Microelectronics Reliability xxx (2015) xxx–xxx

MR-11620; No of Pages 5

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Microelectronics Reliability

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Nitrogen-Vacancy centers in diamond for current imaging at the redistributive layerlevel of Integrated Circuits

A. Nowodzinski a,⁎,1, M. Chipaux b,1,2, L. Toraille b,3, V. Jacques c, J.-F. Roch c, T. Debuisschert b

a CEA, LETI, MINATEC Campus, F-38054 Grenoble, Franceb Thales Research & Technology, 1 Av. Augustin Fresnel, 91767 Palaiseau cedex, Francec Laboratoire Aimé Cotton, bât 505 Campus d'Orsay, 91405 Orsay cedex, France

⁎ Corresponding author.E-mail address: antoine.nowodzinski@cea.fr (A. Nowo

1 These two authors contributed equally to this work.2 Current position: University of Groningen/Universi

Department of Biomedical Engineering, Antonius DeusiThe Netherlands.

3 Present address: Ecole Normale Supérieure de Lyon7000, 69342 Lyon Cedex 07, France.

http://dx.doi.org/10.1016/j.microrel.2015.06.0690026-2714/© 2015 Elsevier Ltd. All rights reserved.

Please cite this article as: A. Nowodzinski, eIntegrated Circuits, Microelectronics Reliabil

a b s t r a c t

a r t i c l e i n f o

Article history:Received 22 May 2015Accepted 11 June 2015Available online xxxx

Keywords:NV color centerMagnetic Current Imaging

We present a novel technique based on an ensemble of Nitrogen-Vacancy (NV) centers of diamond to performMagnetic Current Imaging (MCI) on an Integrated Circuit (IC). NV centers of diamond permit to measure thethree components of the magnetic fields generated by mA range current in an IC structure over a field of50 × 200 μm with sub-micrometric resolution. Vector measurements allow the use of a more robust algorithmthan those used for MCI using GMR or SQUID sensors and it is opening new current reconstruction prospects.Calculated MCI from these measurements shows a very good agreement with theoretical current path. Acquisi-tion time is around 10 s, which is much faster than scanning measurements using Superconducting QuantumInterference Device (SQUID) or Giant Magneto Resistance (GMR). The experimental set-up relies on a standardoptical microscope, and the measurements can be performed at room temperature and atmospheric pressure.These early experiences, not optimized for IC, show that NV centers in diamond could become a real alternativefor MCI in IC.

© 2015 Elsevier Ltd. All rights reserved.

1. Introduction

Magnetic Current Imaging (MCI) has demonstrated its ability toperform efficient failure localization in electron devices whether it is“short” [1] or even “open” failure [2]. Commercial MCI for electrondevices uses either Superconducting Quantum Interference Devices(SQUIDs) or Giant Magneto Resistance (GMR) sensor. Working at cryo-genic temperature in vacuum chamber, SQUID reaches sensitivity aslow as 40 pT/Hz1/2 [6] with microscale spatial resolution. On the otherhand, GMR sensors allowmeasurement at room temperature and stan-dard pressure with sensitivity close to 10 nT/Hz1/2 [6] and submicronicresolution. Magnetic field images obtained with those two techniquescan be converted to current cartography thanks to the Biot–Savart lawinversion as described by Roth in [3].

Recently, the Nitrogen-Vacancy (NV) center in diamond has beenstudied for its remarkable properties. In particular, new types ofmagne-tometer devices have been developed exploiting the spin properties ofthis color center. A first example is scanning field microscopy where a

dzinski).

ty Medical Center Groningen,nglaan 1, 9713 AV Groningen,

, 15 parvis René Descartes, BP

t al., Nitrogen-Vacancy centeity (2015), http://dx.doi.org/1

single NV center placed on an Atomic Force Microscope (AFM) tip,allows magnetic mapping at the nanoscale, with sensitivity downto 10nT=

ffiffiffiffiffiffiHz

p[4]. A second example is far-field magnetic microscopy

with an ensemble of NV centers located at the surface of a diamondplate. It provides directly a diffraction limited image (500 nm) ofthe three spatial components of the magnetic field, with no require-ment of any scanning procedure [5]. A sensitivity of 2μT � μm=

ffiffiffiffiffiffiHz

p4

has been reported.The goal of this paper is to investigate the application of such far-

fieldmagnetic imager forMCI. First, we describe theprinciple of NV cen-ters based magnetic imaging. Then, measurement of the magnetic fieldproduced by an IC is presented, as well as the MCI reconstruction.

