278 Characterization of Thin Films (a) VACUUM M Lz3- L, - K INITIAL STATE X-RAY 3 EMISSION 3s etc. 2P - 2s 1s \: =/e- ELECTRON EJECTED P - 4 AUGER ELECTRON EMISSION Figure 6-14. Schematic of electron energy transitions: (a) initial state; (b) incident photon (or electron) ejects K shell electron; (c) X-ray emission when 2s electron fills vacancy; (d) Auger electron emission. KLL transition shown. For example, hc EKa, = - = E, - E,, 9 XKa, (6-15) where h, c, and X have their usual meaning. 2. The emitted X-rays are characteristic of the particular atom undergoing emission. Thus, each atom in the Periodic Table exhibits a unique set of K, L, M, etc., X-ray spectral lines that serve to unambiguously identify it. These characteristic X-rays are also known as fluorescent X-rays when excited by incident photons (e.g., X-rays and gamma rays). There is, however, an alternative process by which the electron hole in Fig. 6-14b can be filled. This involves a complex transition in which three, rather than two, electron levels, as in EDX, participate. The Auger process, which is the basis of AES, first involves an electron transition from an outer level (e.g., L,) to the K hole. The resulting excess energy is not channeled into the 6.4. Chemical Characterization 279 creation of a photon but is expended in ejecting an electron from yet a third level (e.g., L,). As shown in Fig. 6-14d, the atom finally contains two electron holes after starting with a single hole. The electron that leaves the atom is known as an Auger electron, and it possesses an energy given by EmL = E, - ELI - EL2 = E, - EL, - ELI. (6-16) The last equality indicates KL ,L, and KL, L transitions are indistinguishable. Similarly, other common transitions observed are denoted by LMM and MNN. Since the K, L, and M energy levels in a given atom are unique, the Auger spectral lines are characteristic of the element in question. By measuring the energies of the Auger electrons emitted by a material, we can identify its chemical makeup. To quantitatively illustrate these ideas, let us consider the X-ray and Auger excitation processes in titanium. The binding energies of each of the core electrons are indicated in Fig. 6-15, where electrons orbiting close to the nucleus are strongly bound with large binding energies. Electrons at the Fermi level are far from the pull of the nucleus and therefore taken to have zero binding energy, thus establishing a reference level. They would still have to acquire the work function energy to be totally free of the solid. Some notion of the rough magnitude of the core energy levels can be had from the well-known formula for hydrogen-like levels; Le., E = 13.6Z2/n2 (ev), (6-17) where 2 is the atomic number and n is the principal quantum number. For Ti (2 = 22), the calculated energy of the K shell (n = 1) is 6582 eV. Complex electron-electron interactions and shielding of the nucleus makes this formula far too simplistic for multielectron atoms. Both effects reduce electron binding energies relative to Eq. 6-17. Several of the prominent characteristic X-ray energies and wavelenbths for Ti are Kal: E, - EL, = 4966.4 - 455.5 = 4511 eV, X = 2.75 A; KO,: EK - EM, = 4966.4 - 34.6 = 4932 eV, X = 2.51 A; La: EL, - EM,,, = 455.5 - 3.7 = 452 eV, X = 27.4 A. Similarly, a prominent Ti Auger spectral transition is LMM or ELMM = EL, - EM, - EM4 = 455.5 - 34.6 - 3.7 = 417 eV. The question may arise: When do atoms with electron holes undergo X-ray transitions, and when do they execute Auger processes? The answer is that both processes go on simultaneously. In the low-Z elements, the probability is greater that an Auger transition will occur, whereas X-ray emission is favored for high Z elements. The fractional proportions of the characteristic X-ray 280 Characterization of Thin Films a. X-RAY PROCESS FERMi LEVEL b. AUGER PROCESS 0 3.7 eV 4 34.6 eV 60.3 eV -t ti 455.5 eV L46l.5 eV 563.7 eV 4966.4 e\ EDX I I I 4.0 4.5 5.0 X-RAY ENERGY, keV C. 387 300 4 ELECTRON I d. AES k 151 I 500 NERGY, eV Ti 2p3/2 I 600 500 400 BINDING ENERGY eV Figure 6-15. Electron excitation processes in Ti: (a) energy-level scheme; @) EDX spectrum of Ti employing Si(Li) detector; (c) AES spectral lines for Ti (dN(E)/dE vs. E); (d) a portion of the XPS spectrum for Ti (MgKa! radiation). 