- Email: [email protected]
Breakdown mechanisms in ultra-thin oxides: impact of carrier energy and current through substrate hot carrier stress study
Microelectronic Engineering 72 (2004) 10–15 www.elsevier.com/locate/mee
Breakdown mechanisms in ultra-thin oxides: impact of carrier energy and current through substrate hot carrier stress study G. Ribes
a,b,*
, S. Bruyere a, M. Denais a,c, F. Monsieur a, V. Huard d, D. Roy a, G. Ghibaudo b
a
STMicroelectronics, Central R&D labs, 850 rue Jean Monnet, BP16, 38926 Crolles, France IMEP/ENSERG, UMR CNRS 5531, 23 rue des Martyrs, BP257, 38016 Grenoble, France L2MP/ISEM, UMR CNRS 6137 Maison des Technologies, place G. Pompidou, 83000 Toulon, France d Philips Semiconductors, Central R&D labs, 850 rue Jean Monnet, BP16, 38926 Crolles, France b
c
Abstract An experimental investigation of breakdown phenomenon using substrate hot hole and electron stresses of silicon dioxide ranging in thickness from 2 to 5 nm is reported. First, we demonstrate that the scattering effect is responsible of the low activation energy already observed by other authors [J. Appl. Phys. 90(5) (2001)]. Based on a method of carrier energy measurement we characterize the scattering effect. Second, we demonstrate the decorrelation between carrier energy and carrier density showing that the carriers–carriers scattering is negligible. Finally being capable to confirm the real decorrelation between energy and density we observed a current dependence of the charge to breakdown. Besides, we give a theory using the multiple vibrational excitation of the Si–H bound [Surf. Sci. 368–377 (1996); Science 268 (1995) 1590]. Hence, we demonstrate once again that the hydrogen species behavior is strongly linked to breakdown phenomenon. Ó 2004 Elsevier B.V. All rights reserved.
1. Introduction The reliability of the gate dielectric of metaloxide-semiconductor (MOS) has received increasing attention due to a critical intrinsic behavior of the gate dielectrics. Although a large research on the intrinsic mechanisms of silicon dioxide degradation and breakdown, controversies about the *
Corresponding author. Tel.: +33-476-926-801; fax: +33-476925-732. E-mail address: [email protected] (G. Ribes).
degradation mechanism still remain. Nevertheless some important result as the strong correlation between the total number of defects at breakdown (Nbd ) and the electrons fluence (Qbd ) through the oxide has been demonstrated [1] Qbd ¼
q Nbd ; Pg
ð1Þ
where Qbd is the total electronic charge injected into the oxide, until breakdown event, Nbd is the total number of defects at breakdown, Pg is the defect generation rate, and q is the electron charge.
0167-9317/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2003.12.048
G. Ribes et al. / Microelectronic Engineering 72 (2004) 10–15
The defect generation rate has been shown for quasiballistic/ballistic electrons to have weak thickness dependence but a strong gate voltage one [1]. The aim of this paper is to provide some insights on the physical mechanisms at the origin of breakdown events and especially on the dependence of the defect generation rate (Pg ). A detailed study of substrate hot hole (SHH) and electron (SHE) stresses is performed. First, the low activation energy of charge to breakdown already observed in [2] during SHH experiments will be discussed. Second, an original approach considering the scattering effects on carrier energy is developed. Finally, the injected current dependence (not only carrier energy dependent) of the defect generation rate is demonstrated. This result will be linked to the hydrogen desorption behavior at low field.
11
Ec Ev SHE eN+injector eGate
P substrate
Ef
d (distance)
Fig. 2. Band diagram of a SHE regime stress. d is the distance between the mos transistor and the injector (note that for SHH: N-substrate and P+ injector).
used. The nitrided gate oxide thickness investigated is ranging between 2 and 5 nm issued from a 0:10 lm CMOS technology.
