1. Theory

Definition: Conductive AFM scans a conducting tip in contact mode while a bias is applied between tip and sample, recording the current at each point simultaneously with topography (Porti et al.; Fiorenza et al.).
Nano-MOS: On a dielectric, the tip acts as a gate of about 100 $n m^{2}$ , so leakage, tunnelling and breakdown can be studied on areas a million times smaller than MOS capacitors (Porti et al.).
Tunnelling: Currents through thin oxides follow Fowler-Nordheim or direct tunnelling; fits give barrier height and effective thickness (Porti et al.).
Statistics: Many stressed points give breakdown statistics at the nanoscale (Fiorenza et al.).

2. Working Principle

Tip and bias: Doped-diamond or metal-coated tips contact the surface; the substrate or tip is biased (Porti et al.; Jiang et al.).
Current detection: A sensitive amplifier measures current, from 100 $fA$ to 12 $pA$ in one range (Fiorenza et al.), with an external source meter for milliamperes (Jiang et al.).
Stress and image: Points or lines are stressed at high bias, then imaged at low bias to find new leakage spots (Porti et al.; Fiorenza et al.).
Spectroscopy: I-V curves at fixed points are fitted with tunnelling models (Porti et al.).

3. Applications

Gate-dielectric reliability: Leakage and breakdown spots in SiO2 and high-k stacks (Porti et al.).
Wide-gap MOS: Premature breakdown of oxides on SiC (Fiorenza et al.).
Tip reliability: Checking tip degradation, which can be misread as thicker oxides or shifted onset voltages (Jiang et al.).

