CA2673621A1 - A method for evaluating umg silicon compensation - Google Patents
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- CA2673621A1 CA2673621A1 CA 2673621 CA2673621A CA2673621A1 CA 2673621 A1 CA2673621 A1 CA 2673621A1 CA 2673621 CA2673621 CA 2673621 CA 2673621 A CA2673621 A CA 2673621A CA 2673621 A1 CA2673621 A1 CA 2673621A1
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- C30B—SINGLE-CRYSTAL GROWTH; UNIDIRECTIONAL SOLIDIFICATION OF EUTECTIC MATERIAL OR UNIDIRECTIONAL DEMIXING OF EUTECTOID MATERIAL; REFINING BY ZONE-MELTING OF MATERIAL; PRODUCTION OF A HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; SINGLE CRYSTALS OR HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; AFTER-TREATMENT OF SINGLE CRYSTALS OR A HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; APPARATUS THEREFOR
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Abstract
The present invention relates to a method for the determination of boron (B) and phosphorus (P) concentration in high purity silicon feedstock (5N). More particularly, it is a method applicable for the evaluation of initial dopant compensation in Upgraded Metallurgical Grade silicon (UMG-Si). Using the resistivity (or conductivity) of a directionally solidified ingot made with a particular feedstock batch, the residual resistivity at p/n transition is measured. The resistivity at p/n transition is only related to the amount of compensation in the material and, since of acceptor (N a) is equal to the amount of donor (N d) at that particular location, initial concentration in the feedstock may be calculated by the help of Scheil's equation.
Description
A METHOD FOR EVALUATING UMG SILICON COMPENSATION
Introduction Compensated doping is typical of upgraded metallurgical silicon. Compensation occurs when both donor and acceptor dopant impurities are present in a semiconductor. Highly compensated silicon is still poorly understood and this poses interesting scientific challenges. Reliable data exists for monocristalline silicon doped with either boron or phosphorus, but not both.
The major difficulty by using UMG-Si in the production of solar cells is to have a perfect control of the dopant concentration to produce wafers with a resistivity in between 0.3 and 5 S2.cm. Since dopant density and resistivity are related, the initial dopant density in the feedstock is the first acceptance parameters to consider for the quality control.
There is no Certified Reference Material (CRM) available for calibration for compensated silicon and demonstrate clearly the precision and accuracy needed by the industry.
Therefore, the present invention relates to a method for the determination af boron (B) and phosphorus (P) concentration in high purity silicon feedstock (5N) using resistivity measurement method.
Equilibrium segregation coefficient In crystal growth, a known amount of dopant is added to the melt to obtain the desired doping concentration in the solid silicon. For silicon, boron and phosphorus are the most common dopants for p- and n-type materials, respectively.
When an ingot is directionally solidified, the doping concentration of the crystal (solid) is usually different from the doping concentration of the melt (liquid) at the interface. The ratio of these two concentrations is defined as the equilibrium segregation coefficient ko:
k C (0) (Equation 1) where CS and CI(0) are, respectively, the equilibrium concentrations of the dopant in the solid and liquid near the interface. Table 1 lists values of ko for a selection of elements for silicon.
Table 1: List of equilibrium se re ation coefficients for some elements Element Symbol Type ko Aluminum Al p 0.002 Arsenic As n 0.3 Boron B p 0.8 Carbon C - - - 0.1 Gallium Ga p 0.008 Germanium Ge - - - 0.33 Indium In p 0.0004 Phosphorus P n 0.35 Antimony Sb n 0.023 Tin Sn - - - 0.016 m IV v B c Al Si P
3 Ga 3 Ge 3 As Acceptors (a): p-type;
491n 5 Sn 5 3b Donors (d): n-type.
