AFM Cantilevers Classification

Content

AFM Cantilevers by Shape

AFM Cantilevers by Shape (Top View)

Single Beam AFM Cantilevers

Rectangular/Diving Board AFM Cantilevers
Pyrex-Nitride Diving Board AFM Cantilever
Pyrex-Nitride Diving Board
AFM Cantilever

Rectangular AFM cantilevers with various dimensions for specific applications.
(see Interdependence between Geometry and Application)

Typical AFM cantilever mechanical properties ranges:

  • AFM cantilever force constant: 0.06 to 50 N/m
  • AFM cantilever resonance frequency: 1 kHz to 1 MHz
  • AFM cantilever length:  100 to 500 µm
  • AFM cantilever width: 30 to 50 µm
  • AFM cantilever thickness: 0.5 to 8 µm
» Browse all AFM probes with rectangular AFM cantilevers
Triangular AFM Cantilevers
Arrow™ UHF AFM Cantilever
Arrow™ UHF
AFM Cantilever

Triangular AFM cantilevers.

  • Short triangular AFM cantilever with a high resonance frequency for high speed scanning
» Browse all AFM probes with triangular AFM cantilevers

Double Beam AFM Cantilevers

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Rectangular/Diving Board AFM Cantilevers
Akiyama-Probe AFM Cantilever
Akiyama-Probe
AFM Cantilever

AFM cantilevers with two beams running parallel to each other.

  • AFM cantilever geometry currently used for Akiyama-Probe AFM cantilevers
  • AFM cantilever length: 310 µm
  • AFM cantilever thickness: 3.7 µm
  • AFM cantilever width: 30 µm each
» NANOSENSORS Akiyama-Probe
Triangular AFM Cantilevers
Pyrex-Nitride Triangular AFM Cantilever
Pyrex-Nitride
Triangular AFM Cantilever

V-shaped AFM cantilever geometry with two identical legs.

Typical triangular AFM cantilever mechanical properties ranges:

  • AFM cantilever force constant: 0.08 to 0.3 N/m
  • AFM cantilever resonance frequency: 10 to 70 Khz
  • AFM cantilever length: 100 to 200 µm
  • AFM cantilever width: 10 to 30 µm
  • AFM cantilever thickness: 0.5 to 0.6 µm
» Browse all AFM probes with triangular AFM cantilevers

AFM Cantilevers by Shape (Cross Section)

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Rectangular Cross Section AFM Cantilevers
Rectangular Cross Section AFM Cantilever
Rectangular Cross Section
AFM Cantilever

AFM cantilevers with a rectangular cross section.

» Browse all AFM probes with rectangular cross section AFM cantilevers
Trapezoidal Cross Section AFM Cantilevers (tip on narrow flank)
Trapezoidal Cross Section AFM Cantilever with tip on narrow flank
Trapezoidal Cross Section
AFM Cantilever with tip
on narrow flank

AFM cantilevers with a trapezoidal cross section and the tip on the narrow flank.

» Browse all AFM probes with trapezoidal cross section AFM cantilevers (tip on narrow flank)
Trapezoidal Cross Section AFM Cantilevers (tip on wide flank)
Trapezoidal Cross Section AFM Cantilever with tip on wide flank
Trapezoidal Cross Section
AFM Cantilever with tip
on wide flank

AFM cantilevers with a trapezoidal cross section and the tip of the wide flank.

» Browse all AFM probes with trapezoidal cross section AFM cantilevers (tip on wide flank)
Trapezoidal Cross Section with Curved Sides AFM Cantileverss (tip on narrow flank)
Trapezoidal Cross Section with Curved Sides AFM cantilever with tip on narrow flank
Trapezoidal Cross Section
with Curved Sides
AFM cantilever with
tip on narrow flank

AFM cantilevers with a trapezoidal cross section with curved sides and the tip on narrow flank.

