals (35 μΩ cm).¹⁰ Recent studies from IBM also predict that the resistivity of Weyl semimetal CoSi should decrease with decreasing size, and a weakly decreasing resistivity with decreasing film thickness was experimentally observed in amorphous CoSi films.^11,12 Another promising candidate for interconnect applications is MoP, a triple-point TSM with low resistivity, high carrier density, and high cohesive energy.^13–15 A previous work from our group showed successful synthesis of poly-crystalline MoP nanowires via template-assisted chemical vapor conversion and demonstrated promising resistivity values.¹⁶ 

In this work, we fabricate porous but almost single-crystalline MoP narrow lines using standard fabrication techniques that provide control over the cross-section area of the MoP lines. Narrow molybdenum disulfide (MoS₂) lines were first fabricated from exfoliated single-crystal flakes using electron beam lithography and reactive ion etching. The MoS₂ lines were then converted to MoP lines via chemical vapor conversion.¹⁷ This chemical conversion can be wafer scale since BEOL-compatible wafer-scale synthesis of MoS₂ is already achieved.^18,19 Four-point resistivity measurements and porosity analysis were performed on fabricated MoP lines to investigate the lines’ resistivity and its relationship to porosity, thickness, and cross-section area.

We synthesize highly crystalline MoP lines and flakes by chemically converting MoS₂ lines and flakes using a phosphorus-containing precursor [Fig. 1(a)] following the synthesis protocol of a prior work on MoP for hydrogen evolution reaction.¹⁷ Single-crystal MoS₂ flakes with varying thicknesses were exfoliated from bulk crystals and placed on dry thermal oxide (SiO₂/Si) substrates, which were subsequently placed at the center of a horizontal tube furnace. Sodium hypophosphite monohydrate (Na₂H₂PO₂ · H₂O) powder was put in a crucible upstream and used as the phosphorous (P) source. Argon (Ar) gas was used as the carrier gas and provided an oxygen-free atmosphere. At elevated temperatures, Na₂H₂PO₂ · H₂O decomposes and reactive PH₃ gas is generated²⁰ to induce the conversion of MoS₂ to MoP following the reaction: $MoS2+43PH3↑=MoP+2H2S↑+13P↑$⁠.²¹ The details of the conversion conditions are provided in the Experiment Section.

This conversion transforms the two-dimensional (2D) layered MoS₂ with van der Waals gaps to 3D covalently bonded MoP via atomic substitution [Fig. 1(b)], and the atomic lattice maintains hexagonal symmetry. Figure 1(c) shows the optical microscope image of the flake before and after the conversion. The overall morphology of the flake is retained even after conversion. The thickness of the flake changes significantly during the conversion due to the removal of the van der Waals gaps of 2D structure to form a 3D covalently bonded crystal, as shown in Fig. 1(b). Comparison of the height profiles obtained from atomic force microscopy (AFM) shows this thickness reduction going from an initial 40 nm thick MoS₂ to a final 27 nm thick MoP [Fig. 1(d)]. Supplementary material, Fig. S1, presents more MoP flakes with different thicknesses converted from MoS₂.

To characterize the conversion products, we acquired Raman spectra before and after the conversion [Fig. 1(e)]. Before conversion, the $E1g1$ and A_1g peaks of MoS₂ at 384 and 409 cm⁻¹ are clearly identified.²² After conversion, these two characteristic peaks disappear, and a new broad peak at ∼406 cm⁻¹ emerges, which is consistent with the MoP characteristic peak reported in the literature.^16,17,23 The absence of MoS₂ Raman peaks indicates complete conversion with no residual MoS₂ present in final MoP flakes. Raman spectra for converted MoP flakes with different thicknesses are shown in Fig. S2.

