Microscope The Scanning Tunneling

The Scanning Tunneling Microscope

Fabian Natterer for PHYS 401, 10.12.2019

Fabian Donat Natterer – Curriculum Vitae

10 years of STM

What do you already know about

STM?

G. Binnig, H. Rohrer, RMP 71, S324 (1999)

Swiss Made in 1981 at

IBM

Rueschlikon

G. Binnig, H. Rohrer, RMP 71, S324 (1999) Researchgate.net

Scanning …

… Tunneling …

Julian Chen, Introduction to Scanning Tunneling Microscopy

Figure: Michael Schmid, TU Wien

… Microscope

Atomic resolution!

Why STM?

ibm.com

What’s the surface structure of Si(111)?

Settling a ~25 year old

debate in one STM image.

Si(111)- 7x7 reconstruction

G. Binnig, H. Rohrer, Ch. Gerber, and E. Weibel Phys. Rev. Lett. 50, 120 (1983)

Moving atoms

Crommie et al., Science 262, 218 (1993)

48 Fe atoms on Cu(111)

Kalff et al., Nat. Nanotechnol. 11, 926 (2016)

Cl vacancies on 2x2 Cl/Cu(100)

Density of States (DOS)

http://hoffman.physics.harvard.edu/research/STMintro.php

Approaching Sample and Tip

http://hoffman.physics.harvard.edu/research/STMintro.php

Quantum Tunneling

http://hoffman.physics.harvard.edu/research/STMintro.php

Barrier Penetration, 1 D case

𝛹 _𝑡 𝛹 _𝑏 𝛹 _𝑠

0 𝑤

𝑧 𝐸𝑛𝑒𝑟𝑔𝑦

𝐸

𝑉 ₀

Ψ_𝑡 = 𝐴𝑒^𝑖𝑘𝑧 + 𝐵𝑒^{−𝑖𝑘𝑧} Ψ_𝑏 = 𝐶𝑒^−𝛼𝑧 + 𝐷𝑒^𝛼𝑧 Ψ_𝑠 = 𝐸𝑒^𝑖𝑘𝑧

− ℏ

2𝑚

𝑑

Ψ

𝑑𝑧

+ 𝑈 𝑧 Ψ = 𝐸Ψ Solve Schroedinger Equation

𝑈 𝑧 = 0 𝑈 𝑧 = 𝑉₀ 𝑈 𝑧 = 0

𝑘² = 2𝑚𝐸

ℏ² 𝛼² = 2𝑚(𝑉₀ − 𝐸)

ℏ²

𝑘² = 2𝑚𝐸 ℏ²

Transmission through barrier

• From eqns before: Ψ(𝑧) = Ψ(0)𝑒 ^−𝛼𝑧 𝛼 ² = ^2𝑚(𝑉

^−𝐸)

ℏ

, with V

is workfunction Φ of order 5 eV

• probability: Ψ(𝑧) ² = Ψ(0) ² 𝑒 ^−2𝛼𝑧

• Current: 𝐼 𝑧 = 𝐼 0 𝑒 ^−2𝑎𝑧 , α = 5.1 Φ(𝑒𝑉)𝑛𝑚 ⁻¹

• Current changes by an order of magnitude for every 0.1 nm tip displacement

Julian Chen, Introduction to Scanning Tunneling Microscopy

Bardeen 1D case – understanding spectroscopy

• Ψ(𝑧) ² = Ψ(0) ² 𝑒 ^−2𝛼𝑧

• 𝐼 = ^4𝜋𝑒

ℏ ׬ _−∞ ^∞ 𝑓 𝐸 _𝐹 − 𝑒𝑉 + 𝜀 − 𝑓 𝐸 _𝐹 + 𝜀 ×

𝜚 _𝑠 𝐸 _𝐹 − 𝑒𝑉 + 𝜀 𝜚 _𝑡 𝐸 _𝐹 + 𝜀 𝑀 ² 𝑑𝜀

• 𝑓 𝜀 = Τ 1 1 + 𝑒

^ൗ

, Fermi-Dirac distribution

Phys. Rev. Lett. 6, 57 (1961)

‘Reasonable’ Approximations

• 𝐼 = ^4𝜋𝑒

ℏ ׬ ₀ ^𝑒𝑉 𝜚 _𝑠 𝐸 _𝐹 − 𝑒𝑉 + 𝜀 𝜚 _𝑡 𝐸 _𝐹 + 𝜀 𝑀 ² 𝑑𝜀

• If kT smaller than required energy resolution, Fermi-Dirac approximated by step function

