Comparison of the results of measuring the carrier recombination lifetime in silicon single crystals by contactless HF and microwave μ-PCD methods was carried out. It has been shown that HF method gives a large error compared with a μ-PCD method.
When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3613

Anfimov, I.M.

Kobeleva, S.P.

Orlova, M.N.

Schemerov, I.V.

Electronic Sumy State University Institutional Repository

JOURNAL OF NANO- AND ELECTRONIC PHYSICS ЖУРНАЛ НАНО- ТА ЕЛЕКТРОННОЇ ФІЗИКИ Vol. 6 No 3, 03018(3pp) (2014) Том 6 № 3, 03018(3cc) (2014)   The article was reported at the International Conference «The Advanced Technology, Equipment and Analytical Systems for Materials», Kursk, 13-14 May, 2014 2077-6772/2014/6(3)03018(3) 03018-1  2014 Sumy State University On the Applicability of HF and -PCD Methods for Determination of Carrier Recombination Lifetime in the Non-passivated Single-crystal Silicon Samples   I.М. Anfimov, S.P. Kobeleva, I.V. Schemerov, M.N. Orlova  National University of Science and Technology “MISiS”, 4, Leninsky Pr., 119049 Moscow, Russia  (Received 19 May 2014; published online 15 July 2014)  Comparison of the results of measuring the carrier recombination lifetime in silicon single crystals by contactless HF and microwave -PCD methods was carried out. It has been shown that HF method gives a large error compared with a -PCD method.  Keywords: Single-crystal silicon, Contactless -PCD method, Carrier recombination lifetime, Photocon-ductivity decay.   PACS number: 81.05.Dz   1. INTRODUCTION  The carrier recombination lifetime (τv) is the inverse value of recombination probability of a nonequilibrium electron (electron hole) in a unit of time. Shockley-Read-Hall recombination through deep centers domi-nates in the indirect-gap semiconductors such as silicon and germanium. Such metallic contaminations as iron or copper are typical deep recombination centers in Si and Ge. In silicon with resistivity () in the range from 1 to 1000 Ohmcm τv is inversely proportional to the concen-tration of the recombination centers [1-7] and it can there-fore be considered as the most important parameter of the quality of this semiconductor material. Recombination centers may significantly influence properties of the semi-conductor devices, especially in the structures of submi-crometer and nanometer sizes. So, with change of concen-tration of iron from 1012 cm – 3 to 109 cm – 3 in the most pure silicon τv varies from a few microseconds to millisec-onds, and it is easily detected, while there are no other available methods for the determination of such concen-trations in industrial applications. One of the main methods of determining τv is the measurement of the photoconductivity decay (PCD) [5-10]. More accurate method of determining τv is the con-tact PCD method [2, 3, 10], but it had not been used for industrial applications because of high labor consump-tion. More practically applicable variant of PCD meth-od is the -PCD method owing to its nondestructive nature and high speed of measurement [8, 10, 11]. The decay curve in the -PCD method is strongly influenced by hardware factors and condition of the surface of a sample on which both volume and additional recombi-nation take place. As a result the effective recombina-tion time (τeff) which is measured depends on the ratio of three characteristic lengths — diffusion length (LD), thickness of sample (d) (the size along the direction of the surface illumination), reciprocal light absorption factor and the surface recombination velocity (S) [2-8]. The equipment for the -PCD method demands cal-ibration on referring samples (RS) with known effective time. The only -PCD method-capable RS manufac-tured in Russia was described in [12]. Samples were made of a high-resistance material with identical carri-er recombination time. The certified value of τeff for RS was received by the HF measurement – a method in which the sample was placed between facings of a ca-pacitor and signal attenuation in an RC circuit on kHz frequencies was measured. This method was chosen because there was a possibility of certifying the meas-uring system on measurement of a decay curve of standard capacities. In [12] it is noted that results of measuring RS by the -PCD equipment differ consider-ably from the certified data of a set. The purpose of this work is the analysis of the measurements of a RS package using HF and the -PCD methods and an as-sessment of application possibilities of HF as a method for RS certification.  