Average Matrix Relative Sensitivity Factors (AMRSFs) for Auger Electron Spectroscopy (AES)

Transcription

1 erage Matrx Relatve Senstvty Factors (AMRSFs) for Auger Electron Spectroscopy (AES) These tables and plots contan AMRSFs for AES calculated for the total peak area for the K, L, M and N shells for both 5 kev and 10 kev electron beam energes at 30º ncdence angle. The background to, and use of, AMRSFs, I, s dscussed by Seah and Glmore [1] and also n ISO [2]. For homogeneous solds, the atomc fracton of element A, XA, s gven by X A I Am / I A I m / I where the I m are the measured peak area ntenstes for the element n the sample m. (1) These AMRSFs are based on theory and are thus for use wth spectrometers for whch the ntensty/energy response functon s calbrated [3] or otherwse known [4]. They are unlkely to be as accurate, for quantfcaton, as properly determned expermental senstvty factors, measured on the nstrument wth the correct settngs for whch they are ntended to be used [2]. It should be noted that these AMRSFs are thought to be vald for all systems, rrespectve of the chemcal state, but are only vald for a correct measure of the peak areas. The most correct general background to remove for homogeneous solds s Tougaard's background [5]. It s very common n XPS to use Shrley's background [6] but ths does not gve ntenstes that ether agree wth Tougaard's background or wth the theory for XPS ntenstes [7] These AMRSFs are not for use wth Shrley's background. It s also very common to dfferentate spectra but then the relatve senstvty factors become dependent on the analyser resoluton, the dfferentatng functon and the chemcal state of the elements concerned [8]. The calculatons of the AMRSFs use the procedure of Seah and Glmore[1] n whch the AMRSFs, for the core level X n the element A, are gven by: I AX γ AX sec α N Q λ ( EAX ) nax σ A ( Eo ) [1 + r ( EAX, Eo, α) ] X (2) where γ AX s the probablty that the onsed core level X n element A s flled wth the ejecton of an Auger electron, α s the angle of ncdence of the electron beam from the surface normal, N s the atomc densty of the average matrx, Q s a term allowng for the reducton n overall escape probablty of electrons from the average sold arsng from elastc scatterng, λ (E AX ) s the nelastc mean free path (IMFP) for the Auger electrons wth average energy E AX n the average matrx, σ AX (E o ) s Casnat, Tatar and Barald's onsaton cross secton for the core level X n the element A for electrons of energy E o, n AX s the populaton of the level X, and r E, E, ) s the addtonal onsaton of the core level ( AX o α X arsng from backscattered energetc electrons. In ths work, the parameter γ AX allows for the competng process of X-ray emsson where Page 1 of 13 pages Crown copyrght 2006 Page 1 of 9 Verson AESAMRSFsweb.doc 1 (29/9/06)

2 1 - Z (3) 4 Z + Z o γ AX 4 4 and Z o 32.4 for X K, 89.4 for X L, for X M and 300 for X N [9]. The angle α s 30º. In reference [10], and [11] N atoms m 3 (4) Q (1 ω) (5) (1 ω) and where, for the average matrx, ω 0.3 (6) Thus, Q (7) The nelastc mean free path, λ (E AX ), s taken from the TPP-2M formula [12] λ A E ( E) 2 2 E [ β ln( γe) ( C / E) + ( D / E )] p (8) where ( ρ N / A) 0.5 E 28.8 n ev (9) p v β ( E E ) ρ 0.1 p + g (10) γ ρ (11) C W D W (12) (13) W ρ N / A (14) In these equatons, ρ s the densty (n g cm -3 ), N v s the number of valence electrons per atom and A s the atomc weght. For metals, the value of E g, the band gap, s zero. v Page 2 of 13 pages Crown copyrght 2006 Page 2 of 9 Verson AESAMRSFsweb.doc 1 (29/9/06)