2. Experimental details
3. Temperature effect on SHH stress
Fig. 1 displays the stress configuration of the SHE regime. The gate voltage is fixed at !1 V (inversion regime) source and drain are pined to the ground (surface potential is fixed to the ground thus the oxide field is control by the gate voltage only). The np diode is in forward polarization. Fig. 2 depicts the SHE band diagram: np junction enables to generate carriers (Iinjected : holes for SHH and electrons for SHE) that can be accelerated by bulk bias Vb (carrier energy). Structures with different distances d between the injector and the MOS transistor (W L ¼ 10 10 lm2 ) have been
It has been reported that breakdown induced by SHH stress has a lower temperature dependence as compared to breakdown induced by constant voltage stress (CVS) [2]. Moreover, lower activation energy is observed as the injector/MOS distance increases (Fig. 3). Both experiments can be explained by the carrier scattering effect in the substrate. Indeed during CVS tests, carriers are
Vinj d
n+
n+
nn+
QBD (C/cm2) @ 50%
Vg
Field control
10000 Ea=0.63eV 1000
d=10um Ea=1.11eV
100 d=25um Ea=0.63eV
Ea=1.11eV 10
Densitycontrol
1 p
27
28
29
1/K1 (eV-1) Energy control
Vb
Fig. 1. SHE structure schematic. (Note that for SHH structure : p+ source, drain, injector and n-substrate).
Fig. 3. Activation energy of charge to breakdown measured thick oxide with Vb ¼ 5 V and during SHH stress on 23 A Vinj ¼ 6 V showing an injector-gate distance dependence probably due to a phonon–electron scattering effect (note that for d ¼ 10 lm, the activation energy is well close to CVS one).
12
G. Ribes et al. / Microelectronic Engineering 72 (2004) 10–15
directly injected from the channel into the oxide and scattering effect is negligible. On the contrary in SHH/SHE structures, carriers travel through the substrate and the scattering effect can modulate the injected carrier energy during transport. Besides, the temperature is known to increase the scattering effect (phonon–carrier interaction) and then to induce a loss of carrier energy [3]. Since, the defect generation rate is well to increase with carrier energy, the temperature leads to a less efficient defect generation rate (for a given stress biases). Thus, the defect generation rate is temperature dependent and so the activation energy is impacted. Other results confirm this hypothesis. As it is showed in Fig. 4 the gate current is almost constant with the temperature for high injector/MOS distance (d ¼ 25 lm) and increases for short distance (d ¼ 10 lm). Indeed, the energetic distribution of electrons in the semiconductors (Fermi–Dirac distribution) is raised by temperature and so increases the leakage current for the low distance (channel carrier and d ¼ 10 lm). Nevertheless for high distance (25 lm) the phonon–carriers scattering effect induces a significant loss of carrier energy. This loss drastically increases with temperature and tends to be prevalent when the distance covered by carriers is important. These results are consistent and show
that we have to take into account the energy loss by scattering effect to well understand the uniform hot carrier stress. The following method answers to this need.
4. Method of carrier energy and scattering measurement 4.1. Carrier scattering A barrier height lowering of Fowler–Nordheim thick conduction (on SHH structures with 50 A oxide) is observed as bulk bias increases (Fig. 5). This is attributed to the injection of carrier with higher energy than channel carrier one. Thus, we can extract the carrier energy at the interface as the barrier lowering (Fig. 6). It has been plotted as a function of its energy close to the injector (initial energies, Ei ðeVÞ ¼ Vb þ /np , where Vb is the bulk bias and /np is the contact potential difference of the np junction). This depicts that the scattering (Ei ðeVÞ Eextracted ðeVÞ) leads to a carrier energy reduction in this case of 57%. 4.2. Focus on carrier–carrier scattering (impact on carrier energy and density decorrelation) In other works [2,4,7] the impact of scattering is not taken into account when SHH or SHE stress
2.E-07 2.E-07 2.E-07
1E-21
3V
Ig/E2 (A.cm2/V2)
Iginit (A)
1.E-07 1.E-07 d=10µm
9.E-08 7.E-08 d=25µm
5.E-08 3.E-08
1E-24 Vb (V) 0V 1E-27 6.0E-08
1.E-08 0
50
100 T ˚C
150
200
Fig. 4. Initial gate current measured during the SHH stress (Fig. 2) increases for a MOS–injector distance equal to 10 lm and is almost constant with temperature for a 25 lm distance, explained by the temperature dependence of the scattering.
