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There’s no place like Ohm: conduction in oxide thin films
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 J. Phys.: Condens. Matter 26 142202 (http://iopscience.iop.org/0953-8984/26/14/142202) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 193.255.248.150 This content was downloaded on 23/12/2014 at 08:59
Please note that terms and conditions apply.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 142202 (4pp)
doi:10.1088/0953-8984/26/14/142202
Fast Track Communciations
There’s no place like Ohm: conduction in oxide thin films J F Scott Cavendish Laboratory, Department of Physics, Cambridge University, Cambridge CB3 0HE, UK Received 4 February 2014, revised 18 February 2014 Accepted for publication 20 February 2014 Published 20 March 2014 Abstract
A pedagogical essay is given that alerts researchers to the errors inherent in assigning linear I(V) current–voltage dependences to Ohmic conduction. Such a linear I(V) is necessary but not sufficient, since other mechanisms, including Simmons’ modification of the basic Schottky emission theory, also give linear I(V) at small applied voltages. Discrimination among Ohmic, Schottky, space-charge limited, and other models requires accurate thickness dependence I(d) data, where for Ohmic conduction I = a/d, whereas for interface-limited mechanisms such as Simmons/Schottky, I is nearly independent of d. Keywords: ferroelectrics, thin films, dielectrics, conduction (Some figures may appear in colour only in the online journal)
2. Schottky emission
Recently the present author had some success in alerting readers that apparent P(V) polarization hysteresis curves are not unambiguous proof of ferroelectricity, but can result from electret-like effects and charge injection in a variety of materials, including ordinary banana skins [1]. Although such whimsical essays do not appeal to all tastes, they seem successful in alerting newcomers to special pitfalls in thin-film research and attract more attention than more staid articles [2]. A more strait-laced essay that has proved even more successful is that of Catalan [3] on artifacts due to magnetoresistance that can look like magnetoelectricity (a glaring misinterpretation is given in [4]). In the same vein, the present note is to remind researchers on thin-film oxides that a linear current–voltage I(V) response at low V is not a proof of Ohmic conduction.
Schottky discovered that the Richardson emission of electrons in solids could be strongly enhanced by applying a voltage [5, 6]. Schottky conduction is limited by the interface between the sample and the metallic contacts on each end. In his original work [5] Schottky considered several different situations: the two most important limiting cases are those in which the electron (or hole) mean free path L is >> the Schottky barrier width w, and conversely, that in which L J.
J = Neμ[ε / (ekT *AB )] T */ T d −[2(T */ T )+1]V (T */ T ) +1 . (5) The practical problem in modeling data is that equations (4) and (5) together entail too many fitting parameters. In a typical experiment [24] on SrBi2Ta2O9 on Pt, T* = 315 K at V = 3.0–4.0 V when T = 293 K. For clarity, space-chargelimited current data should exhibit a very abrupt change from linear I(V) to quadratic, as demonstrated for example in figure 1 for PZT at about E = 60 kV cm-1 [18]. Zafar et al initially identified Simmons’ mechanism in ferroelectric thin films [25]; and more recently Martinez et al [26] and Pavunny et al [27] have fitted I(V) data in various oxide thin films and have shown that their conduction is indeed not Simmons form, with the key evidence being reasonable fitted values of dielectric constant and Richardson coefficients. (In [25] it was shown that the conduction is predominantly space-charge-limited at low fields < 100 kV cm-1 but Schottky-limited at higher fields.) This is a satisfactory procedure when processing conditions