Nano-MOS and Tunnelling

Name	Formula	Related Formulae	Variables/Constants
Nano-MOS current density	$J = \frac{I}{A _{e f f}}$	$\frac{A _{M O S}}{A _{t i p}} = \frac{1 0 ^{- 6} c m ^{2}}{100 n m ^{2}} = 1 0^{6}$	$J : c u r r e n t d e n s i t y$ $I : m e a s u r e d c u r r e n t$ $A_{e f f} : e f f ec t i v e e mi ss i o n a r e a u n d er t h e t i p; P or t i e t a l . : b or o n - d o p e d d iam o n d t i p a c t in g a s t h e m e t a l e l ec t r o d e w i t h a t y p i c a l a r e a o f ab o u t 100 n m^{2}, co n v e n t i o na l M O S c a p a c i t or s o f 1 \times 1 0^{- 3} t o 1 \times 1 0^{- 6} c m^{2}, l a t er a l r eso l u t i o n ab o u t 10 nm, c u r r e n t d e n s i t i es u p t o ab o u t 10 A/c m^{2} a l l o w e d, co n t a c t m o d e in ai r w i t h s u b s t r a t e inj ec t i o n; F i or e n z a e t a l . : t i p co n t a c t d iam e t er b e l o w 100 nm (a = 100 nm u se d), c u r r e n t r an g e 100 fA t o 12 pA (see t h e Q / A)$ $(co m p u t e d : 1 pA o v er 100 n m^{2} i s 1 A/c m^{2}, so 10 A/c m^{2} i s 10 pA; a 100 nm d iam e t er co n t a c t i s 7850 n m^{2}, 79 t im es l a r g er)$
Fowler-Nordheim tunnelling	$J = A E_{o x}^{2} exp (- \frac{B}{E _{o x}})$	$A = \frac{1.54 \times 1 0 ^{- 6}}{ϕ _{B}} \frac{m _{0}}{m ^{}} A/ V^{2}, B = 6.83 \times 1 0^{7} \frac{m ^{}}{m _{0}} ϕ_{B}^{3/2} V/cm$	$E_{o x} : o x i d e f i e l d$ $ϕ_{B} : ba r r i er h e i g h t (e V), m^{} : o x i d e e f f ec t i v e ma ss; I s l am o v e t a l . : A = e^{3} / (8 π h ϕ_{B}) an d B = 8 π 2 m^{} ϕ_{B}^{3/2} / (3 h e), w i t h m^{} = 0.5 m_{0} f or t h er ma l S i O 2; n u m er i c a l p r e f a c t or s e v a l u a t e d h er e (co m p u t e d); P or t i e t a l . : F N I - V b e ha v i o u r, ba r r i er f i x e d a t 3.15 eV w i t h e f f ec t i v e t hi c k n ess t_{e f f} a s t h e s in g l e f i t p a r am e t er, t_{e f f} r eso l v e d t o 0.1 nm, ba r r i er l o w er e d t o 2.84 an d 2.96 eV a f t er d e t r a pp in g o n 3 nm o x i d es$ $(a ss u m e d : m^{} = 0.5 m_{0}; co m p u t e d : B = 2.70 \times 1 0^{8} V / c m, J = 1.8 \times 1 0^{- 4} A/c m^{2} a t 10 MV/cm, an d 1 A/c m^{2}, 1 pA t h r o ug h 100 n m^{2}, n ee d s ab o u t 14 MV/cm)$
Oxide field with trapped charge	$E_{o x} = \frac{V _{t i p} - V _{F B}}{t _{o x}} + \frac{q N _{e f f}}{ε _{o x}}$	$E_{B D}^{i d e a l} \approx 10 MV/cm, E_{B D}^{S i C} \approx 6.5 MV/cm$	$V_{t i p} : t i p bia s$ $V_{F B} : f l a t - ban d v o l t a g e$ $t_{o x} : o x i d e t hi c k n ess$ $N_{e f f} : e f f ec t i v e o x i d e c ha r g e p er a r e a$ $ε_{o x} : o x i d e p er mi tt i v i t y; F i or e n z a e t a l . : t hi s e x p r ess i o n (w r i tt e n w i t h t_{o x} in t h e c ha r g e t er m; p er mi tt i v i t y f or m u se d h er e a s m y r e a d in g), N_{e f f} = + 3 \times 1 0^{12} p er s q u a r e ce n t im e t r e, V_{F B} ab o u t - 7.5 V, i d e a l b r e ak d o w n ab o u t 10 MV/cm a g ain s t 6.5 MV/cm m e a s u r e d o n 3 C - S i C, nan osc a l e s t r ess a t 8 MV/cm an d V_{t i p} = 8 V o n ab o u t 10 nm o x i d e, D_{i t} u p t o 8 \times 1 0^{12} c m^{- 2} e V^{- 1}$ $(co m p u t e d : q N_{e f f} / ε_{o x} = 1.39 MV/cm f or 3 \times 1 0^{12} p er s q u a r e ce n t im e t r e)$