» Browse all AFM probes with trapezoidal cross section with curved sides AFM cantilevers
(tip on narrow flank)

AFM Cantilevers by Material

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Silicon AFM Cantilevers
Arrow™ AFM Cantilever
Arrow™ AFM Cantilever

AFM cantilevers made of single crystal silicon.

  • All components of the AFM probe: the AFM tip, the AFM cantilever and the AFM support are made of monolithic single crystal silicon
  • Silicon is highly doped for static charge dissipation
» Browse all AFM probes with silicon AFM cantilevers
Silicon Nitride AFM Cantilevers
Pyrex-Nitride AFM Cantilevers
Pyrex-Nitride
AFM Cantilevers

AFM cantilevers made of silicon nitride.

  • The AFM tip and the AFM cantilever are made of silicon nitride
  • The AFM cantilever is attached to a silicon or borosilicate glass support chip
» Browse all AFM probes with silicon nitride AFM cantilevers
Quartz-like AFM Cantilevers

AFM Cantilevers by Number of Cantilevers per AFM Probe

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1 Single AFM Cantilever per AFM Probe
Arrow™ TL1 AFM Cantilever
Arrow™ TL1
AFM Cantilever

One AFM cantilever on the support chip.

» Browse all AFM probes with single AFM cantilevers
2 AFM Cantilevers on One Side of the AFM Probe
Arrow™ TL2 AFM Cantilevers
Arrow™ TL2
AFM Cantilevers

Two identical AFM cantilevers as a small array on one side of the support chip.

» Browse all AFM probes with two AFM cantilevers
3 AFM Cantilevers on One Side of the AFM Probe
Pierced Cantilever Probe AFM Cantilevers
Pierced Cantilever Probe
AFM Cantilevers

Three different AFM cantilevers on one side of the support chip.

» Browse all standard AFM probes with three AFM cantilevers on one side of the support chip

8 AFM Cantilevers on One Side of the AFM Probe (AFM Cantilever Array)
Arrow™ TL8 AFM Cantilever
Arrow™ TL8
AFM Cantilevers

Arrays of eight identical AFM cantilevers on one side of the support chip.

» Browse all AFM probes with AFM cantilever arrays
4 AFM Cantilevers per AFM Probe (2 cantilevers on each side)
All-In-One AFM Cantilevers
All-In-One AFM Cantilevers

Two AFM cantilevers with different characteristics on one each side of the support chip.

» Browse all AFM probes with multiple AFM cantilevers

AFM Cantilevers by Coating

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Backside Aluminum Coated AFM Cantilevers
Rotated AFM Tip
AFM Cantilever with
Aluminum Reflex coating

Aluminum coating on the detector facing side of the AFM cantilevers for enhanced laser reflectance.

Reflectance of an uncoated AFM cantilever vs reflectance of an aluminum coated AFM cantilever:

Rotated AFM Tip Rotated AFM Tip
Reflectance of an uncoated AFM Cantilever Reflectance of Aluminum coated AFM Cantilever


» Browse all AFM probes with backside aluminum coated AFM cantilevers
Backside Gold Coated AFM Cantilevers
AFM Cantilever with Gold Reflex Coating
AFM Cantilever with Gold Reflex Coating

Gold coating on the detector facing side of the AFM cantilevers for enhanced laser reflectance in ambient atmosphere and chemically aggressive environments.

Reflectance of an uncoated AFM cantilever vs reflectance of a gold coated AFM cantilever:

Rotated AFM Tip Rotated AFM Tip
Reflectance of an uncoated AFM Cantilever Reflectance of a Gold coated AFM Cantilever
» Browse all AFM probes with backside gold coated AFM cantilevers
Topside Gold Coated AFM Cantilevers
AFM Cantilever with Topside Gold Coating
AFM Cantilever with
Topside Gold Coating

Gold coating on the top side of the AFM cantilevers.