8.0E-08 1/E (cm/V)
1.0E-07
thick oxide, d ¼ 10 lm, T ¼ 25 Fig. 5. Extraction (on a 50 A °C, Vinj Vb ¼ 2:1 V) of the barrier height in Fowler–Nordheim. A decrease (decrease of the slope) with bulk voltage (Vb ) is observed. This is induced by the bigger injected carrier energy at the interface than channel carrier one.
G. Ribes et al. / Microelectronic Engineering 72 (2004) 10–15 1.E-04
3 2.5 2 1.5
Ig (A)
Extracted Energy (eV)
13
y = 0.4344x
1
1.E-06 Vb=1 to 3V
0.5 0 0
2
4
6
8
1.E-08
Initial Energy (eV)
are considered. It is important to deeper characterize it, since if carrier–carrier scattering can be incriminated, the assumption that carrier energy (Vb ) and carrier density (Vinj Vb ) can be decorrelated with this structure is no more valid. Nevertheless, for different injected currents (Iinjected ), at fixed gate and bulk voltages the direct tunneling transparency (trapezoidal barrier) only depends of the carrier energy pffiffiffiffiffiffiffiffiffiffi ffi 3=2 3=2 4 2m q ½ðEÞ ðE þ V SiO2 Þ 3 h T ðEÞ ¼ exp F SiO2 ð2Þ [8], where E is the carrier energy, m is the effective carrier mass in the SiO2 , q is the electron charge, F SiO2 is the electric field in the oxide and V SiO2 is the potential in the oxide. Fig. 7 shows that the current injected dependence of the tunnel gate current can be well fitted by a linear relation ship: the slope belong only Vb dependent (Ig ¼ Iinjected T ðVb Þ). That means that the transparency (the slope of the characteristic) remains constant versus injected current. Thus, the carrier energy is clearly decorrelated with carrier current density. In order to check if the both measurement method are self-consistent one), we plot in Fig. 8 the trans(20 and 50 A gate oxide versus. parency extracted on 20 A 3=2 ðEextracted Þ ðEextracted þ V SiO2 Þ3=2 . By taking into account the scattering effect on hole energy ðEextracted ðeVÞ ¼ 0:43 Ei ðeVÞÞ mea-
2.E-02
6.E-02
6.E-02
8.E-02
Iinjected (A) Fig. 7. Gate-leakage current versus injected current measured at different bulk voltage and constant gate on nmos 20 A voltage (1 V) shows a good agreement with experience and a constant transparency versus injected current (constant energy versus injected current).
1.E-02
y = 8E-16e
1.E-03 T (E)
Fig. 6. Hole energy measured at the interface Si/SiO2 by extraction of the barrier height lowering of the FN gate current on SHH structures displays an extracted energy equal to 43% 50-A of the initial energy (Ei ðeVÞ ¼ Vb þ /np ).
3.E-03
11.079x
1.E-04 1.E-05
4
1.E-06 1.E-07
* 2m q
3 1.7
2
2.3
2.6
= 11 .11 FSio2
E^3/2-(E+VSio2)^3/2 Fig. 8. Extraction (using the energy extracted E ¼ Eextracted ¼ 0:57Ei on SHE structure with the method displayed in Fig. 5) at constant oxide field of the constant A showing a good agreement with the theoretic expression (2) and the self-consistence of both measurement methods.
sured with previous analysis (Fig. 6), the slope extracted is A ¼ 11:08 where the theoretical value is pffiffiffiffiffiffiffiffiffiffi ffi 4 2m q 3 h ¼ 11:11: ð3Þ A¼ F SiO2 (Note that A is extracted equal to 3.1 without introducing scattering impact.) Thus, the importance of scattering effect in the substrate is clearly high lighted and the consistence between 50 and 20 A SHH and SHE structure underlined. Besides, we have reproduced the same test for electron ðEextracted ðeVÞ ¼ 0:57 Ei ðeVÞÞ. The different behavior of electron and hole scattering
14
G. Ribes et al. / Microelectronic Engineering 72 (2004) 10–15
obtained can be well explained through the mean free path ratio [3]: Lrh Eextracted ðhÞ ScatðeÞ ¼ ¼ 0:72 Eextracted ðeÞ ScatðhÞ Lre 0:43 ¼ ¼ 0:75 : 0:57 This observation shows the consistence of the measurement for different oxide thickness (50 and and for both carriers (hole and electron). By 20 A) this way we are able to quantify the loss of energy in the substrate and the maximum energy of the injected carrier (electron or hole) at the interface.
