Crystals. Fig From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap ( McGraw-Hill, 2005)

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1 Crystls Mterils will often orgnize themselves by minimizing energy to hve long rnge order. This order results in periodicity tht determines mny properties of the mteril. We represent this periodicity by 3D/2D lttice, which contins repeted unit cell Lttice my or my not be rectngulr A bsis is the geometric specifiction of the lttice. Fig 1.31

2 F C C U n it C e ll ( ) 2R (b ) (c ) () The crystl structure of copper is Fce Centered Cubic (FCC). The toms re positioned t well defined sites rrnged periodiclly nd there is long rnge order in the crystl. (b) An FCC unit cell with closed pcked spheres. (c) Reduced sphere representtion of the FCC unit cell. Exmples: Ag, Al, Au, C, Cu, γ-fe (>912 C), Ni, Pd, Pt, Rh Fig 1.31

3 Crystl Pckings Mny different rrngements re found s determined by the tomic structure. (The number of vlnce electrons). Some re: Fce centered cubic (FCC): Metls (dense) Hexgonl close-pcked (HCP): Metls (dense) Body centered cubic (BCC): Metls (dense) Dimond cubic: Covlent Bonds (Si, Ge) Zinc-blend: Covlent/Ionic Bonds (GAs) Others tht re quite complicted Fig 1.31

4 b Exmples: Alkli metls (Li, N, K, Rb), Cr, Mo, W, Mn, α-fe (< 912 C), β-ti (> 882 C). Body centered cubic (BCC) crystl structure. () A BCC unit cell with closely pcked hrd spheres representing the Fe toms. (b) A reduced-sphere unit cell. Fig 1.32

5 L y e r B L y e r A L y e r B L y e r A L y e r A L y e r A ( ) ( b ) c ( c ) ( d ) Exmples: Be, Mg, α-ti ( < 882 C ), Cr, Co, Zn, Zr, Cd Fig 1.33 The Hexgonl Close Pcked (HCP) Crystl Structure. () The Hexgonl Close Pcked (HCP) Structure. A collection of mny Zn toms. Color difference distinguishes lyers (stcks). (b) The stcking sequence of closely pcked lyers is ABAB (c) A unit cell with reduced spheres (d) The smllest unit cell with reduced spheres.

6 C The α dimond unit cell is cubic. The cell hs eight toms. Grey Sn (α-sn) nd the elementl semiconductors Ge nd Si hve this crystl structure. Fig 1.34

7 S Z n The Zinc blende (ZnS) cubic crystl structure. Mny importnt compound crystls hve the zinc blende structure. Exmples: AlAs, GAs, GP, GSb, InAs, InP, InSb, ZnS, ZnTe. Fig 1.35

8 N + C l A possible reduced sphere unit cell for the NCl (rock slt) crystl. An lterntive unit cell my hve N+ nd Cl interchnged. Exmples: AgCl, CO, CsF, LiF, LiCl, NF, NCl, KF, KCl, MgO Fig 1.37

9 Crystl Properties The crystl structure of mteril determines mny fetures. Surfce fetures (fceting of multi-crystlline films) Surfce energies Trnsport properties (electrons, het, tomic diffusion) Anisotropic mteril properties (conduction, strength, diffusion) The crystl structure cn be experimentlly determined using electron bem diffrction. Often del with plnes with in the crystl. For exmple the mteril my be strong in the plne of mximum density, or electron conduction my be poor perpendiculr to specific plne in the crystl. Geometry is n issue!

10 Left: A polycrystlline dimond film on the (100) surfce of single crystl silicon wfer. The film thickness is 6 microns nd the SEM mgnifiction is Right: A 6-micron-thick CVD dimond film grown on single crystl silicon wfer. SEM mgnifiction is 8000.

