Results of measurement of resistivity of mesoporous silicon formed on n-type substrates in a wide temperature range are presented. Measurements show that at low temperatures there is a growth of resistance of four orders of magnitude compared to that at
room temperature which occurs in a relatively narrow temperature range.
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Attanasio, Carmine

Bondarenko, V.P.

Chubenko, E.B.

Cirillo, Carla

Kholostov, K.I.

Klyshko, A.A.

Prischepa, S.I.

Redko, S.V.

Trezza, Michela

SocioEconomic Challenges Journal (Sumy State University)

320                  Nanomaterials: Applications and Properties (NAP-2011). Vol. 1, Part II             
 
TEMPERATURE DEPENDENCE of RESISTIVITY OF PO-
ROUS SILICON FORMED ON N+ SUBSTRATES 
Sergey V. Redko1*, Eugene B. Chubenko1, Alexey A. Klyshko1,  
Konstantin I. Kholostov1, Vitaly P. Bondarenko1, Sergey L. Prischepa1, 
 Michela Trezza2, Carla Cirillo2, Carmine Attanasio2 
 
1 Belarussian State University of Informatics and Radioelectronics, P. Brovka str. 6, Minsk, 
220013, Belarus 
2 CNR-SPIN and Dipartimento di Fisica “E.R. Caianiello”, Università degli Studi di Salerno, 
Fisciano (Sa), I-84084, Italy 
 
ABSTRACT 
Results of measurement of resistivity of mesoporous silicon formed on n-type sub-
strates in a wide temperature range are presented. Measurements show that at low tem-
peratures there is a growth of resistance of four orders of magnitude compared to that at 
room temperature which occurs in a relatively narrow temperature range.  
 
Key words: porous silicon, resistivity, space charge region 
 
INTRODUCTION 
Electrical properties of porous silicon (PS) are of great importance for en-
gineering of PS-based electronic devices. It is well known that the conductance 
mechanisms of PS differ from that of bulk silicon [1]. Especially it concerns 
temperature dependence of resistivity. But the exact mechanism of the electron-
ic transport in PS layers isn’t ultimately understood up till now. Different ap-
proaches were developed during last years. They are based on the band gap 
modulation via quantum confinement effects in silicon crystallites forming 
porous silicon skeleton, on the hopping at the Fermi level mechanism, on the 
thermionic emission above energy barriers and on the space charge models [2 – 
5]. None of them explains satisfactory the resistivity versus temperature de-
pendencies. 
In  this  work,  in  order  to  clarify  the  conductance  mechanisms  of  PS,  we  
perform the investigation of mesoporous silicon resistivity behavior in a wide 
temperature range: from 300 K down to 10 K. 
SAMPLES CHARACTERIZATION AND MEASURING TECHNIQUE 
PS samples used for the measurements were prepared by electrochemical 
anodization technique. Antimony-doped 0.01 Ohm·cm wafers with (111) orien-
tation and standard thickness of 450 Pm were used. PS layers were formed in 
                                               
* e-mail: ml.redkov@gmail.com, tel: (+375)172938843 
Nanomaterials: Applications and Properties (NAP-2011). Vol. 1, Part II              321 
 