Acceptors L Donors Semiconductors Figure 1: Part of the Periodic table
Introduction Compensated doping is typical of upgraded metallurgical silicon. Compensation occurs when both donor and acceptor dopant impurities are present in a semiconductor. Highly compensated silicon is still poorly understood and this poses interesting scientific challenges. Reliable data exists for monocristalline silicon doped with either boron or phosphorus, but not both.
The major difficulty by using UMG-Si in the production of solar cells is to have a perfect control of the dopant concentration to produce wafers with a resistivity in between 0.3 and 5 S2.cm. Since dopant density and resistivity are related, the initial dopant density in the feedstock is the first acceptance parameters to consider for the quality control.
There is no Certified Reference Material (CRM) available for calibration for compensated silicon and demonstrate clearly the precision and accuracy needed by the industry.
Therefore, the present invention relates to a method for the determination af boron (B) and phosphorus (P) concentration in high purity silicon feedstock (5N) using resistivity measurement method.
Equilibrium segregation coefficient In crystal growth, a known amount of dopant is added to the melt to obtain the desired doping concentration in the solid silicon. For silicon, boron and phosphorus are the most common dopants for p- and n-type materials, respectively.
When an ingot is directionally solidified, the doping concentration of the crystal (solid) is usually different from the doping concentration of the melt (liquid) at the interface. The ratio of these two concentrations is defined as the equilibrium segregation coefficient ko:
k C (0) (Equation 1) where CS and CI(0) are, respectively, the equilibrium concentrations of the dopant in the solid and liquid near the interface. Table 1 lists values of ko for a selection of elements for silicon.
Table 1: List of equilibrium se re ation coefficients for some elements Element Symbol Type ko Aluminum Al p 0.002 Arsenic As n 0.3 Boron B p 0.8 Carbon C - - - 0.1 Gallium Ga p 0.008 Germanium Ge - - - 0.33 Indium In p 0.0004 Phosphorus P n 0.35 Antimony Sb n 0.023 Tin Sn - - - 0.016 m IV v B c Al Si P
3 Ga 3 Ge 3 As Acceptors (a): p-type;
491n 5 Sn 5 3b Donors (d): n-type.
Acceptors L Donors Semiconductors Figure 1: Part of the Periodic table
2 . . . . .... .. .. . . . .. ... . . .. ... ....... .. .... . .. . . . . . . .
Equilibrium segregation coefficient While the crystal is growing, dopants are constantly being rejected into the melt. If the rejection rate is higher than the rate of which the dopant can be transported away by diffusion or convection, then a concentration gradient will develop at the interface.
F Solid Liquixd --- -Ct(0) ~Qx) ----- C
t (ko < 1) C,- keCt ~ x ~ -r Growth direction Figure 2: Doping distribution near the solid-liquid interface.
We can define an effective segregation coefficient ke7 which is the ratio of Cs and the impurity concentration far away from the interface, C,.
Most impurity elements have a very low segregation coefficient in silicon.
This means that the solid will reject the impurities during crystallization. The solid and the liquid phase will as a rule obey to equilibrium at the interface, but the mean content of the phases will normally not be in equilibrium because the rate of impurity transport within the phases is limited.
Equilibrium segregation coefficient While the crystal is growing, dopants are constantly being rejected into the melt. If the rejection rate is higher than the rate of which the dopant can be transported away by diffusion or convection, then a concentration gradient will develop at the interface.
F Solid Liquixd --- -Ct(0) ~Qx) ----- C
t (ko < 1) C,- keCt ~ x ~ -r Growth direction Figure 2: Doping distribution near the solid-liquid interface.
We can define an effective segregation coefficient ke7 which is the ratio of Cs and the impurity concentration far away from the interface, C,.
Most impurity elements have a very low segregation coefficient in silicon.
This means that the solid will reject the impurities during crystallization. The solid and the liquid phase will as a rule obey to equilibrium at the interface, but the mean content of the phases will normally not be in equilibrium because the rate of impurity transport within the phases is limited.
