EBIC and EBAC

1. Theory

• EBIC: The SEM beam creates electron-hole pairs inside a device; pairs generated within or near a depletion region are separated by its field and collected as a current, imaged against beam position (Semitracks; Oxford).
• Gain: Each beam electron creates hundreds to thousands of pairs, so the induced current far exceeds the beam current (Semitracks).
• Diffusion length: The decay of EBIC with distance from a junction gives the minority-carrier diffusion length (Imina; Oxford).
• EBAC: Electron beam absorbed current measures the beam current flowing into a conductor network, revealing opens, shorts and resistive segments in interconnects (Oxford).

2. Working Principle

• Connections: Nanoprobes or package pins connect device nodes to a low-noise current amplifier (Imina; Oxford; Semitracks).
• Beam energy: Chosen to place generation at the depth of the junction or conductor of interest (Semitracks).
• Imaging: The amplified current modulates image brightness at each pixel, overlaid on the SE image (Oxford).
• Line scans: Averaged profiles across a cleaved junction are fitted for diffusion length (Imina).

3. Applications

• Junction delineation: Location and depth of diffusions and implants, even under metal (Semitracks).
• Defect recombination: Dislocations, grain boundaries and stacking faults in silicon, III-V and solar materials (Oxford; Semitracks).
• Failure analysis: ESD and EOS damage, gate-oxide defects and junction leakage (Semitracks).
• Interconnect opens and shorts: EBAC mapping of metal nets (Oxford).

Induced Current

Name	Formula	Related Formulae	Variables/Constants
Generation and gain	$G=\frac{E_0\left(1-\gamma \eta \right)}{E_{eh}}$	$I_{EBIC}=I_{b}G{\eta }_c$	$\begin{array}{r}G:electron-holepairsperincident\\ electron\end{array}$ $E_0:beamenergy$ $\begin{array}{r}\gamma :fractionofenergycarriedawayby\\ backscatteredelectrons(about0.5)\end{array}$ $\eta :backscattercoefficient$ $\begin{array}{r}{E}_{eh}:paircreationenergy(3.621\mathrm{eV}inSi\\ fromPowellandYoo{n}^{\prime }s2.596E_g+0.174;\\ 3.86\mathrm{eV}forGaAsfromthesamerelation\\ withanassumed{E}_g=1.42\mathrm{eV},computed)\end{array}$ $I_b:beamcurrent$ $\begin{array}{r}{\eta }_c:collectionefficiency;PowellandYoon:\\ generationrate{I}_b{E}_b\alpha /(e{E}_{EHP})with\alpha the\\ absorbedfraction,writtenhereas1-\gamma \eta \\ (myreading);Semitracks:a10\mathrm{keV}\\ electroncreatingroughly500to1000\\ pairswithionizationenergiesbelow10\\ \mathrm{eV},EBICmuchlargerthanthebeamcurrent\\ (seetheQ/A)\end{array}$ $\begin{array}{r}(computed:Siat10\mathrm{keV}with\eta =0.16\\ givesG=2540with3.621\mathrm{eV},and920with\\ Semitrack{s}^{\prime }10\mathrm{eV}bound)\end{array}$
Diffusion-length fit	$I\left(x\right)=k{x}^{\alpha }\exp \left(-\frac{x}{L}\right)$	$\ln \left[I\left(x\right)x^{-\alpha }\right]=\ln k-\frac{x}{L}$	$I(x):EBICatdistancexfromthejunction$ $k:constant$ $\alpha :exponentsetbysurfacerecombination$ $\begin{array}{r}L:minority-carrierdiffusionlength;form\\ (myreading,matchingthevariablesImina\\ lists);PowellandYoon:diffusionlength\\ fromanexponentiallydecayingprofile;\\ Imina:\alpha between-0.5(nosurface\\ recombination)and-1.5(infinitesurface\\ recombinationvelocity),slope1/Lwhen\alpha \\ =-0.5,2\mathrm{kV}and3\mathrm{nA},50averagedline\\ profiles,L=570\mathrm{nm}onacleavedGaAs\\ solarcell,nanoproberinaTescanCLARA\\ SEMatabout10degreestiltand4.3\mathrm{mm}\\ workingdistance\end{array}$ $\begin{array}{r}(computed:at2\mathrm{kV}theKanaya-Okayama\\ rangeinGaAsisabout55\mathrm{nm},tentimes\\ smallerthanL,sothepoint-source\\ assumptionholds)\end{array}$
Generation depth	$R_{KO}=\frac{0.0276A{E}_0^{1.67}}{Z^{0.889}\rho }\mu \mathrm{m}$	$R=0.022E_0^{1.65}(\text{Semitracks, units not stated})$	$\begin{array}{r}R:depthofthegenerationvolume;\\ Kanaya-OkayamaformfromtheSEMpage;\\ Semitracks:roughestimateR=0.022E^{1.65},\\ beamenergychosentoplacepairsnear\\ buriedjunctions,depthonly\\ semi-quantitative(seetheQ/A)\end{array}$ $\begin{array}{r}(computedforSiat10\mathrm{keV}:R_{KO}=1.49\mu \mathrm{m}\\ against0.98fromSemitrack{s}^{\prime }formulain\\ micrometres)\end{array}$