do not readily permit varying film thickness d. Good examples of Simmonsmodified Schottky currents are shown [28] in figure 4. Here in figure 4(a) we see that the temperature dependence from 77 to 293 K shows that conduction is Schottky-limited, but the expected exponential dependence on V1/2 does not set in until V = 0.5 V for reverse bias and about 1.0 V for forward bias. In figure 4(b) we see that above 4.0 V the behavior is Simmonslike Schottky emission dominated. In figure 4(c) we also see [29] Simmons behavior above 4.0 V following a negative resistance dip; such a dip in a 200 nm thick BST film with a dielectric constant of about 1000 and a 10 nm depletion width requires an oxygen vacancy concentration of >3 × 1018 cm-3;
5. Conclusions Understanding the conduction mechanisms for leakage currents in oxide thin films is very important for commercializing devices. Linear I(V) current–voltage relationships at low voltage do not in themselves imply Ohmic conduction. Other mechanisms are compatible with that, especially the modification of Schottky emission detailed by Simmons for the common situation in which the electron mean free path L is less than the Schottky barrier width w. We end these comparisons with a final warning from Sze [34]: ‘For large space charge effect, the tunneling characteristic is found to be very similar to the Schottky-type emission’. 3
J. Phys.: Condens. Matter 26 (2014) 142202
References
[19] Pintilie L, Vrejoiu I, Hesse D, LeRhun G and Alexe M 2007 Phys. Rev. B 75 104103 [20] Dey S K and Zuleeg R 1990 Ferroelectrics 112 309 [21] Alexe M, Harnagea C, Hesse D and Goesele U 1999 Appl. Phys. Lett. 75 1793 [22] Rose A 1955 Phys. Rev. 97 1538 [23] Rose A 1978 Concepts in Photoconductivity and Allied Problems (New York: Krieger) [24] Watanabe K, Hartmann A J, Lamb R N and Scott J F 1998 J. Appl. Phys. 24 2170 [25] Zafar S, Jones R E, Jiang B, White B, Kaushik V and Gillespie S 1998 Appl. Phys. Lett. 73 3533 [26] Martinez R, Kumar A, Palai R, Katiyar R S and Scott J F 2010 J. Appl. Phys. 107 114107 [27] Pavunny S P, Misra P, Scott J F and Katiyar R S 2013 Appl. Phys. Lett. 102 252905 [28] Dawber M and Scott J F 2004 J. Phys.: Condens. Matter 16 L515 [29] Watanabe K, Hartmann A J, Lamb R N and Scott J F 1998 J. Appl. Phys. 84 2170 [30] Scott J F 1989 Proc. IEEE Ultrasonics Symp. (Montreal, Canada) vol I p 299 [31] Warren W L, Dimos D and Waser R 1996 MRS Bull. 21 40 [32] Dimmler K, Parris M, Butler D, Eaton S, Pouligny B, Scott J F and Ishibashi Y 1987 J. Appl. Phys. 61 5467 [33] Scott J F, Araujo C A, Melnick B M, McMillan L D and Zuleeg R 1991 J. Appl. Phys. 70 382 [34] Sze S M 1981 Physics of Semiconductor Devices (New York: Wiley) pp 262, 404
[1] Scott J F 2008 J. Phys.: Condens. Matter 20 021001 [2] Eerenstein W, Morrison F D, Sher F, Prieto J L, Attfield J P, Scott J F and Mathur N D 2007 Phil. Mag. Lett. 87 249 [3] Catalan G 2006 Appl. Phys. Lett. 88 102902 [4] Staresinik D, Lunkenheimer P, Hemberger J and Loidl A 2006 Phys. Rev. Lett. 96 046402 [5] Schottky W 1923 Z. Phys. 14 63 [6] Schottky W 1923 Z. Phys. 15 51 [7] Scott J F 1996 Ferroelectrics 183 51 [8] Simmons J G 1963 J. Appl. Phys. 34 1793 [9] Simmons J G 1964 J. Appl. Phys. 35 2472 [10] Dietz G W, Schumacher M, Waser R, Streiffer S K, Basconi C and Kingon A I 1997 J. Appl. Phys. 82 2359 [11] Dietz G W and Waser R 1966 Thin Solid Films 299 53 [12] Guyonnet J, Gaponenko I, Gariglio S and Paruch P 2011 Adv. Mater. 23 5377 [13] Lee K, Rhee B R and Lee C 2001 J. Korean Phys. Soc. 38 723 [14] Scott J F 1999 Ferroelectrics 232 25 [15] Qi X, Ho J, Rumen T, Blamire M G and MacManus-Driscoll J L 2005 Appl. Phys. Lett. 86 062903 [16] Zhu H-W, Wang S-L, Jiang P, Shen J-Q and Tang W-H 2010 J. Korean Phys. Soc. 57 268 [17] Lampert M A and Mark P 1970 Current Injection in Solids (New York: Academic) [18] Melnick B M, Scott J F, Paz de Araujo C A and McMillan L D 1992 Ferroelectrics 135 163
4
