Repetition: Micro Hardness

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Chrystal Baldwin
5 years ago
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1 Repetitio: Micro Hardess Defied by the residual deformatio of a material due to the peetratio of a (ideally) udeformable test body. Test body material: + Diamod Test body geometries: + Vicers: Pyramid with diagoal vs. height :7 + Koop: three sided pyramid + Rocwell: sphere + Wedge Test loads: N

2 Repetitio: Naoideter The Naoideter also allows the determiatio of the elastic (reversible) deformatio (I. e. of the elastic modulus) of the sample. Force Elastic modulus load uload I the case of coatigs care has to be tae that the idetatio depth of the test body is less tha /3 of the film thicess. Oly uder this coditio the ifluece f the substrate ca be eglected. Residual deformatio Peetratio depth

3 Repetitio: No-Destructive Hardess Hertzia Cotact: Poit force actig oto a ideally elastic half-plai: z F w(r)=f(f,g, ν) w(r) correspods to the idetatio depth of the test body. G ad ν result from the elastic costats of the sample: G = c 44 0 w(r) G...Shear modulus ν...poisso ratio r ν= c2 2( c + c ) 44 2

4 Repetitio: Spatial Resolutio By Scaig Force Microscopy the followig mechaical (surface) properties ca be determied spatially resolved o the aometer scale: + Elastic modulus + Hardess + Adhesio stregth This is possible by the so-called force spectroscopy

5 Repetitio: Force Spectroscopy Repated recordig of force/distace curves durig a AFM-sca with electroic aalysis: Force-distace curve: Polymer chais: Topography free catilever oscillatio Adhesio Stiffess

6 Repetitio: Stresses Kids of stress: σ = σ + σ + σ MECH T I Mechaical Stress: σ MECH Ca be triggered by clampig the substrate ad subsequet relaxatio Thermal stress: σ = E ( α α )(T T ) Triggered by differet coefficiets T S S U B M of thermal expasio (CTE) of E S... Elastic modulus coatig substrate ad coatig α S... CTE, coatig α U... CTE. substrate T B... Coatig temperature T M... Temperature of stress measuremet

7 Repetitio: Stress Measuremet Curved Substrate: Tesile stress Compressive Stress Total stress σ of a thi film: σ = Esd 6( ν 2 s s )d F R s R s2 a) Substrate b) Coatig c) Referece plate E S... Elastic Modulus substrate ν S... Poisso Ratio substrate d S... Substrate thicess d F... Film thicess R S, R S2... Radius of curvature before/after coatig, respectively

8 Electroic Properties The properties of the electroic system of a material ifluece: + Coductivity + Optical properties + Magetic properties + Adsorptio ad adhesio For thi films these properties are also modified by the high surface to volume ratio.

9 Bod Types I The electroic system of a material is a direct cosequece of the fudametal chemical bod types: Attetio: 00J meas: 00J/Mol ev!

10 Bod Types II Covalet bod: Trasitio ioic covalet:

11 Bod Types III Relevat for solids: + Ioic (heteropolar) bod + Covalet bod + Metallic bod Ioic: electros strogly localized Metallic: electros delocalized Bods withi solids are strogly characterized by the multi-particle characteristics of codesed matter!

12 Metals Trasitio sigle particle multi-particle system: Sigle atom Multi-particle system Solid

13 Semicoductor Semicoductors represet a trasitioal state betwee covalet ad metallic solids. They ca be described by the bad model. Isulator Semicoductor Coductor coductio bad coductio bad coductio bad valece bad valece bad valece bad

14 Thi Films ad Electroic Compoets Thi film techology allows the realizatio of the followig electroic compoets + Itercoect + Thi film resistor + Codeser Metal Isulator Semicoductor, dopig A Semicoductor, dopig B + Diode + Trasistor + MOSFETS

15 Coductivity of Metals Macroscopic descriptio: Ohm s law I = U R l = Curret U = Voltage R = Resistivity Microscopic descriptio : Drude law r j = e τ 2m e r E 2 r = σ E j = Curret desity E = E-field σ = Coductvity = Number of charges e = Elemetary charge m e = Electro mass τ = Average collisio time

16 Theory of Coductivity Drude-Theory: r j = e τ 2m e r E 2 r = σ E j = Curret desity E = E-field σ = Coductvity = Number of charges e = Elemetary charge m e = Electro mass τ = Average collisio time The cetral poit of the Drude-Theory is the Average collisio time τ

17 The Average Collisio Time The average collisio time τ ca be calculated by "Matthiess's rule": τ = τ G + τ K + τ V +... τ G = Collisio with lattice atoms τ K = Collisio with grai boudaries τ G = Collisio with impurities The magitude of coductivity is defied by the id ad umber of defects at which electros ca be scattered. Also iterfaces of each id ca be cosidered as defects. This promptly leads to a depedece of the coductivity o film thicess!

18 Coductivity of Thi Films Bul: Film: E V K G τ + τ + τ = τ I V K G τ + τ + τ + τ = τ E z x D 0 The iterfaces at z=0 ad z=d are additioal ceters of electro scatterig!

