Oxide in PL5 - Champion Heterojunction Device 1-Sun Light IV

Champion Heterojunction Device 1-Sun Light IV

A.2 Oxide in PL5

The capability to deposit SiOxusing NO2 and 5 % SiH4in Ar was added not long before my arrival to the group, and very little process development had been done. Here you will find some working recipes, approaching the silicon rich suboxide regime. Recipes and growth rates are shown in table A.1 and optical data in figure A.4. Note that a heater temperature of 500^◦C corresponds to a substrate temperature of approximately 350^◦C.

Table A.1: Oxide/Suboxide Depositions from PL5

Heater SiH4 N2O Growth

Growth Pressure Temperature RF Power Flow Rate Flow Rate

Number (mTorr) (^◦C) (Watts) (sccm) (sccm) (nm/min)

143 750 500 3 50 50 28

145 750 500 3 50 25 26.8

146 750 500 3 50 10 19.3

0 0.005 0.01 0.015 0.02

1.45 1.5 1.55 1.6 1.65 1.7 1.75 1.8

300 400 500 600 700 800 900

Wavelength (nm)

Optical Constants for Three SiOx Films Deposited by PECVD in PL5

143 n 145 n 146 n 143 k 145 k 146 k

Figure A.4: Optical Constants of Oxides Deposited in PL5

Appendix B

Transient Simulations using Sentaurus TCAD

Synopsys Sentaurus TCAD was used to interpret the results of photoconductivity decay experiments.

While relatively simple analytical solutions relating the effective lifetime to the surface recombination velocity, bulk lifetime, and thickness exist for wafer geometries, these same expressions only exist for certain limited conditions in cylindrical geometries, and are not solved for tapered structures.

Therefore, we turn to simulations to fit likely material parameters given an effective lifetime for these geometries.

The following code was built off, and borrowed sections from the wire simulations developed by Michael Kelzenberg and adaptions made by Michael Deceglie. The general workflow follows the typical method of device simuation: first, the structure is defined and meshed in the structure editor.

Next, Sentaurus Device is run once to calculate the illumination, and the illumination information is imported into the next Device simulation which calculates the carrier density. Finally Matlab is used to fit either a single or double exponential to the extracted data. An example of the output data and fit are shown in figure B.1

Listing B.1: Sentaurus Device Editor Code

##########################################################################################################

# R a d i a l p−n j u n c t i o n s o l a r c e l l s t r u c t u r e f o r c o r e d e p l e t i o n s t u d i e s

# S e n t a u r u s S t r u c t u r e E d i t o r command f i l e ( a b r i d g e d f o r i n c l u s i o n i n PhD t h e s i s )

# M i c h a e l K e l z e n b e r g , C a l i f o r n i a I n s t i t u t e o f T e c h n o l o g y , 2 0 1 0

# M o d i f i e d f o r p h o t o c o n d u c t i v i t y d e c a y s i m u l a t i o n s by H a l Emmer , 2 0 1 5

##########################################################################################################

#G l o b a l s e t t i n g s ( p r o j e c t v a r i a b l e s ) :

# @R@ w i r e r a d i u s , m i c r o n s

# @L@ l e n g t h o f ’ ’ a b o v e s u b s t r a t e ’ ’ w i r e ( n o t e t h a t t h e a c t u a l s t r u c t u r e i s 1 um l o n g e r )

# @subsdoping@ d o p i n g o f t h e s u b s t r a t e , c o n t r o l s l i f e t i m e on t h e bottom s u r f a c e

#L o c a l s e t t i n g s :

#d e f i n e B a s e D o p i n g 1E+16

# [ cm−3 ]

#d e f i n e t n i t r i d e 0 . 1 5

0 1 2 3 4 5 x 10^-5 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Time (s)

Normalized Electron Density

signal vs. time Exponential Fit

Figure B.1: Example output of a transient simulation, and exponential fit generated by Matlab.

# [ m i c r o n s ] ( o x i d e s h e l l u s e d t o s e t s i d e w a l l SRV v a l u e )

#d e f i n e EMinGrid 0 . 0 1

# [ um ] min. r e f i n e m e n t mesh s i z e i n e m i t t e r r e g i o n

#d e f i n e EMaxGrid 0 . 2

# [ um ] max. r e f i n e m e n t mesh s i z e i n e m i t t e r r e g i o n

#d e f i n e E R a t i o 1 . 5

# g r i d r e l a x a t i o n r a t i o f o r e m i t t e r r e g i o n

#d e f i n e BMinGrid 0 . 0 1

# [ um ] min. r e f i n e m e n t mesh s i z e i n b a s e r e g i o n

#d e f i n e BMaxGrid 0 . 2

# [ um ] max. r e f i n e m e n t mesh s i z e i n b a s e r e g i o n

#d e f i n e B R a t i o 1 . 2

# g r i d r e l a x a t i o n r a t i o f o r b a s e r e g i o n

##########################################################################################################

# C r o s s s e c t i o n o f w i r e m a t e r i a l f o r c y l i n d r i c a l p h o t o c o n d u c t i v i t y d e c a y s i m u l a t i o n s

##########################################################################################################

#MATERIAL

( s d e g e o : c r e a t e−r e c t a n g l e (p o s i t i o n 0 −t n i t r i d e 0 )

(p o s i t i o n (+ @R@ t n i t r i d e ) @L@ 0 ) ” N i t r i d e ” ” N i t r i d e r e g i o n ” )