X-ray photoelectron spectroscopy (XPS) was performed to analyze the chemical composition and surface oxidation states. Figure 1(f) shows the high-resolution XPS scans of flakes before and after the conversion at the Mo 3d edge (right), P 2p edge (middle), and S 2s edge (left). For the Mo 3d edge, the spectrum shows a doublet of peaks at 233.3 and 230.1 eV (Mo 3d_3/2 and Mo 3d_5/2) before conversion, corresponding to the Mo⁴⁺ oxidation state in MoS₂. After conversion, the Mo peaks shift to lower binding energies at 231.7 eV for 3d_3/2 and 228.5 eV for 3d_5/2, corresponding to the Mo³⁺ oxidation state in MoP.^24,25 Before conversion, there is no P signal, as expected; after conversion, the P 2p edge spectrum shows a doublet of P 2p_1/2 and 2p_3/2 peaks at 130.7 and 129.8 eV, respectively, in agreement with the P peak positions of MoP in the literature.²⁵ While the S 2p spectrum of the MoS₂ flake shows the doublet of S 2p_1/2 and S 2p_3/2 peaks at 164.1 and 162.9 eV, respectively, the S 2p scan of MoP did not yield any signal, which indicates a complete conversion from MoS₂ to MoP. The quantification results from XPS show a Mo:P atomic ratio of 1:1.003, which indicates a successful conversion to MoP.

To verify the atomic structure, we performed structural characterization of the converted MoP flakes using scanning transmission electron microscopy (STEM). Figure 2(a) shows a high-angle annular dark-field (HAADF) STEM image of a converted MoP flake that has a triangular shape of the original MoS₂ flake. At a higher magnification [Fig. 2(b)], pores are observed in the MoP flake. These pores are attributed to the lattice mismatch between MoS₂ and MoP as there is a ∼2.2% in-plane lattice change between MoS₂ (a = b = 3.160 Å) and MoP (a = b = 3.231 Å) and a large >250% out-of-plane lattice reduction (MoS₂ c = 12.294 Å, MoP c = 3.207 Å). The significant lattice change, particularly the in-plane mismatch, will likely generate strain during conversion. As the initial MoS₂ flake is mechanically well anchored to the SiO₂/Si substrate, the formation of pores and cracks is likely in the flake to accommodate the change in lattice parameters and release strain generated during conversion. Nanoscale pores were also observed in the prior work.¹⁷ The average pore diameter is around 5 nm (Fig. S3). We observe that the crystallinity of the MoP flake is maintained at the edge of the pores [Fig. 2(c)], and no disordered or amorphous regions are observed near the edge of the pores. These STEM images also show that the pores extend through the entire thickness of the flake. Additional converted MoP flakes and their morphologies are imaged using scanning electron microscopy (SEM) (Fig. S4), where small pores are observed at the edges of the flakes and much larger, long strip-shaped pores are observed in the inner areas of the flakes. The different shapes of the pores at the edge vs the inner area of the flake may be due to the degree to which conversion-induced strain can be released. It is likely that flake edges are not as strongly adhered to the substrate as the center of the flake, making volume contraction easier at the flake edges.

The crystal structure of the converted MoP flakes is confirmed by acquiring selected area electron diffraction (SAED) on the same flake [Fig. 2(d)]. Diffraction spots with hexagonal symmetry indicate the high crystallinity of the converted flake. Atomic resolution HAADF-STEM image of the flake [Fig. 2(e)] shows an exact match with the MoP (0001) plane, with the measured $(01̄10)$ lattice spacing of 0.28(1) nm in agreement with the MoP $(01̄10)$ spacing. From the SAED pattern, we note the co-presence of diffraction rings with weak intensity, which indicates that the flake is not a single crystal but contains some grains with different orientations. We attribute this to the presence of larger pores (Fig. S4) observed in the inner region of the flake, which can create isolated grains of MoP. As the diffraction rings are not as prominent as the diffraction spots, the converted MoP flakes are highly crystalline. This is in contrast with the conversion from e-beam deposited Mo thin films to MoP following the same conversion process, which results in porous and highly polycrystalline MoP films (Fig. S5). HAADF-STEM images and the SAED pattern of another MoP flake are shown in Fig. S6.

The chemical composition of the converted MoP flake was checked by energy dispersive x-ray spectroscopy (EDS), which indicates that the Mo:P atomic ratio is close to 1:1 as the EDS from the converted flake closely overlaps with the spectrum of a MoP bulk crystal synthesized by chemical vapor transport [Fig. 2(f)].¹⁶ This is in agreement with the XPS analysis. EDS mapping of a converted flake shows a uniform distribution of Mo and P in the flake [Figs. 2(g)–2(i)]. These characterizations altogether prove the successful synthesis of porous yet highly crystalline MoP flakes.

