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Sci Rep
Sci Rep
Scientific Reports
2045-2322
Nature Publishing Group UK London

39237567
71177
10.1038/s41598-024-71177-w
Article
Transport diagrams of germanium double quantum dots/Si barriers using photocurrent measurement
Wang I-Hsiang
Chiu Yu-Wen
Lin Horng-Chih
Li Pei-Wen pwli@nycu.edu.tw

grid.260539.b 0000 0001 2059 7017 Institute of Electronics, National Yang Ming Chiao Tung University, Hsin-chu, Taiwan
5 9 2024
5 9 2024
2024
14 2074911 6 2024
26 8 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
We reported transport diagrams of self-assembled germanium (Ge) double quantum-dots (DQDs) using direct current measurement under illumination at wavelength (λ) of 850 nm and at the base temperature of 4.5 K. Ge DQDs with a coupling-barrier of Si, tunneling-barriers of Si3N4, and self-aligned p+-Si reservoirs were fabricated in a self-organized CMOS approach. Charge transport through the Ge-DQDs is facilitated by photon-assisted tunneling. Characteristic gate-controlled hexagonal-shaped cells over a wide range of hole occupancy are acquired thanks to hard-wall confinement. Large dimensions (ΔVG > 200 mV) of hexagonal-shaped cells are favored for the operation of charge states, indicating that our Ge DQDs system is less susceptible to shot noises arising from external voltage sources. Estimated intra-QD and inter-QD charging energies are EC,R/EC,L = 48.9 meV/42.7 meV and ECm = 7.8 meV, respectively.

Keywords

Ge quantum dot
Transport diagram
Photon assisted tunneling
Subject terms

Engineering
Nanoscience and technology
http://dx.doi.org/10.13039/100020595 National Science and Technology Council 112-2119-M-A49-006 issue-copyright-statement© Springer Nature Limited 2024
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pmcIntroduction

Semiconductor qubits are the subject of intense research for implementing practical quantum computers using robust CMOS manufacturing technologies. The physical-level ingredients of semiconductor qubits comprise quantum dots (QDs), inter-QD coupling-barrier (CB), QD-reservoir tunneling-barriers (TBs), and control gates. Among currently pursued technologies for realizing Si-based qubits, gate-defined technique is primarily employed to electrostatically create QDs and CBs/TBs by applying bias voltages to closely-spaced plunger-gates (PGs) and barrier-gates (BGs), respectively, over quantum-well or quantum-wire structures of Si/SiGe1,2, Ge/SiGe3,4, or Si-MOS5,6. To dates, 6 Si QD electron-spin qubits7 and 16 Ge QD hole-spin qubits8 have been demonstrated in linear-chain and cross-bar configurations, respectively, using the gate-defined approach. However, the scale up of gate-defined QD qubits is challenging from practical operation perspectives. The densely-spaced PGs not only modulate the specific QD’s potential that they are designed to control, but also influence parameters of other unintentionally-addressed QDs through capacitive cross-talk. Besides, soft-wall CBs and TBs induced by BGs provide a weak confinement, leading to charge or spin states of QDs susceptible to environmental noises and limiting the QD-qubit operation at milli-Kelvin temperatures.

Physically-defined QDs9,10 promise higher temperature operation and lower quantum leak thanks to the fact that hard-wall barriers presumably result in strong quantum confinement and enlarge energy scales (charging energy (EC) and energy-level spacing (ΔE)). The challenge of implementing physically-defined QD qubits lies in the holistic and meticulous process integration to achieve the high-degree control of (1) QD size and shape, (2) barrier engineering in the CB/TB material and width, and (3) electrical addressability of QDs and CB/TB using individual BGs and PGs with minimum parasitic effects. Moreover, tunneling-current magnitude is typically small (~ pA and even smaller) due to strong confinement of carriers within physically-defined QDs. The pA-scale transport current leads to the difficulty in resolving charge-states and their in-between transition lines by simply using direct current measurement. Thereby, intricate readout techniques such as RF-reflectometry in combination with associated matching networks are necessary9.