J. Bardeen

Phys. Rev. Lett. 6, 57 (1961)

‘Reasonable’ Approximations

• 𝐼 = ^4𝜋𝑒

ℏ ׬ ₀ ^𝑒𝑉 𝜚 _𝑠 𝐸 _𝐹 − 𝑒𝑉 + 𝜀 𝜚 _𝑡 𝐸 _𝐹 + 𝜀 𝑀 ² 𝑑𝜀

• ^𝑑𝐼 Τ _𝑑𝑉 ∝ 𝜚 _𝑠 𝐸 _𝐹 − 𝑒𝑉 𝜚 _𝑡 𝐸 _𝐹

• Differential conductance proportional to local density of states (LDOS)

J. Bardeen

Phys. Rev. Lett. 6, 57 (1961)

𝑅_g = 2.5 × 10⁸Ω

Ti/Au(111): Jamnelaet al., Phys. Rev. B 61, 9990 (2000), Ti/Ag(100): Nagaoka et al., Phys. Rev. Lett.88, 077205 (2002), Ti/CuN/Cu(100): Otteet al., Nat. Phys. 4, 847 (2008).

Kondo features were found for Ti adatoms on:

𝑇_K = (29 ± 3)K

𝑅_g = 2.5 × 10⁸Ω

F. D. Natterer, F. Patthey, and H. Brune, Surf. Sci. 615, 80 (2013)

Measurement Modes:

Tunneling

Spectroscopy

STM Measurement modes: Spectroscopy and Topography Mapping

http://hoffman.physics.harvard.edu/research/STMintro.php

22

Sparse Sampling for STM

J. Oppliger and F.D. Natterer, arxiv 1908.01903

Up to ~50x faster measurements: days → hours

Measurement Modes: Spin-Polarized Tunneling

GMR and TMR concept

wiki.org Forrester et al., RSI 89, 123706 (2018)

Forrester et al., RSI 89, 123706 (2018)

Measurement Modes: Inelastic Electron Tunneling Spectroscopy

𝐼

ℏΩ

𝑒𝑉

𝑑𝐼ൗ 𝑑𝑉

ℏΩ

𝑒𝑉

𝑑²𝐼ൗ

𝑑𝑉²

ℏΩ

𝑒𝑉 ℏΩ 𝑒𝑉

Tip Sample

from Klein (1973)

Measurement Modes: Inelastic Electron Tunneling Spectroscopy

Single Molecule Vibrational Spectroscopy

Stipe et al., Science 280, 1732 (1998)

topo

C

D

𝐼

ℏΩ

𝑒𝑉

𝑑𝐼ൗ 𝑑𝑉

ℏΩ

𝑒𝑉

𝑑²𝐼ൗ

𝑑𝑉²

ℏΩ

𝑒𝑉 ℏΩ 𝑒𝑉

Tip Sample

from Klein (1973)

C

H

358mV

266 mV 311 mV

Measurement Modes: Inelastic Electron Tunneling Spectroscopy

Heinrich et al., Science 306, 466 (2004)

Single Atom Spin Flip Spectroscopy

Mn/Al

0

𝐼

ℏΩ

𝑒𝑉

𝑑𝐼ൗ 𝑑𝑉

ℏΩ

𝑒𝑉

𝑑²𝐼ൗ

𝑑𝑉²

ℏΩ

𝑒𝑉 ℏΩ 𝑒𝑉

Tip Sample

from Klein (1973)

Measurement Modes: Pump-Probe Spectroscopy

Loth et al., Science 329, 1628 (2010) T₁ = 87 ± 1 ns

29

Fe

STM ⚭ ^ESR

S. Baumann, W. Paul et al., Science 350, 417 (2015)

10 MHz energy resolution ≈ 40 neV 1’750 × better than NIST mK STM

30’000 × better than 4 K STM

Measurement Modes: Electron Spin

Resonance

S Baumann, W. Paul et al., Science 350, 417 (2015)

10 MHz energy resolution ≈ 40 neV 1’750 × better than NIST mK STM

30’000 × better than 4 K STM

B_z = 0.2T

f₀

Zeeman

B_z Energy

hf₀ = 2 µ_B g m B_z

f₀

RF excitation

Temperature independent resolution

Measurement Modes: Electron Spin

Resonance

31

10 MHz energy resolution ≈ 40 neV 1’750 × better than NIST mK STM

30’000 × better than 4 K STM

Population

RF Frequency

f₀ 50:50

exp (-hf₀/k_bT)