12 z c U n i t C e l l G e o m e t r y z U n i t c e l l c β O γ b α x () A prllelepiped is chosen to describe geometry of unit cell. We line the x, y nd z xes with the edges of the prllelepiped tking lower-left rer corner s the origin [ ] b y x c [ ] x o z o P [ ] b (b) Identifiction of direction in crystl y o y [ ] [ ] y y [ ] [ ] [ ] [ ] [ ] [ ] x [ ] (c) Directions in cubic crystl system [ ] [ ] [ ] [ ] F m i l y o f < > d i r e c t i o n s Fig 1.40

13 z i n t e r c e p t t b M i l l e r I n d i c e s ( h k ) : x i n t e r c e p t t / 2 z c ( ) y x U n i t c e l l y i n t e r c e p t t b ( ) I d e n t i f i c t i o n o f p l n e i n c r y s t l z ( ) ( ) z ( ) ( ) ( ) x y x ( ) ( ) y ( ) z z ( ) ( ) ( ) y y x y x ( b ) V r i o u s p l n e s i n t h e c u b i c l t t i c e z Lbelling of crystl plnes nd typicl exmples in the cubic lttice Fig 1.41

14 z F C C U n i t c e l l ( ) 2 y = Ð z = O 1 / 2 y A = 2 A = 2 2 x ( ) ( ) p l n e ( b ) ( ) p l n e ( c ) ( ) p l n e The (012) plne nd plnr concentrtions in n FCC crystl. Fig 1.42

15 Crystlline phses Mterils some times chnge their crystl structure s the temperture is chnged. They hve different phses! If the mteril is llowed to nnel (minimize energy over time) the stble phse will become dominnt. Known s poly-morphism or llotropy. Exmple is solid crbon. Low temperture form is grphite High temperture/pressure form is dimond Weird form is buckminsterfullerine If we form dimond nd then cool the dimond phse is frozen in. Over time ( gret del) the dimond will nnel bck to grphite (lower energy t room temperture). Fig 1.42

16 Fig 1.43

18 Crystl Defects No crystl is perfect. The formtion my freeze in defects, temperture will disturb the crystl, unwnted toms mybe present, etc. These defects re very importnt in determining mteril properties. Mny types: Point defects: missing toms, misplced toms, dded toms, impurities Line defects: missing lines of toms, screwed up lines of toms, Plne defects: grin boundries, surfces Over time these defects will nnel out (temperture * time = rte) s the perfect crystl is lowest energy. But t room temperture long time! Fig 1.43

19 () Perfect crystl without vcncies (b) An energetic tom t the surfce breks bonds nd jumps on to new djoining position on the surfce. This leves behind vcncy. (c) An tom in the bulk diffuses to fill the vcncy thereby displcing the vcncy towrds the bulk. (d) Atomic diffusions cuse the vcncy to diffuse into the bulk. Genertion of vcncy by the diffusion of n tom to the surfce nd the subsequent diffusion of the vcncy into the bulk. Fig 1.44

20 () A vcncy in the crystl. (b) A substitutionl impurity in the crystl. The impurity tom is lrger thn the host tom. (c) A substitutionl impurity in the crystl. The impurity tom is smller thn the host tom. (d) An interstitil impurity in the crystl. It occupies n empty spce between host toms. Point defects in the crystl structure. The regions round the point defect become distorted; the lttice becomes strined. Fig 1.45

21 S c h o t t k y d e f e c t F r e n k e l d e f e c t ( ) S c h o t t k y n d F r e n k e l d e f e c t s i n n i o n i c c r y s t l. S u b s t i t u t i o n l i m p u r i t y. D o u b l y c h r g e d ( b ) T w o p o s s i b l e i m p e r f e c t i o n s c u s e d b y i o n i z e d s u b s t i t u t i o n l i m p u r i t y t o m s i n n i o n i c c r y s t l. Point defects in ionic crystls Fig 1.46

22 Equilibrium Concentrtion of Vcncies n = N exp E v v kt n v = vcncy concentrtion N = number of toms per unit volume E v = vcncy formtion energy k = Boltzmnn constnt T = temperture (K)

