Spectroscopic applications of Quantum Mechanics
Scanning Probe Microscopes (SPM) define a abroad group of instruments used to image and measure properties of material, chemical and biological surfaces.
SPM works on the principle of bringing a very sharp probe close to sample surface. Measuring a “local” physical quantity related with the interaction, allows constructing an image of the studied surface. All the data are transferred to a PC, where, with the use of the appropriate software, an image of the surface is created.
Scanning Tunneling Microscope
A scanning tunneling microscope (STM) is an instrument for imaging surfaces at the atomic level. It was invented in 1981 by Gert Binning and Heinrich Rohrer.
It consists of a metal probe (made of tungsten, platinum iridium or gold) with a point so fine that its tip is a single atom which is brought close to the surface of a conducting or semi-conducting material.
description & representation called topography is able to resolve individual atoms on a surface.
In STM electrons are transferred between tip and sample and net transfer is sustained by applying a tunneling voltage across the gap. Since electron transmission probability e-L
where L is gap width. Therefore even a small change in L (0.01nm) means a detectable change in tunneling current. So change in current is a result of a change in the tip-sample separation.
STM works in two Modes (method of using interaction to obtain image):
If the tip is moved across the sample in the x-y plane, the changes in surface height and
density of states cause changes in current. These changes are mapped in images. This change in current with respect to position can be measured itself, or the height, z, of the tip corresponding to a constant current can be measured. These two modes are called constant height mode and constant current mode, respectively.
In constant current mode, feedback electronics adjust the height by a voltage to the piezoelectric height control mechanism maintaining the current constant. This leads to a height variation and thus the image comes from the tip topography across the sample.
In constant height mode, the voltage and height are both held constant while the current changes to keep the voltage from changing; this leads to an image made of current changes over the surface.
The speed of scanning in constant current mode (CCM) is restricted by usage of feedback system. Larger scanning speeds can be obtained by usage of Constant Height mode (CHM), but CCM allows investigating the samples with developed relief.
Advantages of STM:
1. Very high resolution (lateral: 0.1nm depth: 0.01nm)
Disadvantages:
1. STM is limited to conducting and semi-conducting materials.
2. In biological materials, conduction is due to flow of ions not electrons, so cannot be studied by STMs.
Atomic force microscope (AFM)
The first commercially available atomic force microscope (AFM) was introduced in 1989. The AFM is one of the foremost tools for imaging, measuring, and manipulating matter at the nanoscale.
The AFM consists of a cantilever with a sharp tip (probe) at its end that is used to scan the specimen surface. The cantilever is typically silicon or silicon nitride with a tip radius of curvature on the order of nanometers. When the tip is brought into proximity of a sample surface, forces between the tip and the sample lead to a deflection of the cantilever according to Hooke's law. Depending on the situation, forces that are measured in AFM include mechanical contact force, van der Waals forces, capillary forces (due to the water layer often present in an ambient environment), chemical bonding, electrostatic forces, magnetic forces etc. Along with force, additional quantities may simultaneously be measured through the use of specialized types of probe.
Typically, the deflection is measured using a laser spot reflected from the top surface of the cantilever into an array of photodiodes. This set-up is known as an optical lever. The probe is moved over the sample by a scanner, typically a piezoelectric element, which can make extremely precise movements.
The AFM can be operated in a number of modes, depending on the application. In general, possible imaging modes are divided into static (also called contact) modes and a variety of dynamic (or non-contact) modes where the cantilever is vibrated.
Contact mode (Probe-surface separation is< 0.5nm)
In Contact mode of operation the cantilever deflection under scanning reflects repulsive force acting upon the tip. Repulsion force F acting upon the tip is related to the cantilever deflection value x under Hooke's law: F = -kx, where k is cantilever spring constant. The spring constant value for different cantilevers usually varies from 0.01 to several N/m. In contact mode the deflection signal is used as a parameter characterizing the interaction force between the tip and the surface. There is a linear relationship between the deflection value and the force. In Constant Force mode of operation the deflection of the cantilever is maintained by the feedback circuitry on the preset value. So, vertical displacement of the scanner under scanning reflects topography of sample under investigation.
Advantages:
- High scan speeds.
- “Atomic resolution” is possible.
- Easier scanning of rough samples with extreme changes in vertical topography.
Disadvantages:
- Lateral forces (i.e., frictional forces on the surface) can distort the image.
- Capillary forces from a fluid layer can cause large forces normal to the tip sample interaction.
- Combination of these forces reduces spatial resolution and can cause damage to soft samples
Non contact mode (Probe-surface separation is 0.1nm to 10nm)
In this mode, the probe operates in the attractive force region and the tip-sample interaction is minimized.
A stiff cantilever is oscillated with a frequency slightly above its resonant frequency in the attractive regime, meaning that the tip is quite close to the sample, but not touching it (hence, “noncontact”). When an oscillating cantilever is brought near to the surface (in the range of 10nm-100nm), oscillations get modified due to interaction forces between tip and the sample. The forces between the tip and sample are quite low, on the order of pN (10-12 N). The detection scheme is based on measuring changes in the oscillation
characteristics i.e., resonant frequency, amplitude of oscillations, phase shift .Oscillations characteristics can be used to generate a map that characterizes surface of the sample.
Advantage:
- Low force is exerted on the sample surface and no damage is caused to soft samples
Disadvantages:
Tapping mode (Probe-surface separation is 0.5nm to 2nm)
A stiff cantilever is oscillated (close to its resonance frequency) closer to the sample than in noncontact mode. Part of the oscillation extends into the repulsive regime, so the tip intermittently touches or “taps” the surface. Due to interaction of forces on cantilever, when tip comes close to the surface VanderWaal force, dipole-dipole interaction, electrostatic force etc., cause the amplitude of this oscillation to decrease. Digital feedback loop adjust the tip sample separation to maintain constant amplitude and force on the sample.
Very stiff cantilevers are typically used, as tips can get “stuck” in the water contamination layer. In tapping mode image is produced by imaging the force of intermittent contacts of the tip with the sample surface.
The advantage of tapping the surface is improved lateral resolution on soft samples. Lateral forces such as drag, common in contact mode, are virtually eliminated. For poorly adsorbed specimens on a substrate surface the advantage is clearly seen.
Potential energy diagram of a probe and sample.
Advantages:
–Allows high resolution of samples that are easily damaged & loosely held to a surface –Good for biological samples
Disadvantages:
–More challenging to image in liquids –Slower scan speed.
Disadvantages of AFM
–Forces involved change the shape of the specimen (eg DNA)
–The physical probe used in AFM is not ideally sharp. So, AFM image does not reflect the true sample topography, but represents the interaction of the probe with the sample surface. This is called tip convolution.
Note:
**Piezocrystals