( s d e g e o : c r e a t e−r e c t a n g l e (p o s i t i o n 0 0 0 ) (p o s i t i o n @R@ @L@ 0 ) ” S i l i c o n ” ” B a s e r e g i o n ” )

( s d e g e o : c r e a t e−r e c t a n g l e (p o s i t i o n 0 @L@ 0 ) (p o s i t i o n@R@ (+ @L@ 1 . 0 ) 0 ) ” S i l i c o n ” ” S u b s r e g i o n ” )

#PROFILES

( s d e d r : d e f i n e−c o n s t a n t−p r o f i l e ” C o n s t a n t P r o f i l e D e f i n i t i o n f o r B a s e ” ” B o r o n A c t i v e C o n c e n t r a t i o n ” B a s e D o p i n g ) ( s d e d r : d e f i n e−c o n s t a n t−p r o f i l e−r e g i o n ” C o n s t a n t P r o f i l e P l a c e m e n t f o r B a s e ”

” C o n s t a n t P r o f i l e D e f i n i t i o n f o r B a s e ” ” B a s e r e g i o n ” )

( s d e d r : d e f i n e−c o n s t a n t−p r o f i l e ” C o n s t a n t P r o f i l e D e f i n i t i o n f o r S u b s ” ” B o r o n A c t i v e C o n c e n t r a t i o n ” @subsdoping@ ) ( s d e d r : d e f i n e−c o n s t a n t−p r o f i l e−r e g i o n ” C o n s t a n t P r o f i l e P l a c e m e n t f o r S u b s ”

” C o n s t a n t P r o f i l e D e f i n i t i o n f o r S u b s ” ” S u b s r e g i o n ” )

#REFINEMENTS FOR MATERIAL

( s d e d r : d e f i n e−r e f i n e m e n t−s i z e ” R e f i n e m e n t D e f i n i t i o n f o r S i l i c o n ” BMaxGrid BMaxGrid EMinGrid EMinGrid )

( s d e d r : d e f i n e−r e f i n e m e n t−m a t e r i a l ” R e f i n e m e n t P l a c e m e n t f o r S i l i c o n ”

” R e f i n e m e n t D e f i n i t i o n f o r S i l i c o n ” ” S i l i c o n ” )

#REMAINING REFINEMENTS

#POSITION

( s d e d r : d e f i n e−r e f e v a l−w i n d o w ” R e f E v a l W i n B U p p e r ” ” R e c t a n g l e ” (p o s i t i o n 0 0 0 ) (p o s i t i o n @R@ (∗ @L@ 0 . 5 ) 0 ) )

( s d e d r : d e f i n e−r e f e v a l−w i n d o w ” R e f E v a l W i n B L o w e r ” ” R e c t a n g l e ” (p o s i t i o n 0 @L@ 0 ) (p o s i t i o n @R@ (∗ @L@ 0 . 5 ) 0 ) )

#REFINEMENT PITCH

( s d e d r : d e f i n e−m u l t i b o x−s i z e ” M u l t i b o x D e f i n i t i o n B U p p e r ” BMaxGrid BMaxGrid BMinGrid BMinGrid −B R a t i o B R a t i o ) ( s d e d r : d e f i n e−m u l t i b o x−s i z e ” M u l t i b o x D e f i n i t i o n B L o w e r ”

BMaxGrid BMaxGrid BMinGrid BMinGrid −B R a t i o −B R a t i o )

#PLACEMENTS

( s d e d r : d e f i n e−m u l t i b o x−p l a c e m e n t ” M u l t i b o x P l a c e m e n t B U p p e r ”

” M u l t i b o x D e f i n i t i o n B U p p e r ” ” R e f E v a l W i n B U p p e r ” ) ( s d e d r : d e f i n e−m u l t i b o x−p l a c e m e n t ” M u l t i b o x P l a c e m e n t B L o w e r ”

” M u l t i b o x D e f i n i t i o n B L o w e r ” ” R e f E v a l W i n B L o w e r ” )

# NITRIDE SIDEWALL

( s d e d r : d e f i n e−r e f e v a l−w i n d o w ” R e f E v a l W i n N i t r i d e ”

” R e c t a n g l e ” (p o s i t i o n 0 0 0 ) (p o s i t i o n (+ @R@ t n i t r i d e ) @L@ 0 ) ) ( s d e d r : d e f i n e−m u l t i b o x−s i z e ” M u l t i b o x D e f i n i t i o n f o r N i t r i d e ”

BMaxGrid BMaxGrid EMinGrid EMinGrid E R a t i o −E R a t i o ) ( s d e d r : d e f i n e−m u l t i b o x−p l a c e m e n t ” M u l t i b o x P l a c e m e n t f o r N i t r i d e ”

” M u l t i b o x D e f i n i t i o n f o r N i t r i d e ” ” R e f E v a l W i n N i t r i d e ” )

# NITRIDE TOP

( s d e d r : d e f i n e−r e f e v a l−w i n d o w ” R e f E v a l W i n T o p N i t r i d e ”

” R e c t a n g l e ” (p o s i t i o n 0 0 0 ) (p o s i t i o n (+ @R@ t n i t r i d e ) −t n i t r i d e 0 ) ) ( s d e d r : d e f i n e−m u l t i b o x−s i z e ” M u l t i b o x D e f i n i t i o n f o r T o p N i t r i d e ”