2. Measurement of the magnetic field thanks to the NV color centerin diamond

2.1. Principle

The NV center is a crystalline defect of diamond constituted of anitrogen atom (N) substituted to a carbon atom and a vacancy(V) located on an adjacent crystalline site of the lattice (cf. Fig. 1a).

4 The sensitivity is shot noise limited. It depends on the surface over which the signal isintegrated. Here, magnetic fields as low as 2 μT can be detected in 1 s, for a 1 μm2 integra-tion surface.

rs in diamond for current imaging at the redistributive layer level of0.1016/j.microrel.2015.06.069

Fig. 1.NV center in diamond. a) The NV center of diamond is constituted by a nitrogen atom (N) substituted to a carbon atom, and a vacancy in an adjacent site. This quantum object ab-sorbs light in the green (at 532 nm in our case) and emits a perfectly stable photoluminescence in the red domain (between 600 to 800 nm). b) Energetic diagram associated with itsinternal electronic spin. The degeneracy between the zero spin state (ms=0) and the non-zero spin state (ms=±1) is shifted by the spin–spin interaction. In the presence of an externalmagnetic field (in blue), the degeneracy between the state ms = −1 and the state ms = +1 is lifted. The frequency difference, given by Eq. (1) is proportional to the projection of themagnetic field on the NV axis. c) Electron Spin Resonance (ESR) spectrum. Resonances between the state ms = 0 and the state ms = ±1 induced by a microwave field (in purple) canbe detected optically by a decrease of the photoluminescence. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

2 A. Nowodzinski et al. / Microelectronics Reliability xxx (2015) xxx–xxx

The NV center is a perfectly photostable photoluminescent objectwith an internal degree of freedom related to its total spin angular mo-mentum (S=1). It can be optically polarized in itsms=0 state. Its spinstate can be optically read out by its photoluminescence level that islower for the ms = ±1 than for the ms = 0 spin state. Consequently,resonances between those spin states, induced by a microwave signalcan be detected by purely optical means.

Fig. 1c represents the photoluminescence of a NV center submittedto an increasing magnetic field. For a zero field, the states ms = −1and ms = +1 are degenerated, and the spectrum presents only oneresonance at v0 = 2.87 GHz corresponding to the resonance betweenthe states ms = 0 and ms = ±1. With a non-zero magnetic field, thedegeneracy between the states of non-zero spin is lifted.

The two resonances, at v− and v+ correspond to the transitionsbetween thems=0 state and thems=−1 andms=+1 states respec-tively. The frequency difference is given by:

νþ−ν− ¼ 2gμB

hBNV : ð1Þ

BNV is the projection of the magnetic field along the axis of the NVcenter, g is the Landé factor of the NV center, μB is the Bohr magnetonand h is the Planck constant. The projection of the magnetic fieldalong the NV axis can thus be deduced by the measurement of thisfrequency difference.

2.2. Far field magnetic microscopy

Themagnetic imager is described in detail in [5]. It relies on an ultra-pure diamond plate holding an ensemble of NV centers located 10 nmbelow the surface. They are produced by ion implantation. As depictedin Fig. 2a, this layer is pumped by a green laser at 532 nmand submittedto a microwave field. An image of its luminescence signal is obtainedwith a standard optical microscope (cf. Fig. 2b).

Here, the field of view (around 50 × 200 μm) is determined by thesize of the laser spot. In our case, the use of a microscope objectivewith a magnification of 10 and a numerical aperture of 0.1 is welladapted to the object we are investigating.

Please cite this article as: A. Nowodzinski, et al., Nitrogen-Vacancy centeIntegrated Circuits, Microelectronics Reliability (2015), http://dx.doi.org/1

A microwave excitation is applied to the sample. Its frequency isswept in the range around 2.87 GHz and an image of the luminescenceover the region of interest is taken at each step. Consequently, a wholeESR spectrum can be obtained for each single pixel of the image(cf. Fig. 1c).

Each spectrum features four pairs of resonances. They correspond tothe projections of the magnetic field along the four possible NV centeraxis orientations inside the diamond lattice (Eq. (1)). Exploiting thosefour projections allows retrieving the complete vector components ofthe magnetic field.

3. Magnetic Current Imaging

3.1. Principle

In [3], Roth describes how to reverse the law of Biot–Savart and thuscalculate the current density when the magnetic field is measured. It isshown that Bx, By and Bz the three components of the magnetic fieldsare the results of a convolution between filters and the two componentsof the current in the plane: Jx and Jy (the vertical component is assumedto be zero).

GMR and SQUID sensors are only sensitive to Bz which is itselfdependent on two components Jx and Jy. Thanks to the addition of thehypothesis of continuity of current, the current image may be recon-structed since we have a system of two equations with two unknownvariables (Jx and Jy).