2. SAMPLES AND EQUIPMENT FOR  MEASUREMENT  The measurements have been carried out on the GIREDMET 48-0572-260(1-9)-2009 RS set. Samples of n-type silicon single-crystal were cut from a homogene-ous ingot with the resistivity around 1.5 kOhmcm. Various effective lifetimes have been obtained by using slices with different thicknesses. The non-passivated surface has been uniformly processed (polishing) which makes it possible to consider S within the range of 5000 to 15000 cm/s. The calculations of τeff by the HF method were car-ried out by comparing the experimental curve and ex-ponential decay curve with a known parameter on an oscilloscope screen. The standard error of the meas-urements is 10 %. The measurements of τeff using the -PCD method were carried out on the automated -PCD detector APK-TAUMETR [13]. τeff were calculated using the portion of the decay signal in the range from 45-5 % of the peak sig-nal according to recommendations [14-15]. Results of the measurements are presented in the Table 1. The statisti-cal error of measurements does not exceed 8 %.  3. INTERPRETATION  For the analysis of the received results we used the equation for maximum τeff in the so-called infinite S approximation [2, 8, 11]:  I.N. ANFIMOV, S.P. KOBELEVA, I.V. SCHEMEROV, M.N. ORLOVA J. NANO- ELECTRON. PHYS. 6, 03018 (2014)   03018-2 Table 1 – RS data  Sample number 1 2 3 4 5 6 7 8 d, m 9970 3140 2500 2000 1530 1070 760 315 Certified τeff measured by the HF method, s 1590 470 300 170 106 73 45 17 τeff measured by the -PCD method, s 1020 494 350 257 177 93,7 52,9 10,7    Fig. 1 – Correlation between τeff and thickness for samples 1-4    Fig. 2 – Correlation between the diffusion coefficient and the resistivity in single-crystal n-type silicon   221 1eff vdD     (1) where D – diffusion coefficient, m2s – 1. As it was shown in [11], equation (1) provides plau-sible values for thick samples with thickness exceeding diffusion length. As we can see from data of Table 1, τv will exceed 1000 s. This value corresponds to LD of 1100 m for an n-type Si. The LD depends on the square root of τv, so a further increase of τv will lead to an insignificant LD change. Therefore it is possible to assume that d for samples 1-4 exceeds the LD value, and therefore (1) is applicable to samples 1-4. Fig. 1 illustrates a correla-tion between 1 / τeff and 1 / d2 which, in accordance with (1), allows to determine τv and Dp. A high linearity and, as a result, a smaller error is observed for the -PCD method results. For the HF method τv  3600  2000 s and Dp  19  3 cm2/s, for the -PCD method τv  1200  100 s and Dp  12  1 cm2/s. Such τv values correspond to LD of 2000 and 1190 m respectively. Fig. 2 illustrates a correlation between Dp and resistiv-ity from standard data [16]. In the samples with resis-tivity in the range 1-2 kOmcm Dp changes from 11,5 to 12,5 cm2/s, thus Dp values calculated according to the -PCD measurements correspond rather closely to the   ON THE APPLICABILITY OF HF AND -PCD METHODS… J. NANO- ELECTRON. PHYS. 6, 03018 (2014)   03018-3 Table 2 – Comparison of τeff, obtained using equation (2) and measured using the -PCD and HF method  Sample number 1 2 3 4 5 6 7 8 τeff obtained from equation (2), s 1020 494 372 270 178 96 53 10,8 Deviation from the -PCD measurements, % 0,0 0,0 6,3 4,9 0,7 2,5 0,1 1,1 Deviation from the HF measurements, % – 35 5,1 24 58 68 32 17 – 36  standard data for Si single-crystal. This supports the reliability of the values obtained by -PCD method. At the same time the calculations using the HF measure-ments differ considerably from known published data. Equation (1) is not applicable for thin samples 5-8 [11], therefore calculations of τv should be performed on a more correct equation which takes into accountthe sur-face recombination velocity:   221 1 1 1,2v eff s sd dS D         (2)  Usually (2) is not applied for calculations because S is unknown, and its measurement is a labor consuming task. For the results of this paper it is possible to de-termine S due to a large database including thin sam-ples 5-8. Analysis of data obtained by the -PCD meth-od showed that S is equal to 6700 cm/s  17 %.  