Advanced industrial CMOS technology is highly envisaged to facilitate practical implementation of Si- and Ge-qubits. However, off-the-shelf nanometer-scale transistor processes cannot be readily transferred to the fabrication of physically-defined Si- and Ge-QDs qubit structures due to different operation principles and special structural-design requirements. Our previous reports have demonstrated engineered Ge QDs/Si-based barrier system11–14. Ordered and size-controlled Ge spherical QDs with self-organized Si CB, Si3N4 TBs, and self-aligned p+-Si source/drain (S/D) were reproducibly fabricated using combined processes of lithographic patterning, conformal sidewall spacer deposition, and the self-assemble growth in CMOS approaches. These engineering strengths have turned our Ge QD/Si-based barrier system into key ingredients in the design and integration of qubit devices, such as single-electron/-hole transistors (SETs/SHTs)15,16, double QDs (DQDs)13,14, and even multiple QD array10,13,14. Ge-QD SHTs in few-hole regime at T = 40 K15 and even 150 K17 have been demonstrated. Extracted addition energy (Ea) for a single Ge QD with diameter of 20 nm is > 50 meV15.

In this work, we reported experimental fabrication and electrical characterization of Ge self-assembled DQDs that are coupled to each other via a CB of Si and capacitively coupled to p+-Si source/drain reservoirs through TBs of Si3N4. Small Ge QDs with diameter of 20 nm in combination with strong confinement arising from tunneling/coupling barriers of Si3N4/Si results in large ΔE and intra-QD charging energy (EC ~ tens meV), which are conducive for high temperature operation of Ge qubits using the degree of freedom of charge or spin. However, the strong confinement tends to result in transport current too small to be accurately measurable in time when the Ge DQDs is biased in the linear transport regime (i.e., at VDS ≈ 0). In order to obtain a measurable transport current through our Ge DQDs, a large VDS is generally applied across source and drain electrodes so that the DQDs system is biased in a nonlinear transport regime. That is, multiple discrete energy levels are covered within the large bias window since VDS is larger than ΔE. In this case, both ground states and excited states can contribute to the conductance, leading to the difficulty in identifying the full hexagonal cells in the transport diagram since the vertices (or triple points) become blurred. Our experimental observation shows that under nW illumination at wavelength (λ) of 850 nm, charge transport through our Ge DQDs is significantly facilitated by photon-assisted tunneling. Thereby, photon-enhanced transport diagram of Ge DQDs in the linear transport regime shows PG-controlled hexagonal-shaped cells with large dimensions over a wide range of hole occupancy, allowing a quick estimation of charging energies of the individual QDs and identification of charge states within the DQDs.

Results

Plan-view EDS mapping micrographs in Fig. 1a show that Ge DQDs are in spherical shape with a diameter of 20 nm and coupled to each other via a 25 nm-thick CB of Si. Figure 1a clearly reveals the penetration of Si3N4 spacer-layers by the Ge QDs. Our previous reports have already elaborated the kinetic mechanism of Ge QD burrowing the proximal layers of Si3N4 due to “SiO2 deconstruction–construction” processes11,12, which dynamically occur near the QD surface as a result of the exquisite interplay between Ge, Si, and O interstitials during the thermal-oxidation process. Importantly, our Ge DQDs approach provides the structural flexibility of barrier engineering in the CB and TBs by design. The Si ridge serves as the inherent, self-organized CB that physically separates Ge DQDs (Fig. 1b). Additionally, the sidewall spacer layers of Si3N4 act as the self-organized TBs between Ge QDs and p+-Si S/D. Ultimately, the Ge QDs are capacitively coupled to top PGs of p+-poly-Si via a 40 nm-thick gate SiO2 layer.Fig. 1 (a) EDS map micrographs of Ge DQDs with inter-QD coupling barrier of 20 nm-thick Si. Ge QDs are weakly coupled to p+-Si S/D via 12 nm-thick tunneling-barriers of Si3N4. (b) Schematic band diagram of Ge-DQDs/Si-coupling barrier that is coupled to p+-Si S/D via Si3N4 tunneling-barriers.