HF:C3H7OH:H2O = 1:3:1 solution at current density of 65 mA/cm2 using poly-
tetrafluorethylene cell. The resulting PS layers had total thickness 10 ȝm and 
porosity 55%. Vertical pores had diameter in the range 20 nm – 30 nm. Such 
material can be classified as mesoporous.  
In order to carry out the resistivity measurements samples were cut in 
pieces 20 mm × 10 mm. The resistivity measurements were performed with 
four probe method using current-in-plane configuration. Electrical contacts to 
PS layer were made by indium attached directly to PS. In this case the structure 
under  study can  be  treated  as  consisting  of  two layers:  highly  doped N+ sub-
strate and PS itself. The transport measurements were performed in a 4He cryo-
stat in a temperature interval 300 K – 10 K. 
The same measurements were carried out for silicon sample without po-
rous layers in order to clarify their role in the conductance mechanism. 
RESULTS AND DISCUSSION 
The typical curves, representing results of measurements of resistance 
versus temperature for both Si and PS are shown in Fig. 1.  
Two distinctive regions 
can be found in Fig. 1 for 
PS. In the region I 
(10 K < T < 170 K) the resis-
tivity value is approximately 
4 orders of magnitude higher 
that in the region II 
(200 K < T < 300 K), for 
which resistivities of Si and 
PS  are  equal.  Moreover  it  
drops in the rather narrow 
temperature range, 
170 K < T < 200 K. 
We believe that such 
giant increase of resistivity 
of the investigated structure below 200 K is caused mainly by change of the 
space charge region width in PS. 
Indeed, assuming that the Fermi level at the PS surface is fixed at about 
the middle point of the band gap we can calculate the free space charge region 
(SCR) width using the following equation [6] 
 
nq
Vͯͯ2W bir0d 
 ,   (1) 
where Wd is the free space charge region width; İ0 is the dielectric 
constant; İ r is the permittivity of Si; Vbi is the surface potential value; q is the 
 
Fig. 1 – The measured resistance versus tempera-
ture behavior of Si and PS 
322                  Nanomaterials: Applications and Properties (NAP-2011). Vol. 1, Part II             
 
charge of electron, n is the charge carrier concentration. 
The results of calculations of Wd values for three different temperatures 
related to two different temperature regions are presented in a Table 1. Here we 
reasonably assume Vbi = 0.5 eV. 
 
Table 1 – Key PS parameters at different temperatures 
In our estimations the 
variation of the effective 
impurity concentration in 
porous silicon compared to 
that in substrate is neglect-
ed. As we see the SCR width values at room temperature are quite close to the 
pores skeleton dimensions (20 nm – 30 nm). We have to note, that the electron 
mean free path change with temperature is less with respect to the change of the 
SCR width. When temperature lowers, the SCR area in the pores increases, thus 
leading to reduction of the part of the skeleton where the charge carriers have 
less scattering, see Fig. 2. 
The above mentioned fact will have a significant influence on the resis-
tivity of PS and thus the overall structure resistivity, up to the moment of over-
lapping of space regions of neighboring pores. As we suppose it is exactly the 
space charge region overlapping that causes such significant increase of the 
resistivity of the measured structure with lowering the temperature. 
 
 
Fig. 2 – Sketch of the PS representing two pores with SCR and undepleted region at two 
different temperatures. (a) T > 200K, (b) T < 170K. D is the pore inner diameter, d is 
dimension of the undepleted region 
 
CONCLUSIONS 
In the present work the lateral resistivity of mesoporous silicon on the n+ 
substrate was investigated in the wide temperature range. It was found that the 
resistivity value changes by four orders of magnitude while the temperature is 
lowered from 300 K down to 10 K. The most significant change takes place in 
the temperature range 200 K – 170 Ʉ. We believe that such giant growth of 
T, K n, cm-3[6] Wd, nm 
300 3.3·1018 14 
200 2.82·1018 15 
100 1.95·1018 18 
Nanomaterials: Applications and Properties (NAP-2011). Vol. 1, Part II              323 
 
resistivity is related to the overlapping of the SCR of neighboring pores while 
lowering the temperature. Estimations of SCR width at different temperatures 
strongly support this hypothesis. 
 