S value for the HF method is not possible to deter-mine using (2) because at the values of τv more than 1000 s τs asymptotically tends to the τeff which would be less than the d2 / 2D value for samples 5-7. We used S and τv values obtained to calculate the τeff using equation (2) for all samples. Results of calcu-lations and their comparison with the -PCD meas-urements data are given in Table 2. The calculations in Table 2 shows that the -PCD measurement results is more correct than the results of τeff measurements by HF method. The samples for this measurements is comparatively thick that allows to determine a correct volume lifetime. It is known that more accurate results are obtained by contact measurements of photoconductivity decay based on the standard [14]. So for RS manufacturing it is necessary to use this method since the results of the contactless methods HF and -PCD differ dramatically.  4. CONCLUSIONS  The analysis of the measurement results of RS shows that the HF method can give a significant error as compared to the results of the -PCD method for thick samples (sample thickness more than LD) and therefore cannot be used for the RS certification. For correct determination of volume lifetime and effective lifetime of referring samples contact measurements are necessary.  ACKNOWLEDGMENTS  The investigations were carried out on the equip-ment of the Common-Use Scientific Center ―Materials Science and Metallurgy‖ of the NUST ―MISIS‖ and with financial support from the Ministry of Educa-tion and Science of the Russian Federation in the framework of Increase Competitiveness Program of MISIS.   REFERENCES  1. D.K. Schroder, Semiconductor Material and Device Characterization, 2-nd Ed. (John Wileyand Sons: NewYork: 1998) 2. W.R. Runyan, T.J. Shaffner, Semiconductor Measurements & Instrumentation (McGraw-Hill: New York: 1997). 3. S.P. Kobeleva, Zavodskaya Laboratroiya. Diagnostika Materialov 73, No 1, 60 (2007). 4. E. Gaubas, P. Clauws, et al., Physica B 401-402, 222 (2007). 5. V.K. Khanna, Prog. Quantum Electron. 29, 59 (2005). 6. B. Berger, N. Schuler, S. Anger, B. Grundig-Wendrock, J.R. Niklas, K. Dornich, Contactless electrical defect characterization in semiconductors by microwave detected photo induced current transient spectroscopy(MD–PICTS) and microwave detected photoconductivity (MDP), 1 (BIAMS: Halle: 2010). 7. S. Dubois, O. Palaisa, P.J. Ribeyron, et al., J. Appl. Phys. 102, 083525 (2007). 8. T. Pavelka, Problems and Possibilities of comparing different Lifetime measuring instruments and techniques, 206 (Ed. by D.C. Gupta, W.M. Hughes, F.R. Bacher), (Recombination Lifetime Measurements in Silicon: ASTM International: 1998). 9. N. Schuler, S. Anger, K. Dornich, et al., Sol. Energ. Mat. Sol. C. 98, 245 (2012). 10. S.P. Kobeleva, Comments to Standards No 8, 15 (2013). 11. I.M. Anfimov, S.P. Kobeleva, I.V. Schemerov, Zavodskaya Laboratroiya. Diagnostika Materialov 80 No 1, 41 (2014). 12. S.P. Kobeleva, P.B. Lagov, I.V. Schemerov, Standard Samples No 3, 10 (2013). 13. N.N. Goryunov, S.P. Kobeleva, I.A. Kalinin, Zavodskaya Laboratoriya. Diagnostika Materialov 70 No 6, 23 (2004). 14. SEMI MF28. “Test Methods for the Minority-Carrier Lifetime in Bulk Germanium and Silicon by Measurement of Photoconductivity Decay”. 15. SEMI MF1535. «Test method for carrier recombination lifetime in silicon wafers by non-contact measurement of photoconductivity decay by -PCD reflectance». 16. SEMI MF723. «Practice for conversion between resistivity and dopant or carrier density for boron-doped, phosphorus-doped, and arsenic-doped silicon».  