3 The average IMFP functon s not determned by averagng the TPP-2M parameters but by evaluatng λ (E), averagng these and fttng ths average wth Equatons (8) to (14) to gve the parameters to generate λ (E). Thus [1], ( ) N v λ (15) ρ -3 ( ) g cm λ (16) A( λ ) (17) E p ev (18) ( ) β λ (19) γ (20) C (21) D (22) W (23) The sum over the core level onsaton cross sectons s made wth Casnat, Tatar and Barald's formula [13], whch have been found to be n good agreement wth measurements, and the backscatterng wth Shmzu's ftted relaton at 30º. For the use of backscatterng n Shmzu s equatons [1]: Z(r ) (24) The calculated results are gven n Tables I and II for 5 kev and 10 kev electron beams, respectvely, as shown n Fgure 1(a) and (b). Tables III and IV show the AMRSFs ratoed to Ag as unty. For work at 0º and 45º, the backscatterng term and secα need changng. For Tables III and IV the backscatterng changes the AMRSFs. Wthn the approxmatons dscussed above, the rato of the backscatterng term [1 + r ( EAX, Eo, α) ] for 0º and 45º to that at 30º for 5 kev and 10 kev electron beams s shown n Fg 2. The effect s smple to ncorporate but s small and n many crcumstances may be gnored. Page 3 of 13 pages Crown copyrght 2006 Page 3 of 9 Verson AESAMRSFsweb.doc 1 (29/9/06)

4 0.01 K L M N AMRSF (a) 5000 ev Z 0.01 K L M N AMRSF Z (b) 1000 ev Fgure 1 - The AMRSFs for K, L, M and N shell peaks areas n sr -1 unts for 5 kev and 10 kev beams ncdent at 30º. Page 4 of 13 pages Crown copyrght 2006 Page 4 of 9 Verson AESAMRSFsweb.doc 1 (29/9/06)

5 1.04 Backscatterng rato , 5keV 45, 5keV 0, 10keV 45, 10keV Mean core level bndng energy, ev Fgure 2 Rato of the term [1 + r ( EAX, Eo, α) ] for 0º and for 45º to that at 30º to scale the AMRSFs for work at 0º and 45º. [1] M P Seah and I S Glmore, Surface and Interface Analyss (1998). [2] ISO 18118: Surface chemcal analyss - Auger electron spectroscopy and X-ray photoelectron spectroscopy - Gude to the use of expermentally determned relatve senstvty factors for the quanttatve analyss of homogeneous materals, ISO, Geneva (see also S Tanuma, Surface and Interface Analyss (2006)). [3] [4] M P Seah, J. Electron Spectrosc (1995). [5] S Tougaard, Surface and Interface Analyss 11, 453 (1988). [6] D A Shrley, Phys. Rev. B 5, 4709 (1972). [7] M P Seah and I S Glmore, Phys. Rev. B (2006). [8] M P Seah, I S Glmore, H E Bshop and G Lorang, Surface and Interface Analyss (1998). [9] M P Seah and I S Glmore, J. Vacuum Sc. Technolog. A (1996). [10] M P Seah, I S Glmore and S J Spencer, J. Electron Spectrosc (2001). [11] M P Seah and I S Glmore, Surface and Interface Analyss (2001). [12] S Tanuma, C J Powell and D R Penn, Surface and Interface Analyss (1994). [13] M P Seah and I S Glmore, Surface and Interface Analyss (1998). Page 5 of 13 pages Crown copyrght 2006 Page 5 of 9 Verson AESAMRSFsweb.doc 1 (29/9/06)

6 Table I Calculated AMRSFs for 5 kev electron beam Level K L M N Level K L M N Z 1 Z Crown copyrght 2006 Page 6 of 9 Verson 1 (29/9/06)

7 Table II Calculated AMRSFs for 10 kev electron beam Level K L M N Level K L M N Z 1 Z Crown copyrght 2006 Page 7 of 9 Verson 1 (29/9/06)

8 Table III Calculated AMRSFs ratoed to Ag as unty for 5 kev electron beam Level K L M N Level K L M N Z 1 Z Crown copyrght 2006 Page 8 of 9 Verson 1 (29/9/06)

9 Table IV Calculated AMRSFs ratoed to Ag as unty for 10 kev electron beam Level K L M N Level K L M N Z 1 Z Crown copyrght 2006 Page 9 of 9 Verson 1 (29/9/06)