We fabricate narrow MoP metal lines out of the converted MoP flakes to measure their resistivity values as a function of cross-section area. Since small pores were observed at the edges while large streaky pores were found in the inner regions of the MoP flakes, we first fabricate narrow MoS₂ lines out of exfoliated MoS₂ flakes using electron-beam (e-beam) lithography, positive e-beam resist as an etching mask, and reactive ion etching (RIE). The fabricated narrow MoS₂ lines are then converted to narrow MoP lines, where we expect small pores in these narrow lines. Finally, Cr/Au electrodes are patterned and deposited onto the narrow MoP lines for four-point probe resistivity measurements. Figure 3(a) shows optical images of the fabrication process.

Figure 3(b) shows a SEM image of a MoS₂ line obtained by etching a MoS₂ flake and a MoP line after chemical conversion. As before, a non-porous MoS₂ is converted to a porous MoP. MoP lines with different widths are shown in Fig. 3(c) (left: 80 nm, right: 30 nm). Nanoscale pores are uniformly distributed in these MoP lines. Figure 3(d) shows a SEM image of a fabricated four-point probe MoP device.

Room temperature resistance of the MoP lines is measured using the four-point probe method. Linear current (I)-voltage (V) curves were obtained when only pairs of the electrodes were used, indicating Ohmic contacts between the Cr/Au electrodes and MoP lines [Fig. 4(a)]. Resistivity values were calculated from the measured resistance values by obtaining nominal cross-section areas using AFM (height) and SEM (width) first, and then converting to actual cross-section areas by taking porosity into account. The details are provided in the Experiment Section.

We plot measured resistivity values of the porous MoP lines as a function of the cross-section area [Fig. 4(b)]. As the cross-section area decreases, the resistivity values scatter with no obvious scaling behavior. Thus, the measured resistivity does not appear to depend on the cross-section area. We note that the resistivity values measured here are higher than the resistivity values of poly-crystalline MoP nanowires from our previous work (12–35 μΩ cm).¹⁶ To understand the reason for this high resistivity, we examine how the resistivity values are affected by porosity and the thickness of the MoP lines. We first plot the resistivity as a function of porosity [Fig. 4(c)]. The porosity of MoP lines was obtained by analyzing many SEM images (supplementary material for details). Now, the resistivity of the MoP lines scales monotonically with the level of porosity in the lines [Fig. 4(c)]. The MoP line with the lowest porosity shows resistivity (53.13 μΩ cm) that is comparable with the resistivity of polycrystalline MoP nanowires in our previous work. However, as the porosity increases, the resistivity increases rapidly. We attribute this to the increased surface scattering of electrons in these porous lines. Since the presence of pores creates new surfaces, an increase in porosity leads to a larger surface area in the lines, therefore, increased surface scattering as electrons transport in the lines. We confirm that the high and low resistivity values shown in Fig. 4(b) for cross-section areas <4000 nm² correspond to high and low porosity levels. Figure 4(c) shows that there may be two different scattering regimes with porosity as the rate of resistivity increases with porosity appears to change at ∼17% porosity level. Supplementary material, Fig. S7, shows our fit to these data. A possible reason for this may be that higher porosity is associated with thinner flakes, and when thickness decreases below the mean free path of the MoP (10.5 nm),¹⁶ the electron scattering at the top and bottom surfaces may dominate over scattering off pore surfaces, leading to a different slope.

The resistivity also shows an increasing trend with the decreasing thickness of the MoP lines [Fig. 4(d)]. This is because the porosity actually changes with the thickness of the lines. Figure S8(a) shows an SEM image of a flake with varying thicknesses, where the thinner region is more porous than the thicker region. Figure S8(b) shows the porosity vs the thickness of the converted MoP flakes, showing the increase in porosity with decreasing thickness. We think this is because thinner flakes are more confined by the substrate, which will lead to more strain accumulated during conversion, which leads to larger lattice distortion and higher porosity. Indeed, interactions between SiO₂ substrates and 2D materials can hinder synthesis and phase transitions of 2D materials.^26–28 Thicker flakes, on the contrary, are less confined by a substrate because they have more MoS₂ layers and more van der Waals gaps. Due to the easily sliding nature of the van der Waals gaps,²⁹ thicker MoS₂ flakes can better accommodate the lattice distortion and, therefore, have lower porosity levels. We also checked a potential relation between resistivity and linewidth (Fig. S9) and found that the measured resistivity is most strongly influenced by porosity, not linewidth. Based on the resistivity scaling behavior, decreasing the porosity in MoP lines is of utmost importance. Substrates that more weakly interact with Mo atoms than SiO₂, such as Al₂O₃ or hBN,^26,27 may produce fewer pores after chemical conversion, which will require further investigation. More industrial-compatible approaches may be direct growth of MoP thin films using metal–organic chemical vapor deposition or atomic layer deposition (ALD). A recent work achieved thin MoP films by ALD,³⁰ but the measured resistivity was still high. More optimizations are needed to improve the crystalline quality of the ALD-grown MoP film.