5. The injected current dependence of charge to breakdown Previously, we have verified the assumption that in SHH and SHE stress the carrier energy and density is really decorrelated. This enables indubitably us to show that the charge to breakdown is dependent of the injected current on SHE and SHH structures (Fig. 9). In the hypothesis of percolation model [9,10], it means that the total number of defects at breakdown (Nbd ) and/or the defect generation rate (Pg ) in SHH or SHE stress is dependent of the injected current for low energy stress (less than 5 eV Vbnmos ¼ 8 V, Vbnmos ¼ 10 V). Indeed, for higher energy stress (>5 eV) this behavior was not observed 10000
Qbd@50% (C/cm2)
SHE Vb=-4V~2.9eV @ 25˚C
1000
y = 3E-12x-13.95
SHH Vb=5V~2.5eV @125˚C
100
10
1 0.02
y = 4E-12x-10.042
0.04
0.06
0.08
0.1
0.12
[2,4,7]. In the hypothesis of hydrogen release model [4], it is interesting to note that a similar result has been observed on the desorption yield (atoms/ electrons) of hydrogen atoms by a scanning tunneling microscope (STM) tip [5,6]. This current dependence is explained by the multi-vibrational excitation of the Si–H bond. Under the threshold of 5 eV one carrier is not able to break the bond alone and a need of carrier impact frequency is required (current). Thus, a similar behavior between breakdown in SHH–SHE stress and hydrogen desorption is observed. Indeed, defect generation rate has not only a bulk bias dependence (electron energy), but it is also a strong function of the tunneling current (Fig. 9), suggesting that many electrons must cooperate to create a defect, which has the same threshold than the Si–H bond. This observation leads to conclude that the responsible defect of breakdown path has the same behavior that hydrogen desorption and so it is one more argument in favor of the role of hydrogen species in the creation of a percolation path leading to breakdown. 6. Conclusion Using a deeper characterization of the SHH and SHE stress, we explain the low temperature dependence of the SHH stress by a scattering effect. In showing the importance of scattering impact on the understanding of the SHH and SHE results, we verify the good decorelation between carrier energy and density. This enables indubitably us to report a current dependence of the defect generation rate for low carrier energy. Furthermore, we explain this behavior with multiple vibrational state of the Si–H bound. Hence, we demonstrate for the first time a current dependence of the defect generation rate leading us to a better understanding of the oxide and interface degradation.
Iinjected (A) nmos SHE Fig. 9. The charge to breakdown measured on 20 A structure at Vgate ¼ 1 V, Vbulk ¼ 4 V (2.9 eV) and pmos SHH structure at Vgate ¼ 1 V, Vb ¼ 5 V (2.5 eV) at different injected current displays an injected current dependence.
References [1] J.H. Stathis, D.J. Dimaria, Tech. Dig. Int Electron Dev. Meeting 44 (1998) 167.
G. Ribes et al. / Microelectronic Engineering 72 (2004) 10–15 [2] E.M. Vogel, M.D. Edelstein, J.S. Suehle, J. Appl. Phys. 90 (5) (2001). [3] Cromwell, Sze, Appl. Phys. Lett. 9 (1966) 242. [4] D.J. DiMaria, J. Appl. Phys. 86 (4) (1999). [5] Ph. Avouris, R. Walkup, A.R. Rossi, H.C. Akpati, P. Nordlander, T.-C. Shen, G.C. Abeln, J.W. Lyding, Surf. Sci. (1996) 368–377. [6] T.C. Shen, C. Wang, G. Abeln, J.R. Tucker, J.W. Lyding, Ph. Avouris, R. Walkup, Science 268 (1995) 1590.
