Three-dimensional imaging of integrated-circuit activity using quantum defects in diamond

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Three-dimensional imaging of integrated-circuit activity using quantum defects in diamond

Marwa Garsi, Rainer Stöhr, Andrej Denisenko, Farida Shagieva, Nils Trautmann, Ulrich Vogl, Badou Sene, Florian Kaiser, Andrea Zappe, Rolf Reuter, and Jörg Wrachtrup

Phys. Rev. Applied 21, 014055 – Published 29 January 2024

Abstract

The continuous scaling of semiconductor-based technologies to micrometer and submicrometer regimes has resulted in higher device density and lower power dissipation. Many physical phenomena such as self-heating or current leakage become significant at such scales, and mapping current densities to reveal these features is decisive for the development of modern electronics. However, advanced noninvasive technologies either offer low sensitivity or poor spatial resolution and are limited to two-dimensional spatial mapping. Here we use near-surface nitrogen-vacancy centers in diamond to probe Oersted fields created by current flowing within a multilayered integrated circuit in predevelopment. We show the reconstruction of the three-dimensional components of the current density with a magnitude down to about ≈10 µA/µ $m^{2}$ and submicrometer spatial resolution at room temperature. We also report the localization of currents in different layers and observe anomalous current flow in an electronic chip. Our method therefore provides a decisive step toward three-dimensional current mapping in technologically relevant nanoscale electronics chips.

Received 11 September 2023
Accepted 18 December 2023

DOI:https://doi.org/10.1103/PhysRevApplied.21.014055

Physics Subject Headings (PhySH)

Magnetometry Quantum sensing Transport phenomena

3-dimensional systems Devices for digital logic, storage & processing Nanostructures Nitrogen vacancy centers in diamond

Optically detected magnetic resonance

Condensed Matter, Materials & Applied PhysicsQuantum Information, Science & Technology

Authors & Affiliations

Marwa Garsi ^1,2,*, Rainer Stöhr ¹, Andrej Denisenko², Farida Shagieva², Nils Trautmann³, Ulrich Vogl ³, Badou Sene ⁴, Florian Kaiser ^1,†, Andrea Zappe¹, Rolf Reuter¹, and Jörg Wrachtrup ¹

¹Third Institute of Physics, IQST, and Research Center SCoPE, University of Stuttgart, 70569 Stuttgart, Germany
²Solid State Quantum Technologies, TTI GmbH, 70569 Stuttgart, Germany
³Corporate Research and Technology, Carl Zeiss AG, Carl-Zeiss-Straße 22, 73447 Oberkochen, Germany
⁴Mobility Electronics, Robert Bosch GmbH, 72762 Reutlingen, Germany

^*m.garsi@pi3.uni-stuttgart.de
^†Now at Luxembourg Institute of Science and Technology (LIST).

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Vol. 21, Iss. 1 — January 2024