3 Effective segregation coefficient With sufficient convection, the bulk of the melt will be homogeneous, but on the interface between solid and liquid there will be a thin layer with incomplete mixing (8). The transport of impurities to the bulk melt must go through this layer.
The diffusion layer (S) can be minimized by changing crystallization conditions. It will be small with a low solidification rate, strong stirring and high diffusion coefficient. The diffusion coefficient is a property of the impurity element itself and solidification rate has to stay in a practical speed for ingot production. However, we found that convection (natural or forced) is the more important parameter to affect the effective segregation coefficient. In an extreme case, the effective distribution coefficient may approach equilibrium:
ke > ko. For a given method of crystallization, the value of ke must be determined experimentally.
Using an ALD SCU400 crystallization furnace, we sliced two different blocks (from 2 different convection conditions) in 10 mm layers for chemical analysis. Assuming that the signal of the analytical equipment is proportional to element concentration over the range of interest, the chemical results were normalized to eliminate any risk of wrong calibration. The effective segregation coefficient was than calculated from the Scheil's equation by best fitting a curve:
[El ]sa,,,p,e = ke,Er fs )' ke F~ Scheil factor) (Equation 2) [El,oroerage Where:
[El]SQ ,pte: Impurity concentration in the sample (ppma);
[EZ]Q1eYRge: Average impurity concentration in the block (ppma);
f: Solidified fraction (position in the block from bottom);
ke,Er: Effective segregation (or distribution) coefficient of the impurity.
The diffusion layer (S) can be minimized by changing crystallization conditions. It will be small with a low solidification rate, strong stirring and high diffusion coefficient. The diffusion coefficient is a property of the impurity element itself and solidification rate has to stay in a practical speed for ingot production. However, we found that convection (natural or forced) is the more important parameter to affect the effective segregation coefficient. In an extreme case, the effective distribution coefficient may approach equilibrium:
ke > ko. For a given method of crystallization, the value of ke must be determined experimentally.
Using an ALD SCU400 crystallization furnace, we sliced two different blocks (from 2 different convection conditions) in 10 mm layers for chemical analysis. Assuming that the signal of the analytical equipment is proportional to element concentration over the range of interest, the chemical results were normalized to eliminate any risk of wrong calibration. The effective segregation coefficient was than calculated from the Scheil's equation by best fitting a curve:
[El ]sa,,,p,e = ke,Er fs )' ke F~ Scheil factor) (Equation 2) [El,oroerage Where:
[El]SQ ,pte: Impurity concentration in the sample (ppma);
[EZ]Q1eYRge: Average impurity concentration in the block (ppma);
f: Solidified fraction (position in the block from bottom);
ke,Er: Effective segregation (or distribution) coefficient of the impurity.
4 We found:
Table 2: Effective distribution coefficient for boron and phosphorus by changing convection conditions in the liquid silicon during solidification.
Boron Phosphorus 2.80 4.00 -,.
2.60 2.40 3.50 -~~..
2.20 3.00 ~~.
1.00 1.80 S
2 2.50 1.60 .!!
O 1.40 2.00 1.20 -- g .'..
1.00 0.60 0.40 .~.
0.50 0.10 0.00 . ........._ . . . . _--. -.. = -._-.__~ -_.. 000 8 0 0 o g 8 0 0 0 0 8 8 0 0 o g o 0 0 0 0 8 Solidified frection Solidified fraction ke,B = 0.70 ke,p = 0.33 1.80 4.00 1.60 3.50 1.40 3.00 1.20 2.00 O 0.80 -.' 1.50 0.60 - SS
1.00 0.40 -.
030 0.50 ,,.
~4 . . . . . . . . .
0.00 ~'~. . . . . , . . . . . . . 0.00 $ o 0 o B ~ o 0 0 0 8 $ o 0 o S ~ o o ~ 0 8 Solidified fraction Solidified fractlon ke,B=0.85 ke,p=0.50 The effective coefficient measurement can be useful for any element in Table 1.