Acknowledgements 
This work was partially supported by Belarus Government Research Pro-
grams “Crystalline and molecular structures”, project 1.13 and “Functional and 
engineering material, nanomaterials”, project 2.4.12. 
REFERENCES 
[1] S.P. Zimin, Semiconductors, 2000, 34, P.353. 
[2] M. Ben-Chorin, F. Möller, F. Koch, Phys. Rev. B, 1994, 49, P. 2981.  
[3] J. Kocka, A. Fejfar, I. Pelant, Phys. Status Solidi B, 1995, 190, P. 27. 
[4] J. Kocka, A. Fejfar, I. Pelant, J. Non-Cryst. Solids, 1996, 198-200, P. 857. 
[5] Y. Lubianiker, I. Balberg, Phys. Rev. Lett, 1997, 78, P. 2433. 
[6] Physics of Semiconductor Devices (C.M. Sze), John Wiley and Sons, New York, 
1969. 
 
  


Temperature dependence of resistivity of porous silicon formed on N-substrates

Electronic Sumy State University Institutional Repository

320                  Nanomaterials: Applications and Properties (NAP-2011). Vol. 1, Part II              TEMPERATURE DEPENDENCE of RESISTIVITY OF PO-ROUS SILICON FORMED ON N+ SUBSTRATES Sergey V. Redko1*, Eugene B. Chubenko1, Alexey A. Klyshko1,  Konstantin I. Kholostov1, Vitaly P. Bondarenko1, Sergey L. Prischepa1,  Michela Trezza2, Carla Cirillo2, Carmine Attanasio2  1 Belarussian State University of Informatics and Radioelectronics, P. Brovka str. 6, Minsk, 220013, Belarus 2 CNR-SPIN and Dipartimento di Fisica “E.R. Caianiello”, Università degli Studi di Salerno, Fisciano (Sa), I-84084, Italy  ABSTRACT Results of measurement of resistivity of mesoporous silicon formed on n-type sub-strates in a wide temperature range are presented. Measurements show that at low tem-peratures there is a growth of resistance of four orders of magnitude compared to that at room temperature which occurs in a relatively narrow temperature range.   Key words: porous silicon, resistivity, space charge region  INTRODUCTION Electrical properties of porous silicon (PS) are of great importance for en-gineering of PS-based electronic devices. It is well known that the conductance mechanisms of PS differ from that of bulk silicon [1]. Especially it concerns temperature dependence of resistivity. But the exact mechanism of the electron-ic transport in PS layers isn’t ultimately understood up till now. Different ap-proaches were developed during last years. They are based on the band gap modulation via quantum confinement effects in silicon crystallites forming porous silicon skeleton, on the hopping at the Fermi level mechanism, on the thermionic emission above energy barriers and on the space charge models [2 – 5]. None of them explains satisfactory the resistivity versus temperature de-pendencies. In  this  work,  in  order  to  clarify  the  conductance  mechanisms  of  PS,  we  perform the investigation of mesoporous silicon resistivity behavior in a wide temperature range: from 300 K down to 10 K. SAMPLES CHARACTERIZATION AND MEASURING TECHNIQUE PS samples used for the measurements were prepared by electrochemical anodization technique. Antimony-doped 0.01 Ohm·cm wafers with (111) orien-tation and standard thickness of 450 Pm were used. PS layers were formed in                                                * e-mail: ml.redkov@gmail.com, tel: (+375)172938843 Nanomaterials: Applications and Properties (NAP-2011). Vol. 1, Part II              321  HF:C3H7OH:H2O = 1:3:1 solution at current density of 65 mA/cm2 using poly-tetrafluorethylene cell. The resulting PS layers had total thickness 10 ȝm and porosity 55%. Vertical pores had diameter in the range 20 nm – 30 nm. Such material can be classified as mesoporous.  In order to carry out the resistivity measurements samples were cut in pieces 20 mm × 10 mm. The resistivity measurements were performed with four probe method using current-in-plane configuration. Electrical contacts to PS layer were made by indium attached directly to PS. In this case the structure under  study can  be  treated  as  consisting  of  two layers:  highly  doped N+ sub-strate and PS itself. The transport measurements were performed in a 4He cryo-stat in a temperature interval 300 K – 10 K. The same measurements were carried out for silicon sample without po-rous layers in order to clarify their role in the conductance mechanism. RESULTS AND DISCUSSION The typical curves, representing results of measurements of resistance versus temperature for both Si and PS are shown in Fig. 1.  