Breakdown

Name	Formula	Related Formulae	Variables/Constants
Breakdown-spot area	$A_{B D} \approx 1 0^{- 12} to 1 0^{- 13} c m^{2}$	$A_{B D} = 1 0^{- 12} c m^{2} = 100 n m^{2}$	$A_{B D} : a r e a o f a d i e l ec t r i c - b r e ak d o w n s p o t; P or t i e t a l . : b r e ak d o w n in a v er y l oc a l i z e d a r e a o f 1 \times 1 0^{- 12} t o 1 \times 1 0^{- 13} c m^{2}, l e ak y s p o t s m e a s u r e d b y C - A F M c l ose t o t h e es t ima t e d 100 n m^{2}, c u r r e n t s w i t c hin g o f ab o u t 1 pA an d d e t r a pp in g p e ak s o f a f e w p i co am p s a s p r e - b r e ak d o w n n o i se, 5.9 nm o x i d e ima g e d a t 6.4 V$ $(co m p u t e d : 1 \times 1 0^{- 13} c m^{2} i s 10 n m^{2}, a s p o t o n l y ab o u t 3.6 nm a cr oss)$
Stress time per point	$t_{s t r ess} = \frac{T}{L / a}$	$β_{s h or t} = 2.2, β_{l o n g} = 7.1 (Weibull slopes)$	$t_{s t r ess} : d w e l l u n d er t h e t i p p er p o in t w h e n sc annin g a l in e o f l e n g t h L in t im e T w i t h co n t a c t d iam e t er a$ $β : W e ib u l l s ha p e p a r am e t er; F i or e n z a e t a l . : t hi s r e l a t i o n, T f r o m 1 s t o 10 min an d L f r o m 200 nm t o 100 μ m co v er in g ab o u t t h r ee d ec a d es, W e ib u l l s l o p es o f 2.2 an d 7.1 a t s h or t an d l o n g s t r ess t im es, s t r ess t im es o f 2 an d 50 s, b r e ak d o w n e v e n t s r ai s in g c u r r e n t b y u p t o t h r ee or d er s o f ma g ni t u d e; W e ib u l l s t a t i s t i cs o n t h e R e l iabi l i t y p a g es$ $(co m p u t e d : T = 1 s o v er 100 μ m w i t h a = 100 nm g i v es 1 m/s p er p o in t; o v er 200 nm i t g i v es 0.5 s)$
Effective thickness changes	$J \propto \frac{V _{o x}^{2}}{t _{e f f}^{2}} exp (- \frac{2 C ^{'} t _{e f f}}{V _{o x}})$	$Δ t_{e f f} < 0 (trap-assisted tunnelling), Δ t_{e f f} > 0 (negative charge trapping)$	$t_{e f f} : e l ec t r i c a l o x i d e t hi c k n ess f r o m F N f i t s, C^{'} : co n s t an t$ $V_{o x} : o x i d e v o l t a g e; P or t i e t a l . : t hi s f or m (r eco n s t r u c t e d), t_{e f f} d ecr e a s in g o n 3 nm o x i d es a f t er s t r ess (t r a p - a ss i s t e d t u nn e l l in g) an d in cr e a s in g o n 6 nm o x i d es (n e g a t i v e c ha r g e t r a pp in g), e l l i p so m e t r i c t hi c k n esses 2.9, 4.2 an d 5.9 nm$ $(co m p u t e d : in F N, a 0.1 nm c han g e in e f f ec t i v e t hi c k n ess a t 6 V a cr oss 6 nm c han g es c u r r e n t b y e^{0.1 B / E} t im es, ab o u t 1.6 w i t h B = 2.70 \times 1 0^{8} V / c m, m y i l l u s t r a t i v e es t ima t e)$

Instrument Practice

Name	Formula	Related Formulae	Variables/Constants
Current amplifier range	$I_{min} \approx 100 fA, I_{ma x} \approx 12 pA (one range)$	$external source meter for I \sim mA$	$I_{min}, I_{ma x} : d e t ec t i o n l imi t s o f t h e C - A F M am pl i f i er; F i or e n z a e t a l . : 100 fA t o 12 pA, ba r e S i C p r o b e d a t + 0.5 V w i t h 0 t o 20 pA r an g e, c u r r e n t r i s in g b y t h r ee or d er s a t b r e ak d o w n; J ian g e t a l . : C A F M c u r r e n t l imi t e d t o \pm 100 pA, w i t h an e x t er na l so u r ce m e t er u se d t o r e a c h mi l l iam p er e c u r r e n t s$ $(co m p u t e d : 12 pA / 100 fA = 120, ab o u t tw o d ec a d es o f d y nami c r an g e)$
Tips and wear	$PtIr-coated Si, solid doped diamond, solid metal$	$A_{e f f} grows with wear and force$	$J ian g e t a l . : t h ese t i p ma t er ia l s, 20 nm P t I r co a t in g s, co a t e d - t i p co n t a c t r es i s t an ce r i s in g b y 2 t o 3 or d er s b e f or e co n d u c t i v i t y i s l os t; P or t i e t a l . : b or o n - d o p e d d iam o n d t i p s; F i or e n z a e t a l . : S C M o n t h e s am e s am pl es a t 100 kHz w i t h 2 V A C, p ha se c han g in g f r o m 180 t o - 180 d e g r ees a cr oss an t i p ha se b o u n d a r i es; f or ce an d w e a r e f f ec t s o n co n t a c t a r e a (m y r e a d in g; A F M p a g e)$ $(co m p u t e d : d o u b l in g a 10 nm co n t a c t d iam e t er t o 20 nm q u a d r u pl es t h e e f f ec t i v e a r e a an d t h e c u r r e n t a t a g i v e n f i e l d)$

Important Questions

Ques: What does conductive AFM measure?