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My IOPscience
There’s no place like Ohm: conduction in oxide thin films
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 J. Phys.: Condens. Matter 26 142202 (http://iopscience.iop.org/0953-8984/26/14/142202) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 193.255.248.150 This content was downloaded on 23/12/2014 at 08:59
Please note that terms and conditions apply.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 142202 (4pp)
doi:10.1088/0953-8984/26/14/142202
Fast Track Communciations
There’s no place like Ohm: conduction in oxide thin films J F Scott Cavendish Laboratory, Department of Physics, Cambridge University, Cambridge CB3 0HE, UK Received 4 February 2014, revised 18 February 2014 Accepted for publication 20 February 2014 Published 20 March 2014 Abstract
A pedagogical essay is given that alerts researchers to the errors inherent in assigning linear I(V) current–voltage dependences to Ohmic conduction. Such a linear I(V) is necessary but not sufficient, since other mechanisms, including Simmons’ modification of the basic Schottky emission theory, also give linear I(V) at small applied voltages. Discrimination among Ohmic, Schottky, space-charge limited, and other models requires accurate thickness dependence I(d) data, where for Ohmic conduction I = a/d, whereas for interface-limited mechanisms such as Simmons/Schottky, I is nearly independent of d. Keywords: ferroelectrics, thin films, dielectrics, conduction (Some figures may appear in colour only in the online journal)
2. Schottky emission
Recently the present author had some success in alerting readers that apparent P(V) polarization hysteresis curves are not unambiguous proof of ferroelectricity, but can result from electret-like effects and charge injection in a variety of materials, including ordinary banana skins [1]. Although such whimsical essays do not appeal to all tastes, they seem successful in alerting newcomers to special pitfalls in thin-film research and attract more attention than more staid articles [2]. A more strait-laced essay that has proved even more successful is that of Catalan [3] on artifacts due to magnetoresistance that can look like magnetoelectricity (a glaring misinterpretation is given in [4]). In the same vein, the present note is to remind researchers on thin-film oxides that a linear current–voltage I(V) response at low V is not a proof of Ohmic conduction.
Schottky discovered that the Richardson emission of electrons in solids could be strongly enhanced by applying a voltage [5, 6]. Schottky conduction is limited by the interface between the sample and the metallic contacts on each end. In his original work [5] Schottky considered several different situations: the two most important limiting cases are those in which the electron (or hole) mean free path L is >> the Schottky barrier width w, and conversely, that in which L J.
J = Neμ[ε / (ekT *AB )] T */ T d −[2(T */ T )+1]V (T */ T ) +1 . (5) The practical problem in modeling data is that equations (4) and (5) together entail too many fitting parameters. In a typical experiment [24] on SrBi2Ta2O9 on Pt, T* = 315 K at V = 3.0–4.0 V when T = 293 K. For clarity, space-chargelimited current data should exhibit a very abrupt change from linear I(V) to quadratic, as demonstrated for example in figure 1 for PZT at about E = 60 kV cm-1 [18]. Zafar et al initially identified Simmons’ mechanism in ferroelectric thin films [25]; and more recently Martinez et al [26] and Pavunny et al [27] have fitted I(V) data in various oxide thin films and have shown that their conduction is indeed not Simmons form, with the key evidence being reasonable fitted values of dielectric constant and Richardson coefficients. (In [25] it was shown that the conduction is predominantly space-charge-limited at low fields < 100 kV cm-1 but Schottky-limited at higher fields.) This is a satisfactory procedure when processing conditions do not readily