6.4. Chemical Characterization 281 120 - 0- I I 1 I I 0 5 I0 15 20 25 30 ENERGY (keV) Figure 6-1 6. Characteristic X-ray emission energies of the elements. (Courtesy of Princeton Gamma Tech, Inc.) 90 80 70 5 60 m $ 50 p 40 5 30 Z 20 10 0 0 800 1600 2400 ELECTRON ENERGY (eV) Figure 6-1 7. Principal Auger electron energies of elements. (Courtesy Electromcs Industnes, Inc.) 90 80 70 5 60 m $ 50 p 40 5 30 Z 20 10 0 0 800 1600 2400 ELECTRON ENERGY (eV) Figure 6-1 7. Principal Auger electron energies of elements. (Courtesy Electromcs Industnes, Inc.) of Physical and Auger yields for K, L, M transitions can be found in standard references (Ref. 13). The variation of the principal characteristic X-ray and Auger lines with atomic number is shown in Figs. 6-16 and 6-17, respectively. Commercial spectrometers typically operate within the energy range spanned in these 282 Characterization of Thin Films figures. Therefore, in EDX, K X-ray transitions are conveniently measured in low-Z materials, and L series X-rays appear when high-2 elements are involved. Similarly, in AES, KLL and LMM transitions are involved for low-Z elements, and LMM and MNN lines appear for high-Z elements. Although keeping track of the particular shell involved is sometimes annoying, spectra from virtually all of the elements in the periodic table can be detected with a single excitation source and a single detector. Fortunately, the resolu- tion of X-ray or electron detectors is such that prominent lines of neighboring elements do not seriously overlap. This facilitates spectral interpretation and atomic fingerprinting. The basis for understanding XPS lies in the same atomic core electron scheme that we have been considering. Rather than incident electrons in the case of EDX and AES, relatively low-energy X-rays impinge on the specimen in this technique. The absorption of the photon results in the ejection of electrons via the photoelectric effect. Governing this process is the well-known equation expressed by EKE = hv - EB, (6-18) where EKE, hu, and EB are the energies of the ejected electron, incident photon, and the involved bound electron state. Since values of the binding energy are element-specific, atomic identification is possible through measure- ment of photoelectron energies. 6.4.3. X-Ray Energy-Dispersive Analysis (EDX) 6.4.3.1. Equipment. Most energy-dispersive X-ray analysis systems are interfaced to SEMs, where the electron beam serves to excite characteristic X-rays from the area of the specimen being probed. Attached to the SEM column is the liquid-nitrogen Dewar with its cooled Si(Li) detector aimed to efficiently intercept emitted X-rays. The Si(Li) detector is a reverse-biased Si diode doped with Li to create a wide depletion region. An incoming X-ray generates a photoelectron that eventually dissipates its energy by creating electron-hole pairs. The incident photon energy is linearly proportional to the number of pairs produced or equivalently proportional to the amplitude of the voltage pulse they generate when separated. The pulses are amplified and then sorted according to voltage amplitude by a multichannel analyzer, which also counts and stores the number of pulses within given increments of the voltage (energy) range. The result is the characteristic X-ray spectrum shown for Ti in Fig. 6-15. Si(Li) detectors typically have a resolution of about 150 eV, so overlap of peaks occurs when they are not separated in energy by more than this amount. Overlap sometimes 6.4. Chemical Characterization 283 occurs in multicomponent samples or when neighboring elements in the periodic table are present. Several variants of X-ray spectroscopy are worth mentioning. In X-ray wavelength-dispersive analysis (WDX), where wavelength rather than energy is dispersed, a factor of 20 or so improvement in X-ray linewidth resolution is possible. In this case, emitted X-rays, rather than entering a Si(Li) detector, are diffracted from single crystals with known interplanar spacings. From Bragg's law, each characteristic wavelength reflects constructively at different corresponding angles, which can be measured with very high precision. As the goniometer-detector assembly rotates, the peak is swept through as a function of angle. The electron microprobe (EMP) is an instrument specially designed to perform WDX analysis. This capability is also available on an SEM by attaching a diffractometer to the column. The high spectral resolution of WDX is offset by its relatively slow speed. Characteristic X-rays can also be generated by using photons and energetic particles rather than electrons as the excitation source. For example, conven- tional X-ray tubes, and radioactive sources such as 24'Am (60-keV gamma ray, 26.4-keV X-ray) and '@Cd (22.1-keV Ag-K X-ray) can excite fluorescent X-rays from both thin-film and thick specimens. Unlike electron-beam sources, they have virtually no lateral spatial resolution. 