B_z Energy

hf₀ = 2 µ_B g m B_z

f₀

Population driven to 50/50 at resonance Zeeman

ESR with STM

32

Measuring magnetic moments

Fe

B

B

B

33

Fe

B

B

B

Measuring magnetic moments

34

Fe

B

B

B

Measuring magnetic moments

35

Calibrating the Fe sensor

23.0 23.1 23.2 23.3

0 5 10

ESR signal (fA)

Frequency (GHz)

f_↑

f_↓

Δf = f_↓-f_↑

Fe-Fe r ≈ 2.5 nm

1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 0.1

1

f (GHz)

Fe-Fe distance (nm)

Δf = a m_Fem_Fe/r³

Calibrating Fe sensor atom m

= (5.44 ± 0.03) µ

T. Choi et al., Nat. Nano. 12, 450 (2017)

36

10 Å Fe Mg O

Nano GPS

Trilateration from known sensor atoms

T. Choi et al., Nat. Nano. 12, 450 (2017)

37

Model system: MgO on Ag(100)

Figure from: Donati et al. Science 352, 318 (2016)

top view

Science 352, 318 (2016)

What did we know about stable Ho magnets so far?

Prediction of a Ho moment of ~5.7µ

On 7 ML MgO

39

Measuring the Ho bit moment

ESR line only jumps after we deliberately switch the Ho atom

→Ho on MgO is a stable magnet

m_Ho = (10.1 ± 0.1) µ_B

F.D. Natterer et al., Nature 543, 226 (2017) f₀ f_↓

f_↑

Δf = a m_Hom_Fe/r³

40

A two “Ho bit” memory

2 bit memory:

• Designed with dipole-dipole coupling to Fe sensor in mind

• read out via TMR and via Fe sensor

Fe (sensor)

Ho

Ho

1 nm

y x

Ho

Ho

F.D. Natterer et al., Nature 543, 226 (2017)

41

A four “Ho bit” memory

“multiplexing” allows reading of N bits simultaneously

Courtesy of William Paul

75 100 125 150 0.01

0.1 1 10

Switching rate (s-1 )

V (mV)

42

Tunnel Magnetoresistance on Ho

Magnetic Switching

0 20 40 60

24 25

I (pA)

Time (s)

10 100

0.01 0.1 1 10

Switching rate (s-1 )

I (pA)

Ho

Ho Fe

Ho

MgO/Ag(100) tip

B_z

I V

V = 150 mV I= 1.5 nA

V = 150 mV

Controlling the magnetic state

F.D. Natterer et al., Nature 543, 226 (2017)

IETS on magnetic atoms

Baumann et al., Phys. Rev. Lett. 115, 237202 (2015)

IETS on magnetic atoms

B=0T

Baumann et al., Phys. Rev. Lett. 115, 237202 (2015)

IETS on magnetic atoms

Baumann et al., Phys. Rev. Lett. 115, 237202 (2015) B=0T

B=4T

Instrumentation

• Vibrations

• Acoustic noise

• Low temperature

• Ultra-high vacuum

• RF cabling

• magnets

arXiv:1810.03887

47

IBM 1.2 K STM

48

-1000 -500 0 500 1000

0.0 0.5 1.0 1.5 2.0

dI/dV (normalized)

V (V)

T_eff= 232 mK

ΔE = 3.3 k_b T ≈ 70 µeV

Aluminum in a dilution refrigerator at 10 mK

Song et al. RSI 81, 121101 (2010)

Ultra low temperature STM

STM@EPFL

T

= 400 mK, B

= ±8.5 T, B

= 0.8 T

Outlook: Atomic Details Matter

Stable Single Atom Magnet Paramagnetic Atom

Mgo Ho

How to access the individual magnets?

m

= (1.004 ± 0.001) µ

arXiv:1810.03887

Graphene Field Effect Device and Navigation

52 250 μm

MLG

BLG

SLG

1 nm

100 μm

5 μm

V

53

Scanning Tunneling Microscopy on Graphene Devices

53

Empty States

Filled States

Tip DOS Graphene DOS

dI/dV

SiO₂ h-BN

Graphene

V

V

- Scanning Tunneling Spectroscopy (STS)

• Density of state information

- Scanning Tunneling Microscopy (STM)

• Spatial information of samples

Tunneling current

E

SiO₂ h-BN

Graphene

V

V

Gate Voltage as a Tuning Knob

54

dI /dV

dI /dV

dI /dV

E

E

E

E_F

E_F E_F

V

V

V

How to Compose a Spectroscopic “Gate Map” ?