15
[7] H. Satake, S. Takagi, A. Toriumi, in: Proceedings of International Reliability Physics Symposium, Denver, CO, IEEE, NJ, 1997, p. 156. [8] M. Depas, B. Vermeire, P.W. Mertens, R.L. Van Meirhaeghe, M.M. Heyns, Solid-State Electron. 38 (1995) 1465. [9] D.J. Dumin, S.K. Mopuri, S. Vanchinathan, R.S. Scott, R. Subamoniam, T.G. Lewis, IEEE Trans. Electron Dev. 42 (4) (1995). [10] J.H. Stathis, J. Appl. Phys. 86 (10) (1999).
Breakdown mechanisms in ultra-thin oxides: impact of carrier energy and current through substrate hot carrier stress study G. Ribes
a,b,*
, S. Bruyere a, M. Denais a,c, F. Monsieur a, V. Huard d, D. Roy a, G. Ghibaudo b
a
STMicroelectronics, Central R&D labs, 850 rue Jean Monnet, BP16, 38926 Crolles, France IMEP/ENSERG, UMR CNRS 5531, 23 rue des Martyrs, BP257, 38016 Grenoble, France L2MP/ISEM, UMR CNRS 6137 Maison des Technologies, place G. Pompidou, 83000 Toulon, France d Philips Semiconductors, Central R&D labs, 850 rue Jean Monnet, BP16, 38926 Crolles, France b
c
Abstract An experimental investigation of breakdown phenomenon using substrate hot hole and electron stresses of silicon dioxide ranging in thickness from 2 to 5 nm is reported. First, we demonstrate that the scattering effect is responsible of the low activation energy already observed by other authors [J. Appl. Phys. 90(5) (2001)]. Based on a method of carrier energy measurement we characterize the scattering effect. Second, we demonstrate the decorrelation between carrier energy and carrier density showing that the carriers–carriers scattering is negligible. Finally being capable to confirm the real decorrelation between energy and density we observed a current dependence of the charge to breakdown. Besides, we give a theory using the multiple vibrational excitation of the Si–H bound [Surf. Sci. 368–377 (1996); Science 268 (1995) 1590]. Hence, we demonstrate once again that the hydrogen species behavior is strongly linked to breakdown phenomenon. Ó 2004 Elsevier B.V. All rights reserved.
1. Introduction The reliability of the gate dielectric of metaloxide-semiconductor (MOS) has received increasing attention due to a critical intrinsic behavior of the gate dielectrics. Although a large research on the intrinsic mechanisms of silicon dioxide degradation and breakdown, controversies about the *
Corresponding author. Tel.: +33-476-926-801; fax: +33-476925-732. E-mail address: [email protected] (G. Ribes).
degradation mechanism still remain. Nevertheless some important result as the strong correlation between the total number of defects at breakdown (Nbd ) and the electrons fluence (Qbd ) through the oxide has been demonstrated [1] Qbd ¼
q Nbd ; Pg
ð1Þ
where Qbd is the total electronic charge injected into the oxide, until breakdown event, Nbd is the total number of defects at breakdown, Pg is the defect generation rate, and q is the electron charge.
0167-9317/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2003.12.048
G. Ribes et al. / Microelectronic Engineering 72 (2004) 10–15
The defect generation rate has been shown for quasiballistic/ballistic electrons to have weak thickness dependence but a strong gate voltage one [1]. The aim of this paper is to provide some insights on the physical mechanisms at the origin of breakdown events and especially on the dependence of the defect generation rate (Pg ). A detailed study of substrate hot hole (SHH) and electron (SHE) stresses is performed. First, the low activation energy of charge to breakdown already observed in [2] during SHH experiments will be discussed. Second, an original approach considering the scattering effects on carrier energy is developed. Finally, the injected current dependence (not only carrier energy dependent) of the defect generation rate is demonstrated. This result will be linked to the hydrogen desorption behavior at low field.
11
Ec Ev SHE eN+injector eGate
P substrate
Ef
d (distance)
Fig. 2. Band diagram of a SHE regime stress. d is the distance between the mos transistor and the injector (note that for SHH: N-substrate and P+ injector).
used. The nitrided gate oxide thickness investigated is ranging between 2 and 5 nm issued from a 0:10 lm CMOS technology.