Absorbed Current, Sensitivity and Damage

Name	Formula	Related Formulae	Variables/Constants
Absorbed current (EBAC)	$I_{abs}=I_b\left(1-\eta -\delta \right)$	$I_A=I_{abs}\frac{G_A}{G_A+G_B}(\text{two paths to ground})$	$\begin{array}{r}{I}_{abs}:currentabsorbedintheirradiated\\ conductor\end{array}$ $\delta :secondaryyield$ $\begin{array}{r}{I}_A:sharecollectedthroughtheprobedpath\\ Awithconductance{G}_{A}againstan\\ alternativepathB;relations(computed);\\ Oxford:EBACmeasurescurrentabsorbed\\ fromthebeamintointerconnectsfor\\ opens,shorts,high-resistivityareasand\\ layernon-uniformities\end{array}$ $\begin{array}{r}(assumed:\eta =0.3,\delta =0.2forCu;\\ computed:halfthebeamcurrentis\\ absorbed,andanopenlinedownstreamofa\\ breakshowszeroEBAC)\end{array}$
Sensitivity and speed	$I_{min}\approx 100\mathrm{fA},A_v=10^3\text{to}10^{10}V/A$	${\tau }_{amp}\approx \frac{1}{2\pi B}$	$I_{min}:smallestdetectablecurrent$ $A_v:transimpedancegain$ ${\tau }_{amp}:amplifiertimeconstant$ $\begin{array}{r}B:bandwidth;Oxford:coaxialprobe\\ detectingdownto100\mathrm{fA},gains1\times 10^{3}to\\ 1\times 10^{10}V/A,plusorminus1\mathrm{V}offset,plus\\ orminus10\mathrm{V}bias,0.5\mathrm{MHz}bandwidth,\\ 1\times 10^{9}V/Alow-noiseamplifierwith200\mathrm{ns}\\ to6m/sdwelltimes;time-constant\\ relation(computed)\end{array}$ $\begin{array}{r}(computed:0.5\mathrm{MHz}gives\tau =318\mathrm{ns},\\ comparabletothe200\mathrm{ns}shortestdwell;\\ 100\mathrm{fA}at1\times 10^{10}V/Ais1\mathrm{mV})\end{array}$
Beam damage to MOS devices	$\Delta V_T\text{of volts after EBIC exposure}$	$\text{anneal}\approx 120{}^{\circ }\mathrm{C},\approx 4\mathrm{h}$	$\begin{array}{r}\Delta V_T:threshold-voltageshiftfromoxide\\ chargeandinterfacetrapsgeneratedby\\ thebeam;Semitracks:shiftsofvolts,\\ usuallyannealableatabout120{}^{\circ }Cfor\\ aboutfourhours,EBICtofollowgentler\\ techniquesonMOSdevices,bipolar\\ structurestoleratinghighbeamenergy\end{array}$ $\begin{array}{r}(computed:a1\mathrm{V}shiftona2\mathrm{nm}oxide\\ with{C}_{ox}=1.7\times 10^{-6}F/c{m}^{2}correspondstoabout\\ 1\times 10^{13}chargespersquarecentimetre)\end{array}$

