Magnetic Field Fingerprinting of Integrated-Circuit Activity with a Quantum Diamond Microscope

Current density distributions in active integrated circuits result in patterns of magnetic fields that contain structural and functional information about the integrated circuit. Magnetic fields pass through standard materials used by the semiconductor industry and provide a powerful means to fingerprint integrated-circuit activity for security and failure analysis applications. Here, we demonstrate high spatial resolution, wide field-of-view, vector magnetic field imaging of static magnetic field emanations from an integrated circuit in different active states using a quantum diamond microscope (QDM). The QDM employs a dense layer of fluorescent nitrogen-vacancy (N-$V$) quantum defects near the surface of a transparent diamond substrate placed on the integrated circuit to image magnetic fields. We show that QDM imaging achieves a resolution of approximately $10\mu \mathrm{m}$ simultaneously for all three vector magnetic field components over the $3.7\times 3.7{\mathrm{mm}}^2$ field of view of the diamond. We study activity arising from spatially dependent current flow in both intact and decapsulated field-programmable gate arrays, and find that QDM images can determine preprogrammed integrated-circuit active states with high fidelity using machine learning classification methods.

Figure 1

(a) Schematic of the QDM experimental setup with insets showing the diamond in contact with intact and decapsulated FPGAs. The diamond is positioned such that the N-$V$ layer is in direct contact with the FPGA, as indicated by the red layer in the insets. (b) Diamond crystal lattice with the nitrogen (red) vacancy (grey) defect. Lab frame coordinates ($X,Y,Z$) and N-$V$ frame coordinates for a single defect ($x,y,z$) are shown. (c) The ground state energy level diagram for a N-$V$ with fine structure and Zeeman splitting. (d) Example ODMR spectral data for an applied bias field of $(B_X,B_Y,B_Z)=(2.01.60.7)\mathrm{mT}$, showing the measured N-V fluorescence contrast, i.e., photoluminescence (PL) contrast, and resonant microwave frequencies of $f_{\pm ,i}$ with $i=1,2,3,4$ indicating each of the four N-$V$ axes. Hyperfine interactions between the N-$V^{-}$ electrons and the spin-1 ${}^{14}\mathrm{N}$ nucleus result in the splitting of each N-$V$ resonance into three lines.

Figure 2

(a) Intact Xilinx 7-series Artix FPGA with die location and dimensions indicated in red. (b) X-ray image of the FPGA package determining the position and size of die outlined in red. (c) A high-resolution image of the decapsulated FPGA with the fixed diamond measurement field of view indicated with a blue box, and the location of ring oscillator clusters indicated by red boxes labeled R1–R4. (d) Scanning electron microscope (SEM) image of the FPGA cross section showing the $500\mu \mathrm{m}$ standoff distance between the chip die and the top layer. (e) Close-up of the SEM focusing on the metal layers of die. The thickness of the passivation layer is $5\mu \mathrm{m}$ and sets the minimum standoff distance for the decapsulated measurements.

Figure 3

(a) QDM vector magnetic field maps of the decapped FPGA for different ring oscillator (RO) clusters activated in regions R1 and R2. The location of the $3.7\times 3.7{\mathrm{mm}}^2$ diamond field of view is fixed on the FPGA for all magnetic field images [see Fig. 2]. State-dependent magnetic field changes ($\mathrm{\Delta }{B}_X,\mathrm{\Delta }{B}_Y,\mathrm{\Delta }{B}_Z$) are calculated by subtracting background idle magnetic field images from active magnetic field images. Wires on the top metal layer are generally oriented in the $Y$ direction, yielding prominent $\mathrm{\Delta }{B}_X$ and $\mathrm{\Delta }{B}_Z$ fields. $\mathrm{\Delta }{B}_Y$ magnetic field maps show contributions from deeper sources. Background magnetic field maps of the idle FPGA with zero ring oscillators show variations of the field from the mean. Several different background fields are evident: a gradient from the bias magnet, distortion of the bias field from the ball grid array, and background current delivery. (b) The $\mathrm{\Delta }{B}_Z$ data for 200 ring oscillators in R1 plotted in transparency over a high-resolution optical image of circuit die. Regions of interest discussed in the text are indicated by (i), (ii), (iii), and (iv).

Figure 4

(a) QDM magnetic images indicate sensitivity to changing the number of ring oscillators in different regions for the decapsulated (decap) and intact chips when performing overlapped measurements. Different scale bars are used for feature clarity. (b) Decapsulated QDM data of $\mathrm{\Delta }{B}_{z,1}$ for a single active ring oscillator in region 1, demonstrating measurement sensitivity to the magnetic field from current supplying a single ring oscillator. Inset: Overlay of the magnified single ring oscillator magnetic field image with a high-resolution optical image of the circuit die. Each image is the average of 10 QDM (nominally identical) measurements.

Figure 5

Principal component analysis and support vector machine classification of QDM images. Region 1 is active with 0, 1, 5, 10, 50, 100, or 200 ring oscillators. (a) Example principal component basis vectors plotted as images for both decapsulated (labeled “decap” in the figure) and intact data sets. PC1 and PC2 are shown to exemplify principal components that resemble magnetic field images and thus will be useful in chip state classification. PC4 is shown as an example principal component that captures activity state-independent variations and thus will not be useful in chip state classification. (b) The PCA score for PC1, $S^{1,j}$, is plotted against the score for PC2, $S^{2,j}$, for each magnetic field image, ${\mathbf{B}}^j$, as a demonstration of state distinguishability . This distinguishability is evidenced by the separation of colors representing differing numbers of active ring oscillators. Insets magnify the scores for small numbers of ring oscillators, and show greater fidelity of state separation in the decapsulated data set compared to the intact data set. (c) Table of SVM predictions on the test set for the intact images. For each unique value of active ring oscillators, there are 12 images in the test set. Rows indicate the fraction of images predicted for each of the possible chip states. All but one prediction [indicated by the red boxes in (b) and (c)] lie on or near the main diagonal, demonstrating the high predictive power of the SVM classifier. The corresponding table for the decapsulated data set is not shown, as the main diagonal would contain 1’s and the off diagonals would contain 0’s owing to the perfect separability of each state (see Table 1).

Figure 6

Subset of the extended QDM magnetic field dataset with two ring oscillators active in region 5, region 6, or region 5 and region 6 simultaneously. The top row is high SNR data of 100 measurements taken from the decapsulated chip. Subsequent rows show the calculated magnetic image at different standoff distances of $\mathrm{\Delta }z=50\mu \mathrm{m}$, $250\mu \mathrm{m}$, $500\mu \mathrm{m}$, and $1000\mu \mathrm{m}$. The $\mathrm{\Delta }z=500\mu \mathrm{m}$ row is the closest approximation of measurements taken of an intact chip.

Figure 7

$\mathrm{PCA}+\mathrm{SVM}$ model performance metrics of the extended dataset. (a) Model accuracy is plotted as a function of the size of the dataset for both the training and test sets. A standoff distance of $500\mu \mathrm{m}$ is chosen to most closely replicate the intact dataset in the main text. (b) Model accuracy is plotted as a function of the standoff distance. The full dataset is used (100 samples per state). (c) Matrix of state predictions versus active state on chip at a standoff distance of $1000\mu \mathrm{m}$. The matrix is row normalized to 1 so that each element represents the fraction of measurements of a given state that are predicted to be any state. The red boxes enclose predictions for which the predicted region and active region are the same.