NV color centers provide also Bx and By the two other components ofthe magnetic field which build thus an overdetermined system of fourequations and two unknown variables. This adds constraints on thecurrent image and therefore should reduce noise.

In Eq. (2), theBiot–Savart law iswritten as an integral of a vector prod-

uct where μ0 is the vacuum permeability, j!

is the current density that

generates the magnetic field B!

at a position defined by the vector r!.

B!

r!� �

¼ μ0

4π

Z j!

r 0!� �

∧ r!−r 0!� �

r!−r 0!������ d3 r 0

!: ð2Þ

rs in diamond for current imaging at the redistributive layer level of0.1016/j.microrel.2015.06.069

a)

c)

b)

d)

Fig. 2. Far field photoluminescence microscopy of ensemble of NV centers. a) An ultrapure 4 mm × 4 mm × 250 μm diamond parallelepiped (yellow) holds and ensemble of NV centers(red) located close to itsmain face. This active layer is placed in contact to the sample (purple). Then, a pumping beam(green) is propagated inside the diamond and illuminates an area ofthis active layer. Amicrowavefield is applied through an antenna. Thephotoluminescence signal is collected indirection z by a standard opticalmicroscope and imaged on a digital camera.b) Image of photoluminescence of the NV center layer. c) ESR spectrum for one given pixel. d) Spatial components of themagnetic field calculated from the images of photoluminescence.(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

3A. Nowodzinski et al. / Microelectronics Reliability xxx (2015) xxx–xxx

It can be viewed as the convolution of the current density with a fil-ter function. Since z is fixed to zmes, it is a two dimensional problem in xand y direction of the space. It takes a simpler expression in the (kx, ky)Fourier space:

B!T F kx; ky; zmes

� � ¼ μ0

4 � π J!T F∧ F

! ð3Þ

where B!T F and J

!T F are the Fourier transform of the magnetic field and

current density respectively. F!

is the Fourier transform of vector f!

whose components are given by:

f l x; y; zmesð Þ ¼ lffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffix2 þ y2 þ zmes

2p l ¼ x; y; zmesð Þ: ð4Þ

In addition to the expressions of the components of the magneticfield, one can use the continuity of current expressed in the frequencydomain by:

i � kx � Jx T F þ i � ky � JyT F ¼ 0 ð5Þ

where we have considered an in-plane current ð Jz T F ¼ 0Þ: The overde-termined system of 4 equations and two unknowns (Jx and Jy) can beexpressed in matrix form by:

B ¼ M � J ð6Þ

with

B ¼BT Fx

BT Fy

BT Fz0

���������

���������M ¼

0 Fzmes

−Fzmes 0Fy −Fx

i � kx i � ky

��������

��������J ¼ Jx

T F

JyT F

����������: ð7Þ

In this paper, standard matlab@ QR solver is used to find the matrixof current density JTF. Once the two components of the current densityare found in the space frequency, an inverse FFT is applied to obtainthe current in the real space.

Our component used for the evaluation of MCI calculated from NVcolor center is only a 2D structure but it worth noting that the systemof Eq. (7) can be transformed into a system of 4 equations with 3

Please cite this article as: A. Nowodzinski, et al., Nitrogen-Vacancy centeIntegrated Circuits, Microelectronics Reliability (2015), http://dx.doi.org/1

unknowns ( JxT F , Jy

T F and JzT F ) in order to calculate the 2D image of

the JzT F , the out of plane component of a current flowing in a 3D

structure.It is clear that the vector magnetic field measurement authorized by

the use of NV color centers opens new current reconstruction prospects.

3.2. Measurements

The sample used forMCI is depicted Fig. 3a and b. It consists ofmetallines deposited over resin and forming serpentines. One of theseserpentines is far enough from the pads to accommodate the size ofthe diamond (4 × 4 mm).

Fig. 3c to f shows the good agreement between assumed currentpath and calculated MCI. In Fig. 3e and f, areas bounded by the dashedlines highlight the shape of the laser spot, the lack of light outside ofthe laser spot inducing automatically an increase of the measurementnoise.

For eachMCI, the magnetic field acquisition time is 10 s and calcula-tion time for the reconstitution of the magnetic field is 1 min. This veryshort measurement time should be compared to the case of sensorscanning instruments whose acquisition time may exceed several tensof minutes.