In this work, we report the fabrication of highly crystalline yet porous MoP lines using standard fabrication techniques and template-assisted chemical vapor conversion. The converted MoP flakes show the expected atomic structure and stoichiometry of MoP, but contain nanoscale pores, likely due to the lattice constant mismatch between MoP and MoS₂. The pore morphology changes between the edges and inner areas of the MoP flake due to varying degrees of strain release conditions in these regions. The porosity also depends on the thickness of the flake because of different degrees of vertical confinement during conversion. From resistivity measurements as a function of cross-section areas of the fabricated MoP lines, we found that porosity was the main factor that affected the resistivity of these MoP lines. Resistivity increased with increasing porosity, suggesting increased surface scattering of electrons from the additional surfaces created by the pores.

Because of the flexibility of pattern design in e-beam lithography, we were able to investigate the resistivity of MoP under various cross-section areas. This research thus provides a facile method for the fabrication of TSM lines with different dimensions to investigate their resistivity scaling behavior. The template-assisted chemical vapor conversion used in this work can be extended to the synthesis of other metal phosphides using metal sulfides as the starting materials. This conversion process could be wafer scale, as wafer-scale growth of MoS₂ and WS₂ thin films has already been achieved.^18,31 The porous MoP nanostructure that we synthesize may be useful for hydrogen evolution reaction (HER) for its large surface area with abundant dangling bonds.^32,33

The whole process flow is shown in Fig. S10. MoS₂ flakes with various thicknesses were mechanically exfoliated onto the SiO₂/Si substrate with alignment grids using commercially available MoS₂ (HQ Graphene) and the Scotch tape method. Then, positive tone e-beam resist 495 K PMMA A4 was spin-coated onto the substrate at 4000 rpm for 2 min. Then, JEOL 6300 (JEOL JBX-6300FS 100 kV electron beam lithography system) was used for patterning the resist and creating a dumbbell-shaped resist mask, with the linewidth as small as 30 nm in the center of the dumbbell. After e-beam writing, the wafer was developed in MIBK:IPA 1:3 solution for 1 min to remove the e-beam exposed resist. Then, reactive ion etching was performed using the PlasmaTherm720/740 etcher to remove the uncovered MoS₂ area and get MoS₂ lines. SF₆ was used as the etchant with a flow rate of 20 and 10 sccm Ar was also flowed. The chamber pressure was set to 6 mTorr, and the etching time was 135 s with 20 W power. Then, the wafer was soaked in acetone overnight to remove the PMMA resist.

A 1-inch horizontal tube furnace (Lindberg/Blue M) was used for the conversion process. The wafer containing MoS₂ lines was put at the center of the tube, while a crucible with 1 g of Na₂H₂PO₂ · H₂O (Sigma-Aldrich, ≥99%) was placed upstream (15 cm from the center of the tube furnace). The system was first pumped down and purged with Ar carrier gas at 250 sccm for 10 min to remove all the air inside the tube furnace. Then, the tube furnace was brought to atmospheric pressure by continuing to flow Ar gas. The furnace was heated to 670 °C for 30 min, held at 670 °C for 30 min, and then naturally cooled to room temperature. During this process, Na₂H₂PO₂ · H₂O was thermally decomposed and released phosphine gas, which reacts with MoS₂ and forms MoP. A bubbler containing copper sulfate was used between the gas outlet and the building exhaust pipe to neutralize the phosphine gas generated in this process. After conversion, the substrate was rinsed with DI water.