55

-30 -20 -10 0 10 20 30 40

-300 -200 -100 0 100 200 300

Sample bias (mV)

Gate Voltage (V)

E

dI/dV dI/dV

dI/dV

Unoccupied States

Occupied States

Color Coding dI/dV data for all Gate Voltages

56

-30 -20 -10 0 10 20 30 40

-300 -200 -100 0 100 200 300

Sample bias (mV)

Gate Voltage (V)

E

dI/dV dI/dV

dI/dV

Unoccupied States

Occupied States

Fully Developed Gate Map with dI/dV data

57

E

Unoccupied States

Occupied States

-30 -20 -10 0 10 20 30 40

-300 -200 -100 0 100 200 300

Sample bias (mV)

Gate Voltage (V)

Averaging only Helps with Noise…

58

-100 -50 0 50 100

-2 0 2

V_g=+45V L_42501

IETS signal

Bias (mV)

-100 -50 0 50 100

-2 -1 0 1 2

V_g=+25V L_42482

Bias (mV)

IETS, 3mVrms, 200ms, 135pts, SP: ±100mV/500pA (- for V_g<0)

11h 15h

Lots of Spectral Features…

59

-100 -50 0 50 100

-2 0 2

V_g=+45V L_42501

IETS signal

Bias (mV)

-100 -50 0 50 100

-2 -1 0 1 2

V_g=+25V L_42482

Bias (mV)

IETS, 3mVrms, 200ms, 135pts, SP: ±100mV/500pA (- for V_g<0)

Where are the phonons?

? ? ?

? ? ? ?

? ?

? ? ?

?

?

?

“There is no such thing as a free lunch.”

61

-30 -20 -10 0 10 20 30 40

-300 -200 -100 0 100 200 300

Sample bias (mV)

Gate Voltage (V)

condensing/averaging all spectra into one

The Bill:

no gate resolution

𝑑𝐼ൗ 𝑑𝑉

ℏω

𝑒𝑉

−ℏω

𝑑²𝐼ൗ

𝑑𝑉²

ℏω

−ℏω 𝑒𝑉

Inelastic excitations at constant threshold

ℏ𝜔

−ℏ𝜔

“There is no such thing as a free lunch.”

62

𝑑𝐼ൗ 𝑑𝑉

ℏω

𝑒𝑉

−ℏω

𝑑²𝐼ൗ

𝑑𝑉²

ℏω

−ℏω 𝑒𝑉

Inelastic excitations at constant threshold

Zoom into Exposed Excitations

63

Extracting threshold energies

How does it Compare to Phonon Dispersion and Density of States?

64

Excellent agreement with maxima in phonon DOS

ћ𝝎 IETS (meV) DFT (meV) Symmetry

1 56.8 ± 0.9 58 M₃₊

2 80.9 ± 1.3 78.1 M_2±

3 152.8 ± 1.2 148.9 K₅ 4 176.9 ± 1.5 172.6 M_3-

5 195 ± 2 198.7 Γ₅₊

6 359 ± 1 356.2 Γ₅₊ + K₁

Flat dispersion→ large DOS

large electron-phonon coupling

Gate (Density) Resolved Phonon Spectroscopy

65

-40 -20 0 20 40

-500 -250 0 250 500

V b (mV)

V_g (V)

Natterer et al. Phys. Rev. Lett. 114, 245502 (2015) ℏ𝜔

1-2 1-2 3-5 6

3-5 6

We know where to look at:

Phonons appear as “faint” horizontal lines

ћ𝝎 IETS (meV) DFT (meV) Symmetry

1 56.8 ± 0.9 58 M₃₊

2 80.9 ± 1.3 78.1 M_2±

3 152.8 ± 1.2 148.9 K₅ 4 176.9 ± 1.5 172.6 M_3-

5 195 ± 2 198.7 Γ₅₊

6 359 ± 1 356.2 Γ₅₊ + K₁

Phonon Intensities Show Asymmetries

66

Two asymmetries in phonon intensity:

• With respect to charge carrier concentration

• With respect to bias

-40 -20 0 20 40

-500 -250 0 250 500

V b (mV)

V_g (V)

-40 -20 0 20 40

-0.5 0.0 0.5 1.0

d2 I/dV2 (nS/V)-d2 I/dV2 (nS/V)

V_g (V)

-40 -20 0 20 40

-0.5 0.0 0.5 1.0

𝑉_𝑏 = 359 meV

𝑉_𝑏 = −359 meV

Natterer et al. Phys. Rev. Lett. 114, 245502 (2015)

