Homework #2 Solutions, EE/MSE 486, Spring 2017 Problem 1:

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Audra Atkins
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1 Homework # Solutos, EE/MSE 486, Sprg 017 Problem 1: P o p N N A ( N N A) Here / for type dopg; 4 p p N A N ( N A N) / for p type dog. 4 At 1000C, 3.1* / From the table the otes, we have T 0.603eV exp( ) cm kt 3 5.8*10 18 cm 3 o (cm /s) + (cm /s) - (cm /s) = (cm /s) B 7.04e e-14 P 1.7e e-16.5e-16 As.68e e-15 Sb 7.70e e-15 The plot for p type s:

2 dffusvty (cm /s) B P As Sb The plot for type s: N A -N (cm -3 )

3 dffusvty (cm /s) B P As Sb N -N A (cm -3 ) Problem The trsc carrer cocetrato Slco s gve by 3.1*10 16 T 3/ The electrc feld ehacemet factor for dffuso s 0.603eV exp( ) cm kt 3 h 1 N N 4 where N s 1*10 19 cm -3 the problem. Cosderg the cocetrato depedet dffuso for As, we have As o Here, = N + N + 4

4 The method to get o ad - s the same as the problem 1. We ca defe the ehacemet from the cocetrato depedet dffuso as: Ehacemet o o We ca plot the ehacemet from electrc feld effect ad from the cocetrato-depedet dffuso together as a fucto of temperature, as show below. Whe the temperature s lower the 1300C, both of the ehacemet factor s larger tha 1.. At 1300C, / s about 1.5. Whe reducg temperature, / would crease remarkably. Thus the ehacemet factor wll also crease Electrc feld effects Cocetrato depedet Ehacemet 6 4 Problem 3: Setaurus put fle s: T ( o C) le x locato=0 spacg=0.01 tag=sevtop le x locato=1 spacg=0.01 le x locato=5 spacg=0.1 tag=sevbot rego slco xlo=sevtop xh=sevbot t cocetrato=e18<cm-3> feld=phosphorus wafer.oret=100

depost materal=oxde type=sotropc thckess=1 Boro coc=1e dffuse temperature=900<c> tme=<m> struct tdr=predep strp oxde dffuse temperature=1000<c> tme=60<m> struct tdr=drve select z=boro layers prt.

5 depost materal=oxde type=sotropc thckess=1 Boro coc=1e dffuse temperature=900<c> tme=<m> struct tdr=predep strp oxde dffuse temperature=1000<c> tme=60<m> struct tdr=drve select z=boro layers prt.1d I ths put fle, we ca tue the predeposto tme to match the dose requremet. The layers commad would output the dose (cm - ) at certa layer the termal wdow as show below: The trsc dffusvty for boro at 900 C s: 900 C B exp kt 16 cm s 1 The relato betwee dose ad predeposto tme wth fxed surface cocetrato s:

6 Q C S t Cs s the surface cocetrato whch s about 6*10 19 /cm -3 from the Setaurus smulato. To get Q=*10 14 cm -, we eed t=9.*10-1 cm - So the predeposto tme for trsc should be: 1 9.*10 3 t 9.9*10 s *10 The extrsc dffusvty for boro at 900 C s: p h 0.05exp 0.95exp cm s 900C 14 1 B kt kt wth h~ So the predeposto tme for extrsc should be: 1 9.*10 t.7*10 s *10 Based o TCA smulato, the predeposto tme s about m whch s smaller tha the value based o the costat trsc dffusvty whle larger the value usg extrsc dffusvty. Ths s because Setaurus use par dffuso model as default, whch cosder electrcal feld effect, cocetrato depedece ad coupled dffuso betwee dopat ad pot defects. Problem 4: Based o the mass relato for the chemcal reacto, equlbrum the cocetrato of actve As ad actve As4V has the relato below: 4 C As4V = kc V C As (1) Here C X stads for the cocetrato of x ad k s the equlbrum costat. C As s the cocetrato of actve As ad we wll use C As,tot to stad the total cocetrato of As. C As,tot = C As + 4 C As4V () Whe C As,tot = 10 0 cm 3, the actve As4V s 10% of the total As. So we have Put (3) back to (1), we ca get kc V = cm 9 () the becomes 4 C As4V = cm 3 ad C As = cm 3 (3) C As,tot = C As C As (4) (4) descrbes the relato betwee C As ad C As,tot whch ca be plotted as follows:

7 Actve As Cocetrato (cm ( -3)) Total As Cocetrato (cm -3 ) X:.004e+1 Y: 5.67e+0 The peak stable electro desty before precptato s 5.67*10 0 cm -3 whe C As,tot = 10 1 cm 3. Problem 5. Setaurus put fle: le x locato=0 spacg=0.01 tag=sevtop le x locato=1 spacg=0.01 le x locato=5 spacg=0.1 tag=sevbot rego slco xlo=sevtop xh=sevbot t cocetrato=e16<cm-3> feld=phosphorus wafer.oret=100 pdbset Slco opat ffmodel Ferm #pdbset Slco opat ffmodel Par pdbset Gas_Slco Phosphorus BoudaryCodto rchlet pdbsetouble Slco Phosphorus Cstar 3e0 dffuse temperature=900<c> tme=1<hr> struct tdr=ferm # struct tdr=par

8 select z=phosphorus prt.1d The comparso betwee par model ad Ferm model s show followg plots: Phosphorus cocetrato (cm -3 ) depth (m) Par model Ferm model

9 upared tersttal cocetrato (cm -3 ) depth (m) Par model Ferm model There s strog tersttal supersaturato the bulk rego the Par model whle the upared tersttal s equlbrum for Ferm model. The supersaturato of tersttal of Par model s due to the dffuso of PI pars to the bulk ad dssocated to phosphorus ad upared tersttal (chemcal pumpg effect). Whle the small dp of It profle for Fem model s due to the dopg depedece of tersttal equlbrum cocetrato. Kk of phosphorus profle s due to the egatve gradet of It ear surface, whle the tal s the result of ehaced dffuso caused by tersttal supersaturato.

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

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