Since both donor and acceptor impurities are present simultaneously, the impurity that is present in a greater concentration determines the type of conductivity in the semiconductor. When atomic boron concentration is higher than phosphorus concentration, the silicon is p-type and, when boron concentration is lower than phosphorus, n-type. The p/n transition can be calculated by doing a modification to Scheil's equation:
I
k4,P-k4,B
fs =1- B ke B (Equation 3) [P],, ' kp
Table 2: Effective distribution coefficient for boron and phosphorus by changing convection conditions in the liquid silicon during solidification.
Boron Phosphorus 2.80 4.00 -,.
2.60 2.40 3.50 -~~..
2.20 3.00 ~~.
1.00 1.80 S
2 2.50 1.60 .!!
O 1.40 2.00 1.20 -- g .'..
1.00 0.60 0.40 .~.
0.50 0.10 0.00 . ........._ . . . . _--. -.. = -._-.__~ -_.. 000 8 0 0 o g 8 0 0 0 0 8 8 0 0 o g o 0 0 0 0 8 Solidified frection Solidified fraction ke,B = 0.70 ke,p = 0.33 1.80 4.00 1.60 3.50 1.40 3.00 1.20 2.00 O 0.80 -.' 1.50 0.60 - SS
1.00 0.40 -.
030 0.50 ,,.
~4 . . . . . . . . .
0.00 ~'~. . . . . , . . . . . . . 0.00 $ o 0 o B ~ o 0 0 0 8 $ o 0 o S ~ o o ~ 0 8 Solidified fraction Solidified fractlon ke,B=0.85 ke,p=0.50 The effective coefficient measurement can be useful for any element in Table 1.
Since both donor and acceptor impurities are present simultaneously, the impurity that is present in a greater concentration determines the type of conductivity in the semiconductor. When atomic boron concentration is higher than phosphorus concentration, the silicon is p-type and, when boron concentration is lower than phosphorus, n-type. The p/n transition can be calculated by doing a modification to Scheil's equation:
I
k4,P-k4,B
fs =1- B ke B (Equation 3) [P],, ' kp
5 where:
f: Solidified fraction at p/n transition;
[B]o: Initial boron concentration in feedstock (ppma);
[P]o: Initial phosphorus concentration in feedstock (ppma);
ke,B: Effective distribution coefficient of boron;
ke,P: Effective distribution coefficient of phosphorus.
The phosphorus to boron ratio in the initial feedstock may be precisely determined by knowing the position of the p/n transition and the effective segregation coefficient for boron and phosphorus:
at p/n transition: [P], =[B]j and, (Equation 4) fi!B.(l_f)kB_kP (Equation 5) B ke,P
where:
[B],-: Boron concentration at p/n transition (ppma);
[P];: Phosphorus concentration at p/n transition (ppma);
.-' ~' 1 $ ... :__.-.. . ..;. _...._.... .; . _... ... . ........:.......
iii -..:__ .__.___~_ .____. ...... ...... ... :.. .
1.0 ~+L
c.r~ . ~ ~.$ _. ~ ......___"- .=____......: ___.........____ ....._____ =_._____ ~~..~ `.. , .
00 ...... ........:. ...........:............. ._......._.__.,...._._ ~ 0.30hmcm ~... 2.50hncm 0 aoo -$o o so Ioo oistence (mn]
Figure 3: Typical p/n transition in a compensated multicrystalline silicon ingot.
f: Solidified fraction at p/n transition;
[B]o: Initial boron concentration in feedstock (ppma);
[P]o: Initial phosphorus concentration in feedstock (ppma);
ke,B: Effective distribution coefficient of boron;
ke,P: Effective distribution coefficient of phosphorus.