On the Applicability of HF and μ-PCD Methods for Determination of Carrier Recombination Lifetime in the Non-passivated Single-crystal Silicon Samples

SocioEconomic Challenges Journal (Sumy State University)

JOURNAL OF NANO- AND ELECTRONIC PHYSICS ЖУРНАЛ НАНО- ТА ЕЛЕКТРОННОЇ ФІЗИКИ 
Vol. 6 No 3, 03018(3pp) (2014) Том 6 № 3, 03018(3cc) (2014) 
 
 
The article was reported at the International Conference «The Advanced Technology, Equipment and Analytical Systems for Materials», Kursk, 13-14 May, 2014 
2077-6772/2014/6(3)03018(3) 03018-1  2014 Sumy State University 
On the Applicability of HF and -PCD Methods for Determination of Carrier Recombination 
Lifetime in the Non-passivated Single-crystal Silicon Samples  
 
I.М. Anfimov, S.P. Kobeleva, I.V. Schemerov, M.N. Orlova 
 
National University of Science and Technology “MISiS”, 4, Leninsky Pr., 119049 Moscow, Russia 
 
(Received 19 May 2014; published online 15 July 2014) 
 
Comparison of the results of measuring the carrier recombination lifetime in silicon single crystals by 
contactless HF and microwave -PCD methods was carried out. It has been shown that HF method gives a 
large error compared with a -PCD method. 
 
Keywords: Single-crystal silicon, Contactless -PCD method, Carrier recombination lifetime, Photocon-
ductivity decay. 
 
 PACS number: 81.05.Dz 
 
 
1. INTRODUCTION 
 
The carrier recombination lifetime (τv) is the inverse 
value of recombination probability of a nonequilibrium 
electron (electron hole) in a unit of time. Shockley-
Read-Hall recombination through deep centers domi-
nates in the indirect-gap semiconductors such as silicon 
and germanium. Such metallic contaminations as iron or 
copper are typical deep recombination centers in Si and 
Ge. In silicon with resistivity () in the range from 1 to 
1000 Ohmcm τv is inversely proportional to the concen-
tration of the recombination centers [1-7] and it can there-
fore be considered as the most important parameter of the 
quality of this semiconductor material. Recombination 
centers may significantly influence properties of the semi-
conductor devices, especially in the structures of submi-
crometer and nanometer sizes. So, with change of concen-
tration of iron from 1012 cm – 3 to 109 cm – 3 in the most 
pure silicon τv varies from a few microseconds to millisec-
onds, and it is easily detected, while there are no other 
available methods for the determination of such concen-
trations in industrial applications. 
One of the main methods of determining τv is the 
measurement of the photoconductivity decay (PCD) [5-
10]. More accurate method of determining τv is the con-
tact PCD method [2, 3, 10], but it had not been used for 
industrial applications because of high labor consump-
tion. More practically applicable variant of PCD meth-
od is the -PCD method owing to its nondestructive 
nature and high speed of measurement [8, 10, 11]. The 
decay curve in the -PCD method is strongly influenced 
by hardware factors and condition of the surface of a 
sample on which both volume and additional recombi-
nation take place. As a result the effective recombina-
tion time (τeff) which is measured depends on the ratio 
of three characteristic lengths — diffusion length (LD), 
thickness of sample (d) (the size along the direction of 
the surface illumination), reciprocal light absorption 
factor and the surface recombination velocity (S) [2-8]. 
The equipment for the -PCD method demands cal-
ibration on referring samples (RS) with known effective 
time. The only -PCD method-capable RS manufac-
tured in Russia was described in [12]. Samples were 
made of a high-resistance material with identical carri-
er recombination time. The certified value of τeff for RS 
was received by the HF measurement – a method in 
which the sample was placed between facings of a ca-
pacitor and signal attenuation in an RC circuit on kHz 
frequencies was measured. This method was chosen 
because there was a possibility of certifying the meas-
uring system on measurement of a decay curve of 
standard capacities. In [12] it is noted that results of 
measuring RS by the -PCD equipment differ consider-
ably from the certified data of a set. The purpose of this 
work is the analysis of the measurements of a RS 
package using HF and the -PCD methods and an as-
sessment of application possibilities of HF as a method 
for RS certification. 
 
2. SAMPLES AND EQUIPMENT FOR  
MEASUREMENT 
 
The measurements have been carried out on the 
GIREDMET 48-0572-260(1-9)-2009 RS set. Samples of 
n-type silicon single-crystal were cut from a homogene-
ous ingot with the resistivity around 1.5 kOhmcm. 
Various effective lifetimes have been obtained by using 
slices with different thicknesses. The non-passivated 
surface has been uniformly processed (polishing) which 
makes it possible to consider S within the range of 5000 
to 15000 cm/s. 
The calculations of τeff by the HF method were car-
ried out by comparing the experimental curve and ex-
ponential decay curve with a known parameter on an 
oscilloscope screen. The standard error of the meas-
urements is 10 %. 
The measurements of τeff using the -PCD method 
were carried out on the automated -PCD detector APK-
TAUMETR [13]. τeff were calculated using the portion of 
the decay signal in the range from 45-5 % of the peak sig-
nal according to recommendations [14-15]. Results of the 
measurements are presented in the Table 1. The statisti-
cal error of measurements does not exceed 8 %. 
 