Current through the sample under a conducting tip, point by point. In contact mode, a bias between tip and substrate drives current that a sensitive amplifier records alongside topography (Porti et al.). On thin dielectrics, the tip acts as the gate of a tiny MOS structure: Porti et al. used boron-doped diamond tips with a typical electrical area of about 100 $n m^{2}$ and lateral resolution of about 10 $nm$ , compared with $1 \times 1 0^{- 3}$ to $1 \times 1 0^{- 6}$ cm^2 for conventional capacitors, a million times larger at the small end (computed). Over 100 $n m^{2}$ , 1 $pA$ is already 1 $A/c m^{2}$ (computed), so picoamp sensitivity reaches device-relevant current densities. Fiorenza et al.’s amplifier spans 100 $fA$ to 12 $pA$ . Reference: M. Porti, M. Nafria, X. Aymerich, A. Olbrich and B. Ebersberger, ‘Nanometer-scale electrical characterization of stressed ultrathin SiO2 films using conducting atomic force microscopy’, Appl. Phys. Lett. 78, 4181 (2001) (FN equations partly garbled) (fetch-tool summary); P. Fiorenza, E. Schiliro, F. Giannazzo, C. Bongiorno, M. Zielinski, F. La Via and F. Roccaforte, ‘On the origin of the premature breakdown of thermal oxide on 3C-SiC probed by electrical scanning probe microscopy’, arXiv:2005.01290 (fetch-tool summary).

Ques: Is the C-AFM contact about 100 square nanometres or 100 nanometres across?

The sources differ by nearly two orders of magnitude. Porti et al. give a typical tip area of about 100 $n m^{2}$ , about 11 $nm$ across, matching their 10 $nm$ resolution and breakdown spots of $1 \times 1 0^{- 12}$ to $1 \times 1 0^{- 13}$ cm^2, while Fiorenza et al. describe a contact diameter below 100 $nm$ and use 100 $nm$ , about 7850 $n m^{2}$ , in their stress-time estimate, 79 times larger (computed). Both may be right for their purposes: the mechanical contact of a worn or blunt tip can approach 100 $nm$ , while current flows mainly through a much smaller effective area where the field and contact are best (my reading). For current density, the smaller electrical area is more likely correct; for stress-time geometry, the larger mechanical contact matters (my reading). Reference: M. Porti, M. Nafria, X. Aymerich, A. Olbrich and B. Ebersberger, ‘Nanometer-scale electrical characterization of stressed ultrathin SiO2 films using conducting atomic force microscopy’, Appl. Phys. Lett. 78, 4181 (2001) (FN equations partly garbled) (fetch-tool summary); P. Fiorenza, E. Schiliro, F. Giannazzo, C. Bongiorno, M. Zielinski, F. La Via and F. Roccaforte, ‘On the origin of the premature breakdown of thermal oxide on 3C-SiC probed by electrical scanning probe microscopy’, arXiv:2005.01290 (fetch-tool summary).

Ques: How are tunnelling currents analysed?