The phosphorus to boron ratio in the initial feedstock may be precisely determined by knowing the position of the p/n transition and the effective segregation coefficient for boron and phosphorus:
at p/n transition: [P], =[B]j and, (Equation 4) fi!B.(l_f)kB_kP (Equation 5) B ke,P
where:
[B],-: Boron concentration at p/n transition (ppma);
[P];: Phosphorus concentration at p/n transition (ppma);
.-' ~' 1 $ ... :__.-.. . ..;. _...._.... .; . _... ... . ........:.......
iii -..:__ .__.___~_ .____. ...... ...... ... :.. .
1.0 ~+L
c.r~ . ~ ~.$ _. ~ ......___"- .=____......: ___.........____ ....._____ =_._____ ~~..~ `.. , .
00 ...... ........:. ...........:............. ._......._.__.,...._._ ~ 0.30hmcm ~... 2.50hncm 0 aoo -$o o so Ioo oistence (mn]
Figure 3: Typical p/n transition in a compensated multicrystalline silicon ingot.
6 Perfectly Compensated Silicon The intrinsic conductivity of ultrapure silicon is about 4.4x 10-6 S/cm. Such a low conductivity is a proof of its very high purity. However, if some impurities are introduced, conductivity should increase significantly.
When producing a multicrystalline ingot with compensated silicon (UMG-Si), in most cases, we can observe a p/n junction (p/n transition) in the ingot height (figures 3 and 4). As we have seen, the position of this transition may differ according to the initial chemical ratio [P]/[B] of the silicon feedstock (Equation 3). At the p/n transition, silicon is locally perfectly compensated (NQ=Nd). It means that, at this precise location, only one degree of freedom exists and the system can be perfectly described by one of the parameters NQ+Nd, NQ or Nd.
The resistivity at p/n junction can be measured precisely by Eddy-current using Semilab WT-2000. This equipment is preferred because of the high quantity of measurements it can take in a very small surface area and its good reproducibility. Its accuracy should however be check on a regular basis.
18.0 15.6 -rRaster0.5mm 154 Raztero.5mm .-... __ =
'.. '. .., ....'j .. , .= .. - ,,, 140 `Rartrlmm Rarter i mm = Raster 2 mm Raster 2 mm =^ \., 12.0 . 15.2 aloo = y d ~
t L 15.0 6.0 14.8 Sr e 4.0 } .,. ..
14.6 2.0 ro 00 . .. . . . . xux's*,w~mm = .:~. 14.4 : ~ -__:- . : . . . . . . ,,= . .
$ 8 8 8 8 8 8 8 8 8 $
o d d o o d o 0 o d .. o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Solidified fraction Solidified fraction Figure 4: Measurement of the resistivity of a multicrystalline ingot made with UMG-Si and an enlargement at the p/n transition to show the reproducibility of 3 different mapping with different sampling-area size.
With experimentation, we can observe that higher is the compensation at p/n junction, the lower will be the associated resistivity (and inversely, higher is conductivity). We can easily come to the conclusion that like the conductivity of a neutral electrolyte solution may be an indication of the total amount of ionic salts dissolved in de-ionized water, the conductivity at p/n junction can indicate the level of compensation at this precise location.
When producing a multicrystalline ingot with compensated silicon (UMG-Si), in most cases, we can observe a p/n junction (p/n transition) in the ingot height (figures 3 and 4). As we have seen, the position of this transition may differ according to the initial chemical ratio [P]/[B] of the silicon feedstock (Equation 3). At the p/n transition, silicon is locally perfectly compensated (NQ=Nd). It means that, at this precise location, only one degree of freedom exists and the system can be perfectly described by one of the parameters NQ+Nd, NQ or Nd.
The resistivity at p/n junction can be measured precisely by Eddy-current using Semilab WT-2000. This equipment is preferred because of the high quantity of measurements it can take in a very small surface area and its good reproducibility. Its accuracy should however be check on a regular basis.
18.0 15.6 -rRaster0.5mm 154 Raztero.5mm .-... __ =
'.. '. .., ....'j .. , .= .. - ,,, 140 `Rartrlmm Rarter i mm = Raster 2 mm Raster 2 mm =^ \., 12.0 . 15.2 aloo = y d ~
t L 15.0 6.0 14.8 Sr e 4.0 } .,. ..