Fig. 3c shows the interest to calculate the MCI from the vector mag-netic field rather than just the vertical component of the magnetic fieldas it is donewith classical MCI. To calculate the MCI with only the verti-cal component, we use the same matrices B and M but removing thefirst two lines of M and B in order to build a system of 2 equations and2 unknowns (Jx

T F , JyT FÞ. Moreover, it was applied a Blackman window

before calculating the inverse FFT of current density components. Thisoperation is not necessary when the MCI is calculated from the threecomponents of the magnetic field but help to suppress high frequencynoise generated by current step at the edge of frequency domain ofJx

T F and JyT F .

The quality difference between the MCI calculated from the threecomponents of the magnetic field and the MCI calculated from onlythe vertical magnetic field can be explained because overdeterminedsystem define in Eq. (7) provides redundant information to calculatethe current density. Thus, MCI obtained from the three components ofthe magnetic field is much more tolerant to noise measurement thanthe MCI obtained with only vertical component of the magnetic field.

rs in diamond for current imaging at the redistributive layer level of0.1016/j.microrel.2015.06.069

a)

c)

b)

d)

e)

f)

Fig. 3. Sample used for the MCI and MCI. a) View of the Integrated Circuit used for the test, the dashed line encloses the area where the measurements were made. b) Details of the areaused for themeasurements. Three serpentines are used forMCI testing, for all the line is 10 μmwide, but thepitches can be15 μmfor the narrowest, 20 μmor 40 μmfor thewidest. c)MCI ofa current of 6 mA using the three components of the magnetic field (upper figure) or using only the component in the z direction of the space (figure below), in the latter case theserpentine is hardly recognizable d) and e) MCI of a current of 10 mA. f) MCI of a current of 8 mA. The dashed lines delimit area beyond which the noise increases.

4 A. Nowodzinski et al. / Microelectronics Reliability xxx (2015) xxx–xxx

Besides the sensor is closer to the current, it is one of the reasons thatdespite large measurement noise (compared with GMR or SQUIDsensors) MCI remains feasible at milliampere range.

Fig. 4 is an attempt to determine theminimumdetectable current forthe sample and for themeasurement configuration used in this paper. Ithas been found that minimum detectable current is 0.5 mA, which isvery encouraging for a first non-optimized setup and with an acquisi-tion time of 10 s.

4. Conclusion

The MCI described in this paper with a non-optimized setup for ICshows remarkable results. The instrument providing the vectormagnet-icfield for theMCI calculation is very simple andusable at room temper-ature and atmospheric pressure. It enablesmeasuring themagneticfieldvector over a field of 50 × 200 μm in less than 10 s. The field of viewbeing limited by the laser spot size, it can be easily expanded by

a)

Fig. 4. Comparison ofMCI using Bz andMCI using Bx, By and Bz. a) Fig 3c after offset subtractionMeasured standard deviation is 0.15 mA, it was considered that the minimumdetectable currenfrom the sensor to the sample, geometry of the conductive line and measuring conditions of fi

Please cite this article as: A. Nowodzinski, et al., Nitrogen-Vacancy centeIntegrated Circuits, Microelectronics Reliability (2015), http://dx.doi.org/1

increasing the height of the diamond in order to enlarge the laserspot. The surface of the diamond plate can be reduced to performmea-surement on smaller IC. Then the spatial resolution can be decreaseddown to 500 nm, at the limit given by optical diffraction.

Vectormeasurements allow the use of amore robust algorithm thanthose used for MCI using GMR or SQUID sensors and may suggest thatnew reconstruction algorithm could be developed to characterize cur-rent in 3D structures.

With the setup and sample used in this paper the current resolutionis estimated to be 0.5 mA. Several ways to improve it can be investigat-ed. For example, differential measurements can eliminate the back-ground noise [5], which would directly result in an improvement ofthe sensitivity and lead to a total time of acquisition and treatmentbelow the second. In addition, several ways to improve the perfor-mances of the wide-field magnetic imager itself can be foreseen, usingeither optimized diamond crystals [7,8] or pulsed measurement tech-niques [9,10].

b)

and normalization to 6mA. b) Histogram of the zone surrounded by awhite line in Fig. 4a.t is 0.5 mA (≈3σ). It is important to note that this threshold is dependent on the distanceeld B.

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Acknowledgments

The magnetic field measurements were performed in Thales TRT(Palaiseau, Fr.). The MCI reconstruction was performed in CEA-Leti(Grenoble, Fr.). The research leading to these results has receivedfunding from the European Union Seventh Framework Programme(FP7/2007-2013) under the project DIADEMS (Grant agreement No.611143) and from the Agence Nationale de la Recherche (ANR) underthe project ADVICE (Grant ANR-2011-BS04-021).

References

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Please cite this article as: A. Nowodzinski, et al., Nitrogen-Vacancy centeIntegrated Circuits, Microelectronics Reliability (2015), http://dx.doi.org/1

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