Four-point electrodes were patterned and deposited for MoP line resistance measurements, excluding the parasitic contact resistance between the electrode and the MoP.³⁴ 495 K PMMA A8 resist was first spin-coated on the substrate at 2500 rpm for 2 min. Then, the Nabity Nanometer Pattern Generator System (NPGS) was used to pattern the electrodes used for four-point probe measurement. Zeiss Supra 55VP SEM was used in combination with the NPGS to provide the electron beam used for exposure. The SEM is operated at 20 keV acceleration voltage and 30 μm aperture. The distance between the electrodes was designed to be 500 nm. The wafer was then developed in MIBK:IPA 1:3 solution for 1.5 min to remove the e-beam exposed resist. Then, 10 nm Cr (adhesion layer) and 100 nm Au (electrode) were deposited by e-beam evaporation (CVC SC4500 evaporation system). Lift-off was done by soaking the wafer in acetone overnight. I-V characteristics were measured using the Agilent B1500A semiconductor device analyzer. 4-probe resistance measurement was performed using the Lakeshore CRX-VF cryogenic probe station. Resistance data were recorded using Stanford Research 830 DSP Lock-In Amplifier with applied current amplitudes from 100 nA to 1 μA.

Optical images were taken using Microscope Central Olympus BX51M. AFM characterization was carried out using the Veeco Icon Atomic Force Microscope. Raman spectra were acquired using the WITec Alpha300R Confocal Raman Microscope with a 532 nm laser source and 1 mW laser power. XPS characterization was performed using the Thermo Nexsa G2 Surface Analysis System. HAADF-STEM images and EDS were taken using Thermo-Fisher Scientific Spectra 300 S/TEM at 300 keV. SEM images and EDS mapping were taken using the Zeiss Sigma 500 scanning electron microscope.

Porosity analysis of the MoP lines was done using an image processing Python script with the “Watershed” algorithm, which is an image segmentation algorithm that can recognize pores by finding the local intensity minimum in the gray-scaled image. We use the Watershed algorithm implemented in scikit-image’s Python package.³⁵ Porosity (f) represents the area fraction of the pores in the lines. Images of the MoP lines used for porosity analysis were taken by SEM. Figure S11 shows the pore recognition results using the algorithm compared to the unprocessed image. Pore diameter analysis was done using ImageJ software.³⁶ The cross section of the narrow MoP lines is rectangular considering its fabrication process. Therefore, the actual cross-section area (A) was calculated as A = dt(1 − f), where t is the thickness of the line measured by AFM, d is the wire width measured by SEM, and f is the porosity obtained from image analysis. Resistivity (ρ) was calculated from resistance (R) using the following equation: $ρ=RAL$⁠, where L is the channel length of the line measured using SEM.

See the supplementary material for supporting Figs. S1–S11.

H.W. acknowledges the support from SRC JUMP2.0 SUPREME for device measurements. Q.P.S. was supported by the National Science Foundation (NSF) GRFP under Grant No. 2139899. A.D.K. was supported by the NSF National Nanotechnology Coordinated Infrastructure (NNCI)-2025233 under its REU program. J.J.C. acknowledges support from the Gordon and Betty Moore Foundation (EPiQS Synthesis Investigator Award No. GBMF9062.01). This work made use of the Cornell Center for Materials Research shared instrumentation facility. This work was performed in part at the Cornell NanoScale Facility, a member of the NNCI supported by NSF (Grant No. NNCI-2025233). We also thank Dr. Ching-Tzu Chen at IBM T. J. Watson Research Center for the technical discussions and suggestions in fabricating devices.

The authors have no conflicts to disclose.

Han Wang: Conceptualization (equal); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Project administration (lead); Software (lead); Validation (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (equal). Gangtae Jin: Conceptualization (equal); Investigation (supporting); Methodology (supporting); Validation (supporting); Visualization (supporting). Quynh P. Sam: Investigation (supporting). Stephen D. Funni: Software (supporting); Validation (supporting). Roberto R. Panepucci: Methodology (supporting); Validation (supporting). Astrid D. Kengne: Data curation (supporting); Formal analysis (supporting). Saif Siddique: Investigation (supporting). Nghiep Khoan Duong: Investigation (supporting); Validation (supporting). Yeryun Cheon: Validation (supporting). Mehrdad T. Kiani: Validation (supporting). Judy J. Cha: Conceptualization (equal); Investigation (supporting); Methodology (supporting); Supervision (lead); Writing – review & editing (lead).

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