With Fowler-Nordheim fits. The current density follows $A E_{o x}^{2} exp (- B / E_{o x})$ , with $A = e^{3} / (8 π h ϕ_{B})$ and $B$ set by the barrier height and effective mass (Islamov et al.). Porti et al. fixed the barrier at 3.15 $eV$ and fitted only the effective thickness, resolving changes as small as 0.1 $nm$ ; after stress, it decreased on 3 $nm$ oxides, indicating trap-assisted tunnelling, and increased on 6 $nm$ oxides, indicating negative charge trapping. With an assumed effective mass of 0.5, the FN expression gives only $1.8 \times 1 0^{- 4}$ $A/c m^{2}$ at 10 $MV/cm$ , and 1 $pA$ through 100 $n m^{2}$ needs about 14 $MV/cm$ (computed), which shows how small areas push measurable currents close to breakdown fields. Reference: M. Porti, M. Nafria, X. Aymerich, A. Olbrich and B. Ebersberger, ‘Nanometer-scale electrical characterization of stressed ultrathin SiO2 films using conducting atomic force microscopy’, Appl. Phys. Lett. 78, 4181 (2001) (FN equations partly garbled) (fetch-tool summary); D. R. Islamov, V. A. Gritsenko, T. V. Perevalov, O. M. Orlov and G. Ya. Krasnikov, ‘The charge transport mechanism and electron trap nature in thermal oxide on silicon’, arXiv:1604.03353: J_FN = A F^2 exp(-B sqrt(m*) Phi0^{3/2}/F), A = e^3/(8 pi h Phi0), B = 8 pi sqrt(2)/(3 h e), Phi0 = 2.9 eV, m* = 0.5 m_e (fetch-tool summary).

Ques: What does C-AFM reveal about dielectric breakdown?

That breakdown is extremely localized and preceded by current noise. Porti et al. found breakdown confined to areas of about $1 \times 1 0^{- 12}$ to $1 \times 1 0^{- 13}$ cm^2, 100 down to 10 $n m^{2}$ , the smaller only about 3.6 $nm$ across (computed), and leaky spots measured by C-AFM close to the estimated 100 $n m^{2}$ . Before breakdown, current switched by about 1 $pA$ and showed detrapping peaks of a few picoamps, linked to the pre-breakdown noise seen in macroscopic tests. Barrier heights fell to 2.84 and 2.96 $eV$ after detrapping on 3 $nm$ oxides. Breakdown mostly occurred at voltages where current peaks were most frequent. Mapping before and after stress shows which spots fail, information hidden in the averaged current of a large capacitor. Reference: M. Porti, M. Nafria, X. Aymerich, A. Olbrich and B. Ebersberger, ‘Nanometer-scale electrical characterization of stressed ultrathin SiO2 films using conducting atomic force microscopy’, Appl. Phys. Lett. 78, 4181 (2001) (FN equations partly garbled) (fetch-tool summary).

Ques: How is breakdown stress controlled in a scan?

Through the time the tip spends over each point. Fiorenza et al. write $t_{s t r ess} = T / (L / a)$ for a line of length L scanned in time T with contact size a; with T from 1 $s$ to 10 min and L from 200 $nm$ to 100 $μ m$ , stress time spans about three decades: 1 $s$ over 100 $μ m$ gives 1 $m/s$ per point, while over 200 $nm$ it gives 0.5 $s$ (computed). At 8 $MV/cm$ on 10 $nm$ oxide on 3C-SiC, breakdown raised current by up to three orders of magnitude. The Weibull slope changed from 2.2 at short stress times to 7.1 at long ones, indicating different failure populations. Comparing 2 and 50 $s$ stresses separates extrinsic, defect-related failures from intrinsic wear-out. Reference: P. Fiorenza, E. Schiliro, F. Giannazzo, C. Bongiorno, M. Zielinski, F. La Via and F. Roccaforte, ‘On the origin of the premature breakdown of thermal oxide on 3C-SiC probed by electrical scanning probe microscopy’, arXiv:2005.01290 (fetch-tool summary).

Ques: Why do oxides on SiC break down early?

