Periodic Table of Elements. EE105 - Spring 2007 Microelectronic Devices and Circuits. The Diamond Structure. Electronic Properties of Silicon

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1 EE105 - Srg 007 Mcroelectroc Devces ad Crcuts Perodc Table of Elemets Lecture Semcoductor Bascs Electroc Proertes of Slco Slco s Grou IV (atomc umber 14) Atom electroc structure: 1s s 6 3s 3 Crystal electroc structure: 1s s 6 3(s) 4 Damod lattce, wth 0.35 m bod legth Very oor coductor at room temerature: why? The Damod Structure 3s Tetrahedral Bod.35A (1s) 5.43A (s) () 6 (3s) 4 Hybrdzed State 3 4

2 States of a Atom Slco Eergy. E 3 E Forbdde Bad Ga Allowed Eergy Levels E 1 Atomc Sacg Lattce Costat Quatum Mechacs: The allowed eergy levels for a atom are dscrete ( electros wth ooste s ca occuy a state) Whe atoms are brought to close cotact, these eergy levels slt If there are a large umber of atoms, the dscrete eergy levels form a cotuous bad 5 S has four valece electros. Therefore, t ca form covalet bods wth four of ts eghbors. Whe temerature goes u, electros the covalet bod ca become free. 6 Electro-Hole Par Iteracto Free Electro Desty as a Fucto of Temerature E g 15 3/ kt T e electros / cm ( T 300 K ) electros / cm ( T 600 K ) electros / cm Wth free electros breakg off covalet bods, holes are geerated. Holes ca be flled by absorbg other free electros, so effectvely there s a flow of charge carrers. 7 E g, or badga eergy, determes how much effort s eeded to break off a electro from ts covalet bod. There exsts a exoetal relatosh betwee the free-electro desty ad badga eergy. 8

3 Tye Dog P Tye Dog If S s doed wth grou-v elemets such as hoshorous (P) or arsec (As), the t has more electros ad becomes tye (electro). Grou-V murtes are called Doors If S s doed wth grou-iii elemets such as boro (B), the t has more holes ad becomes P tye. Grou-III murtes are called Accetors 9 10 Summary of Charge Carrers Thermal Equlbrum (Pure S) Balace betwee geerato ad recombato determes o o Strog fucto of temerature: T 300 K G Gth( T) + Got R k( ) G R k ( ) Gth( T) Gth( T)/ k ( T) 10-3 ( T) 10 cm at 300K 11 1

4 Mass Acto Law The roduct of electro ad hole destes s ALWAYS equal to the square of trsc electro desty, regardless of dog levels ( T 300 K, 10 cm ) 10 3 o o -Tye P-Tye Majorty Carrer Coc. Dog Coc d d a a Morty Carrer Coc. (Mass Acto Law) 0 d 0 a 13 Comesated Dog S s doed wth both door ad accetor atoms: More doors tha accetors: d > a tye o d a o More accetors tha doors: a > d P tye o a d o d a a d 14 Frst Charge Trasortato Mechasm: Drft Moblty Moblty vs. Dog Slco at 300K v v h e μ E μ E The rocess whch charge artcles move because of a electrc feld s called drft. Charge artcles wll move at a velocty that s roortoal to the electrc feld. 15 Tycal values μ 1350 μ 450 V-sec / cm V-sec / cm 16

5 Curret Flow: Geeral Case I v W h q I J v q Wh Electrc curret s calculated as the amout of charge v meters that asses thru a cross-secto f the charge travel wth a velocty of v m/s. Curret Flow: Drft J μe q J μ E q Jtot μe q+ μe q q( μ + μ ) E Sce velocty s equal to μe, drft characterstc s obtaed by substtutg v wth μe the geeral curret equato. The total curret desty cossts of both electros ad holes Velocty Saturato Secod Charge Trasortato Mechasm: Dffuso μ0 μ 1 + be μ0 vsat b v μ0e 1+ v sat E A toc treated more advaced courses s velocty saturato. I realty, velocty does ot crease learly wth electrc feld. It wll evetually saturate to a crtcal value. 19 Charge artcles move from a rego of hgh cocetrato to a rego of low cocetrato. 0

6 Curret Flow: Dffuso Examle: Lear vs. olear Charge Desty Profle Dffuso Coeffcet J d qd dxd J qd dx d d Jtot q( D D ) dx dx Dffuso curret s roortoal to the gradet of charge (d/dx) alog the drecto of curret flow. Total dffuso curret desty cossts of both electros ad holes. J qd d qd dx L d qd qd ex dx Ld Lear charge desty rofle meas costat dffuso curret, whereas olear charge desty rofle meas varyg dffuso curret. J x L d 1 Este's Relato Resstvty of Uformly Doed S D kt μ q Whle the uderlyg hyscs behd drft ad dffuso currets are totally dfferet, Este s relato rovdes a lk betwee the two. 3 J μ E q σ E σ qμ 1 1 ρ σ q μ V R I Ohm's Law V E L I J tw I V EL L J E σ E A RtW RtW RtW 1 L L R ρ σ tw tw 4

7 Sheet Resstace (R s ) IC resstors have a secfed thckess ot uder the cotrol of the crcut desger Elmate thckess, t, by absorbg t to a ew arameter: the sheet resstace (R s ) Usg Sheet Resstace (R s ) Io-mlated (or dffused ) IC resstor L ρ R L R L ρ S Wt t W W umber of Squares 5 6 Idealzatos Why does curret desty J tur? What s the thckess of the resstor? What s the effect of the cotact regos? 7