3. INTERPRETATION 
 
For the analysis of the received results we used the 
equation for maximum τeff in the so-called infinite S 
approximation [2, 8, 11]: 
 I.N. ANFIMOV, S.P. KOBELEVA, I.V. SCHEMEROV, M.N. ORLOVA J. NANO- ELECTRON. PHYS. 6, 03018 (2014) 
 
 
03018-2 
Table 1 – RS data 
 
Sample number 1 2 3 4 5 6 7 8 
d, m 9970 3140 2500 2000 1530 1070 760 315 
Certified τeff measured by the HF 
method, s 
1590 470 300 170 106 73 45 17 
τeff measured by the -PCD method, s 1020 494 350 257 177 93,7 52,9 10,7 
 
 
 
Fig. 1 – Correlation between τeff and thickness for samples 1-4 
 
 
 
Fig. 2 – Correlation between the diffusion coefficient and the resistivity in single-crystal n-type silicon 
 
 
2
2
1 1
eff v
d
D  
   (1) 
where D – diffusion coefficient, m2s – 1. 
As it was shown in [11], equation (1) provides plau-
sible values for thick samples with thickness exceeding 
diffusion length. 
As we can see from data of Table 1, τv will exceed 
1000 s. This value corresponds to LD of 1100 m for an 
n-type Si. The LD depends on the square root of τv, so a 
further increase of τv will lead to an insignificant LD 
change. Therefore it is possible to assume that d for 
samples 1-4 exceeds the LD value, and therefore (1) is 
applicable to samples 1-4. Fig. 1 illustrates a correla-
tion between 1 / τeff and 1 / d2 which, in accordance with 
(1), allows to determine τv and Dp. A high linearity and, 
as a result, a smaller error is observed for the -PCD 
method results. For the HF method τv  3600  2000 s 
and Dp  19  3 cm2/s, for the -PCD method 
τv  1200  100 s and Dp  12  1 cm2/s. Such τv values 
correspond to LD of 2000 and 1190 m respectively. 
Fig. 2 illustrates a correlation between Dp and resistiv-
ity from standard data [16]. In the samples with resis-
tivity in the range 1-2 kOmcm Dp changes from 11,5 to 
12,5 cm2/s, thus Dp values calculated according to the 
-PCD measurements correspond rather closely to the  
 ON THE APPLICABILITY OF HF AND -PCD METHODS… J. NANO- ELECTRON. PHYS. 6, 03018 (2014) 
 
 
03018-3 
Table 2 – Comparison of τeff, obtained using equation (2) and measured using the -PCD and HF method 
 
Sample number 1 2 3 4 5 6 7 8 
τeff obtained from equation (2), s 1020 494 372 270 178 96 53 10,8 
Deviation from the -PCD measurements, % 0,0 0,0 6,3 4,9 0,7 2,5 0,1 1,1 
Deviation from the HF measurements, % – 35 5,1 24 58 68 32 17 – 36 
 
standard data for Si single-crystal. This supports the 
reliability of the values obtained by -PCD method. At 
the same time the calculations using the HF measure-
ments differ considerably from known published data. 
Equation (1) is not applicable for thin samples 5-8 [11], 
therefore calculations of τv should be performed on a 
more correct equation which takes into accountthe sur-
face recombination velocity: 
 
 
2
2
1 1 1 1
,
2v eff s s
d d
S D    
     (2) 
 
