Lecture 23 X-Ray & UV Techniques

Transcription

1 Lecture 23 X-Ray & UV Techniques Schroder: Chapter /50 Announcements Homework 6/6: Will be online on later today. Due Wednesday June 6th at 10:00am. I will return it at the final exam (14 th June). I will make the solutions available on June 6 th. Office Hours Next week office hours will be Today 13:00-14:00. 2/50 1

2 Announcements Final Exam The final is scheduled for Thursday June 14 th at 14:00. Strand Agriculture Hall 113. The exam will be 90 minutes long. More information will be provided next week. The next lecture with content will be today. Wednesday June 6 th will be a review lecture. I will go through some examples. There will be no lecture on Friday June 8 th. It will be treated as an opportunity to prepare for the exam. 3/50 Lecture 23 X-Ray Fluorescence. X-Ray Photoelectron Spectroscopy. Ultraviolet Photoelectron Spectroscopy. X-Ray Diffraction Spectroscopy. 4/50 2

3 X-Ray Fluorescence 5/50 X-Rays X-rays are just photons (like light). Defined in the range of λ = 10 pm to 10 nm In terms of energy this is: ~100 ev to 100 kev. A lot of materials are transparent to X-rays. Hence it is a good bulkprobe, since X-rays can travel a long way in materials. 6/50 3

4 X-Ray Fluorescence X-ray fluorescence (XRF) involves x-ray-induced ionization of inner core electrons and detection of secondary x-rays emitted as a consequence of relaxation from an excited state. X-rays hν L hν Also X-rays The x-ray energy and intensity establish the atomic identity and concentration, respectively. Atomic identification is readily accomplished, since x- ray energies are well known and x-ray lines are relatively few in number. K 7/50 X-Ray Fluorescence XRF is a bulk technique. In Si for example the penetration depth is ~ 1 10 μm. XRF is a nondestructive elemental analysis technique and is applicable to solids, liquids, and thin films. It has a sensitivity of ~0.01% or ~5 X cm -3 and an analysis area of ~1 cm 2. 8/50 4

5 Total Reflection XRF Total Reflection XRF X-ray fluorescence (TXRF) is a surface-sensitive version of XRF. We use of a grazing incidence angle of θ < 0.1. incident x-ray beam θ detector secondary x-ray beam substrate reflected x-ray beam This results in a theoretical beam penetration distance of ~2-3 nm. This may be slightly higher due to finite roughness, wafer warpage or beam divergence. 9/50 Total Reflection XRF TXRF has a detection sensitivity of ~ cm -2 for metallic impurities in silicon, which can be enhanced by about an order of magnitude by HF vapor-etching of the surface native oxide, which is allowed to dry and then analyzed by TXRF. 10/50 5

6 Applications of XRF In reality XRF is ideally suited to rapidly survey samples, for more detailed analysis later. It is non-destructive and can be used in air. Can be used for thickness measurements if standards are used. 11/50 X-Ray Photoelectron Spectroscopy 12/50 6

7 XPS X-Ray Photoelectron Spectroscopy (XPS) is sometimes also known as Electron Spectroscopy for Chemical Analysis (ESCA). We use it to evaluate elemental composition and properties of chemical bonds. As usual we fire radiation (X-Rays) at the sample and measure what comes off. In this case we measure electrons coming emitted (hence the term photoelectron). Typically energies are ~1,250 1,500 ev. We are probing core levels. 13/50 XPS Normally the X-Ray beam is large, but we can use focused beam to provide spatial information. 14/50 7

8 XPS The photon comes in and kicks off a core (e.g. L level) electron. E vacuum hν The electron then will be detected with a metal spectrometer. L K 15/50 Binding Energy Emitted electrons are energy analyzed and then plotted in terms of the binding energy E B : Where: known h = Planck Constant. E B = hν KE eφ sp measured ν = Frequency of incoming photon. KE = Kinetic energy of emitted electron. e = Fundamental unit of charge. calibrated φ sp = Work function of detector (in V). 16/50 8

9 XPS Spectrum Below is what a typical XPS spectrum looks like 17/50 Bonding The primary reason why XPS is of interest (rather than the many other elemental analysis techniques) is that it can provide information on bonding and local environment. The figure to the right shows what happens as Pb bonds with O. Schroder p /50 9