BMaxGrid BMaxGrid EMinGrid EMinGrid E R a t i o −E R a t i o ) ( s d e d r : d e f i n e−m u l t i b o x−p l a c e m e n t ” M u l t i b o x P l a c e m e n t f o r T o p N i t r i d e ”

” M u l t i b o x D e f i n i t i o n f o r T o p N i t r i d e ” ” R e f E v a l W i n T o p N i t r i d e ” )

# DONE. GENERATE MESH .

( s d e : s a v e−m o d e l ”n@node@” )

( s d e : b u i l d−m e s h ” snmesh ” ”−y 1 e 5 −numThreads 8 ” ”n@node@” )

Listing B.2: Sentaurus Device illumination code for uniform monochromatic illumination

# O p t i c a l G e n e r a t i o n w i t h T r a n s f e r M a t r i x Method

#s e t d e p @node| −1 : a l l @

#s e t t a u p 1

#s e t S0 1

# R e q u i r e d t o read t h e p a r a m e t e r f i l e . T h e s e w i l l b e m o d i f i e d i n t h e d e v i c e s i m u l a t i o n

∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗

∗ FILE

F i l e {

G r i d = ” n@node|−1@ msh . t d r ”

P a r a m e t e r s = ” @parameter@ ”

p l o t = ” @tdrdat@ ”

c u r r e n t = ” @plot@ ”

O p t i c a l G e n e r a t i o n O u t p u t = ” optgen des R@R@ L@L@ I@Power@ . t d r ” }

∗ ELECTRODES

∗ PLOT

P l o t {

e C u r r e n t / V e c t o r h C u r r e n t / V e c t o r c u r r e n t /v e c t o r

S p a c e C h a r g e e D e n s i t y h D e n s i t y P o t e n t i a l E l e c t r i c F i e l d

SRH Auger T o t a l R e c o m b i n a t i o n S u r f a c e R e c o m b i n a t i o n C o n d u c t i o n B a n d V a l e n c e B a n d D o p i n g C o n c e n t r a t i o n e Q u a s i F e r m i h Q u a s i F e r m i

E f f e c t i v e I n t r i n s i c D e n s i t y I n t r i n s i c D e n s i t y O p t i c a l G e n e r a t i o n R a y T r a c e I n t e n s i t y ∗ R a y T r e e s }

∗ PHYSICS

P h y s i c s { O p t i c s (

C o m p l e x R e f r a c t i v e I n d e x ( WavelengthDep ( r e a l imag ) ) O p t i c a l G e n e r a t i o n (

C o m p u t e F r o m M o n o c h r o m a t i c S o u r c e ) ∗ end O p t i c a l G e n e r a t i o n

E x c i t a t i o n ( Window ( ” L1 ” ) (

O r i g i n = ( 0 , 0 ) L i n e ( Dx = @<2∗@R@>@) )∗End Window

W a v e l e n g t h = 1 . 0 6 4 ∗ um , Nd :YAG l a s e r o u t p u t I n t e n s i t y = @Power@ ∗W/cmˆ 2

T h e t a = 0 . ∗ d e g r e e s P h i = 3 0 . ∗ d e g r e e s )∗End E x c i t a t i o n

O p t i c a l S o l v e r ( TMM (

L a y e r S t a c k E x t r a c t i o n ( WindowName = ” L1 ” ) ∗ end L a y e r S t a c k

) ∗ end TMM

) ∗ end O p t i c a l S o l v e r ) ∗end O p t i c s

} ∗ end p h y s i c s

∗MATH

Math{

E x t r a p o l a t e D e r i v a t i v e s A v a l D e r i v a t i v e s R e l E r r C o n t r o l D i g i t s =18 RhsMin=1E−15 E x t e n d e d P r e c i s i o n I t e r a t i o n s =300 Notdamped =300 E x i t O n F a i l u r e S t a c k S i z e =20000000 C y l i n d r i c a l ( 0 . 0 )

}

∗ SOLVE

S o l v e {

O p t i c s }

Listing B.3: Sentaurus Device code for transient photoconductivity decay

#s e t d e p @node| −1 : a l l @

# s e t Nto @<@Nt@/100>@

∗ FILE

F i l e {

G r i d = ” n@node|−2@ msh . t d r ”

P a r a m e t e r s = ” @parameter@ ”

p l o t = ” @tdrdat@ ”

c u r r e n t = ” @plot@ ”

O p t i c a l G e n e r a t i o n I n p u t = ” optgen des R@R@ L@L@ I@Power@ . t d r ” }

∗ ELECTRODES

∗

∗ No e l e c t r o d e s a r e u s e d i n t h e c o n t a c t l e s s p h o t o c o n d u c t i v i t y e x p e r i m e n t

∗

∗ PLOT

P l o t {

e C u r r e n t / V e c t o r h C u r r e n t / V e c t o r c u r r e n t /v e c t o r

E l e c t r i c F i e l d / V e c t o r e D r i f t V e l o c i t y / V e c t o r h D r i f t V e l o c i t y / V e c t o r S p a c e C h a r g e e D e n s i t y h D e n s i t y

P o t e n t i a l C o n d u c t i o n B a n d E n e r g y V a l e n c e B a n d E n e r g y

SRH Auger T o t a l R e c o m b i n a t i o n S u r f a c e R e c o m b i n a t i o n / R e g i o n I n t e r f a c e e G a p S t a t e s R e c o m b i n a t i o n h G a p S t a t e s R e c o m b i n a t i o n