  • Electrically conductive
» Browse all AFM probes with topside gold coated AFM cantilevers
Overall Gold Coated AFM Cantilevers
AFM Cantilever with Overall Gold Coating
AFM Cantilever with
Overall Gold Coating

Gold coating on both sides of the AFM cantilevers.

  • Electrically conductive
  • Often used for tip functionalization
  • Protects the cantilever in chemically aggressive measurement environments
» Browse all AFM probes with overall gold coated AFM cantilevers
Platinum Coated AFM Cantilevers
AFM Cantilever with Electrically Conductive Platinum Coating
AFM Cantilever with
Electrically Conductive
Platinum Coating

Platinum coating on both sides of the AFM cantilevers.

  • Enhances laser reflectance
  • Electrically conductive
  • Used for electric mode measurements
» Browse all AFM probes with platinum coated AFM cantilevers
Platinum/Iridium Coated AFM Cantilevers
AFM Cantilever with Electrically Conductive Platinum/Iridium Coating
AFM Cantilever with
Electrically Conductive
Platinum/Iridium Coating

Platinum/Iridium coating on both sides of the AFM cantilevers.

  • Enhances laser reflectance
  • Electrically conductive
  • Used for electric mode measurements
» Browse all AFM probes with platinum/iridium coated AFM cantilevers
Conductive Diamond Coated AFM Cantilevers
AFM Cantilever with Conductive Diamond Coating
AFM Cantilever with
Conductive Diamond Coating

High wear resistance and electrically conductive real doped diamond coating on the tip side of the AFM cantilevers.

  • Electrically conductive
  • Used fo electric mode measurements
  • Detector facing side of the AFM cantilevers is coated with aluminum
» Browse all AFM probes with conductive diamond coated AFM cantilevers
Silicide Coated AFM Cantilevers
AFM Cantilever with Silicide Coating
AFM Cantilever
with Silicide Coating

Silicide coating on both sides of the AFM cantilevers.

  • Electrically conductive

» Browse all AFM probes with silicide coated AFM cantilevers

Note:

Other coating materials can cover the cantilevers, but as they don't play an active role in the measurement, they haven't been listed above.

Relation between AFM Cantilever Geometry and Application Mode

There is no common definition on the exact force constant values of stiff (or hard) and soft AFM cantilevers. Our own definition of these terms is the following:

An AFM cantilever with force constant above 40 N/m is referred to as a ‘stiff’ AFM cantilever. Such an AFM cantilever allows maximum scanning speeds in tapping/non-contact mode AFM measurements.

 An AFM cantilever with force constant in the range 3-15 N/m is referred to as an ‘intermediately stiff’ AFM cantilever. Such an AFM cantilever is usually preferred for soft intermittent contact mode AFM measurements with reduced tip-sample interaction (5-15 N/m) and for force modulation measurements (3 N/m).

An AFM cantilever with a force constant below 1 N/m is referred to as a ‘soft’ AFM cantilever. Such an AFM cantilever allows high sensitivity contact mode AFM measurements.

For more information on AFM cantilevers, please contact us.

* We are referring to the normal force constant of the AFM cantilever. For more information about the different AFM cantilever force constants, check the next chapter.

 

Relation between AFM Cantilever Geometry and Application Mode

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Definitions of AFM Cantilever Resonance Frequency and Force Constants

The normal resonance frequency (or simply the resonance frequency) f of an AFM cantilever refers to the resonance frequency for small amplitude oscillations in the direction normal to the sample facing surface of the AFM cantilever. This parameter neglects the mass of the tip.

The corrected resonance frequency fcorr of an AFM cantilever takes the AFM tip mass into account. Here, the AFM tip is modeled as a cone with height H and a base diameter H.

The normal force constant (or simply the force constant) C of an AFM cantilever is the ratio of the applied force from the top or the bottom side at the free cantilever end to the free end’s displacement for small displacements (Fig. 1). This force constant is most relevant for determining the tip-sample interaction during the majority of AFM operation modes.