Usually (2) is not applied for calculations because S 
is unknown, and its measurement is a labor consuming 
task. For the results of this paper it is possible to de-
termine S due to a large database including thin sam-
ples 5-8. Analysis of data obtained by the -PCD meth-
od showed that S is equal to 6700 cm/s  17 %.  
S value for the HF method is not possible to deter-
mine using (2) because at the values of τv more than 
1000 s τs asymptotically tends to the τeff which would 
be less than the d2 / 2D value for samples 5-7. 
We used S and τv values obtained to calculate the 
τeff using equation (2) for all samples. Results of calcu-
lations and their comparison with the -PCD meas-
urements data are given in Table 2. 
The calculations in Table 2 shows that the -PCD 
measurement results is more correct than the results of 
τeff measurements by HF method. The samples for this 
measurements is comparatively thick that allows to 
determine a correct volume lifetime. 
It is known that more accurate results are obtained 
by contact measurements of photoconductivity decay 
based on the standard [14]. So for RS manufacturing it 
is necessary to use this method since the results of the 
contactless methods HF and -PCD differ dramatically. 
 
4. CONCLUSIONS 
 
The analysis of the measurement results of RS 
shows that the HF method can give a significant error 
as compared to the results of the -PCD method for 
thick samples (sample thickness more than LD) and 
therefore cannot be used for the RS certification. For 
correct determination of volume lifetime and effective 
lifetime of referring samples contact measurements are 
necessary. 
 
ACKNOWLEDGMENTS 
 
The investigations were carried out on the equip-
ment of the Common-Use Scientific Center ―Materials 
Science and Metallurgy‖ of the NUST ―MISIS‖ 
and with financial support from the Ministry of Educa-
tion and Science of the Russian Federation in the 
framework of Increase Competitiveness Program of 
MISIS. 
 
 
REFERENCES 
 
1. D.K. Schroder, Semiconductor Material and Device 
Characterization, 2-nd Ed. (John Wileyand Sons: 
NewYork: 1998) 
2. W.R. Runyan, T.J. Shaffner, Semiconductor Measurements 
& Instrumentation (McGraw-Hill: New York: 1997). 
3. S.P. Kobeleva, Zavodskaya Laboratroiya. Diagnostika 
Materialov 73, No 1, 60 (2007). 
4. E. Gaubas, P. Clauws, et al., Physica B 401-402, 222 
(2007). 
5. V.K. Khanna, Prog. Quantum Electron. 29, 59 (2005). 
6. B. Berger, N. Schuler, S. Anger, B. Grundig-Wendrock, 
J.R. Niklas, K. Dornich, Contactless electrical defect 
characterization in semiconductors by microwave detected 
photo induced current transient spectroscopy(MD–PICTS) 
and microwave detected photoconductivity (MDP), 1 
(BIAMS: Halle: 2010). 
7. S. Dubois, O. Palaisa, P.J. Ribeyron, et al., J. Appl. Phys. 
102, 083525 (2007). 
8. T. Pavelka, Problems and Possibilities of comparing 
different Lifetime measuring instruments and techniques, 
206 (Ed. by D.C. Gupta, W.M. Hughes, F.R. Bacher), 
(Recombination Lifetime Measurements in Silicon: ASTM 
International: 1998). 
9. N. Schuler, S. Anger, K. Dornich, et al., Sol. Energ. Mat. 
Sol. C. 98, 245 (2012). 
10. S.P. Kobeleva, Comments to Standards No 8, 15 (2013). 
11. I.M. Anfimov, S.P. Kobeleva, I.V. Schemerov, Zavodskaya 
Laboratroiya. Diagnostika Materialov 80 No 1, 41 (2014). 
12. S.P. Kobeleva, P.B. Lagov, I.V. Schemerov, Standard 
Samples No 3, 10 (2013). 
13. N.N. Goryunov, S.P. Kobeleva, I.A. Kalinin, Zavodskaya 
Laboratoriya. Diagnostika Materialov 70 No 6, 23 (2004). 
14. SEMI MF28. “Test Methods for the Minority-Carrier 
Lifetime in Bulk Germanium and Silicon by Measurement 
of Photoconductivity Decay”. 
15. SEMI MF1535. «Test method for carrier recombination 
lifetime in silicon wafers by non-contact measurement of 
photoconductivity decay by -PCD reflectance». 
16. SEMI MF723. «Practice for conversion between resistivity 
and dopant or carrier density for boron-doped, phosphorus-
doped, and arsenic-doped silicon». 
 


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On the Applicability of HF and μ-PCD Methods for Determination of Carrier Recombination Lifetime in the Non-passivated Single-crystal Silicon Samples

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SocioEconomic Challenges Journal (Sumy State University)