6.4.3.2. Quantification. Quantitative analysis of an element in a multicom- ponent matrix is a complicated matter. The expected X-ray yield, Y,(d), originating from some depth d below the surface depends on a number of factors: Io(d), the intensity of the electron beam at d; C, the atomic concen- tration; u, the ionization cross section; w, , the X-ray yield; p, the X-ray absorption coefficient; and E, Q, and 8, the detector efficiency, solid angle, and angle with respect !a the beam, respectively. Therefore, Y,(d) - Zo(d)Cwxe~~d~cos~ E dQ/h, (6-19) and the total signal detected is the sum contributed by all atomic species present integrated over the depth range. It is sometimes simpler to calibrate the yields against known composition standards. Excellent computer programs, both standardless and employing standards, are available for analysis, and compositions are typically computed to approximately 0.1 at%. 6.4.4. Auger Electron Spectroscopy (AES) 6.4.4.7. Equipment. The typical AES spectrometer, shown schematically in Fig. 6-18, is housed within an ultrahigh vacuum chamber maintained at COMPUTER ANALYZER SYSTEM CONTROL FIRST ANGULAR RESOLVED S'ECOND APERTURE APERTURE APERTURE Figure 6-18. Electronics Industries, Inc.) Schematic of spectrometer with combined AES and XPS capabilities. (Courtesy of Physical 6.4. Chemical Characterization 285 - lo-'' torr. This level of cleanliness is required to prevent surface coverage by contaminants (e.g., C,O) in the system. The electron-gun source aims a finely focused beam of - 2-keV electrons at the specimen surface, where it is scanned over the region of interest. Emitted Auger electrons are then energy- analyzed by a cylindrical (or hemispherical in some systems) analyzer. The latter consists of coaxial metal cylinders (or hemispheres) raised to different potentials. The electron pass energy E is proportional to the voltage on the outer cylinder, and the incremental energy range AE of transmitted electrons determines the resolution (AE/E), which is typically 0.2 to 0.5%. Electrons with higher or lower energies (velocities) than E either hit the outer or inner cylinders, respectively. They do not exit the analyzer and are not counted. By a sweep of the bias potential on the analyzer, the entire electron spectrum is obtained. Complete AES spectrometers are commercially available and cost about a half-million dollars. Auger electrons are but a part of the total electron yield, N( E), intermediate between low-energy secondary and high-energy elastically scattered electrons. They are barely discernible as small bumps above the background signal. Therefore, to accentuate the energy and magni- tude of the Auger peaks, the spectrum is electronically or numerically differen- tiated, and this gives rise to the common AES spectrum, or dN(E)/dE vs. E response, shown in Fig. 6-1% for Ti. The reader should verify that differentia- tion of a Gaussian-like peak yields the wiggly narrow double-peak response. By convention, the Auger line energy is taken at the resulting peak minimum. Two very useful capabilities for thin-film analysis are depth profiling and lateral scanning. The first is accomplished with incorporated ion guns that enable the specimen surface to be continuously sputtered away while Auger electrons are being detected. Multielement composition depth profiles can thus be determined over total film thicknesses of several thousand angstroms by sequentially sampling and analyzing arbitrarily thin layers. Although depth resolution is extremely high, the frequently unknown sputter rates makes precise depth determinations problematical. Through raster or line scanning the electron beam, the AES is converted into an SEM and images of the surface topography are obtained. By modulating the imaging beam with the Auger electron signal, we can achieve lateral composition mapping of the surface distribution of particular elements. Unlike EDX-SEM composition mapping, only the upper few atom layers is probed in this case. 6.4.4.2. Quantification. The determination of the Auger electron yield from which atomic concentrations can be extracted is expressed by a formula similar in form to Eq. 6-19 for the X-ray yield. The use of external standards 286 Characterization