The lateral force constant Clat of an AFM cantilever is the ratio of the applied force from the side at the free end of the AFM cantilever to its displacement for small displacements (Fig. 2).

The torsional force constant Ctor of an AFM cantilever is the ratio of the applied lateral force at the AFM tip to the lateral displacement of the AFM tip for small displacements (Fig. 3).

Resonance Frequency and Force Constants of AFM Cantilevers

Definitions of AFM Cantilever Resonance Frequency and Force Constants

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Calculator for the Resonance Frequency and the Force Constants of Silicon AFM Cantilevers

The calculator below calculates important parameters of silicon AFM cantilevers based on their geometric dimensions.

Calculated Constants Entered by user
f fcorr C Clat Ctor E G ρ T L W H
kHz kHz N/m N/m N/m N/m2 N/m2 kg/m3 µm µm µm µm
1.69*1011 5.00*1011
2330

f [kHz] – resonance frequency of the AFM cantilever (neglecting tip mass)
fcorr [kHz] – resonance frequency of the AFM cantilever taking tip mass into account
C [N/m] – (normal) force constant of the AFM cantilever
Clat [N/m] – lateral force constant of the AFM cantilever
Ctor [N/m] – torsional force constant of the AFM cantilever
T [µm] – AFM cantilever thickness
W [µm] – AFM cantilever width
L [µm] – AFM cantilever length
H [µm] – AFM tip height
ρ = 2.33g/cm3 = 2330kg/m3 - density of silicon
E = 1.69*1011 N/m2 - modulus of elasticity / Young’s modulus in the <110> direction of silicon
G = 0.5*1011 N/m2 modulus of rigidity / modulus of elasticity in shear of silicon

The calculator calculates the resonance frequencies and the force constants according to the following formulas:

Formulas

Formulas are derived from “Roark’s Formulas for Stress and Strain”, 6th edition, Waren C. Young, McGraw Hill.

Calculator for the Resonance Frequency and the Force Constants of Silicon AFM Cantilevers

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Content

AFM Cantilevers by Shape

AFM Cantilevers by Shape (Top View)

Single Beam AFM Cantilevers

Rectangular/Diving Board AFM Cantilevers
Pyrex-Nitride Diving Board AFM Cantilever
Pyrex-Nitride Diving Board
AFM Cantilever

Rectangular AFM cantilevers with various dimensions for specific applications.
(see Interdependence between Geometry and Application)

Typical AFM cantilever mechanical properties ranges:

  • AFM cantilever force constant: 0.06 to 50 N/m
  • AFM cantilever resonance frequency: 1 kHz to 1 MHz
  • AFM cantilever length:  100 to 500 µm
  • AFM cantilever width: 30 to 50 µm
  • AFM cantilever thickness: 0.5 to 8 µm
» Browse all AFM probes with rectangular AFM cantilevers
Triangular AFM Cantilevers
Arrow™ UHF AFM Cantilever
Arrow™ UHF
AFM Cantilever

Triangular AFM cantilevers.

  • Short triangular AFM cantilever with a high resonance frequency for high speed scanning
» Browse all AFM probes with triangular AFM cantilevers

Double Beam AFM Cantilevers

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Rectangular/Diving Board AFM Cantilevers
Akiyama-Probe AFM Cantilever
Akiyama-Probe
AFM Cantilever

AFM cantilevers with two beams running parallel to each other.

  • AFM cantilever geometry currently used for Akiyama-Probe AFM cantilevers
  • AFM cantilever length: 310 µm
  • AFM cantilever thickness: 3.7 µm
  • AFM cantilever width: 30 µm each
» NANOSENSORS Akiyama-Probe
Triangular AFM Cantilevers
Pyrex-Nitride Triangular AFM Cantilever
Pyrex-Nitride
Triangular AFM Cantilever

V-shaped AFM cantilever geometry with two identical legs.

