Relationship between image contrast and electron dose

As a means of offering more background on my radiation damage study, this quick post will highlight some relevant information from the paper Experimental high-resolution electron microscopy of polymers by David C. Martin and Edwin L. Thomas.

The main takeaway is that high resolution electron microscopy of organic materials is limited because of their sensitivity to radiation damage. In order to understand the relationship between image contrast and radiation damage more quantitatively, let us take a look at a few simple equations. The number of electrons Q which are incident on an area d² is

where J is the total electron dose (electrons per unit of area) and d is the smallest resolvable feature size of the object of interest. Since the standard deviation in the intensity of an object illuminated with Q electrons is the square root of Q (this is simply the square root of the variance, which is the number of electrons Q), the noise of an electron microscopy image is given by

From this equation we can see that the noise is minimized as the electron dose J is increased – and herein lies our problem. Since organic materials, such as the polymers that I am studying, are especially sensitive to radiation damage, my current goal is to determine a critical electron dose at which high contrast can be achieved without destroying the material’s structure.

According to this paper, the critical dose J_c can be obtained by fitting the intensity of diffraction peaks as a function of electron dose to the following exponential function:

Thus, as explained in my research update post, the critical dose can be obtained by taking the inverse of the decay rate. As for the extra background intensity term, I am still working on whether that should be included in the fit because I’m not sure if I can assume the decay goes to zero.

Radiation damage study of P3HT and P3HT-b-PFTBT

A couple of weeks ago, I obtained my first set of TEM electron diffraction data with the help of another lab member, Thinh Le. Much like how electrons passing through a grating will produce an interference pattern due to particle-wave duality, electrons accelerated through a TEM sample’s periodic structure will result in a diffraction pattern. As seen in the examples below, a crystalline specimen will produce a spot pattern whereas a semi-crystalline or amorphous specimen will produce diffraction rings. Ring formation occurs because each randomly oriented domain produces its own diffraction pattern, and the superposition of these patterns forms rings.

http://www.ammrf.org.au/myscope/tem/background/concepts/imagegeneration/diffractionimages.php

Since the samples I was studying were polymers (P3HT and P3HT-b-PFTBT), their electron diffraction patterns were rings. However, they are very sensitive to electron beam damage – in fact, every time I moved the electron beam to a new location on the sample, I could see the diffraction ring fading away right before my eyes the longer it was exposed to the beam. For this very reason, the first milestone that I hope to achieve is to calculate a critical dose D_c at which soft materials such as P3HT and P3HT-b-PFTBT can be imaged with maximum contrast without destroying their structure.

To characterize this radiation damage, I took 10 consecutive electron diffraction images at one sample location at regular time intervals for both P3HT and P3HT-b-PFTBT (with increasing time, the electron dose also increases proportionally). By extracting the intensity of the diffraction rings using the software Digital Micrograph, I was then able to plot the intensity of the rings against the electron dose. The resulting data can be fitted to an exponential curve and D_c can be calculated as the inverse of the decay rate.

Unfortunately, the values for D_c that I calculated did not agree with values previously calculated by my lab. Possibilities for this discrepancy could be an inaccurate electron dose calibration or imprecise intensities. The first of these issues is out of my hand, but I will attempt to remedy the second by calculating radially integrated intensities using Mathematica.