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Images

Figure 1
Mapping integrated circuit (IC) activity with quantum sensors. (a) Schematic of the experiment. A microfabricated diamond plate contains a layer of near-surface $N − V$ centers and is glued to an integrated circuit. The sample is mounted to an inverted microscope where laser and microwave (MW) radiations excite the $N − V$ centers. A charge coupled device camera records the emitted photoluminescence (PL). (b) Photograph of the IC microchip. The top picture shows the overall chip with different circuit designs. The diamond plate is glued to a region of interest outlined by a blue square. A copper wire carrying MWs is placed next to the diamond, and wire bonds connect the chip to a power supply. The bottom picture shows a zoom-in on the diamond plate. Scale bars are 200 µm for the top photograph and 20 µm for the bottom one. (c) Visualization of the cross-section of the experiment. The current-carrying wires generate Oersted fields sensed by a layer of $N − V$ centers represented in red and separated by a protective overcoat from the leads. Solid lines with arrows represent the magnetic flux lines, and dashed lines represent magnetic field isolines. (d) Representation of the four possible tetrahedral orientations of the $N − V$ bond (A, B, C, D) in the x-y-z reference frame. (e) ODMR spectra from a single pixel near the edge of a semiconductor stripe indicated by the white cross in (b). The blue spectrum is obtained with a bias magnetic field B₀ used to split the eight resonances lines of the $N − V$ ensemble. The orange spectrum is acquired when current flows in the IC, creating a shift in the resonances due to the Zeeman interaction of the $N − V$ centers with the Oersted field. Solid lines are multiple-Lorentzian fits. Each resonance is labeled according to the corresponding $N − V$ orientation, defined in (d).
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Figure 2
Vectorial magnetic field produced by the current-carrying wires: device 1 versus device 2 and corresponding current density maps. (a),(b) Optical images of device 1 and device 2, respectively. (c),(d) Mapping of the three vectorial magnetic field components B_x, B_y, B_z produced by the operational and defective IC, respectively. The sign gives the direction of the field. Linecuts at y_A, y_A_′, y_B, y_B_′ are shown in Figs. 3 and 3 for further analysis. Linecuts at x_C, x_C_′ are shown in the Supplemental Material [38]. (e),(f) Corresponding in-plane current density map reconstructed from B_x and B_y in (a) and (b) respectively. The orange labels indicate the sections where the current amplitudes in Fig. 3 are estimated. Scale bars are 10 µm.
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Figure 3
Experimental contributions of Oersted fields originating from different layers. (a) Schematic view of the x-z plane of the experiment. The variables used to fit the data with Eq. (2) are labeled according to an arbitrarily chosen observation point Obs. (b) Linecuts of experimental data (blue dots) outlined in Fig. 2 along the x-axis at a vertical position y_A (left panel) and at a vertical position y_B (right panel). The fit (solid red line) returns a current amplitude of I_A = 11.77(6) mA where the source-sensor distance is fixed at Δz_A = 4.5 µm for the left panel and current amplitudes of I_B₁= 5.64(5) mA, I_B₂= 3.49(8) mA, I_B₃= 5.76(5) mA where the source-sensor distances are fixed at Δz_B_1,B3= 4.5 µm and Δz_B₂= 8.5 µm for the right panel. (c) Linecuts of experimental data (blue dots) outlined in Fig. 2 along the x-axis at a vertical position y_A_′ (left panel) and at a vertical position y_B_′ (right panel). The fit (solid red line) returns a current amplitude I_A_′= 1.18(4) mA where the source-sensor distance is fixed at Δz_A_′= 4.5 µm for the left panel and current amplitudes of I_B'₁= 0.50(3) mA, I_B'₂= 0.73(5) mA, I_B'₃= 0.39(3) mA where the source-sensor distances are fixed at Δz_B'_1,B'3= 4.5 µm and Δz_B'₂= 8.5 µm for the right panel. Error bars correspond to one standard deviation. Plain colors underline the contribution of each single wire.
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Figure 4
Simulation of Oersted field contributions originating from different layers. (a) Geometry of the simulated structure. A layer of $N − V$ centers is separated from the chip by 0.8 µm. The structure is composed of 12 layers comprising the two ALs and TSVs. A current of amplitude I_α = 11.8 mA goes to the main branch of the first AL, flows down to the bottom layer of the structure where it splits into two subpaths with an amplitude of I_α₂= I_α/2 and flows back to the first AL. In the second AL, a current of amplitude I_β = 2 mA is injected into each of the two branches which combine to a single one afterwards. (b) Top view of each AL of the structure. The first AL, second AL, and the bottom layer of the structure are located at z₁= 4.5 µm, z₂ = 7.9 µm and z₃= 12.2 µm respectively from the sensors. (c) Top: Oersted field in the x-y plane generated by all active components at the sensors layer position. Bottom: Separate contribution from each AL where the vertical axis shows the lateral magnetic field amplitude |B_xy|.
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Figure 5
Current density maps. (a)–(c) Images of the three vectorial components of the current density J_x, J_y, J_z for device 1. Scale bars are 10 µm. (d) Three-dimensional representation of the current flow in the outer layer of the IC. The thickness of the arrow scales with the total current density magnitude and the color scales with the magnitude of J_z.
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