Typical triangular AFM cantilever mechanical properties ranges:

  • AFM cantilever force constant: 0.08 to 0.3 N/m
  • AFM cantilever resonance frequency: 10 to 70 Khz
  • AFM cantilever length: 100 to 200 µm
  • AFM cantilever width: 10 to 30 µm
  • AFM cantilever thickness: 0.5 to 0.6 µm
» Browse all AFM probes with triangular AFM cantilevers

AFM Cantilevers by Shape (Cross Section)

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Rectangular Cross Section AFM Cantilevers
Rectangular Cross Section AFM Cantilever
Rectangular Cross Section
AFM Cantilever

AFM cantilevers with a rectangular cross section.

» Browse all AFM probes with rectangular cross section AFM cantilevers
Trapezoidal Cross Section AFM Cantilevers (tip on narrow flank)
Trapezoidal Cross Section AFM Cantilever with tip on narrow flank
Trapezoidal Cross Section
AFM Cantilever with tip
on narrow flank

AFM cantilevers with a trapezoidal cross section and the tip on the narrow flank.

» Browse all AFM probes with trapezoidal cross section AFM cantilevers (tip on narrow flank)
Trapezoidal Cross Section AFM Cantilevers (tip on wide flank)
Trapezoidal Cross Section AFM Cantilever with tip on wide flank
Trapezoidal Cross Section
AFM Cantilever with tip
on wide flank

AFM cantilevers with a trapezoidal cross section and the tip of the wide flank.

» Browse all AFM probes with trapezoidal cross section AFM cantilevers (tip on wide flank)
Trapezoidal Cross Section with Curved Sides AFM Cantileverss (tip on narrow flank)
Trapezoidal Cross Section with Curved Sides AFM cantilever with tip on narrow flank
Trapezoidal Cross Section
with Curved Sides
AFM cantilever with
tip on narrow flank

AFM cantilevers with a trapezoidal cross section with curved sides and the tip on narrow flank.

» Browse all AFM probes with trapezoidal cross section with curved sides AFM cantilevers
(tip on narrow flank)

AFM Cantilevers by Material

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Silicon AFM Cantilevers
Arrow™ AFM Cantilever
Arrow™ AFM Cantilever

AFM cantilevers made of single crystal silicon.

  • All components of the AFM probe: the AFM tip, the AFM cantilever and the AFM support are made of monolithic single crystal silicon
  • Silicon is highly doped for static charge dissipation
» Browse all AFM probes with silicon AFM cantilevers
Silicon Nitride AFM Cantilevers
Pyrex-Nitride AFM Cantilevers
Pyrex-Nitride
AFM Cantilevers

AFM cantilevers made of silicon nitride.

  • The AFM tip and the AFM cantilever are made of silicon nitride
  • The AFM cantilever is attached to a silicon or borosilicate glass support chip
» Browse all AFM probes with silicon nitride AFM cantilevers
Quartz-like AFM Cantilevers

AFM Cantilevers by Number of Cantilevers per AFM Probe

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1 Single AFM Cantilever per AFM Probe
Arrow™ TL1 AFM Cantilever
Arrow™ TL1
AFM Cantilever

One AFM cantilever on the support chip.

» Browse all AFM probes with single AFM cantilevers
2 AFM Cantilevers on One Side of the AFM Probe
Arrow™ TL2 AFM Cantilevers
Arrow™ TL2
AFM Cantilevers

Two identical AFM cantilevers as a small array on one side of the support chip.

» Browse all AFM probes with two AFM cantilevers
3 AFM Cantilevers on One Side of the AFM Probe
Pierced Cantilever Probe AFM Cantilevers
Pierced Cantilever Probe
AFM Cantilevers

Three different AFM cantilevers on one side of the support chip.

» Browse all standard AFM probes with three AFM cantilevers on one side of the support chip

8 AFM Cantilevers on One Side of the AFM Probe (AFM Cantilever Array)
Arrow™ TL8 AFM Cantilever
Arrow™ TL8
AFM Cantilevers

Arrays of eight identical AFM cantilevers on one side of the support chip.