23 E d g e d is lo c tio n lin e ( ) D is lo c tio n is lin e d e f e c t. T h e d is lo c tio n s h o w n r u n s in to th e p p e r. C o m p re s s io n T e n s io n ( b ) A r o u n d th e d is lo c tio n th e r e is s tr in fie ld s th e to m ic b o n d s h v e b e e n c o m p r e s s e d b o v e n d s tr e tc h e d b e lo w th e is lo c tio n lin e Disloction in crystl is line defect which is ccompnied by lttice distortion nd hence lttice strin round it. Fig 1.47

24 A C D D i s l o c t i o n l i n e ( ) A s c r e w d i s l o c t i o n i n c r y s t l. D i s l o c t i o n l i n e A B A t o m s i n t h e l o w e r p o r t i o n. A t o m s i n t h e u p p e r p o r t i o n. D ( b ) T h e s c r e w d i s l o c t i o n i n ( ) s v i e w e d f r o m b o v e. C A screw disloction involves shering one portion of perfect crystl with respect to nother portion on one side of line (AB). Fig 1.48

25 D i s l o c t i o n l i n e A mixed disloction. Fig 1.49

26 Effects of defects Defects cuse mny phenomen's Surfce structure Growth of crystl t surfces is dominted by: Nucletion nd subsequent growth t steps, holes nd edges Grin boundries re very messy, llowing diffusion, movement nd nneling (grin growth driven by surfce energy) Surfces hve dngling bonds (function of surfce curvture), bsorbed toms. Chemi-bsorbed (fixed by strong bond). Physi-bsorbed (mobile due to wek vn der Wlls forces. Non stoichiometric solids hve extr toms usully interstitilly. Fig 1.49

29 N e w m o l e c u l e Screw disloction ids crystl growth becuse the newly rriving tom cn ttch to two or three toms insted of one tom nd thereby form more bonds. Fig 1.50

30 E d g e S t e p A t o m o n s u r f c e H o l e C r e v i c e C o r n e r S c r e w d i s l o c t i o n Typiclly crystl surfce hs mny types of imperfections such s steps, ledges, kinks, crevices, holes nd disloctions. Fig 1.54

31 N u c l e i C r y s t l l i t e L iq u i d ( ) (b ) G r i n G r i n b o u n d r y ( c ) Solidifiction of polycrystlline solid from the melt. () Nucletion. (b) Growth. (c) The solidified polycrystlline solid. For simplicity, cubes represent toms. Fig 1.51

32 F o r e i g n i m p u r i t y S e l f - i n t e r s t i t i l t y p e V o i d, v c n c y t o m S t r i n e d b o n d G r i n b o u n d r y B r o k e n b o n d ( d n g l i n g b o n d ) The grin boundries hve broken bonds, voids, vcncies, strined bonds nd "interstitil" type toms. The structure of the grin boundry is disordered nd the toms in the grin boundries hve higher energies thn those within the grins. Fig 1.52

33 H D n g lin g b o n d R e c o n s tru c te d A b so rb ed su rf c e O xygen H 2 O H 2 O S u rf c e S u rf c e to m s B u lk c ry s t l At the surfce of hypotheticl two dimensionl crystl, the toms cnnot fulfill their bonding requirements nd therefore hve broken, or dngling, bonds. Some of the surfce toms bond with ech other; the surfce becomes reconstructed. The surfce cn hve physisorbed nd chemisorbed toms. Fig 1.53

34 ( ) S t o i c h i o m e t r i c Z n O c r y s t l w i t h e q u l n u m b e r o f n i o n s n d c t i o n s n d n o f r e e e l e c t r o n s. O 2 Z n 2 + " F r e e " ( o r m o b i l e ) e l e c t r o n w i t h i n t h e c r y s t l. ( b ) N o n - S t o i c h i o m e t r i c Z n O c r y s t l w i t h e x c e s s Z n i n i n t e r s t i t i l s i t e s s Z n 2 + c t i o n s. Stoichiometry nd nonstoichiometry nd the resulting defect structure. Fig 1.55

35 Phses of mterils As remrked mterils cn hve more then one phse. At different temperture it will be liquid or solid. For exmple ice nd wter. Mterils cn lso be in non-equilibrium phse. This is phse tht is not stble but is qusi-stble. An exmple of this is morphous or glss films. These films do not exhibit long rnge order but do posses crystl like structure on short scle lengths. Usully, formed by quickly quenching or freezing liquid to solid. Cn be done with Si to form Si-. Not usully good electronic mteril, lots of dngling bonds, defects, etc. However, we cn pssivte the Si- with Hydrogen to form Si-:H which is better if not perfect mteril for electronics. Good for lrge substrtes.