10 XPS is a Surface Technique X-rays are photons and observe the Beer Lambert law. For inelastic scattering only: Where: I x = I 0 exp x l cos θ I x = X-Ray intensity at distance x into sample. I 0 = X-Ray intensity at sample surface. l = Inelastic mean free path. θ = Angle to surface normal (0 is normal to surface). 19/50 XPS is a Surface Technique At 1000 ev, λ = 1.6 nm. For example if θ = 0 the intensity received as a function of depth could look like this: 95% of X-Ray absorption takes place within first 5nm. 95% of electrons will be emitted from first 5nm. This is a surface technique. 20/50 10

11 XPS vs AES XPS depth profiling is analogous to Auger electron spectroscopy (AES) depth profiling. However, in conventional XPS the x-ray excitation area is quite large (~mm s). Modern XPS systems offer a small-spot option (~1-100 μm), either by restricting the size of the x-ray source or modifying the detector design to accept photoelectrons from a restricted portion of the sample surface. 21/50 XPS vs AES XPS, rather than AES, is better suited to the surface assessment of delicate materials such as polymers, since x-rays induce less surface damage than electrons. In angle-resolved XPS, the surface sensitivity may be modified by varying the take-off angle. I x = I 0 exp x l cos θ XPS elemental sensitivity is ~1%. 22/50 11

12 XPS vs AES Quantitative XPS is accomplished using relative sensitivity factors and standards and has an accuracy of ~10%. The two most common XPS x-ray sources are the Kα lines of Al and Mg at ev and ev, respectively. One disadvantage of these sources are their relatively large linewidths of 0.85 ev and 0.7 ev for Al and Mg, respectively. Also, the lineshapes of these x-ray sources are asymmetric. 23/50 XPS vs AES A broad and asymmetric line results in poorer resolution. Resolution improves with the use of an x-ray monochromator to reduce the linewidth to ~0.1 ev. However, this drastically decreases the x-ray intensity and the signal-to-noise ratio. 24/50 12

13 Ultraviolet Photoelectron Spectroscopy 25/50 UPS Ultraviolet photoelectron spectroscopy (UPS) is another type of photoemission. UPS is basically the same technique as XPS, but employing ultraviolet radiation rather than X-rays. UPS is usually accomplished using a helium lamp emitting at either 21.2 ev (He I radiation) or 40.8 ev (He II radiation). He linewidths are very narrow, ~1 mev, so that resolution is determined by the analyzer. 26/50 13

14 UPS The process is the same as XPS, but we are now looking at much lower energies shallower states (including valence band states). E vacuum VB hν VB /50 UPS Data This is an example of real data. We are looking for the energy after which no electrons are emitted top of valence band. This can be tricky and subjective. Secondary electron edge Note VBE here is relative to Fermi Energy. Intensity a.u. Intensity a.u. He I Source Energy SEE ev VBE EF Evac Binding Energy w.r.t. E Fermi ev VBE Valence band edge Work Function VBE 0.82 ev EFermi Evac 4.69 ev Binding Energy w.r.t. E Fermi ev 28/50 14

15 UPS Data We can combine our knowledge of the valence band energy with other techniques. E.g. using Tauc analysis of optical absorption data can give us band gap. Together this allows us to produce a basic band structure of our material. This information is critically important for device design. 29/50 ARPES Up to now the UPS measurements that we have discussed have implicitly been angle-integrated, since most photoelectron energy analyzers accept electrons over a wide range of take-off angles. More detailed information is available from angleresolved photoemission spectroscopy (ARPES) measurements, in which you can map out the valence band structure in k-space. 30/50 15

16 ARPES Data This information can be used to reconstruct, experimentally, the density of states in the semiconductor. This is something that traditionally is calculated and direct access is very difficult. B.B.Y. Hsu, Adv. Mater. 27 (2015) /50 ARPES Data By measuring the emission as a function of angle we can evaluate the entire band structure (in k-space). T. Cuk, PRL. 93 (2004) This allows us to evaluate the effective mass of carriers in this material. 32/50 16

17 X-Ray Diffraction 33/50 XRD The final technique we will talk about is X-ray diffraction (XRD). We primarily use XRD for crystal structure determination and chemical identification. It is a routine technique for many materials (not just electronic materials) because it is reasonably quick and unambiguous. 34/50 17