D o p i n g C o n c e n t r a t i o n O p t i c a l G e n e r a t i o n C u r r e n t P o t e n t i a l ∗ B e a m G e n e r a t i o n OptBeam N o n L o c a l h B a r r i e r T u n n e l i n g e B a r r i e r T u n n e l i n g }

C u r r e n t P l o t {

S u r f a c e R e c o m b i n a t i o n ( I n t e g r a t e ( R e g i o n I n t e r f a c e=” B a s e r e g i o n / N i t r i d e r e g i o n ” ) ) O p t i c a l G e n e r a t i o n ( ( 0 , @<@L@∗ @samplespot@>@) ) ,

e D e n s i t y ( A v e r a g e ( R e g i o n=” B a s e r e g i o n ” ) ) #p l o t t h e a v e r a g e e l e c t r o n d e n s i t y i n t h e b a s e

# e D e n s i t y ( ( 0 , @<@L@∗ @samplespot@>@) ) #or p l o t i t a t a s p e c i f i c p o i n t }

∗ PHYSICS

P h y s i c s {

E f f e c t i v e I n t r i n s i c D e n s i t y ( NoBandGapNarrowing ) F e r m i

A r e a=@<1e 8 / ( 2∗@R@)>@

O p t i c s (

O p t i c a l G e n e r a t i o n (

R e a d F r o m F i l e ( S c a l i n g = 0 )

TimeDependence (

WaveTime= ( 0 e−4 @ t l i g h t o f f @ ) WaveTsigma= 1e−6

S c a l i n g= 1 . 0 ∗ T r a n s i e n t S c a l i n g

) ∗end TimeDependence

) ) }

P h y s i c s ( M a t e r i a l=” S i l i c o n ” ) { R e c o m b i n a t i o n (

SRH Auger Band2Band (

Model=S c h e n k )

)∗end R e c o m b i n a t i o n M o b i l i t y ( DopingDep ) }

P h y s i c s ( R e g i o n I n t e r f a c e=” B a s e r e g i o n / N i t r i d e r e g i o n ” ){

R e c o m b i n a t i o n ( S u r f a c e S R H ) #u s e a s u r f a c e r e c o m b i n a t i o n v e l o c i t y d e f i n e d i n t h e

} #p a r a m e t e r f i l e t o b e t a k e n f r o m t h e w o r k b e n c h

∗MATH

Math{

Method = P a r D i S o T r a n s i e n t = Be

N u m b e r o f T h r e a d s = maximum E x t r a p o l a t e

D e r i v a t i v e s A v a l D e r i v a t i v e s R e l E r r C o n t r o l D i g i t s =6 RhsMin=1E−15 E x t e n d e d P r e c i s i o n I t e r a t i o n s =300 Notdamped =300 E x i t O n F a i l u r e S t a c k S i z e =4000000 C y l i n d r i c a l ( 0 . 0 )

C u r r e n t P l o t ( I n t e g r a t i o n U n i t= cm )

}

∗ SOLVE

S o l v e {

∗−−F i r s t s o l v e t h e d a r k , V=0 c a s e ( s h o r t c i c u i t c o n d i t i o n ) C o u p l e d { p o i s s o n }

C o u p l e d { p o i s s o n e l e c t r o n } C o u p l e d { p o i s s o n e l e c t r o n h o l e }

P l o t ( F i l e P r e f i x = ” n @ n o d e @ d a r k ” )

N e w C u r r e n t P r e f i x=” l i g h t ”

Q u a s i s t a t i o n a r y ( I n i t i a l S t e p = 0 . 1 M i n S t e p = 0 . 0 0 1 MaxStep = 0 . 5

G o a l{ M o d e l P a r a m e t e r = ” O p t i c s / O p t i c a l G e n e r a t i o n / R e a d F r o m F i l e / S c a l i n g ” V a l u e = 1 } ) { C o u p l e d { p o i s s o n e l e c t r o n h o l e } }

P l o t ( F i l e P r e f i x = ” n @ n o d e @ l i g h t ” )

N e w C u r r e n t P r e f i x= ” S w i t c h ”

##−f r o m 0 t o T1 T r a n s i e n t (

I n i t i a l t i m e = 0 F i n a l t i m e= 5e−4

I n i t i a l s t e p = 1e−7 I n c r e m e n t= 1 . 5 D e c r e m e n t= 4 M i n s t e p= 1 e−11 Maxstep= 1e−4

){ C o u p l e d{ P o i s s o n E l e c t r o n H o l e }

C u r r e n t P l o t ( Time= ( #g e n e r a t e more d a t a a r o u n d t h e d e c a y

Range= ( 0 . 0 e−4 2 . 0 e−4 ) i n t e r v a l s = 2 0; Range= ( 2 . 0 e−4 2 . 5 e−4 ) i n t e r v a l s = 2 0; Range= ( 2 . 5 e−4 3 . 0 e−4 ) i n t e r v a l s = 3 0; Range= ( 3 . 0 e−4 3 . 5 e−4 ) i n t e r v a l s = 2 5;

Range= ( 3 . 5 e−4 4 . 0 e−4 ) i n t e r v a l s = 2 0; Range= ( 4 . 0 e−4 5 . 0 e−4 ) i n t e r v a l s = 1 5 ) ) }

}

Listing B.4: Matlab code for fitting transient photoconductivity simulations

#s e t d e p @node| −1 : a l l @

%% I n i t i a l i z e v a r i a b l e s .

s t a r t t i m e = @ t l i g h t o f f @ ;

f i l e n a m e = ’ . / S w i t c h n @ n o d e|−1 @ d e s . p l t ’ s t a r t R o w = 1 1 ;

%% R e a d c o l u m n s o f d a t a a s s t r i n g s :

% F o r m o r e i n f o r m a t i o n , s e e t h e TEXTSCAN d o c u m e n t a t i o n . f o r m a t S p e c = ’ %26 s %23 s %23 s %23 s%s %[ˆ\n\r ] ’ ;

%% O p e n t h e t e x t f i l e . f i l e I D = fopen( f i l e n a m e , ’ r ’ ) ;

%% R e a d c o l u m n s o f d a t a a c c o r d i n g t o f o r m a t s t r i n g .