36 S i l i c o n ( o r A r s e n i c ) t o m O x y g e n ( o r S e l e n i u m ) t o m ( ) A c r y s t l l i n e s o l i d r e m i n i s c e n t t o c r y s t l l i n e S i O 2. ( D e n s i t y = 2. 6 g c m - 3 ) ( b ) A n m o r p h o u s s o l i d r e m i n i s c e n t t o v i t r e o u s s i l i c ( S i O 2 ) c o o l e d f r o m t h e m e l t ( D e n s i t y = 2. 2 g c m - 3 ) Crystlline nd morphous structures illustrted schemticlly in two dimensions. Fig 1.57

37 Dngling bond ( ) T w o d i m e n s i o n l s c h e m t i c r e p r e s e n t t i o n o f s i l i c o n c r y s t l ( b ) T w o d i m e n s i o n l s c h e m t i c r e p r e s e n t t i o n o f t h e s t r u c t u r e o f m o r p h o u s s i l i c o n. T h e s t r u c t u r e h s v o i d s n d d n g l i n g b o n d s n d t h e r e i s n o l o n g r n g e o r d e r. H H H H H ( c ) T w o d i m e n s i o n l s c h e m t i c r e p r e s e n t t i o n o f t h e s t r u c t u r e o f h y d r o g e n t e d m o r p h o u s s i l i c o n. T h e n u m b e r o f h y d r o g e n t o m s s h o w n i s e x g g e r t e d. H Silicon cn be grown s semiconductor crystl or s n morphous semiconductor film. Ech line represents n electron in bond. A full covlent bond hs two lines nd broken bond hs one line. Fig 1.59

39 Solid phses A phse of mteril is when the mteril is uniform in structure nd composition. If mteril is n lloy or mix then for phse to form they must mix. Like wter nd lcohol, not wter nd oil. Solid lloys do form, but the type of phse present is strongly dependent on the stoichiometry. The liquid/solid trnsition will differ, the structure my chnge nd more then one phse my be present. Use phse digrm to disply effects. Processing is importnt: s you cn freeze in phse which is out of equilibrium.

40 ( ) D i s o r d e r e d S u b s t i t u t i o n l S o l i d S o l u t i o n. E x m p l e : C u - N i l l o y s ( { } p l n e s ) ( b ) O r d e r e d S u b s t i t u t i o n l S o l i d S o l u t i o n. E x m p l e : C u - Z n l l o y o f c o m p o s i t i o n 5 0 % C u % Z n. ( { } p l n e s ). ( c ) I n t e r s t i t i l S o l i d S o l u t i o n. E x m p l e : S m l l n u m b e r o f C t o m s i n F C C F e ( u s t e n i t e ). ( { } p l n e s ) Solid solutions cn be disordered substitutionl, ordered substitutionl nd interstitil substitutionl. There is only one phse within the lloy which hs the sme composition, structure nd properties everywhere. Fig 1.62

41 P u r e C u 8 0 % C u % N i L i q u i d L i q u i d S o l i d F o r m t i o n o f f i r s t s o l i d L C C L 0 S C S 2 0 H e t e r o g e n e o u s m i x t u r e o f l i q u i d n d s o l i d S o l i d C r y s t l g r i n s T i m e () Solidifiction of n isomorphous lloy such s Cu-Ni. Typicl cooling curves. Fig 1.63

42 Cooling of 80%Cu-20%Ni lloy from the melt to the solid stte. Fig 1.64

43 The lloy with the eutectic composition cools like pure element exhibiting single solidifiction temperture t 183 C. The solid hs the specil eutectic structure. The lloy with the composition 60%Pb-40%Sn when solidified is mixture of primry nd eutectic solid. Fig 1.70

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