14.6 2.0 ro 00 . .. . . . . xux's*,w~mm = .:~. 14.4 : ~ -__:- . : . . . . . . ,,= . .
$ 8 8 8 8 8 8 8 8 8 $
o d d o o d o 0 o d .. o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Solidified fraction Solidified fraction Figure 4: Measurement of the resistivity of a multicrystalline ingot made with UMG-Si and an enlargement at the p/n transition to show the reproducibility of 3 different mapping with different sampling-area size.
With experimentation, we can observe that higher is the compensation at p/n junction, the lower will be the associated resistivity (and inversely, higher is conductivity). We can easily come to the conclusion that like the conductivity of a neutral electrolyte solution may be an indication of the total amount of ionic salts dissolved in de-ionized water, the conductivity at p/n junction can indicate the level of compensation at this precise location.
7 Method for back-calculating initial concentration of boron and phosphorus in the feedstock For the purpose of quality control and to know the boron and phosphorus concentration in the initial silicon feedstock, a multicrystalline ingot is made out of every batch coming from production. In the crystallization furnace (model SCU400), 16 small crucibles may be grown in the same time, each being a representative sample of a production batch.
The crucibles may have a dimension such as 220x220x420 mm. The ingot height is an important parameter:
the higher it is, better is the precision to measure the solid fraction (fs) at which the p/n transition happens.
The boron or phosphorus density at p/n transition is established by the relation:
5.00 ,===o 4.50 4.00 -, E 3.50 - = , a a p 3.00 -E! 2.50 y= 82.03x RZ = 0.993 a 2.00 z 1.50 -Z
1.00 0.50 0.00 =' - _ 0.0000 0.0100 0.0200 0.0300 0.0400 0.0500 0.0600 Conductivity at p/n transition (S.cm-1) Figure 5: Calibration curve for determination of boron and phosphorus at p/n junction.
[B]j = [P]j = (82.0). 6j = 82.0 (Equation 6) P;
where:
pj: Resistivity at p/n transition (S2.cm);
6j: Conductivity at p/n transition (S/cm).
The crucibles may have a dimension such as 220x220x420 mm. The ingot height is an important parameter:
the higher it is, better is the precision to measure the solid fraction (fs) at which the p/n transition happens.
The boron or phosphorus density at p/n transition is established by the relation:
5.00 ,===o 4.50 4.00 -, E 3.50 - = , a a p 3.00 -E! 2.50 y= 82.03x RZ = 0.993 a 2.00 z 1.50 -Z
1.00 0.50 0.00 =' - _ 0.0000 0.0100 0.0200 0.0300 0.0400 0.0500 0.0600 Conductivity at p/n transition (S.cm-1) Figure 5: Calibration curve for determination of boron and phosphorus at p/n junction.
[B]j = [P]j = (82.0). 6j = 82.0 (Equation 6) P;
where:
pj: Resistivity at p/n transition (S2.cm);
6j: Conductivity at p/n transition (S/cm).
8 The initial boron and phosphorus density in the feedstock was:
[BI = [B]j k, e.(1 _ f~ke B ~
(Equation 7) [Pl ~ =
~P~' keP'0-fPP
To convert ppma to ppm,,,,, we use the equation: [Bi [B]PPmw1o - 2 60 l (Equation 8) - rPb [P] L
PPmw,a 0.907 The weak point of the method is that a p/n transition has to exhibits during crystallization. If only n-type is found, there is the possibility to add a p-type dopant (B or Ga for instance) in a known quantity to create one p/n transition (or more in the case of more than 2 doping species).