of Thin Films is very important in quantifying elemental analysis, particularly because stan- dardless computer programs for AES are rather imprecise when compared with those available for EDX analysis. An approximate formula that has been widely used to determine the atomic concentration of a given species A in a matrix of m elements is (6-20) i= I The quantity I, represents the intensity of the Auger line and is taken as the peak-to-peak span of the spectral line. The relative Auger sensitivity 3, also enters Eq. 6-20. It has values ranging from - 0.02 to 1 and depends on the element in question, the particular transition selected, and the electron-beam voltage. Uncertainties in C values so determined are perhaps a few atomic percent at best. 6.4.5. X-Ray Photoelectron Spectroscopy (XPS) In order to capitalize on the X-ray-induced photoelectron effect, a spectrome- ter like the one used for AES and shown in Fig. 6-18 is employed. The only difference is the excitation source, which is now a beam of either Mg or A1 Ka X-rays. These characteristic X-rays have relatively low energy (e.g., hv,, = 1254 eV and hv,, = 1487 eV) and set an upper bound to the kinetic energy of the detected photoelectrons z- NGaAs UI- 6- 4 I1 Ill1 I Ill1 Ill1 I II 0 3 6 9 12 15 18 21 24 27 30 SPUTTER TIME (MIN) Figure 6-19. AES depth protila ol AI and Ga through GaAs and AI,Ga, ,A\ films Signal for As not shown (Courtc.\y of R Kopf, AT&T Bell Laboratories ) 6.4. Chemical Characterization 287 A portion of the XPS spectrum for Ti is shown in Fig. 6-15d, where 2s, 2p,,, , and 2p,,, peaks are evident. Interestingly, characteristic Auger electron transitions (not shown) frequently appear at precisely the energy locations indicated in Fig. 6-1%. The XPS peak positions, however, are shifted slightly by a few electron volts from those predicted by Eq. 6-18 because of work function differences between the specimen and detector. It is beyond our scope to discuss spectral notation, the chemistry and physics of transitions, and position and width of the lines. What is significant is that linewidths are considerably narrower than those associated with Auger transi- tions. This fact makes it possible to gain useful chemical bonding information that can also be attained with less resolution by AES, but not by the other surface analytical techniques. It is for this reason that XPS is also known as electron spectroscopy for chemical analysis (ESCA). Effects due to chemical bonding originate at the valence electrons and ripple beyond them to alter the energies of the core levels in inverse proportion to their proximity to the nucleus. As a result, energy shifts of a few electron volts occur and are resolvable. For example, in the case of pure Ti, the 2p,,, line has a binding energy of 454 eV. In compounds this electron is more tightly bound to the Ti nucleus; apparently the electron charge clouds of the neighbor- ing atoms “repel” it. In Tic, TiN, and TiO, the same line is located at EB = 455 eV. Similarly, for the compounds TiO, , BaTiO, , PbTiO, , SrTiO, , CaTiO, , and (C,H5),TiC1, the transition occurs between EB = 458 and 459 eV. Clearly the magnitude of the chemical shift alone is not a sufficient condition to establish the nature of the compound. Aside from chemical bonding information, XPS has an important advantage relative to AES. X-rays are less prone to damage surfaces than are electrons. For example, electron beams can reduce hydrocarbon contaminants to carbon, destroying the sought-after evidence. For this reason, XPS tends to be pre- ferred in assessing the cleanliness of semiconductor films during MBE growth. 6.4.6. A Couple of Applications in GaAs Films 6.4.6.7. AES. As an example of AES, consider the depth profiles for Ga and A1 shown in Fig. 6-’,9. The structure represents a single-crystal GaAs substrate onto which a 2000-A thick, compositionally graded film of Al,Ga,-,As was grown by molecular-beam epitaxy methods (Chapter 7). At first, the deposition rate of Al was increased linearly while that of Ga correspondingly decreased until AlAs formed; then the deposition rates were reversed until the GaAs composition was attained after 2000 A. Finally, a 1000-A-cap film of GaAs was deposited resulting in a 2000-i-wide, V-shaped quantum well sandwiched [...]... Structural Aspects of Epitaxial Films 7. 3 Lattice Misfit and Imperfections in Epitaxial Films 7. 4 Epitaxy of Compound Semiconductors 7. 5 Methods for Depositing Epitaxial Semiconductor Films 7. 