Semiconductors materials

Transcription

1 Semicoductos mteils Elemetl: Goup IV, Si, Ge Biy compouds: III-V (GAs,GSb, ISb, IP,...) IV-VI (PbS, PbSe, PbTe,...) II-VI (CdSe, CdTe,...) Tey d Qutey compouds: G x Al -x As, G x Al -x As y P -y III IV V VI II

2 Cystl Lttices Cystl Lttices Solids: Amophous Cystllie: ios e ged i peiodic y o micoscopic scle. Bvis lttices cosist of ll lttice poits geeted by: D exmple ot i the sme ple e D vectos (pimitive),, e positive o egtive iteges,, R Q P

3 Exmples D: Simple Cubic The most fmili of D Bvis lttice is the simple cubic. It c be sped by thee mutully pepedicul pimitive vectos of equl legth. SC

4 Exmples i D: BCC Body Ceteed Cubic Lttices (BCC) e fomed by ddig to simple cubic lttice (A) dditiol poit t the cete of ech cube (B). Poits A d B e equivlet: both c be tke fom the oigi of the simple cubic lttice.

5 Exmples Exmples i D: BCC i D: BCC If the oigil simple cubic lttice is geeted by pimitive vectos x,y,z ( is clled lttice pmete) set of pimitive vectos fo BCC could be A moe symmetic set is ˆ) ˆ ( ˆ ˆ ˆ z y x y x ˆ) ˆ ( ˆ ˆ) ˆ ( ˆ ˆ) ˆ ˆ ( z y x y x z x z y

6 Exmples i D: FCC A simple cubic lttice with poit i the cete of ech sque fce. All poits e equivlet d c be tke s the oigi of the simple cubic lttice. A symmetic set of pimitive vectos fo FCC lttice is: Fig. 4.9 ( yˆ ( zˆ ( xˆ zˆ) xˆ) yˆ)

7 Pimitive cell Pimitive Cell: volume which, whe tslted, fills exctly the spce (o ovelps, o voids) cotiig oe lttice poit. Not uique! Fig. 4.0 Sevel possible choices of pimitive cell fo D Bvis lttice

8 Uit Cell The uit cell (o pimitive uit cell) is covetiol cell which cotis moe the oe poit i the Bvis lttice. Fig. 4. e 4. Pimitive (pllelogm) d covetiol uit (lge cube) cell fo FCC Bvis lttice. Pimitive d covetiol uit cell fo BCC Bvis lttice. The covetiol uit cell is geelly chose to be bigge th the pimitive cell.

9 Wige-Seitz Cell The most commo choice fo pimitive cell is the Wige-Seitz cell. The Wige- Seitz cell bout lttice poit is the egio of spce tht is close to tht poit th to y othe lttice. It is obtied by bisectig with ple ech lie coectig poit with its eighbos d tkig the smllest polyhedo cotiig the poit. Fig. 4.5 e 4.6 BCC: tucted octhedo FCC: hombic dodechedo

10 Cystl Stuctue Ech lttice poit my cosists of sigle tom (mootomic lttice) o set of toms (lttice with bsis). Also mootomic o-pimitive Bvis lttices e ofte descibed s lttice with bsis (to emphsize give symmety): BCC: simple cubic (0,0,0); /(,,) FCC: simple cubic (0,0,0); /(0,,); /(,,0); /(,0,)

11 Cystllie Stuctue of Semicoductos Dimod Cystl Stuctue Fo the most usul semicoductos the cell cosists of two toms, oe t the positio (0,0,0) d the othe_(,,). The pimitive cell cotis bsis of two toms. Two FCC compeettig lttices Elemets C,57 Å Si 5,4 Å Ge 5,66 Å Fig.. luth I III-V d II-VI the two toms e diffeet species: Zicblede Cystl Stuctue GAs 5.65 Å ZSe Å

12 Molecul Cystls Metl-fee phthlocyie (left) d diethyl hydzoe (ight)

13 Recipocl Recipocl Lttice Lttice The ecipocl lttice is defied by ll poits geeted by the pimitive vectos b, b, b such tht Thee of such vectos e ( ) Recipocl Lttice Diect Lttice This popeties is usully tke s defiig ecipocl lttice poits (G). j i j i b, πδ ( ) V ) ( ) ( ) ( V b V b V b π π π ) ( R G iteges,, with iteges,, with R ig e h h h R h h h b h b h h b G π

14 Recipocl lttice vectos e ig( R) e ig >The G epeset ll wve vectos tht yield ple wves with the peiodicity of the el spce lttice. the ecipocl lttice of ecipocl lttice is the diect lttice. Diect d ecipocl lttices give complete, ltetive d equivlet geometicl desciptio of the cystllie solid, eithe i el o Fouie spce.

15 Exmples Relevt exmples Diect lttice: SC (with cubic pimitive cell of side ); Recipocl lttice: SC (with cubic pimitive cell of side π/). Diect lttice: FCC (covetiol cubic cell ); Recipocl lttice: BCC (covetiol cubic cell 4π/ ). Diect lttice: BCC (covetiol cubic cell ); Recipocl lttice: FCC (covetiol cubic cell 4π/ ).

16 st Billoui Zoe The fist Billoui zoe is the volume obtied i the sme wy s the Wige-Seitz cell, but i the ecipocl spce. > the fist Billoui zoe of the FCC lttice is just the BCC Wige-Seitz cell

17 Mille idices of lttice ples The coespodece betwee ecipocl lttice vectos d fmilies of lttice ples povides coveiet wy to specify the oiettio of lttice ple. Usully the oiettio of the ple is descibed by givig vecto oml to the ple. Sice we kow thee e ecipocl lttice vectos oml to y fmily of lttice ples it is tul to use ecipocl lttice vecto to epeset the oml. To mke the choice uique oe uses the shotest. The Mille idices of lttice ple e the coodites of the shotest ecipocl lttice vecto oml to the ple.

18 Lttice Ples Theoem Ay ecipocl lttice vecto is oml to ple of the diect lttice; its compoets e the Mille idices of the ple Poof: A vecto G hb kb lb is oml to ple with itecepts m,, p if { G ( m ) 0 { G ( m p) 0 { G ( p ) 0 Theefoe we eed to stisfy { { mh k mh pl { k pl m,,l e the Mille idices except fo itege commo fcto.

19 Mille idices Mille idices e thee iteges epesetig fmily of el lttice ples by thei oml xis: ) fid the itecepts of the ple with xis log,, i tems of lttice costts, ) fid the smllest iteges which e i the sme tio s thei ecipocls. Exmple: Itecepts:,, Recipocls: /, _, _. Mille idices:,,

20 Lttice ples Sice the ecipocl lttice of simple cubic lttice is gi simple cubic lttice d the Mille idices e the coodites of vecto oml to the ples, thei use is vey simple i lttices with cubic symmety. Lttice ples e usully specified by givig thei Mille idices i petheses: (h,k,l)