Contrast and Collection

Name	Formula	Related Formulae	Variables/Constants
Junction and defect contrast	$I_{EBIC}\left(x\right)\text{peaks in the depletion region}$	$C=\frac{I_0-I_d}{I_0}(\text{defect contrast})$	$C:recombinationcontrastofadefect$ $\begin{array}{r}{I}_0,I_d:EBICawayfromandatthedefect;\\ contrastdefinition(computed);\\ Semitracks:localizingdiffusionsburied\\ belowpassivationormetal,stacking\\ faults,dislocations,EOS/ESDdamage,\\ diffusionspikesandpipes,gate-oxide\\ defects,emitter-baseshorts,whole-die\\ imagingwithVDDandVSSasnodes;Oxford:\\ recombinationcentressuchas\\ dislocations,grainboundariesand\\ inclusions,recombinationstrengthand\\ surfacerecombinationvelocity\end{array}$ $\begin{array}{r}(computed:adefectreducingthelocal\\ signalfrom100to70\mathrm{nA}has30percent\\ contrast)\end{array}$
Collection from a depletion region	${\eta }_c=1(\text{generated inside }W),{\eta }_c\approx e^{-x/L}(\text{outside})$	$W=\sqrt{\frac{2{\epsilon }_s\left(V_{bi}+V_R\right)}{qN}}$	${\eta }_c:collectionefficiency$ $W:depletionwidth$ $V_{bi}:built-involtage$ $V_R:reversebias$ $\begin{array}{r}N:dopingonthelightlydopedside;\\ PowellandYoon:collectioncloseto100\\ percentinthedepletionregion,\\ exponentialdecayoutside(myreading);\\ Doolittle:depletionwidthgrowingasthe\\ squarerootofthevoltage;Semitracks:\\ carriersseparatedonlywherea\\ space-chargeregionexists,thedevice\\ itselfactingasdetector\end{array}$ $\begin{array}{r}(assumed:GaAs,N=1\times 10^{17}\mathrm{c}{\mathrm{m}}^{-3},V_{bi}=1.3\mathrm{V};\\ computed:W=0.14\mu \mathrm{m}atzerobias)\end{array}$

Important Questions

Ques: How does EBIC produce an image?

By using the device itself as the detector. The beam deposits energy that creates electron-hole pairs; where a depletion region exists, its field separates them and a current flows in the external circuit, while elsewhere they recombine (Semitracks). The amplified current is displayed against beam position, so junctions appear bright and recombining defects dark. Because each beam electron creates many pairs, the signal is much larger than the beam current. Semitracks lists diffusions buried under passivation or metal, stacking faults, dislocations, ESD and EOS damage, diffusion spikes and gate-oxide defects among what EBIC localizes; Oxford adds grain boundaries and inclusions, recombination strength and surface recombination velocity. A defect reducing a 100 $\mathrm{nA}$ signal to 70 $\mathrm{nA}$ shows 30 per cent contrast (computed). Reference: Semitracks, ‘Electron Beam Induced Current’, failure and yield analysis reference page (fetch-tool summary); Oxford Instruments, ‘E3 Electrical Microanalysis System’ brochure (fetch-tool summary).

Ques: How many electron-hole pairs does one beam electron create?

Semitracks says a 10 $\mathrm{keV}$ electron creates roughly 500 to 1000 pairs, reasoning from ionization energies below 10 $\mathrm{eV}$. Using Powell and Yoon’s pair-creation energy for silicon, about 3.621 $\mathrm{eV}$, and correcting for energy lost to backscattering, $E_0(1-\gamma \eta )/E_{eh}$ gives about 2540 pairs at 10 $\mathrm{keV}$, while Semitracks’ 10 $\mathrm{eV}$ bound gives 920 (computed). For silicon the higher figure is more likely correct, as the pair energy is well below 10 $\mathrm{eV}$, so Semitracks’ range is an underestimate by a factor of about 2.5 to 5, although collection losses can reduce the measured gain toward its range (my reading). For GaAs, the same empirical relation gives 3.86 $\mathrm{eV}$ with an assumed 1.42 $\mathrm{eV}$ gap (computed), so the gain is somewhat lower. Either way, the EBIC current is hundreds to thousands of times the beam current. Reference: Semitracks, ‘Electron Beam Induced Current’, failure and yield analysis reference page (fetch-tool summary); K. M. Powell and H. P. Yoon, ‘Depth-Dependent EBIC Microscopy of Radial-Junction Si Micropillar Arrays’, arXiv:2007.05620: generation rate beta = I_b E_b alpha/(e E_EHP) with alpha the absorbed energy fraction, E_EHP = 2.596 E_g + 0.174 (Kobayashi 1972), about 3.621 eV for Si, collection efficiency close to 100 per cent in the depletion region, diffusion length from an exponential decay of the EBIC profile (fetch-tool summary).