% T h i s c a l l i s b a s e d o n t h e s t r u c t u r e o f t h e f i l e u s e d t o g e n e r a t e t h i s

% c o d e . I f a n e r r o r o c c u r s f o r a d i f f e r e n t f i l e , t r y r e g e n e r a t i n g t h e c o d e

% f r o m t h e I m p o r t T o o l .

t e x t s c a n ( f i l e I D , ’ %[ˆ\n\r ] ’ , s t a r t R o w−1 , ’ R e t u r n O n E r r o r ’ , f a l s e ) ;

d a t a A r r a y = t e x t s c a n ( f i l e I D , f o r m a t S p e c , ’ D e l i m i t e r ’ , ’ ’ , ’ W h i t e S p a c e ’ , ’ ’ , ’ R e t u r n O n E r r o r ’ , f a l s e ) ;

%% C l o s e t h e t e x t f i l e . f c l o s e( f i l e I D ) ;

%% C o n v e r t t h e c o n t e n t s o f c o l u m n s c o n t a i n i n g n u m e r i c s t r i n g s t o n u m b e r s .

% R e p l a c e n o n−n u m e r i c s t r i n g s w i t h NaN .

raw = r e p m a t ({’ ’},l e n g t h( d a t a A r r a y{1}) ,l e n g t h( d a t a A r r a y )−1 ) ; f o r c o l =1:l e n g t h( d a t a A r r a y )−1

raw ( 1 :l e n g t h( d a t a A r r a y{c o l}) , c o l ) = d a t a A r r a y{c o l};

end

n u m e r i c D a t a =NaN(s i z e( d a t a A r r a y{1}, 1 ) ,s i z e( d a t a A r r a y , 2 ) ) ;

f o r c o l = [ 1 , 2 , 3 , 4 , 5 ]

% C o n v e r t s s t r i n g s i n t h e i n p u t c e l l a r r a y t o n u m b e r s . R e p l a c e d n o n−n u m e r i c

% s t r i n g s w i t h NaN . rawData = d a t a A r r a y{c o l};

f o r row =1:s i z e( rawData , 1 ) ;

% C r e a t e a r e g u l a r e x p r e s s i o n t o d e t e c t a n d r e m o v e n o n−n u m e r i c p r e f i x e s a n d

% s u f f i x e s .

r e g e x s t r = ’ (?<p r e f i x>.∗?)(?<numbers>( [−]∗(\d + [\, ]∗) + [\. ]{0 , 1} \d∗[ eEdD ]{0 , 1}[−+ ]∗ \d∗[ i ]{0 , 1})|( [−]

∗(\d + [\, ]∗)∗[\. ]{1 , 1} \d +[eEdD ]{0 , 1}[−+ ]∗ \d∗[ i ]{0 , 1}) ) ( ?<s u f f i x>.∗) ’ ; t r y

r e s u l t = r e g e x p ( rawData{row}, r e g e x s t r , ’ names ’ ) ; numbers = r e s u l t . numbers ;

% D e t e c t e d c o m m a s i n n o n−t h o u s a n d l o c a t i o n s . i n v a l i d T h o u s a n d s S e p a r a t o r = f a l s e ;

i f any( numbers== ’ , ’ ) ;

t h o u s a n d s R e g E x p = ’ ˆ\d + ? (\,\d{3})∗ \.{0 , 1} \d∗$ ’ ; i f isempty( r e g e x p ( t h o u s a n d s R e g E x p , ’ , ’ , ’ o n c e ’ ) ) ;

numbers =NaN;

i n v a l i d T h o u s a n d s S e p a r a t o r = t r u e ; end

end

% C o n v e r t n u m e r i c s t r i n g s t o n u m b e r s . i f ˜ i n v a l i d T h o u s a n d s S e p a r a t o r ;

numbers = t e x t s c a n (s t r r e p( numbers , ’ , ’ , ’ ’ ) , ’%f ’ ) ; n u m e r i c D a t a ( row , c o l ) = numbers{1};

raw{row , c o l}= numbers{1};

end

c a t c h me end end end

%% R e p l a c e n o n−n u m e r i c c e l l s w i t h NaN

R = c e l l f u n (@( x ) ˜ i s n u m e r i c ( x ) && ˜ i s l o g i c a l ( x ) , raw ) ; % F i n d n o n−n u m e r i c c e l l s raw (R) ={NaN}; % R e p l a c e n o n−n u m e r i c c e l l s

%% A l l o c a t e i m p o r t e d a r r a y t o c o l u m n v a r i a b l e n a m e s Time = c e l l 2 m a t ( raw ( : , 1 ) ) ;

VarName2 = c e l l 2 m a t ( raw ( : , 2 ) ) ; VarName3 = c e l l 2 m a t ( raw ( : , 3 ) ) ; VarName4 = c e l l 2 m a t ( raw ( : , 4 ) ) ; S i g n a l = c e l l 2 m a t ( raw ( : , 5 ) ) ;

f o r c o l =1:l e n g t h( Time)−1

i f Time ( c o l )>= s t a r t t i m e s t a r t i n d e x = c o l ; break;

end end

%% A l l o c a t e i m p o r t e d a r r a y t o c o l u m n v a r i a b l e n a m e s

Time = Time− s t a r t t i m e ; S i g n a l = S i g n a l / max( S i g n a l ) ;

%% F i t : ’ D o u b l e E x p o n e n t i a l ’ .