Figure 2 shows ID-VGL-VGR characteristics and the transport diagram when Ge DQDs are biased at VDS = − 250 mV and measured at the base temperature of 4.5 K in the darkness. Sweeping VGR and VGL induces characteristic oscillatory tunneling current behaviors when VGR < − 4 V and VGL < − 3 V (Fig. 2a). The current peaks emerge as a consequence of single-hole transport through the DQDs due to Coulomb blockade, which is allowed only when energy levels of QDL and QDR falling within the VDS bias window are simultaneously in resonance and alignment with the fermi-level of source reservoir. The tunneling current peaks marked by “A”, “B”, … in Fig. 2a correspond to the triple points in the transport diagram of Fig. 2b. In the vicinity of the triple points, current flows due to the co-existence of three charge states, namely, (N, M), (N + 1, M), and (N, M + 1) where the parentheses indicate the charge configuration of the DQDs and N/M denotes the absolute number of holes in the left/right QDs. The triple points in Fig. 2b appear to be blurred since multiple energy levels are covered within the large VDS bias window of 250 mV. In this case, resonance conductance, inelastic processes, and co-tunneling are possibly involved. Thereby, it is not easy to accurately outline the hexagonal-shaped features in the transport diagram. Thanks to strong confinement in our Ge DQDs/Si/Si3N4 system, we are able to sketch the hexagonal features based on the tunneling current peaks marked in Fig. 2a in combination with the boundaries appearing in the color-mapping transport diagram (Fig. 2b).Fig. 2 (a) ISD-VGR-VGL and (b) transport diagrams of Ge DQDs/20 nm-thick Si barrier measured at VD = − 250 mV and the base temperature of 4.5 K in the darkness. In (b), the current is plotted in logarithmic-scale for better clarity.

Photon spectroscopy has been reported to be a valuable tool for studying the energy spectra of QDs18. Figure 3a shows that illumination at λ = 850 nm with power of 0.3 nW (48.4 pW/μm2) enhances the transport current magnitude (> 10×) and makes charge states associated with fewer hole numbers observable at smaller VGR (− 2 to − 3.5 V) and VGL (− 3 to − 4 V) as compared to that measured in the darkness. Our previous report on Ge-QD SHTs has also observed that illumination at λ = 850 nm indeed facilitates charge transport through the QD under 3.8 nW optical pumping via photon-assisted tunneling19.Fig. 3 (a) ISD-VGR-VGL and (b) transport diagrams of Ge DQDs/20 nm-thick Si barrier measured at VD = − 50 mV and the base temperature of 4.5 K under illumination at λ = 850 nm with optical power of 0.3 nW. In (b), the current is plotted in logarithmic-scale for better clarity.

The transport diagram of DQDs under 0.3 nW, λ = 850 nm illumination in Fig. 3b reveals several characteristic hexagonal-shaped cells due to Coulomb blockade. The slopes of transition lines between neighboring charge states measured in the darkness (Fig. 2b) and under illumination (Fig. 3b) are nearly identical. It is clearly seen in Fig. 3b that the dimensions of hexagonal charge states are large, indicating that large intra-QD charge energies (ECL and ECR) are large in the left and right QDs. A typical gate-voltage spacing of (ΔVGR, ΔVGL) = (0.32 V, 0.27 V) suggests a small gate capacitance of CGR = 0.5 aF and CGL = 0.59 aF using ΔVGR(L) = e/CGR(L)20, where CGR and CGL are the gate capacitance of QDR and QDL capacitively coupled to plunger gate-R and plunger gate-L, respectively. Estimated diameters of QDR and QDL from CGR and CGL are 19.2 nm and 20.8 nm, respectively, which agree well with the values of QD diameter (~ 20 nm) obtained from TEM examinations (Figs. 1 and 4f).Fig. 4 Plan-view SEM micrographs of (a) the AA mesa with a fanout ridge of Si. Inset highlights the included-angle locations of the Si-ridge. Cross-sectional SEM micrographs of (b) a bi-layer deposition of 12 nm-thick Si3N4 and 25 nm-thick poly-Si0.85Ge0.15 on the Si-ridge and (c) the formation of poly-Si0.85Ge0.15 spacer layers with width/height of 25 nm/30 nm at each sidewall of the Si3N4-encapsulated Si-fanout ridge using an etch back process. Poly-Si0.85Ge0.15 spacer islands were produced via (d) lithographic patterning and (e) HBr/O2 plasma etching. (f) Thermal oxidation produced Ge DQDs that have self-aligned Si reservoirs and self-organized Si coupling barrier. (g) Ge DQDs/Si-CB/Si S/D equipped with controlled gates.