Ques: How is the minority-carrier diffusion length measured?

From how EBIC falls off with distance from the junction. Scanning the beam away from a junction on a cross-section, the current decays as $k{x}^{\alpha }\exp (-x/L)$; Imina lists these variables, with $\alpha$ between -0.5 for no surface recombination and -1.5 for infinite surface recombination velocity, and notes that with $\alpha =-0.5$ the slope of the linearized plot is exactly $1/L$. Imina measured a cleaved GaAs solar cell at 2 $\mathrm{kV}$ and 3 $\mathrm{nA}$, averaging 50 line profiles, and obtained 570 $\mathrm{nm}$. Low voltage keeps the generation volume small, about 55 $\mathrm{nm}$ in GaAs at 2 $\mathrm{kV}$, ten times smaller than L (computed), as the point-source model requires. Surface recombination on the cleaved face must be accounted for through $\alpha$. Reference: Imina Technologies, ‘Quantitative EBIC on GaAs solar cell p-n junction’, application note (fit equation not legible) (fetch-tool summary); K. M. Powell and H. P. Yoon, ‘Depth-Dependent EBIC Microscopy of Radial-Junction Si Micropillar Arrays’, arXiv:2007.05620: generation rate beta = I_b E_b alpha/(e E_EHP) with alpha the absorbed energy fraction, E_EHP = 2.596 E_g + 0.174 (Kobayashi 1972), about 3.621 eV for Si, collection efficiency close to 100 per cent in the depletion region, diffusion length from an exponential decay of the EBIC profile (fetch-tool summary).

Ques: How deep does EBIC probe, and which depth formula should be used?

Generation extends to roughly the electron range, so beam energy sets depth, and Semitracks notes that raising the energy reaches junctions under opaque layers. Semitracks gives a rough estimate $R=0.022E^{1.65}$ without units, while the Kanaya-Okayama formula on the SEM page gives 1.49 $\mu \mathrm{m}$ in silicon at 10 $\mathrm{keV}$ against 0.98 from Semitracks’ form read in micrometres (computed). The Kanaya-Okayama value is the more likely total range, since it includes atomic weight, number and density; Semitracks’ form resembles depth-of-maximum-generation estimates and so gives where most pairs are created (my reading). Semitracks itself cautions that variations in beam energy, density and current make accurate depth measurement difficult, so depth from EBIC is only semi-quantitative. Reference: Semitracks, ‘Electron Beam Induced Current’, failure and yield analysis reference page (fetch-tool summary); Scanning Electron Microscope (SEM) page of this vault.

Ques: What is EBAC, and how does it find opens and shorts?

It measures how much beam current flows into a conductor network. Oxford describes EBAC as measuring current absorbed from the beam into device interconnects, for physical analysis of opens, shorts, high-resistivity areas and layer non-uniformities. The absorbed current is the beam current minus backscattered and secondary electrons, about half for copper with assumed coefficients of 0.3 and 0.2 (computed), and it splits between paths in proportion to their conductances (computed). With a probe on one end of a line, every part of the net still connected appears bright; beyond an open the signal drops to zero, locating the break, and an unexpected bright net reveals a short. Oxford’s coaxial probes detect down to 100 $\mathrm{fA}$. Reference: Oxford Instruments, ‘E3 Electrical Microanalysis System’ brochure (fetch-tool summary).

Ques: What limits EBIC on MOS devices?