[ xData , yData ] = p r e p a r e C u r v e D a t a ( Time ( s t a r t i n d e x :end) , S i g n a l ( s t a r t i n d e x :end) ) ;

% S e t u p f i t t y p e a n d o p t i o n s . f t d o u b l e = f i t t y p e ( ’ e x p 2 ’ ) ; o p t s 2 = f i t o p t i o n s ( f t d o u b l e ) ; o p t s 2 . D i s p l a y = ’ O f f ’ ;

o p t s 2 . Lower = [−I n f −I n f −I n f −I n f] ; o p t s 2 . Upper = [I n f I n f I n f I n f] ;

% S e t u p f i t t y p e a n d o p t i o n s . f t s i n g l e = f i t t y p e ( ’ e x p 1 ’ ) ;

o p t s 1 = f i t o p t i o n s ( ’ Method ’ , ’ N o n l i n e a r L e a s t S q u a r e s ’ ) ; o p t s 1 . D i s p l a y = ’ O f f ’ ;

[ f i t r e s u l t 1 , g o f 1 ] = f i t ( xData , yData , f t s i n g l e , o p t s 1 ) ; f i t r e s u l t 1

g o f 1

% F i t m o d e l t o d a t a .

[ f i t r e s u l t 2 , g o f 2 ] = f i t ( xData , yData , f t d o u b l e , o p t s 2 ) ; f i t r e s u l t 2

g o f 2

i f ( g o f 1 . r s q u a r e < . 9 ) % i f w e d i d n ’ t g e t a g o o d f i t , t r y r e m o v i n g a l l t h e z e r o e s

f o r c o l =1:l e n g t h( yData )−1

i f yData ( c o l ) <= . 0 0 0 1 s t a r t i n d e x = c o l ; break;

end end

xData = xData ( 1 : s t a r t i n d e x ) ; yData = yData ( 1 : s t a r t i n d e x ) ;

o p t s 1 = f i t o p t i o n s ( f t s i n g l e ) ; o p t s 1 . D i s p l a y = ’ O f f ’ ;

[ f i t r e s u l t 1 , g o f 1 ] = f i t ( xData , yData , f t s i n g l e , o p t s 1 ) ; f i t r e s u l t 1

g o f 1

end

i f ( g o f 1 . r s q u a r e < . 9 ) % i f t h e s i n g l e e x p o n e n t i a l f i t i s g o o d , o u t p u t t h a t .

f p r i n t f( ’\nDOE : R2 %.3 f \nDOE : t a u 1 %.2 f u s \nDOE : t a u 2 %.2 f u s \nDOE : a %.2 f \nDOE : b %.2 f\n ’ , g o f 2 . r s q u a r e , −1/ f i t r e s u l t 2 . b ∗ 1 0 ˆ 6 , −1/ f i t r e s u l t 2 . d ∗ 1 0 ˆ 6 , f i t r e s u l t 2 . a , f i t r e s u l t 2 . c ) ; e l s e % O t h e r w i s e , o u t p u t t h e d o u b l e e x p o n e n t i a l f i t

f p r i n t f( ’\nDOE : R2 %.3 f \nDOE : t a u 1 %.2 f u s \nDOE : t a u 2 %.2 f u s \nDOE : a %.2 f \nDOE : b %.2 f\n ’ , g o f 1 . r s q u a r e , −1/ f i t r e s u l t 1 . b ∗ 1 0 ˆ 6 , 0 , f i t r e s u l t 1 . a , 2 7 ) ;

end

% P l o t f i t w i t h d a t a .

f i g u r e( ’ Name ’ , ’ u n t i t l e d f i t 1 ’ ) ; h = p l o t( f i t r e s u l t 1 , xData , yData ) ;

l e g e n d( h , ’ s i g n a l v s . t i m e ’ , ’ u n t i t l e d f i t 1 ’ , ’ L o c a t i o n ’ , ’ N o r t h E a s t ’ ) ;

% L a b e l a x e s x l a b e l( ’ t i m e ’ ) ; y l a b e l( ’ s i g n a l ’ ) ; g r i d on

Appendix C

Excel VBA Code for Limiting Efficiency Calculations

Listing C.1: Excel VBA Solver Code

Dim count Dim m i n e r r o r Dim m i n e r r o r r o w Dim s t a r t c o u n t Dim s t e p

S h e e t 6 .A c t i v a t e

m i n e r r o r = 5 s t a r t c o u n t = 3

For count= s t a r t c o u n t To s t a r t c o u n t + 5 ’ g e n e r a t e i n i t i a l s e e d g u e s s e s o v e r 5 o r d e r s o f m a g n i t u d e S h e e t 6 . Range ( ”E” & count) . V a l u e = 0 . 0 0 0 0 0 0 1 ∗ 1 0 ˆ (count− s t a r t c o u n t )