permit varying film thickness d. Good examples of Simmonsmodified Schottky currents are shown [28] in figure 4. Here in figure 4(a) we see that the temperature dependence from 77 to 293 K shows that conduction is Schottky-limited, but the expected exponential dependence on V1/2 does not set in until V = 0.5 V for reverse bias and about 1.0 V for forward bias. In figure 4(b) we see that above 4.0 V the behavior is Simmonslike Schottky emission dominated. In figure 4(c) we also see [29] Simmons behavior above 4.0 V following a negative resistance dip; such a dip in a 200 nm thick BST film with a dielectric constant of about 1000 and a 10 nm depletion width requires an oxygen vacancy concentration of >3 × 1018 cm-3;
5. Conclusions Understanding the conduction mechanisms for leakage currents in oxide thin films is very important for commercializing devices. Linear I(V) current–voltage relationships at low voltage do not in themselves imply Ohmic conduction. Other mechanisms are compatible with that, especially the modification of Schottky emission detailed by Simmons for the common situation in which the electron mean free path L is less than the Schottky barrier width w. We end these comparisons with a final warning from Sze [34]: ‘For large space charge effect, the tunneling characteristic is found to be very similar to the Schottky-type emission’. 3
J. Phys.: Condens. Matter 26 (2014) 142202
References
[19] Pintilie L, Vrejoiu I, Hesse D, LeRhun G and Alexe M 2007 Phys. Rev. B 75 104103 [20] Dey S K and Zuleeg R 1990 Ferroelectrics 112 309 [21] Alexe M, Harnagea C, Hesse D and Goesele U 1999 Appl. Phys. Lett. 75 1793 [22] Rose A 1955 Phys. Rev. 97 1538 [23] Rose A 1978 Concepts in Photoconductivity and Allied Problems (New York: Krieger) [24] Watanabe K, Hartmann A J, Lamb R N and Scott J F 1998 J. Appl. Phys. 24 2170 [25] Zafar S, Jones R E, Jiang B, White B, Kaushik V and Gillespie S 1998 Appl. Phys. Lett. 73 3533 [26] Martinez R, Kumar A, Palai R, Katiyar R S and Scott J F 2010 J. Appl. Phys. 107 114107 [27] Pavunny S P, Misra P, Scott J F and Katiyar R S 2013 Appl. Phys. Lett. 102 252905 [28] Dawber M and Scott J F 2004 J. Phys.: Condens. Matter 16 L515 [29] Watanabe K, Hartmann A J, Lamb R N and Scott J F 1998 J. Appl. Phys. 84 2170 [30] Scott J F 1989 Proc. IEEE Ultrasonics Symp. (Montreal, Canada) vol I p 299 [31] Warren W L, Dimos D and Waser R 1996 MRS Bull. 21 40 [32] Dimmler K, Parris M, Butler D, Eaton S, Pouligny B, Scott J F and Ishibashi Y 1987 J. Appl. Phys. 61 5467 [33] Scott J F, Araujo C A, Melnick B M, McMillan L D and Zuleeg R 1991 J. Appl. Phys. 70 382 [34] Sze S M 1981 Physics of Semiconductor Devices (New York: Wiley) pp 262, 404
[1] Scott J F 2008 J. Phys.: Condens. Matter 20 021001 [2] Eerenstein W, Morrison F D, Sher F, Prieto J L, Attfield J P, Scott J F and Mathur N D 2007 Phil. Mag. Lett. 87 249 [3] Catalan G 2006 Appl. Phys. Lett. 88 102902 [4] Staresinik D, Lunkenheimer P, Hemberger J and Loidl A 2006 Phys. Rev. Lett. 96 046402 [5] Schottky W 1923 Z. Phys. 14 63 [6] Schottky W 1923 Z. Phys. 15 51 [7] Scott J F 1996 Ferroelectrics 183 51 [8] Simmons J G 1963 J. Appl. Phys. 34 1793 [9] Simmons J G 1964 J. Appl. Phys. 35 2472 [10] Dietz G W, Schumacher M, Waser R, Streiffer S K, Basconi C and Kingon A I 1997 J. Appl. Phys. 82 2359 [11] Dietz G W and Waser R 1966 Thin Solid Films 299 53 [12] Guyonnet J, Gaponenko I, Gariglio S and Paruch P 2011 Adv. Mater. 23 5377 [13] Lee K, Rhee B R and Lee C 2001 J. Korean Phys. Soc. 38 723 [14] Scott J F 1999 Ferroelectrics 232 25 [15] Qi X, Ho J, Rumen T, Blamire M G and MacManus-Driscoll J L 2005 Appl. Phys. Lett. 86 062903 [16] Zhu H-W, Wang S-L, Jiang P, Shen J-Q and Tang W-H 2010 J. Korean Phys. Soc. 57 268 [17] Lampert M A and Mark P 1970 Current Injection in Solids (New York: Academic) [18] Melnick B M, Scott J F, Paz de Araujo C A and McMillan L D 1992 Ferroelectrics 135 163
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