Because trapped charge and defects raise the local field. Fiorenza et al. write the oxide field as the applied term $(V_{t i p} - V_{F B}) / t_{o x}$ plus a contribution from effective positive charge of + $3 \times 1 0^{12}$ per square centimetre; written with the oxide permittivity, that charge adds about 1.39 $MV/cm$ (computed; permittivity form as my reading). With a flat-band voltage near -7.5 $V$ and interface trap densities up to $8 \times 1 0^{12}$ $c m^{- 2} e V^{- 1}$ , macroscopic breakdown occurred at about 6.5 $MV/cm$ rather than the ideal 10 $MV/cm$ . C-AFM located the weak spots, and SCM on the same samples, at 100 $kHz$ with 2 V AC modulation, showed phase reversals at antiphase boundaries, linking premature breakdown to crystal defects in 3C-SiC. Reference: P. Fiorenza, E. Schiliro, F. Giannazzo, C. Bongiorno, M. Zielinski, F. La Via and F. Roccaforte, ‘On the origin of the premature breakdown of thermal oxide on 3C-SiC probed by electrical scanning probe microscopy’, arXiv:2005.01290 (fetch-tool summary).

Ques: What practical issues affect C-AFM measurements?

Tip wear, contact force, current range and the environment. Solid diamond tips are so stiff they can damage samples, while PtIr-coated tips degrade, their contact resistance rising 2 to 3 orders before conduction is lost (Jiang et al.). Wear and force enlarge the contact: doubling a 10 $nm$ contact diameter quadruples the effective area and the current at a given field (computed), which can be mistaken for a material change. A single amplifier range such as 100 $fA$ to 12 $pA$ covers only about two decades (computed), so breakdown events saturate it; Jiang et al. switched to an external source meter for milliampere currents. In air a water layer about 1.2 $nm$ thick can block the tip, and Jiang et al. biased the tip positive with the sample grounded to avoid local anodic oxidation. Reference: P. Fiorenza, E. Schiliro, F. Giannazzo, C. Bongiorno, M. Zielinski, F. La Via and F. Roccaforte, ‘On the origin of the premature breakdown of thermal oxide on 3C-SiC probed by electrical scanning probe microscopy’, arXiv:2005.01290 (fetch-tool summary); L. Jiang, J. Weber, F. M. Puglisi, P. Pavan, L. Larcher, W. Frammelsberger, G. Benstetter and M. Lanza, ‘Understanding current instabilities in conductive atomic force microscopy’, Materials 12, 459 (2019): PtIr-coated (20 nm) Si tips, stiff solid doped-diamond tips that can damage samples, durable but costly solid metal tips with larger radius, coated-tip contact resistance rising by 2 to 3 orders before conductivity is lost, CAFM current limited to +/-100 pA with an external source meter for mA currents, a 1.2 nm water layer the tip could not penetrate, tip biased positive and sample grounded to avoid local anodic oxidation, CAFM first designed for tunnelling through thin dielectrics (fetch-tool summary); Atomic Force Microscope (AFM) page of this vault.

References

M. Porti, M. Nafria, X. Aymerich, A. Olbrich and B. Ebersberger, “Nanometer-scale electrical characterization of stressed ultrathin SiO2 films using conducting atomic force microscopy,” Applied Physics Letters, vol. 78, 4181, 2001. Available: https://ddd.uab.cat/pub/artpub/2001/116266/appphylet_a2001m5v78n26p4181.pdf
P. Fiorenza, E. Schiliro, F. Giannazzo, C. Bongiorno, M. Zielinski, F. La Via and F. Roccaforte, “On the origin of the premature breakdown of thermal oxide on 3C-SiC probed by electrical scanning probe microscopy,” arXiv:2005.01290. Available: https://arxiv.org/pdf/2005.01290
L. Jiang, J. Weber, F. M. Puglisi, P. Pavan, L. Larcher, W. Frammelsberger, G. Benstetter and M. Lanza, “Understanding current instabilities in conductive atomic force microscopy,” Materials, vol. 12, no. 3, p. 459, 2019. Available: https://www.mdpi.com/1996-1944/12/3/459/html
D. R. Islamov, V. A. Gritsenko, T. V. Perevalov, O. M. Orlov and G. Ya. Krasnikov, “The charge transport mechanism and electron trap nature in thermal oxide on silicon,” arXiv:1604.03353. Available: https://arxiv.org/pdf/1604.03353
Atomic Force Microscope (AFM), page in this vault.

Quartz 5

Explorer

Conductive AFM (C-AFM)