Beam damage and node selection. Semitracks warns that the energies needed for EBIC can shift MOS threshold voltages by volts through oxide charge and interface traps, usually annealable at about 120 ${}^{\circ }\mathrm{C}$ for about four hours, so EBIC should follow gentler techniques on MOS devices; bipolar structures tolerate high energy. A 1 $\mathrm{V}$ shift on a 2 $\mathrm{nm}$ oxide with $1.7\times 10^{-6}$ F per square centimetre corresponds to about $1\times 10^{13}$ charges per square centimetre (computed). Signals appear only relative to the chosen nodes, and with power and ground most diffusions contribute, which can hide the anomaly; Semitracks suggests narrowing the search area first with light emission or liquid crystal. Its advantage is that surface layers often need not be removed. Reference: Semitracks, ‘Electron Beam Induced Current’, failure and yield analysis reference page (fetch-tool summary); K. M. Powell and H. P. Yoon, ‘Depth-Dependent EBIC Microscopy of Radial-Junction Si Micropillar Arrays’, arXiv:2007.05620: generation rate beta = I_b E_b alpha/(e E_EHP) with alpha the absorbed energy fraction, E_EHP = 2.596 E_g + 0.174 (Kobayashi 1972), about 3.621 eV for Si, collection efficiency close to 100 per cent in the depletion region, diffusion length from an exponential decay of the EBIC profile (fetch-tool summary); W. A. Doolittle, ECE 4813 lecture ‘Doping Profiling’, Georgia Tech: depletion width growing as the square root of V_bi - V (fetch-tool summary, equations garbled).

Ques: What amplifier performance does EBIC and EBAC need?

Femtoamp sensitivity with fast enough response for imaging. Oxford’s E3 system detects down to 100 $\mathrm{fA}$ through coaxial probes, offers gains from $1\times 10^3$ to $1\times 10^{10}$ $V/A$ with plus or minus 1 $\mathrm{V}$ offset and 10 $\mathrm{V}$ bias, and has a 0.5 $\mathrm{MHz}$ bandwidth, with a $1\times 10^9$ $V/A$ low-noise amplifier supporting dwell times from 200 $\mathrm{ns}$ to 6 $m/s$. At $1\times 10^{10}$ $V/A$, 100 $\mathrm{fA}$ becomes 1 $\mathrm{mV}$ (computed). The bandwidth implies a time constant of 318 $\mathrm{ns}$ (computed), close to the shortest dwell, so faster scanning would smear the image along the scan direction. Bias on the junction widens the depletion region and changes collection; for a GaAs junction doped at $1\times 10^{17}$ $\mathrm{c}{\mathrm{m}}^{-3}$, the zero-bias width is about 0.14 $\mu \mathrm{m}$ (computed). Reference: Oxford Instruments, ‘E3 Electrical Microanalysis System’ brochure (fetch-tool summary).

References

1. Semitracks, “Electron Beam Induced Current,” failure and yield analysis reference. Available: https://www.semitracks.com/reference-material/failure-and-yield-analysis/failure-analysis-die-level/electron-beam-induced-current.php
2. Oxford Instruments NanoAnalysis, “E3 Electrical Microanalysis System,” brochure. Available: https://nano.oxinst.com/assets/uploads/products/nanoanalysis/documents/Brochures/E3.pdf
3. K. M. Powell and H. P. Yoon, “Depth-dependent EBIC microscopy of radial-junction Si micropillar arrays,” arXiv:2007.05620. Available: https://arxiv.org/abs/2007.05620
4. W. A. Doolittle, “Doping Profiling,” ECE 4813 Semiconductor Device and Material Characterization, lecture 3, Georgia Institute of Technology. Available: https://alan.ece.gatech.edu/ECE4813/Lectures/Lecture3DopingProfiling.pdf
5. Imina Technologies, “Quantitative EBIC on GaAs solar cell p-n junction,” application note. Available: https://imina.ch/storage/app/media/Application-Notes/IminaTechnologies_AppNote_Quantitative-EBIC-on-gaas-solar-cell-pn-junction.pdf
6. Scanning Electron Microscope (SEM), page in this vault.

Related pages in this vault: Scanning Electron Microscope (SEM), Cathodoluminescence (SEM-CL), Emission Microscope, OBIRCH and Lock-In Thermography, Lifetime Testers, Electron Backscatter Diffraction (EBSD), CD-SEM, Auger Electron Spectrometer (AES), Focused Ion Beam (FIB), Solar Cell Loss Mechanisms and Characterization, E-Beam Inspection and Defect Review, Electron-Matter Interaction.