Observation of monocrystallic silicone crystal using TEM Kristian SagmoNTNU, 22. april 2013

AbstractThe distance d022 was measured to be 1.853 0.067 .

IntroductionThe purpose of this report will be to briey summarize the observation of a multicrystalline silicone crystal using Bright Field (BF) and High resolution (HR) TEMmodes, as well as to exhibit a basic understanding of some of the physics involvedin the mechanisms of the microscope and basic observation theory. The rst TEMmicroscope was invented by Max Knoll and Ernst Ruska in 1931 shoving promise ofhigher resolutions than that possible with light. This remains one of the main benets of the instrument to date, being capable of resolutions down to around 0,05 nm[2]. Problematically, lens imperfections leading to unwanted optical eects caused byspherical and chromatic abberration, is now one of the main limiting factors of theresoluton power of TEM.For simplicity, no section regarding method will be included in this report, as it islargely described here in the introduction and the theory section.

TheoryAbout TEMTEM is a method of imaging using engergized electrons, oscillating with a specic

wavelength, to penetrate a thin sample of material. The wavelength, , may bemodeled by the De Broglie relation and the relativistic momentum of the electron (forhigh voltage), to produce the equation= q

h2m0 E(1 +

.E2m0 c2 )

(1)

Here, h is the planck constant, m0 the rest mass of an electron, c the speed of lightand E the energy of the accelerated electron. We may then begin to appreciate thepracticality of using a charged particle for imaging, as one may by applying a specicvoltage across the electron accelerator, produce probing particles with wavelengthssmaller than that of light.As electrons are highly interactive particles, the material needs to be thin, 200nm or less, to prevent too many scattering events in the sample. A specifc ray oftransmitted electrons may then be selected by the use of a specic aperture in theback of the sample, usually after the electrons have been focused. This selction oftransmitted electrons denes the dierent imaging modes commonly used.

Lab assignment in course TFY 4220; Solid State Physics, S2013

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BF-TEM is among the most commonly used modes. It involves selecting only the

directly transmitted electrons by the positioning of a magnetic gathering lens, andan aperture in its focal plane. An area of the sample with a denser concentrationof atoms, as seen by the electron, will appear darker than an area with less atomsalong the linear path of the electron. In addition, in a crystal structure, braggs lawsuggests that areas oriented more symmetrically towards line of motion for a particle,will diract, meaning it will appear darker than more randomized areas.

HR-TEM involves selecting all transmitted electrons to produce an image.Diraction-mode TEM, involves selecting only diracted electrons to form an image.

In a crystal structiure this provides an image of the diraction pattern formed by theelectrons, giving information of the alignment of the symmetry planes in the sample.By selecting dierent incoming waves, tilting the sample, and selcting diracted waves,one may for instance identify imperfections in a crystal structure, as well as identifythe dierent orientations in a multicrystalline structure.

Diraction and diraction pattern indexingBy introducing Miller indexes (hkl), the real space distance between atomic planes ina cubic crystal might be describeddhkl =

a,h2 + k 2 + l2

(2)

where a is the lattice constant of the cubic planes. Further, the vector in the reciprocalspace indexed ghkl = hi a + ki a + li a is related with the real space distance by1,| ghkl |

dhkl =

(3)

thus illustrating that the interplanar atomic spacings and the diraction pattern image is inversely related [1].In indexing diraction patterns, dierent approaches may be used, but here preeredis the relationship between the ratio of the lengths between two diraction points andtheir respective hkl values. By exploiting that tan 2 = 2 for very small angles andthereby 2 = RLhkl , Braggs law gives(4)

Rhkl dhkl = L.

The value Rhkl is the distance of the diraction point hkl from the origin, so againthis illustrates that the distance between diraction points in a diraction image isinversely related to the real space between lattice planes in the crystal. Using theabove equation for dhkl one arrives at the desired equationd2h2 + k12 + l12R12.= 22 = 122R2d1h2 + k22 + l22

The vector relationcos 12 =

R1 R2,R1 R2

(5)(6)

may be used as a check. Lastly to calculate the zone axis of an indexed diractionpattern

i

R1 R2 = h1h2

2

jk1k2

k l1 l2

(7)

ResultsIndexing of diraction patternsFor the diraction pattern shown in gure 1 , given that our silicone sample is a diamond crystal with a fcc Bravais lattice with a two atom basis, all visible points mustfulll Fhkl = 4f , meaning that h, k and l are all even or all odd. Furthermore, inthe image, R is measured R1 = R2 = 2 cm, so equation (5) = 1.The angle betweenpoints gives cos 12 = 12 . Then, by method of trial and error the pattern was indexedas illustrated, validated with equation (6). By equation (7) this corresponds to a zoneaxis [111].

Figure 1: Diraction pattern image 1, with miller indexesIn the second diraction image, gure 2, the fact that cos 12 = 0 equation (6)gives the only options h1 k1 l1 =[111], [111], [111] and [111]. Again, by trial and errorusing equation (5) the indexes were calculated as illustrated in gure... Then the zoneaxis was evaluated to [211].

Measurement of real space distance between lattice planes fora specic crystal orientationAs we see on the HR image, in gure 3, a hexagonial pattern is evident, pointingtoward the [111] lattice family. On the scale 2 nm = 1.4 cm, the distance between2nmpoints in the image was measured to be B = 0.15 1.4cm, which by equation (2) givesa real space distance d = 1.853 .

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Figure 2: Diraction pattern image 2, with miller indexes, a 2-dim square Bravais lattice

Figure 3: High resolution mode image, illustrating hexagonial symmetry

DiscussionAs a comparison to the measured value of d, by the given values of the lattice parameters a = b = c = 5.431 , the real space distances; d111 = 3.136 , d022 = 1.920 ,

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Figure 4: BF- TEM image, illustrating oxidation of sample edgesd113 = 1.638 . Thereby we would expect to be looking at the [022]-family, which ts

with the chosen indexing of the diraction pattern.

In gure 4 the edges of the sample is displaying a dark rim. It is suscpected thatthis is due to oxidation of the silicone, resulting in a disoriented atomic array close tothe edges. Further, in the indexing of the cubic diraction pattern, index 222 is seenas an incident of double diraction, due to relative large thickness of the sample.

ConclusionThis exercise has contributed to the basic understanding of TEM, and the operations ofan TE- microscope. Also one has undergone training in miller indexing of diractionpatterns from a crystal, and gained an understanting of its theoretical use. Thedistance d022 was measured to be 1.853 0.067 , wich may be used to descibe thecubic lattice parametres a = b = c of the crystal.

References[1] Hanne Kauko, TFY4220 Solid State Physics: Electron Diraction. NTNU January24, 2013.[2] Transmission electron microscope manufacturer FEI, An introduction toelectron microscopy. http://www.fei.com/resources/student-learning/introduction-to-electron-microscopy/intro.aspx[3] Wikipedia, Transmission electron microscopy. http://en.wikipedia.org/wiki/Transmission_electron_microscopy[4] Wikipedia, Crystal structure. http://en.wikipedia.org/wiki/Crystal_structure

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