Measuring Apparent Barrier Heights

• Current: 𝐼 𝑧 = 𝐼 0 𝑒 ^−2𝑎𝑧 , α = 5.1 Φ(𝑒𝑉)𝑛𝑚 ⁻¹

• ^{𝑑𝑙𝑛( ൗ}

⁾

𝑑𝑧 = −2𝛼

• Φ = ^ℏ

8𝑚

𝑑𝑙𝑛( ൗ

) 𝑑𝑧

2

≈ 0.95 ^{𝑑𝑙𝑛( ൗ}

𝐼 𝐼0

) 𝑑𝑧

2

H ₂ on h-BN/Ni(111)

Condensation around Ti atoms 3 × 3 𝑅30

unit cell

5 nm 1 L H₂, T_D = 10 K, h-BN/Ni(111)

F. D. Natterer, F. Patthey, and H. Brune, Phys. Rev. Lett. 111, 175303 (2013)

Molecular Rotations

• Hydrogen dosing at 10 K

• 𝑇

= 4.7 K

10 Å

H

Natterer et al., ACS nano 8, 7099 (2014)

Rotational Excitation Spectroscopy

𝑅_g = 1 × 10⁹ Ω

F. D. Natterer, F. Patthey, and H. Brune, Phys. Rev. Lett. 111, 175303 (2013)

11% ≤ ∆𝜎 ൗ

𝜎 ≤ 37%

Scaling Behavior for Molecular Motion

𝑅_g = 1 × 10⁹ Ω

Examining scaling of threshold

excitations with isotopic substitution

Vibrational Excitations:

➢ scale with √mass

Rotational Excitations:

➢ scale with mass

Stipe et al., Science 280, 1732 (1998)

C

H

C

D

STM - RES

F. D. Natterer, F. Patthey, and H. Brune, Phys. Rev. Lett. 111, 175303 (2013) See also Li et al. Phys. Rev. Lett. 111, 146102 (2013) for H₂/Au(110)

Examining scaling of threshold

excitations with isotopic substitution

Vibrational Excitations:

➢ scale with √mass

Rotational Excitations:

➢ scale with mass

STM - RES

Examining scaling of threshold

excitations with isotopic substitution

Vibrational Excitations:

➢ scale with mass

Rotational Excitations:

➢ scale with mass

F. D. Natterer, F. Patthey, and H. Brune, Phys. Rev. Lett. 111, 175303 (2013) See also Li et al. Phys. Rev. Lett. 111, 146102 (2013) for H₂/Au(110)

Rotational constant:

𝐵 = ℏ²ൗ 2𝐼

Homonuclear Diatomics

Ψ _𝑡𝑜𝑡 = Ψ _𝑒𝑙 Ψ _𝑣𝑖𝑏 Ψ _𝑛𝑢𝑐 Ψ _𝑟𝑜𝑡

𝐼_𝑁 𝐼_𝑁

Example: Hydrogen; nucleons are Fermions

Symmetric nuclear triplet state, 𝜳

➢ Antisymmetric rotational state, 𝜳

➢ Ortho-hydrogen

↑↑

(↓↓)

(↑↓+↓↑)/ 2

Antisymmetric singlet state, 𝜳

➢ Symmetric rotational state, 𝜳

➢ Para-hydrogen

(↑↓−↓↑)/ 2

are interdependent

→ Forbidden transition between ortho-para isomers

→ Molecules remain in their rotational subspace

Homonuclear Diatomics

Ψ _𝑡𝑜𝑡 = Ψ _𝑒𝑙 Ψ _𝑣𝑖𝑏 Ψ _𝑛𝑢𝑐 Ψ _𝑟𝑜𝑡

𝐼_𝑁 𝐼_𝑁

Example: Hydrogen; nucleons are Fermions

are interdependent

→ Forbidden transition between ortho-para isomers

→ Molecules remain in their rotational subspace

Energy Assignment in STM-RES

F. D. Natterer, F. Patthey, and H. Brune, Phys. Rev. Lett. 111, 175303 (2013) 76

➢ Excitations at 20.9±0.1, 32.8±0.4, and 43.8 ±0.1 meV are ∆𝐽 = 2 transitions of ortho-D

, HD, and para-H

➢ STM-RES energies equivalent to 3D rigid rotors in the gas phase

➢ Distinction of nuclear spin states Initial state ∆𝑱 = 𝟏 ∆𝑱 = 𝟐

p-H₂ (𝐽 = 0) - 43.9 o-H₂ (𝐽 = 1) - 72.8 o-D₂ (𝐽 = 0) - 22.2 p-D₂ (𝐽 = 1) - 36.9

HD (𝐽 = 0) 11.1 33.1

I. F. Silvera, Rev. Mod. Phys. 52, 393 (1980)