» Browse all AFM probes with AFM cantilever arrays
4 AFM Cantilevers per AFM Probe (2 cantilevers on each side)
All-In-One AFM Cantilevers
All-In-One AFM Cantilevers

Two AFM cantilevers with different characteristics on one each side of the support chip.

» Browse all AFM probes with multiple AFM cantilevers

AFM Cantilevers by Coating

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Backside Aluminum Coated AFM Cantilevers
Rotated AFM Tip
AFM Cantilever with
Aluminum Reflex coating

Aluminum coating on the detector facing side of the AFM cantilevers for enhanced laser reflectance.

Reflectance of an uncoated AFM cantilever vs reflectance of an aluminum coated AFM cantilever:

Rotated AFM Tip Rotated AFM Tip
Reflectance of an uncoated AFM Cantilever Reflectance of Aluminum coated AFM Cantilever


» Browse all AFM probes with backside aluminum coated AFM cantilevers
Backside Gold Coated AFM Cantilevers
AFM Cantilever with Gold Reflex Coating
AFM Cantilever with Gold Reflex Coating

Gold coating on the detector facing side of the AFM cantilevers for enhanced laser reflectance in ambient atmosphere and chemically aggressive environments.

Reflectance of an uncoated AFM cantilever vs reflectance of a gold coated AFM cantilever:

Rotated AFM Tip Rotated AFM Tip
Reflectance of an uncoated AFM Cantilever Reflectance of a Gold coated AFM Cantilever
» Browse all AFM probes with backside gold coated AFM cantilevers
Topside Gold Coated AFM Cantilevers
AFM Cantilever with Topside Gold Coating
AFM Cantilever with
Topside Gold Coating

Gold coating on the top side of the AFM cantilevers.

  • Electrically conductive
» Browse all AFM probes with topside gold coated AFM cantilevers
Overall Gold Coated AFM Cantilevers
AFM Cantilever with Overall Gold Coating
AFM Cantilever with
Overall Gold Coating

Gold coating on both sides of the AFM cantilevers.

  • Electrically conductive
  • Often used for tip functionalization
  • Protects the cantilever in chemically aggressive measurement environments
» Browse all AFM probes with overall gold coated AFM cantilevers
Platinum Coated AFM Cantilevers
AFM Cantilever with Electrically Conductive Platinum Coating
AFM Cantilever with
Electrically Conductive
Platinum Coating

Platinum coating on both sides of the AFM cantilevers.

  • Enhances laser reflectance
  • Electrically conductive
  • Used for electric mode measurements
» Browse all AFM probes with platinum coated AFM cantilevers
Platinum/Iridium Coated AFM Cantilevers
AFM Cantilever with Electrically Conductive Platinum/Iridium Coating
AFM Cantilever with
Electrically Conductive
Platinum/Iridium Coating

Platinum/Iridium coating on both sides of the AFM cantilevers.

  • Enhances laser reflectance
  • Electrically conductive
  • Used for electric mode measurements
» Browse all AFM probes with platinum/iridium coated AFM cantilevers
Conductive Diamond Coated AFM Cantilevers
AFM Cantilever with Conductive Diamond Coating
AFM Cantilever with
Conductive Diamond Coating

High wear resistance and electrically conductive real doped diamond coating on the tip side of the AFM cantilevers.

  • Electrically conductive
  • Used fo electric mode measurements
  • Detector facing side of the AFM cantilevers is coated with aluminum
» Browse all AFM probes with conductive diamond coated AFM cantilevers
Silicide Coated AFM Cantilevers
AFM Cantilever with Silicide Coating
AFM Cantilever
with Silicide Coating

Silicide coating on both sides of the AFM cantilevers.

  • Electrically conductive

» Browse all AFM probes with silicide coated AFM cantilevers

Note:

Other coating materials can cover the cantilevers, but as they don't play an active role in the measurement, they haven't been listed above.