19 Coductivity Approximatios,0 0,8 σ 3 = σ 0 8 σ/σ 0 0,6 0,4 λ0 00Å= τv f Electro desity [Å -3 ] λ 0 = 0 40 m at RT 0,2 σ = σ 0 34 l 0,0 E-4 E-3 0,0 0, 0 = D/λ 0,

20 Real Thi Film Systems Ideal: Real: Film Substrate d d Experimet: σ << σ e A B σ = σ(e) σ = σ(r,d) dis σ ot / T r Reaso: D Discotiuity Thermioic emissio Field emissio Tuel effect

21 Coductivity ad Film Thicess - Real,0 0,8 σ/σ 0 0,6 0,4 separated islads Percolatio threshold 0,2 Ideal curve 0,0 E-4 E-3 0,0 0, 0 = D/λ 0,

22 Applicatio: Thi Film Resistors Iterval of resistivity: 00 Ω 00 MΩ Covered by: + Film thicess variatio + Choice of material Prerequisites: + Low temperature coefficiet + Low cost

23 Temperature Coefficiets Cermets

24 Optical Properties Fudametals: The optical properties of materials result from the reactio of the electroic system to the presece of alteratig electromagetic fields. Static: Dyamic: r j r = σ E Geeral: & u r 2r + Γu&r + ω u = 0 Q m r r E(u, t) Perpedicular plae wave, z=0: 2 e && x + Γx& + ω0x = E0 exp(iωt) m

25 Optics Frequecy Idepedet Refractio For optics the followig coservatio law is valid: T + R + A + S = T Trasmissio R Reflectio A Absorptio S Scatterig For geometric optics the refractio idex ca be cosidered as frequecy idepedet.

26 Optics Iterfaces Reflectio: α = α α β α' 2 Refractio: si si α β = 2 Wavelegth: λ i = λ Va i

27 Fresel's Equatios Most geeral descriptio of the passage of a light ray (plae electromagetic wave) through a iterface Reflectio: r p = cos ϕ cos ϕ + cos ϕ cos ϕ Normal Light ray r = cosϕ cosϕ + cosϕ cosϕ Plae ormal/ray Normal compoet, Parallel compoet p, Trasmissio: t p = 2 cosϕ cosϕ + cosϕ Iterface t = 2 cos ϕ cos ϕ + cos ϕ 2

28 Fresel's Equatios: Simplificatio 2 Media, idices of refractio, 2, perpedicular impigemet, i. e.: ϕ = ϕ 2 = 0 Reflectio: 2 2 p r r + = = Trasmissio: 2 p 2 t t + = =

29 Ideal ud Real Thi Film System o absorptio, ifiite thicess absorptio, fiite thicess, reflexio at lower iterface Trasmitted itesity [%] d=00 m = =.25 = ,4 0,5 0,6 0,7 0,8 Wavelegth [µm]

30 Sigle Coatig - Geeral Reflectio/Wavelegth Reflectio/Thicess

31 Multi Coatig - Reflectio Suppressio Sigle coatigs do ot allow for reflectio suppressio i a broad rage of wavelegths. Applicatio of systems cosistig of multiple coatigs With multiple coatig systems it is possible to geerate reflectio suppressig coatigs i a wide spectral rage o substrates with low idices of refractio (,5-,7).

32 Multiple Coatigs - Example a) λ/4 - λ/2-3λ/4 b) λ/4 - λ/2 - λ/4 0 = =.38 2 = 2. 3 =.7 4 =.52

33 Reflectio Ehacemet: Metal Films

34 Reflectio Ehacemet: Dielectric Mirror I System cosistig of λ/4-coatigs with alteratig idices of refractio: t 2 t t 0 < 2 2 > 3 2 3

35 Reflectio Ehacemet: Dielectric Mirror II A dielectric mirror cosists of a multilayer made from λ/4-coatigs with alteratig high (H) ad low (L) idices of refractio.

36 Filters ad Optical Elemets With the thi film systems discussed so far it is possible to maufacture filter systems with almost arbitrary properties. The basic elemets are: + Reflectio suppressig coatigs + Iterferece coatigs + Metal mirrors + Dielectric mirrors + Naocluster (color ceters ad pigmets) These elemets allow the realizatio of may optical systems.

37 Characterizatio of Optical Coatigs I geeral, reflectio ad trasmissio of thi optical coatigs ad scatterig of electromagetic radiatio at surfaces allow to evaluate the refractive idex, coatig thicess ud roughess of a give optical system. These quatities ca be determied odestructively ad i situ, which allows for the reproducable maufacturig of high quality optical coatigs.

38 Mechaic/Abrasive Characterizatio + Alteratig humidity: 2 hours at 40 C, 00% humidity, the 2 hours coolig equals oe cycle. The umber of cycles is varied. + Spray test: sprayig of a aqueous solutio of 5% NaCl at 50 C. + Sad abrasio: 3g sad of graular class 0,4 to 0,8mm impige o the sample from 650mm heigth through a pipe. The sample is mouted o a turtable with a icliatio of Cooig i salt water ad deioized water: the sample remais 5 to 60 mi i the salt solutio.

Repetition: Refractive Index

$Repetition: Refractive Index$ Repetitio: Refractive Idex (ω) κ(ω) 1 0 ω 0 ω 0 The real part of the refractive idex correspods to refractive idex, as it appears i Sellius law of refractio. The imagiary part correspods to the absorptio