[BI = [B]j k, e.(1 _ f~ke B ~
(Equation 7) [Pl ~ =
~P~' keP'0-fPP
To convert ppma to ppm,,,,, we use the equation: [Bi [B]PPmw1o - 2 60 l (Equation 8) - rPb [P] L
PPmw,a 0.907 The weak point of the method is that a p/n transition has to exhibits during crystallization. If only n-type is found, there is the possibility to add a p-type dopant (B or Ga for instance) in a known quantity to create one p/n transition (or more in the case of more than 2 doping species).
9 Exemple 1:
The ingot was solidified in "pulse mode". What is the initial concentration of boron and phosphorus ?
6j = i= 1= 0.0597 S
pj 16.76 cm 18.0 2.50 [B]j _ [P]j _ (82.0).(0.0597) = 4.90 ppmQ 16.0 14.0 a 2.00 SfB= (0.85)= (1- 0.627)1.85-1 = 0.986 12.0 SfP =(0.50) (1- 0.627)1.50-1 = 0.819 1.50 cs 10.0 -4.90 8.0 ~B] - = 4.97 ppma 1.00 -Resistivity 0.986 6.0 4.90 -Conductivity [P] 5.98ppm 4.0 ' 0.50 0.819 2.0 '!.
~]PPmw, = 4.97 2.60 - w o.oo.oo 0.10 o. 0.00 B 1.91ppm 20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 fraction Solidified IP] = 5.98 = 6.60 ppmw PP"'w, 0.907 Results Boron Phosphorus Resistivity at p/n junction 16.76 16.76 Conductivity at p/n junction 0.0597 0.0597 fs at p/n junction 0.627 0.627 ke,Er 0.85 0.50 Scheil factor (Sf) 0.986 0.819 [EI]j 4.90 4.90 [El]o 4.97 5.98 EE l o mH, 1.91 6.60 Exemple 2:
The ingot was solidified in "stirring mode". What is the initial concentration of boron and phosphorus ?
6i = 1= = 0.0398 S
pi 25.10 cm 30.0 - 2.00 [B]j = [P]j = (82.0)= (0.0398) = 3.26 ppma 1.80 25.0 1.60 SfB = (0.70)= (1- 0.677)0.70-' = 0.983 1.40 SfP =(0.33)=(1- 0.677)0.33-1 20.0 = 0.704 E
1.20 a C ' r+
Z' 15.0 1.00 3.26 [B]0 3.32ppmQ 0.80 0.983 50.0 -Resistivity [P]O - 3.26 = 4.63 ppma -Conductivity 0.60 0.704 0.40 5.0 0.20 3.32 =1.28 mw 0.0 [B]nnmw,0 = pp 2.60 o.oo 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 _ 4.63 = 5.10 ppmx, Solidified fraction [P]Prm ~ 0.907 Results Boron Phosphorus Resistivityat p/n junction 25.10 25.10 Conductivity at p/n junction 0.0398 0.0398 fs at p/n junction 0.677 0.677 ke,E1 0.70 0.33 Scheil factor 0.983 0.704 [ECJj, 3.26 3.26 [EIJo 3.32 4.63 EE l o mw 1.28 5.10
The ingot was solidified in "pulse mode". What is the initial concentration of boron and phosphorus ?
6j = i= 1= 0.0597 S
pj 16.76 cm 18.0 2.50 [B]j _ [P]j _ (82.0).(0.0597) = 4.90 ppmQ 16.0 14.0 a 2.00 SfB= (0.85)= (1- 0.627)1.85-1 = 0.986 12.0 SfP =(0.50) (1- 0.627)1.50-1 = 0.819 1.50 cs 10.0 -4.90 8.0 ~B] - = 4.97 ppma 1.00 -Resistivity 0.986 6.0 4.90 -Conductivity [P] 5.98ppm 4.0 ' 0.50 0.819 2.0 '!.