I f S h e e t 6 . Range ( ”N” &count) . V a l u e < m i n e r r o r Then ’ k e e p t r a c k o f t h e c l o s e s t s o l u t i o n m i n e r r o r = S h e e t 6 . Range ( ”N” &count) . V a l u e

m i n e r r o r r o w = count End I f

Next count

s t e p = 1 0

Do While ( m i n e r r o r > 0 . 0 0 1 ) ’ k e e p g e n e r a t i n g n e w g u e s s e s u n t i l e r r o r < 0 . 0 0 1

s t a r t c o u n t =count

For count = s t a r t c o u n t To s t a r t c o u n t + 2 0

S h e e t 6 . Range ( ”E” &count) . V a l u e = S h e e t 6 . Range ( ”E” & m i n e r r o r r o w ) . V a l u e ∗ 1 0 ˆ ( (count− s t a r t c o u n t − 1 0 ) / s t e p )

I f S h e e t 6 . Range ( ”N” & count) . V a l u e < m i n e r r o r Then ’ k e e p t r a c k o f t h e c l o s e s t s o l u t i o n m i n e r r o r = S h e e t 6 . Range ( ”N” & count) . V a l u e

m i n e r r o r r o w = count End I f

Next count s t e p = s t e p ∗ 1 0 Loop

’ c o p y s o l u t i o n s t o t h e r i g h t c e l l s

S h e e t 6 . Range ( ” C22 ” ) . V a l u e = S h e e t 6 . Range ( ”E” & m i n e r r o r r o w ) S h e e t 6 . Range ( ” C23 ” ) . V a l u e = S h e e t 6 . Range ( ”F” & m i n e r r o r r o w )

S h e e t 6 . Range ( ”E1 : N1” ) . V a l u e = S h e e t 6 . Range ( ”E” & m i n e r r o r r o w & ” : N” & m i n e r r o r r o w ) . V a l u e S h e e t 6 . Range ( ” B29 ” ) . V a l u e = S h e e t 6 . Range ( ” C24 ” ) . V a l u e / 1 0 0 0

’ i f w a n t e d , s o l v e f o r l i f e t i m e a n d v o l t a g e a t max p o w e r p o i n t .

’ T h i s s l o w s d o w n t h e c a l c u l a t i o n s f a i r l y s i g n i f i c a n t l y , t h o u g h .

’ S o l v e r O k S e t C e l l : = ”$C$2 9 ” , M a x M i n V a l : = 3 , V a l u e O f : = 0 ,

’ B y C h a n g e : = ”$B$2 9 ” , E n g i n e : = 1 , E n g i n e D e s c : = ” GRG N o n l i n e a r ”

’ S o l v e r S o l v e T r u e

’ A c t i v e S h e e t . R a n g e ( ” E ” & c o u n t + 1 ) . V a l u e = m i n e r r o r r o w

’ A c t i v e S h e e t . R a n g e ( ” E ” & c o u n t + 1 ) . N u m b e r F o r m a t = ” G e n e r a l ”

Listing C.2: VBA Code to Generate Sweeps

Sub Sweep ( )

’ S w e e p s t h i c k n e s s , a n d r e f i n e s t h e c a l c u l a t i o n a r o u n d t h e maximum e f f i c i e n c y t h i c k n e s s

Dim t h i c k n e s s Dim m a x e f f i c i e n c y

m a x e f f i c i e n c y = 0 t h i c k n e s s = 1 . 5 I n d e x = 3

Do While ( t h i c k n e s s < 1 0 0 0 )

S h e e t 1 . Range ( ”B” & I n d e x ) . V a l u e = t h i c k n e s s

S h e e t 6 . Range ( ” C10 ” ) . V a l u e = S h e e t 1 . Range ( ”B” & I n d e x ) . V a l u e Module1 . S o l v e r

S h e e t 1 . Range ( ”C” & I n d e x ) . V a l u e = S h e e t 6 . Range ( ” C27 ” ) . V a l u e ’ e f f i c i e n c y I f S h e e t 1 . Range ( ”C” & I n d e x ) . V a l u e > m a x e f f i c i e n c y Then

m a x e f f i c i e n c y = S h e e t 1 . Range ( ”C” & I n d e x ) . V a l u e m a x e f f i c i e n c y c e l l = I n d e x

m a x e f f i c i e n c y t h i c k n e s s = t h i c k n e s s End I f

S h e e t 1 . Range ( ”D” & I n d e x ) . V a l u e = S h e e t 6 . Range ( ” C24 ” ) . V a l u e ’ v o c S h e e t 1 . Range ( ”E” & I n d e x ) . V a l u e = S h e e t 6 . Range ( ” C17 ” ) . V a l u e ’ C u r r e n t

S h e e t 1 . Range ( ”F” & I n d e x ) . V a l u e = S h e e t 6 . Range ( ” C22 ” ) . V a l u e ’ E f f e c t i v e L i f e t m e S h e e t 1 . Range ( ”G” & I n d e x ) . V a l u e = S h e e t 6 . Range ( ” C23 ” ) . V a l u e ’ C a r r i e r C o n c e n t r a t i o n S h e e t 1 . Range ( ”H” & I n d e x ) . V a l u e = S h e e t 6 . Range ( ” B29 ” ) . V a l u e ’ V o l t a g e a t MPP

