Positron Annihilation Lifetime Spectroscopy
In addition to the changes in the electron momentum distribution, a trapped positron also experiences a decrease in electron density, which is accompanied by a corresponding increase in lifetime. This is the basis of Positron Annihilation Lifetime Spectroscopy (PALS), in which one measures the distribution of positron lifetimes and their intensities. In classic PALS setups, the timing start signal is provided by a gamma-ray that is released coincidentally from a radioactive source with the positron. The stop signal is one of the annihilation gamma-rays. Two phototubes are used to detect the start and stop gamma-rays. The advantages of this type of PALS is a high count rate and a relatively simple experimental apparatus. This disadvantage is that the positrons are implanted very deeply and in an uncontrolled fashion so that only average properties of the sample can be studied with positrons.
On the other hand, in beam PALS, the timing start signal is provided by the secondary electrons produced when the positron beam strikes the sample surface. A CEMA plate detects the secondary electrons and provides the start pulse. The stop signal is still provided by one of the annihilation gamma-rays. The major advantage of beam PALS is the ability to control positron implantation. Samples can be depth-profiled by varying the incident beam energy. This technique has been used to determine the free-volume hole size distributions in various polymers as a function of temperature, pressure, and physical aging. It is a relatively new technique, which holds great promise, particularly in the study of porous films, such as low-k thin films.
Doppler Broadening Spectroscopy
When a thermalized positron annihilates with an electron in a solid, the annihilation gamma-rays are doppler-shifted in order to conserve momentum. Since the thermalized positron is almost at rest compared to the electron, the momentum-related energy shift is due primarily to the momentum of the annihilating electron. Typical energy shifts are of order a keV. This effect tends to broaden the 511 keV annihilation gamma peak and since the energy resolution of a typical germanium detector is of order a keV this can result in a virtual doubling of the experimental line width. Positrons trapped in defects have a smaller probability of annihilating with deeply bound core electrons and a larger probability of annihilating with lower momenta valence electrons. This results in a smaller average energy shift. Thus, defects tend to narrow the experimental line width.
In Doppler Broadening Spectroscopy (DBS), one generally characterizes the width of the energy distribution by the sharpness or S-parameter. This parameter is defined as the ratio of the number of events in some fixed central region of the peak to the total number, and is very sensitive to small changes in the width. DBS may be employed to perform depth-profiled defect analysis by varying the incident beam energy. Due to its relative ease of implementation and its high defect sensitivity, this technique accounts for most of the condensed matter work done with slow positrons today.
Three types of positron microscopes have been constructed to date. The first type to be reported is analogous to the transmission electron microscope (TEM) and is called the transmission positron microscope In it, positrons passing through a thin sample are focused on a channel electron multiplier array (CEMA), and the resulting magnified image is accumulated by a computer. Since this technique cannot readily make use of any of the unique positron characteristics discussed above, it offers only a few potential advantages over a TEM. Shortly thereafter, however, a much more useful type of direct imaging microscope called the positron reemission microscope (PRM) was reported, which does exploit unique positron characteristics. In the PRM (shown schematically in the figure on the right), positrons are implanted in a thick sample and allowed to thermalize and diffuse. Those that reach the surface and are reemitted are then accelerated, magnified, and focused on a CEMA to form an image. Thus the imaged signal is related to the number of particles reemitted, a signal which is unique to positrons.
The PRM offers potential resolutions below 10 angstroms, and should be particularly useful in studies of surfaces and thin overlayers, as well as in biological applications. Any process in the solid that either enhances or suppresses the probability of positron reemission from a particular point on the target surface can be a contrast mechanism for this microscope. Defect trapping, work function changes, surface trapping, positronium formation, and other positron interaction mechanisms can thus be imaged. The reemission probability can be a very sensitive measure of surface conditions in some cases. It may be possible to image overlayers having thicknesses of only 1-2 monolayers, and thus to observe such phenomena as islanding or adsorbate segregation. Depth profiling using the PRM may be feasible, but the actual depth from which information can be obtained is limited by the requirement that positrons be able to reach the surface and be reemitted in order to be imaged. This limits the depth to which the beam positrons can be usefully implanted to roughly a diffusion length (100-1000 angstroms) depending on sample conditions).
The third type of positron microscope, analagous to the scanning electron microscope, is called the scanning positron microscope (SPM). In the SPM (shown schematically in the figure on the right), a beam of positrons of microscopic diameter is rastered across a surface, and a positron-related signal is recorded synchronously. An image is built up in a computer by recording the amplitude of the signal at each point in the raster. The signal can be any of the unique positron signals, for example, reemitted positron rate, energy of the reemitted positrons, positronium fraction, annihilation gamma-ray energy or angle, or positron lifetime.
The advantages of the SPM are the wide variety of signals available and the ability to examine target properties at various depths from the surface. Moreover one is not limited to materials that reemit positrons. Since some of the signals of the SPM (such as gamma-rays) can easily be detected even if they originate from the interior of a target, subsurface features can be imaged without the need to destroy the sample by thinning or delayering. The implantation depth can be varied up to a maximum of several microns by varying the incident energy. Thus the SPM can be used to produce a depth profile of a target and should be particularly useful in the study of such samples as semiconductor devices where buried junctions and interfaces determine the properties of interest. The disadvantages of the SPM are the fact that ultimate resolution is limited by the diffusion spreading of positrons in the incident beam spot to roughly a diffusion length (100-1000 angstroms) as mentioned above), and the need for more intense beams to provide sufficient rate to produce full two-dimensional images. Since the SPM is essentially a PRM with a smaller, rastered, positron beam, it is relatively simple to extend the PRM to include SPM capability.