6 Epitaxial Film Growth and Characterization 7. 2 STRUCTURAL ASPECTS OF EPITAXIAL FILMS 7. 2.1 SingleCrystal Surfaces Prior to consideration of epitaxial films, it is instructive to examine the nature of the topmost surface... with the value obtained from Eq 6-23? Assume e = 170 0 b If the initial order of film stacking were reversed, what would the resulting RBS spectrum look like initially and after annealing? 304 Characterizationof Thin Films c Are the stoichiometries of Au,Al and AuAl, consistent with the value for uAU /aA,? 12 Refer to the RBS spectra of Fig 13-9 - a What is the significance of the yield counts of lo00... Eisen, Thin Solid Films 17, 1, 1963) relates the energy of emergent ions to that of the incident ions The term K , is known as the kinematic factor and can be calculated from Eq 6-21 Once the incident ion, e.g., 4 He+(M, = 4) at E, = 2 MeV, and angular position of the ion detector are selected (e is typically 170 "), K , just depends on the atomic weight of the target atom For example, under the conditions... epitaxy (VPE) of Si on Si (see Chapter 4) The reader may well ask why the underlying Si wafer is not sufficient; why must the single-crystal Si be extended by means of the epi film layer? The reason is that the epilayer is generally freer of defects, purer than the substrate, and can be doped independently of the wafer A dramatic improvement in the yield of early bipolar transistors was the result of incorporating... know about the chemistry of these materials? 10 a Sketch the RBS spectrum for a 900-A-thick Pt film on a Si wafer How does it differ from the spectrum of 900 A of PtSi on Si? In both cases 2.0-MeV 4He+ ions are employed b Sketch the RBS spectrum for the case of a 9 0 0 4 Si film on a thick Pt substrate 11 Consider the RBS spectra of Fig 8-12 a Calculate the value of a /uAl from the initial Au and Al data... analysis Films with rough surfaces yield broadened RBS peaks The maximum film depth that can be probed depends on the ion used, its energy, and the nature of the matrix Typically, 1 pm is an upper limit for 2-MeV 4He+ On the other hand, 3 H + beams of 2 MeV penetrate 5 pm deep in Si O, O - - 6.4 .7. 5 Quantification Despite the limitations noted, RBS enjoys the status of being the preferred method of analysis... the nature of the topmost surface layers of a crystalline solid film The reason the surface will generally have different properties than the interior of the film can be understood by a schematic cross-sectional view as shown in Fig 7- 3 If the surface structure is the predictable extension of the underlying lattice, we have the case shown in Fig 7- 3a The loss of periodicity in one direction will tend... that the unit cell is primitive Similarly, for an overlayer of the same geometry but oriented at 90" with respect to the first case, the notation is P(l x 2) Other examples are shown in Fig 7- 6b, c Note that in Fig 7- 6c the overgrowth layer is rotated with respect to the substrate coordinates and is identified by the letter R Similarly, C is used to denote the centered lattice It is the geometry of the. .. each Si spectrum? b What is the width of the a-Si layer after 15 min at 515 "C? c How does the total number of Au atoms partitioned in a-Si change as a function of annealing time? d From the width and height of spectral features calculate the solubility of Au in a-Si after 85 min 13 The implanted P dopant distribution shown in the SIMS spectrum of Fig 6-26 can be described by the equation 4 C(2)= AR,... (3/4)Ry c h ( Z - l)', where Ry = Rydberg constant (Ry = 1.0 974 c = speed of light h = Planck constant X lo5 cm-') 305 References a Calculate the energy of the K a line for Ti b Make a plot of v vs Z (Moseley diagram) utilizing the data of Fig % 6-16 Calculate the slope of the line c Relative to Ti how are the spectral lines of Fe positioned in the energy-level scheme? REFERENCES l.* J B Bindell, in VLSZ . reference level. They would still have to acquire the work function energy to be totally free of the solid. Some notion of the rough magnitude of the core energy levels can be had from the well-known. 17, 20) 6.4 .7. 1. Physical Principles. This popular thin- film characterization tech- nique relies on the use of very high energy (MeV) beams of low mass ions. These have the property of. G. Amsel, and F. Eisen, Thin Solid Films 17, 1, 1963). relates the energy of emergent ions to that of the incident ions. The term K, is known as the kinematic factor and can