Relation between AFM Cantilever Geometry and Application Mode

There is no common definition on the exact force constant values of stiff (or hard) and soft AFM cantilevers. Our own definition of these terms is the following:

An AFM cantilever with force constant above 40 N/m is referred to as a ‘stiff’ AFM cantilever. Such an AFM cantilever allows maximum scanning speeds in tapping/non-contact mode AFM measurements.

 An AFM cantilever with force constant in the range 3-15 N/m is referred to as an ‘intermediately stiff’ AFM cantilever. Such an AFM cantilever is usually preferred for soft intermittent contact mode AFM measurements with reduced tip-sample interaction (5-15 N/m) and for force modulation measurements (3 N/m).

An AFM cantilever with a force constant below 1 N/m is referred to as a ‘soft’ AFM cantilever. Such an AFM cantilever allows high sensitivity contact mode AFM measurements.

For more information on AFM cantilevers, please contact us.

* We are referring to the normal force constant of the AFM cantilever. For more information about the different AFM cantilever force constants, check the next chapter.

 

Relation between AFM Cantilever Geometry and Application Mode

^ go top
Definitions of AFM Cantilever Resonance Frequency and Force Constants

The normal resonance frequency (or simply the resonance frequency) f of an AFM cantilever refers to the resonance frequency for small amplitude oscillations in the direction normal to the sample facing surface of the AFM cantilever. This parameter neglects the mass of the tip.

The corrected resonance frequency fcorr of an AFM cantilever takes the AFM tip mass into account. Here, the AFM tip is modeled as a cone with height H and a base diameter H.

The normal force constant (or simply the force constant) C of an AFM cantilever is the ratio of the applied force from the top or the bottom side at the free cantilever end to the free end’s displacement for small displacements (Fig. 1). This force constant is most relevant for determining the tip-sample interaction during the majority of AFM operation modes.

The lateral force constant Clat of an AFM cantilever is the ratio of the applied force from the side at the free end of the AFM cantilever to its displacement for small displacements (Fig. 2).

The torsional force constant Ctor of an AFM cantilever is the ratio of the applied lateral force at the AFM tip to the lateral displacement of the AFM tip for small displacements (Fig. 3).

Resonance Frequency and Force Constants of AFM Cantilevers

Definitions of AFM Cantilever Resonance Frequency and Force Constants

^ go top
Calculator for the Resonance Frequency and the Force Constants of Silicon AFM Cantilevers

The calculator below calculates important parameters of silicon AFM cantilevers based on their geometric dimensions.

Calculated Constants Entered by user
f fcorr C Clat Ctor E G ρ T L W H
kHz kHz N/m N/m N/m N/m2 N/m2 kg/m3 µm µm µm µm
1.69*1011 5.00*1011
2330

f [kHz] – resonance frequency of the AFM cantilever (neglecting tip mass)
fcorr [kHz] – resonance frequency of the AFM cantilever taking tip mass into account
C [N/m] – (normal) force constant of the AFM cantilever
Clat [N/m] – lateral force constant of the AFM cantilever
Ctor [N/m] – torsional force constant of the AFM cantilever
T [µm] – AFM cantilever thickness
W [µm] – AFM cantilever width
L [µm] – AFM cantilever length
H [µm] – AFM tip height
ρ = 2.33g/cm3 = 2330kg/m3 - density of silicon
E = 1.69*1011 N/m2 - modulus of elasticity / Young’s modulus in the <110> direction of silicon
G = 0.5*1011 N/m2 modulus of rigidity / modulus of elasticity in shear of silicon

The calculator calculates the resonance frequencies and the force constants according to the following formulas:

Formulas

Formulas are derived from “Roark’s Formulas for Stress and Strain”, 6th edition, Waren C. Young, McGraw Hill.

Calculator for the Resonance Frequency and the Force Constants of Silicon AFM Cantilevers

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