S h e e t 1 . Range ( ” I ” & I n d e x ) . V a l u e = S h e e t 6 . Range ( ” B30 ” ) . V a l u e ’ C a r r i e r C o n c e n t r a t i o n a t MPP t h i c k n e s s = Round ( t h i c k n e s s ∗ 1 . 1 , 1 )

I n d e x = I n d e x + 1 Loop

For t h i c k n e s s = Round ( m a x e f f i c i e n c y t h i c k n e s s , 0 ) − 1 0 To Round ( m a x e f f i c i e n c y t h i c k n e s s , 0 ) + 1 0 S h e e t 1 . Range ( ”B” & I n d e x ) . V a l u e = t h i c k n e s s

S h e e t 6 . Range ( ” C10 ” ) . V a l u e = S h e e t 1 . Range ( ”B” & I n d e x ) . V a l u e Module1 . S o l v e r

m a x e f f i c i e n c y = S h e e t 1 . Range ( ”C” & I n d e x ) . V a l u e m a x e f f i c i e n c y c e l l = I n d e x

m a x e f f i c i e n c y t h i c k n e s s = t h i c k n e s s End I f

S h e e t 1 . Range ( ” I ” & I n d e x ) . V a l u e = S h e e t 6 . Range ( ” B30 ” ) . V a l u e ’ C a r r i e r C o n c e n t r a t i o n a t MPP

I n d e x = I n d e x + 1 Next t h i c k n e s s

S h e e t 1 . Range ( ”B1” ) . V a l u e = m a x e f f i c i e n c y t h i c k n e s s S h e e t 1 . Range ( ”C1” ) . V a l u e = m a x e f f i c i e n c y

S h e e t 1 .A c t i v a t e

End Sub

Sub SweepSRV ( )

DimSRV

SRV = 1 . 5 I n d e x = 3

Do While (SRV< 1 0 0 )

S h e e t 2 . Range ( ”B” & I n d e x ) . V a l u e = SRV

S h e e t 6 . Range ( ” C11 ” ) . V a l u e = S h e e t 2 . Range ( ”B” & I n d e x ) . V a l u e Module1 . S o l v e r

S h e e t 2 . Range ( ”C” & I n d e x ) . V a l u e = S h e e t 6 . Range ( ” C27 ” ) . V a l u e ’ e f f i c i e n c y

S h e e t 2 . Range ( ”D” & I n d e x ) . V a l u e = S h e e t 6 . Range ( ” C24 ” ) . V a l u e ’ v o c S h e e t 2 . Range ( ”E” & I n d e x ) . V a l u e = S h e e t 6 . Range ( ” C17 ” ) . V a l u e ’ C u r r e n t SRV = Round (SRV ∗ 1 . 1 , 1 )

I n d e x = I n d e x + 1 Loop

S h e e t 2 .A c t i v a t e

End Sub

Sub SweepParams ( )

’ g e n e r a t e s w e e p s f o r a n y p a r a m e t e r s , a s e n t e r e d i n t h e w o r k s h e e t

Dim RowIndex , ColumnIndex

Dim P a r a m e t e r s ( 1 To 5 ) As S t r i n g

For ColumnIndex = 1 To 5

I f ( S h e e t 3 . C e l l s ( 2 , ColumnIndex )<> ” ” ) Then S e l e c t Case S h e e t 3 . C e l l s ( 2 , ColumnIndex ) . V a l u e

Case ”SRH Tau”

P a r a m e t e r s ( ColumnIndex ) = ”C7”

Case ”Na”

P a r a m e t e r s ( ColumnIndex ) = ”C9”

Case ” T h i c k n e s s ”

P a r a m e t e r s ( ColumnIndex ) = ” C10 ”

Case ”SRV”

P a r a m e t e r s ( ColumnIndex ) = ” C11 ” Case ” I n t e r n a l C o n c e n t r a t i o n ”

P a r a m e t e r s ( ColumnIndex ) = ” C14 ” End S e l e c t

End I f

Next ColumnIndex

RowIndex = 3

Do While ( S h e e t 3 . Range ( ”B” & RowIndex ) )

For ColumnIndex = 1 To 5 ’ l e n g t h o f p a r a m e t e r s

S h e e t 6 . Range ( P a r a m e t e r s ( ColumnIndex ) ) . V a l u e = S h e e t 3 . C e l l s ( RowIndex , ColumnIndex ) . V a l u e

Next ColumnIndex

Module1 . S o l v e r

S h e e t 3 . C e l l s ( RowIndex , ColumnIndex + 1 ) . V a l u e = S h e e t 6 . Range ( ” C27 ” ) . V a l u e ’ e f f i c i e n c y S h e e t 3 . C e l l s ( RowIndex , ColumnIndex + 2 ) . V a l u e = S h e e t 6 . Range ( ” C24 ” ) . V a l u e ’ v o c S h e e t 3 . C e l l s ( RowIndex , ColumnIndex + 3 ) . V a l u e = S h e e t 6 . Range ( ” C17 ” ) . V a l u e ’ C u r r e n t

RowIndex = RowIndex + 1 Loop

S h e e t 3 .A c t i v a t e

End Sub

Sub SweepTwoParams ( )

’ g e n e r a t e s w e e p s f o r a n y t w o p a r a m e t e r s , a s e n t e r e d i n t h e w o r k s h e e t

Dalam dokumen Paths Towards High Efficiency Silicon Photovoltaics (Halaman 115-129)