Discussion

The experimental identification of charge-stability diagram of DQDs is crucial for practical operations of qubits using the degree of freedoms of charge and spin. The charge-stability diagram visualizes the equilibrium charge states and provides the information of bias-voltage conditions to accurately control the charge occupancy within the DQD system. Also, the charge-stability diagram is of great value in characterizing the energy scales of a DQD system including the intra-QD charging energy, inter-QD charging energy (ECm), and inter-QD coupling energy19. However, an absolute determination of charge occupancy within DQDs is difficult by simply using a direct current method. In general, it requires the integration of charge sensors (for example, SETs or quantum point-contact devices) with DQDs so that DQDs could be biased in the linear regime (that is, VDS ~ 0)21. Our Ge DQDs are equipped with TBs of Si3N4 and CB of Si by design. A large barrier height of 2.6 eV from Si3N4 TBs imposes strong confinement onto holes within the DQDs, whereas the Si CB with a smaller barrier height of 0.26 eV facilitates hole shuttling between DQDs. A combination of a small Ge QD in diameter and strong confinement arising from barriers of Si3N4 results in a large addition energy (Ea) of > 50 meV in the Ge QD15,17. Thereby, a direct measurement of VG-scan photo-current spectra by applying a small dc bias (VDS ≤ 50 meV) across the DQDs under illumination allows a quick estimation of charging energies of the individual QDs and identifies preliminary bias conditions of charge states within DQDs.

Large ΔVGR and ΔVGL (> 200 mV) of hexagonal cells suggest large charging energy for right and left QDs, respectively, which are favored for practical initialization, manipulation, and even readout22 of charge states within DQDs since the participating charge states are less susceptible to shot noises from external bias sources. For comparison, typical gate-voltage spacings of honeycomb cells for the gate-defined DQDs are in the range of few mV–tens mV1–6, imposing strict requirements on the noise levels of plunger-gate voltage sources (≤ sub-mV scales). The detuning line, located between the neighboring charge states with the same total charge number, signifies one charge shuttling between DQDs and can be experimentally determined by connecting the nearest triple points. The voltage spacings (ΔVgR or ΔVgL) of the detuning line relates to the inter-QD charging energy, that is, the change in the potential energy of one QD when a charge is added to/from the other QD. The experimental values of (ΔVgR, ΔVgL) = (0.05 V, 0.049 V) in Fig. 3b are much smaller than (ΔVGR, ΔVGL) = (0.32 V, 0.27 V), representing our Ge DQDs being in weak-intermediate coupling conditions. The voltage spacing ΔVgR(L) relates to the coupling capacitance Cm between DQDs via ΔVgR(L) = eCm/(CGR(L) × CL(R)) = ΔVGR(L) × Cm/CL(R), where CR(L) is the sum of all capacitances attached to the QDR(L) via CR(L) = CD(S) + CGR(L) + Cm20. CD(S) is the capacitance of QDR(L) coupled to drain (source) through a tunnel barrier of 12 nm-thick Si3N4 and Cm is the coupling capacitance of DQDs through the coupling barrier of 25 nm-thick Si in this work. Estimated intra-QD and inter-QD charging energies are EC,R = 48.9 meV, EC,L = 42.7 meV, and ECm = 7.8 meV, using EC, R(L) = (e2/CR(L))/(1−Cm2/(CL × CR)) and ECm = (e2/Cm)/(CL × CR/Cm2−1). Both intra-QD charging energy and inter-QD charging energy are large, indicating that our Ge DQDs system is insensitive to the fluctuations arising from applied voltage sources and environment temperature.

Conclusion

Our physically-defined, self-organized Ge DQDs/Si3N4/Si system comes with an inherent advantage of large intra-QD and inter-QD charging energies thanks to strong confinement, which are conducive for higher temperature operation in comparison to the gate-defined QD system. However, the strong confinement and weak coupling make it difficult to acquire the transport diagram of our Ge DQDs/Si3N4/Si system in the linear transport regime since a large VDS bias is needed to obtain measurable transport current. Our experimental discovery shows that charge transport through our Ge DQDs system is significantly facilitated by photon-assisted tunneling under illumination at λ = 850 nm with a low power density of 48.4 pW/μm2. Thereby, photon-assisted transport diagram of Ge DQDs in the linear transport regime was measured at the base temperature of 4.5 K, Plunger gate-controlled hexagonal-shaped features were observed over a wide range of hole occupancy. The dimensions (ΔVGL and ΔVGR ~ 0.3 V) of the hexagonal charge states of our Ge DQDs are considerably larger than that (few–tens mV) of gate-defined QDs, suggesting that our Ge DQDs system has better immunity to shot noises arising from external voltage sources. Our study reveals that a direct photocurrent measurement offers a quick estimation of intra-QD charging energies of the individual QDs and facilitates the identification of charge states from the transport diagram.