Two distinctive regions can be found in Fig. 1 for PS. In the region I (10 K < T < 170 K) the resis-tivity value is approximately 4 orders of magnitude higher that in the region II (200 K < T < 300 K), for which resistivities of Si and PS  are  equal.  Moreover  it  drops in the rather narrow temperature range, 170 K < T < 200 K. We believe that such giant increase of resistivity of the investigated structure below 200 K is caused mainly by change of the space charge region width in PS. Indeed, assuming that the Fermi level at the PS surface is fixed at about the middle point of the band gap we can calculate the free space charge region (SCR) width using the following equation [6]  nqVͯͯ2W bir0d  ,   (1) where Wd is the free space charge region width; İ0 is the dielectric constant; İ r is the permittivity of Si; Vbi is the surface potential value; q is the  Fig. 1 – The measured resistance versus tempera-ture behavior of Si and PS 322                  Nanomaterials: Applications and Properties (NAP-2011). Vol. 1, Part II              charge of electron, n is the charge carrier concentration. The results of calculations of Wd values for three different temperatures related to two different temperature regions are presented in a Table 1. Here we reasonably assume Vbi = 0.5 eV.  Table 1 – Key PS parameters at different temperatures In our estimations the variation of the effective impurity concentration in porous silicon compared to that in substrate is neglect-ed. As we see the SCR width values at room temperature are quite close to the pores skeleton dimensions (20 nm – 30 nm). We have to note, that the electron mean free path change with temperature is less with respect to the change of the SCR width. When temperature lowers, the SCR area in the pores increases, thus leading to reduction of the part of the skeleton where the charge carriers have less scattering, see Fig. 2. The above mentioned fact will have a significant influence on the resis-tivity of PS and thus the overall structure resistivity, up to the moment of over-lapping of space regions of neighboring pores. As we suppose it is exactly the space charge region overlapping that causes such significant increase of the resistivity of the measured structure with lowering the temperature.   Fig. 2 – Sketch of the PS representing two pores with SCR and undepleted region at two different temperatures. (a) T > 200K, (b) T < 170K. D is the pore inner diameter, d is dimension of the undepleted region  CONCLUSIONS In the present work the lateral resistivity of mesoporous silicon on the n+ substrate was investigated in the wide temperature range. It was found that the resistivity value changes by four orders of magnitude while the temperature is lowered from 300 K down to 10 K. The most significant change takes place in the temperature range 200 K – 170 Ʉ. We believe that such giant growth of T, K n, cm-3[6] Wd, nm 300 3.3·1018 14 200 2.82·1018 15 100 1.95·1018 18 Nanomaterials: Applications and Properties (NAP-2011). Vol. 1, Part II              323  resistivity is related to the overlapping of the SCR of neighboring pores while lowering the temperature. Estimations of SCR width at different temperatures strongly support this hypothesis.  Acknowledgements This work was partially supported by Belarus Government Research Pro-grams “Crystalline and molecular structures”, project 1.13 and “Functional and engineering material, nanomaterials”, project 2.4.12. REFERENCES [1] S.P. Zimin, Semiconductors, 2000, 34, P.353. [2] M. Ben-Chorin, F. Möller, F. Koch, Phys. Rev. B, 1994, 49, P. 2981.  [3] J. Kocka, A. Fejfar, I. Pelant, Phys. Status Solidi B, 1995, 190, P. 27. [4] J. Kocka, A. Fejfar, I. Pelant, J. Non-Cryst. Solids, 1996, 198-200, P. 857. [5] Y. Lubianiker, I. Balberg, Phys. Rev. Lett, 1997, 78, P. 2433. [6] Physics of Semiconductor Devices (C.M. Sze), John Wiley and Sons, New York, 1969.    

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Temperature dependence of resistivity of porous silicon formed on N-substrates

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