Download Problem Set IV - Solutions

Problem 1
Make a table (e.g. in Excel) with a row for the observation tools
§ Optical Microscopy
§ SEM
§ TEM § AFM
§ STM where you describe briefly the following properties: § Basic operating principle § Approximate sensor resolution (10-­xm) § Applications (i.e. specimen type) § Prominent limitations 1
Problem 1
§ Optical Microscopy
§ Operating principle: Visible light (electromagnetic radiation in the visible spectrum) and a system of lenses is used to magnify images of small objects.
§ Resolution: Around 200 nm § Applications: Everyday lab use, observe samples directly without altering them, determine protein concentrations in living cells using UV-­fluorescence imaging, image samples where no resolution lower than 200 nm is needed
§ Limitations: Resolution limited by diffraction. The resolution limit is a function of the wavelength of light. Theoretical optical resolution: d = 0.61 λ / N.A. Transparent samples or different samples with similar transparencies are difficult to image.
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Problem 1
§ Scanning Electron Microscopy (SEM)
§ Operating principle: An electron beam is focused onto a conductive sample using electromagnetic coils. The beam is scanned over the sample and the interaction products (often SE) are detected. These signals are used to create an image where each pixel corresponds to the signal strength on the corresponding position on the sample.
§ Resolution: Few nanometers
§ Applications: Image microstructures, surface topography, material compositions
§ Limitations: The samples must be solid. It is not possible to observe wet samples and living cells. Often a high vacuum and a conducting coating is needed, which both can alter the sample. Due to electron scattering, the electrons from the electron beam interacts with a larger area than just on the focused spot. This limits the resolution. 3
Problem 1
§ Transmission Electron Microscopy (TEM)
§ Operating principle: A beam of electrons interacts with and eventually passes through an ultrathin sample and is magnified by using electromagnetic lenses.
§ Resolution: Few nanometers (better than SEM) § Applications: Observing thin samples (e.g. thin slices of brain tissue), Crystallography (atomic arrangement) § Limitations: Long sample preparation time, a thin sample is needed, sample preparation can alter the sample, resolution limited by electron diffraction, higher acceleration voltage (smaller wavelength) increase the resolution, but simultaneously increase the damage introduced in the sample. High vacuum is needed.
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Problem 1
§ Scanning Tunneling Microscopy (STM)
§ Operating principle: Quantum mechanical tunneling of electrons from the probe through the sample. § Resolution: Sub nanometer
§ Applications: Obtaining atomic level details of samples, manipulation of atoms
§ Limitations: Electrically conductive sample needed. Slow scanning rate and small scanning area. Sharp edges and overhangs cannot be imaged. The size of the probe tip sets a resolution limit (smallest tip = one atom), needs to operate under ultra-­high vacuum.
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Problem 1
§ Atomic Force Microscopy (AFM)
§ Operating principle: A laser diode is used to detect the deflection of a cantilever probe moving in very close proximity to the surface
§ Resolution: Sub nanometer
§ Applications: Observing and manipulating nanometer-­sized objects, nanolithography, measuring magnetic surface pattern (MFM), measuring biological samples in a wet environment
§ Limitations: Slow scanning rate and small scanning area. Sharp edges and overhangs cannot be imaged. The size
of the probe tip sets a resolution limit (smallest tip = one atom). The tip can crush into the sample when large
topological heights differences are present. The tip can damage the sample. Friction and adhesion can influence the measurement. 6
Problem 2
Given an oil immersion objective with 63x magnification, Numerical Aperture (N.A.) = 1.4, a standard 10x eyepiece, and a UV laser of 405 nm
a. What resolving power does system have, i.e. what is the minimal distance between two points you can theoretically distinguish? b. What resolving power does system have, i.e. what is the minimal distance between two points you can theoretically distinguish? c.
What does depth of field mean and how does this relate to N.A.? 7
Problem 2
a. What resolving power does system have, i.e. what is the minimal distance between two points you can theoretically distinguish? § Theoretical resolution: d = 0.61 λ / N.A. = 176.5 nm
b. How large would an object of 800 nm length appear? § M=M1M2 with M1, M2 = magnification of objective and ocular
§ 0.8 μm x 63 x 10 = 504 μm c.
What does depth of field mean and how does this relate to N.A.? § DOF is the range of distance along the optical axis in which the specimen can move without losing the sharpness of the image. This depends on the resolution of the microscope
§ The higher the N.A. the shallower this distance
Comparison of a lense with s maller N.A. to one with a larger N.A.
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Problem 3
How do images taken with optical and transmission electron microscopy differ? What influences whether you see an area as being bright or dark? § The basic principles of both microscopes are very similar but in the TEM electrons are used instead of light
§ In optical microscopy you therefore see things like you see them with your eyes, i.e. reflection and refraction appear as in real life (but with a lower resolution than TEM)
§ In electron microscopy, the interaction between the electrons and the sample is observed. The resulting images can look similar but have a higher resolution and can be influenced by material properties such as conductivity and electromagnetic effects etc.
§ Bright Field: The areas which absorb light (e.g. electrons) appear dark whereas the areas with a low interaction between sample and light (e.g. electrons) appear bright.
§ Dark Field: The light (e.g. electron beam) which barely interacts with the sample does not hit the detector (dark area). Only the light (e.g. electron beam) which is scattered at the sample can reach the detector. These areas appear bright. 9
Problem 4
AFM and STM: a. What properties are needed for AFM cantilevers in the different modes? b. What is the main advantage of using tapping mode compared to using contact mode? c.
What is a key advantage of Scanning Probe Microscopes over Electron or Optical Microscopes? 10
Problem 4
a. What properties are needed for AFM cantilevers in the different modes? § Three operation modes: Contact, tapping and non-­contact
§ In the contact mode, the static deflection of the cantilever is used to calculate the force. Because the measurement of a static signal is prone to noise and drift, low stiffness cantilevers are used to boost the deflection signal. Silicon nitride probes are often used. § For the tapping mode and non-­contact mode the stiffness needs to be higher to get higher resonance frequencies. Operating at higher frequencies results in lower noise levels. Silicon probes are typically used. 11
Problem 4
b. What is the main advantage of using tapping mode compared to using contact mode? § In the tapping mode, the image is obtained by measuring the forces generated by the intermittent contact of the tip with the sample
§ This lessens the damage to the sample compared to the contact mode. Hence, it is possible to image more delicate structures using tapping mode
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Problem 4
c.
What is a key advantage of Scanning Probe Microscopes over Electron or Optical Microscopes? § The resolution is not limited by diffraction. § Scanning Probe Microscopes use a physical probe to scan the specimen to obtain information of samples. Only the size of the probe limits the resolution.
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Problem 5
You have an SEM and an AFM. Which instrument do you use in the following applications and why (explain)?
a. To investigate the vertical surfaces of your etch trenches. The Trench is 3 micron in width and 15 micron in depth b. To investigate the surface of nanotubes lying horizontally on a substrate. The nanotubes are 20 nm in diameter and 100 nm in length 14
Problem 5
a. To investigate the vertical surfaces of your etch trenches. The Trench is 3 micron in width and 15 micron in depth § You use an SEM and tilt the stage so that you can see the vertical surfaces. The AFM cantilever tip cannot access the vertical surfaces of etch trenches. 15
Problem 5
b. To investigate the surface of nanotubes lying horizontally on a substrate. The nanotubes are 20 nm in diameter and 100 nm in length § Investigating the surface of nanotubes needs atomic resolution. § AFM should be chosen. 16