Methods

The fabrication of self-organized Ge DQDs/Si CB/Si3N4 TB with self-aligned p+-Si S/D

Starting with an SOI substrate with a 100 nm-thick unintentionally-doped c-Si (100) layer, a circular-shaped active-area (AA) mesa with diameter of 40 μm was patterned using lithographic patterning and C4F8/SF6 plasma etching. A Si fanout-ridge was then delineated within the AA mesa using combined processes of electron-beam lithography (EBL) on PMMA A2 positive resist, cold development of MIBK/IPA at T = − 5 °C, and C4F8/SF6 plasma etching (Fig. 4a). Enlarged SEM micrograph in Fig. 4a highlights the included-angle locations of the Si-ridge, at which Ge DQDs were to be created by the subsequent processes. Conformal layers of 12 nm-thick Si3N4 and 25 nm-thick poly-Si0.85Ge0.15 were sequentially deposited using LPCVD (Fig. 4b). Following a direct etch-back process using HBr/O2 plasma, poly-Si0.85Ge0.15 spacer layers with a height of 30 nm were produced at each sidewall of the Si3N4-encapsulated Si-ridge (Fig. 4c). To produce poly-Si0.85Ge0.15 spacer islands, a 200 × 100 nm2 ellipsoidal-shaped pattern was created at the included-angle locations of the Si-ridge using EBL on NEB-22 negative resist, 2.38% TMAH development at T = 25 °C (Fig. 4d), followed by HBr/O2 plasma etching. Notably, the Ge-QD diameter is essentially determined by the width, height, and length of poly-Si0.85Ge0.15 spacer islands, which are controllably tuned by adjusting process times of poly-Si0.85Ge0.15 deposition, HBr/O2 etch-back, and EBL exposure, respectively. For the formation of Si CB and S/D, a square trench was produced using EBL and CHF3/CH4/Ar and HBr/O2 plasma etching processes to remove Si3N4 and Si, respectively (Fig. 4e). Following thermal oxidation in an H2O ambient at T = 900 °C, Ge DQDs with diameter of 20 nm were created at the designated included-angle locations via selective oxidation of poly-Si0.85Ge0.15 spacer islands (Fig. 4f). Notably, exposed sidewalls of the Si square trench were simultaneously oxidized. Thereby, concurrent with the formation of Ge DQDs, the conjunction of Si CB and S/D was completely disconnected. In this way, Ge DQDs, Si CB, and Si-S/D were simultaneously formed in a single process step of oxidation. Bi-layers of 25 nm-thick SiO2 and 100 nm-thick in-situ boron-doped poly-Si layer were sequentially deposited using LPCVD for forming the gate-oxide and PG layers. Next, boron-doped poly-Si PGs were produced using EBL on NEB-22, TMAH development at T =  + 4 °C, and then C4F8/SF6 plasma etching. A 400 nm-thick SiO2 layer was deposited to passivate Ge DQDs. Finally, the fabrication of Ge DQDs was completed by contact-hole patterning, 500-nm-thick aluminum metal-pads formation, and forming gas (95% N2/5% H2) anneal at T = 400 °C (Fig. 4g).

Electrical characterization

Steady-state transport diagrams of Ge DQDs measured in the darkness and under illumination were conducted in a Lake Shore CRX-4K probe station. While the base temperature is set at T = 4.5 K, the effective hole temperature in the electrodes is higher and varies between 10 and 16 K. Current through Ge DQDs was characterized by independently sweeping PG voltages, VGL and VGR, to control potential energy of Ge QDL and QDR, respectively, at small drain bias (VDS), using Keysight B1500A semiconductor analyzer equipped with B1517A high-resolution source monitor unit (HRSMU), E5288A atto sense and switch unit (ASU). The null current measured at the base temperature of 4.5 K is 4 ± 4 fA. A laser source at wavelength (λ) of 850 nm is nearly normal-incident (80 degrees from the horizon) onto the Ge DQDs through a lens fiber with a spot size of 10 × 10 μm2.

Acknowledgements

This work was supported by the National Science and Technology Council, Taiwan, under Grants NSTC 112-2119-M-A49-006 and 113-2119-M-A49-007and tsmc.

Author contributions

W.I.H. conducted Ge-DQDs fabrication and performed electrical measurements. C.Y.W. conducted Ge-DQDs fabrication. L.H.C. contributed to data analysis. L.P.W. conceived the study, supervised the work, contributed to data analysis and manuscript preparation. All authors read and approved the final manuscript.

Data availability

The datasets used and/or analyzed during the current study available from the corresponding author on reasonable request.

Competing interests

The authors declare no competing interests.

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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