18 XRD Consider a monochromatic beam of x-rays incident upon a crystal surface at an angle θ. incident θ θ reflected d Under certain circumstances this incident beam is specularly reflected from the surface. Constructive interference occurs for certain angles θ, depending on the separation of crystal planes d. 35/50 XRD The incident and reflected beams are described by their wave vectors k i and k r, respectively, where: k = 2π λ λ is wavelength of the incident X-rays. The incident x-ray beam penetrates the lattice and scatters from atoms in the lattice. If the crystal is represented as a series of parallel atomic planes (as indicated on the previous page) the incident beam is partially reflected at each plane. 36/50 18

19 Bragg s Law If the reflected rays from each plane to the detector have a difference in path length equal to an integral number of x-ray wavelengths, these rays constructively interfere, resulting in specular reflection. This requirement leads to Bragg s Law: 2d sin θ = nλ Where: n N. 37/50 Bragg s Law Note two important ramifications of Bragg s Law. First, the interplanar spacing may be found from the angle and the wavelength. Second, diffraction (i.e., scattering and constructive interference) can occur only if λ < 2d. An alternative way to express Bragg s Law involves an Ewald construction in reciprocal space. Reciprocal space is the Fourier transform of real space. 38/50 19

20 Ewald Construction An alternative way to express Bragg s Law involves an Ewald construction in reciprocal space. Reciprocal space is the Fourier transform of real space. reciprocal space k r k i Ewald sphere G hkl 39/50 Ewald Construction The Ewald construction is accomplished as follows: (i) Draw k i in reciprocal space. (ii) Use k i to generate an Ewald sphere. (iii) Draw k r as a vector from the center of the Ewald sphere to another point located on the sphere surface. (iv) Draw a vector from k i to k r, and identify this vector as the reciprocal lattice vector G hkl, where (hkl) specifies the diffraction plane Miller indices. 40/50 20

21 Ewald Construction The utility of the Ewald construction is that the diffraction condition equivalent to Bragg s law is k r k i = G hkl This equation is particularly interesting when it is recognized that: d hkl = 2π G hkl d hkl is the interplanar distance. 41/50 Bragg Reflection The geometry of Bragg reflection is summarized as follows. real space incident θ k i k r θ θ reflected G hkl d hkl = 2π d hkl G hkl 42/50 21

22 Powder XRD There are several ways to accomplish XRD, such as the powder method, shown below. focussing circle incident x-ray beam θ sample detector scattered x-ray beam 2θ rotate sample & detector relative to x-ray source in a θτ2θ manner intensity (counts) d hkl λ 2sin θ θ 43/50 Powder Database Bragg s Law specifies XRD peak locations. We can use this information to fingerprint compounds and structures. Tens of thousands of XRD powder diffraction files are available for crystal identification from the Joint Committee on Powder Diffraction Standards (JCPDS). The best known database is maintained by Cambridge University: 44/50 22

23 Real Data Typically one would calculate an XRD pattern from a known structure then compare it with experimental data. This can be used to confirm that you have the material / phase / orientation that you think you do. 45/50 Real Data Often when plotted on a linear scale a small number of peaks dominate, and obscure a lot of information. Experimental XRD specialists often will require XRD data plotted on a logarithmic scale to make convincing statements on structure. Red = experimental asterisks = unidentified peaks Blue = calculated 46/50 23

24 Scherrer Formula The width of an XRD peak also provides interesting information. The maximum grain size of a polycrystalline thin film can be estimated from the Scherrer formula: Where: d grain = 0.9λ Δ cos θ d grain = maximum grain size. Δ = full-width-at-half-maximum (in radians) of the XRD peak. 47/50 Rocking Curve For an epitaxial film, the degree of crystalline perfection is estimated from a rocking curve assessment in which the intensity of a diffraction peak is monitored as a function of a small rotation along an axis perpendicular to the sample surface. sample normal ~0.1 ω sample sample rocking 48/50 24

25 Rocking Curve sample normal ~0.1 ω sample sample rocking The sharpness of this rocking curve is a measure of crystalline perfection. A perfectly flat surface at T=0K would in theory have a delta function as its rocking curve. 49/50 Next Time Course Summary. Review Lecture for Final Exam. Exam structure / regulations. Example questions. 50/50 25