~]PPmw, = 4.97 2.60 - w o.oo.oo 0.10 o. 0.00 B 1.91ppm 20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 fraction Solidified IP] = 5.98 = 6.60 ppmw PP"'w, 0.907 Results Boron Phosphorus Resistivity at p/n junction 16.76 16.76 Conductivity at p/n junction 0.0597 0.0597 fs at p/n junction 0.627 0.627 ke,Er 0.85 0.50 Scheil factor (Sf) 0.986 0.819 [EI]j 4.90 4.90 [El]o 4.97 5.98 EE l o mH, 1.91 6.60 Exemple 2:
The ingot was solidified in "stirring mode". What is the initial concentration of boron and phosphorus ?
6i = 1= = 0.0398 S
pi 25.10 cm 30.0 - 2.00 [B]j = [P]j = (82.0)= (0.0398) = 3.26 ppma 1.80 25.0 1.60 SfB = (0.70)= (1- 0.677)0.70-' = 0.983 1.40 SfP =(0.33)=(1- 0.677)0.33-1 20.0 = 0.704 E
1.20 a C ' r+
Z' 15.0 1.00 3.26 [B]0 3.32ppmQ 0.80 0.983 50.0 -Resistivity [P]O - 3.26 = 4.63 ppma -Conductivity 0.60 0.704 0.40 5.0 0.20 3.32 =1.28 mw 0.0 [B]nnmw,0 = pp 2.60 o.oo 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 _ 4.63 = 5.10 ppmx, Solidified fraction [P]Prm ~ 0.907 Results Boron Phosphorus Resistivityat p/n junction 25.10 25.10 Conductivity at p/n junction 0.0398 0.0398 fs at p/n junction 0.677 0.677 ke,E1 0.70 0.33 Scheil factor 0.983 0.704 [ECJj, 3.26 3.26 [EIJo 3.32 4.63 EE l o mw 1.28 5.10
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP2425454A1 (en) * | 2009-04-29 | 2012-03-07 | Calisolar, Inc. | Quality control process for umg-si feedstock |
| WO2013014342A1 (en) | 2011-07-27 | 2013-01-31 | Commissariat A L'energie Atomique Et Aux Energies Alternatives | Determining the dopant content of a compensated silicon sample |
| WO2013014341A1 (en) | 2011-07-27 | 2013-01-31 | Commissariat à l'Energie Atomique et aux Energies Alternatives | Determining the dopant content of a compensated silicon sample |
| CN103376277A (en) * | 2012-04-23 | 2013-10-30 | 中冶建筑研究总院有限公司 | Method for evaluating corrosion situations of steel reinforcement |
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2009
- 2009-07-21 CA CA 2673621 patent/CA2673621A1/en not_active Abandoned
Cited By (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP2425454A1 (en) * | 2009-04-29 | 2012-03-07 | Calisolar, Inc. | Quality control process for umg-si feedstock |
| EP2467329A1 (en) * | 2009-04-29 | 2012-06-27 | Calisolar, Inc. | Process control for umg-si material purification |
| EP2467329A4 (en) * | 2009-04-29 | 2014-06-25 | Silicor Materials Inc | Process control for umg-si material purification |
| EP2425454A4 (en) * | 2009-04-29 | 2014-07-23 | Silicor Materials Inc | Quality control process for umg-si feedstock |
| WO2013014342A1 (en) | 2011-07-27 | 2013-01-31 | Commissariat A L'energie Atomique Et Aux Energies Alternatives | Determining the dopant content of a compensated silicon sample |
| WO2013014341A1 (en) | 2011-07-27 | 2013-01-31 | Commissariat à l'Energie Atomique et aux Energies Alternatives | Determining the dopant content of a compensated silicon sample |
| FR2978548A1 (en) * | 2011-07-27 | 2013-02-01 | Commissariat Energie Atomique | DETERMINATION OF DOPING CONTENT IN A SILICON COMPENSATION SAMPLE |
| CN103376277A (en) * | 2012-04-23 | 2013-10-30 | 中冶建筑研究总院有限公司 | Method for evaluating corrosion situations of steel reinforcement |
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