2. Experimental details
3. Temperature effect on SHH stress
Fig. 1 displays the stress configuration of the SHE regime. The gate voltage is fixed at !1 V (inversion regime) source and drain are pined to the ground (surface potential is fixed to the ground thus the oxide field is control by the gate voltage only). The np diode is in forward polarization. Fig. 2 depicts the SHE band diagram: np junction enables to generate carriers (Iinjected : holes for SHH and electrons for SHE) that can be accelerated by bulk bias Vb (carrier energy). Structures with different distances d between the injector and the MOS transistor (W L ¼ 10 10 lm2 ) have been
It has been reported that breakdown induced by SHH stress has a lower temperature dependence as compared to breakdown induced by constant voltage stress (CVS) [2]. Moreover, lower activation energy is observed as the injector/MOS distance increases (Fig. 3). Both experiments can be explained by the carrier scattering effect in the substrate. Indeed during CVS tests, carriers are
Vinj d
n+
n+
nn+
QBD (C/cm2) @ 50%
Vg
Field control
10000 Ea=0.63eV 1000
d=10um Ea=1.11eV
100 d=25um Ea=0.63eV
Ea=1.11eV 10
Densitycontrol
1 p
27
28
29
1/K1 (eV-1) Energy control
Vb
Fig. 1. SHE structure schematic. (Note that for SHH structure : p+ source, drain, injector and n-substrate).
Fig. 3. Activation energy of charge to breakdown measured thick oxide with Vb ¼ 5 V and during SHH stress on 23 A Vinj ¼ 6 V showing an injector-gate distance dependence probably due to a phonon–electron scattering effect (note that for d ¼ 10 lm, the activation energy is well close to CVS one).
12
G. Ribes et al. / Microelectronic Engineering 72 (2004) 10–15
directly injected from the channel into the oxide and scattering effect is negligible. On the contrary in SHH/SHE structures, carriers travel through the substrate and the scattering effect can modulate the injected carrier energy during transport. Besides, the temperature is known to increase the scattering effect (phonon–carrier interaction) and then to induce a loss of carrier energy [3]. Since, the defect generation rate is well to increase with carrier energy, the temperature leads to a less efficient defect generation rate (for a given stress biases). Thus, the defect generation rate is temperature dependent and so the activation energy is impacted. Other results confirm this hypothesis. As it is showed in Fig. 4 the gate current is almost constant with the temperature for high injector/MOS distance (d ¼ 25 lm) and increases for short distance (d ¼ 10 lm). Indeed, the energetic distribution of electrons in the semiconductors (Fermi–Dirac distribution) is raised by temperature and so increases the leakage current for the low distance (channel carrier and d ¼ 10 lm). Nevertheless for high distance (25 lm) the phonon–carriers scattering effect induces a significant loss of carrier energy. This loss drastically increases with temperature and tends to be prevalent when the distance covered by carriers is important. These results are consistent and show
that we have to take into account the energy loss by scattering effect to well understand the uniform hot carrier stress. The following method answers to this need.
4. Method of carrier energy and scattering measurement 4.1. Carrier scattering A barrier height lowering of Fowler–Nordheim thick conduction (on SHH structures with 50 A oxide) is observed as bulk bias increases (Fig. 5). This is attributed to the injection of carrier with higher energy than channel carrier one. Thus, we can extract the carrier energy at the interface as the barrier lowering (Fig. 6). It has been plotted as a function of its energy close to the injector (initial energies, Ei ðeVÞ ¼ Vb þ /np , where Vb is the bulk bias and /np is the contact potential difference of the np junction). This depicts that the scattering (Ei ðeVÞ Eextracted ðeVÞ) leads to a carrier energy reduction in this case of 57%. 4.2. Focus on carrier–carrier scattering (impact on carrier energy and density decorrelation) In other works [2,4,7] the impact of scattering is not taken into account when SHH or SHE stress
2.E-07 2.E-07 2.E-07
1E-21
3V
Ig/E2 (A.cm2/V2)
Iginit (A)
1.E-07 1.E-07 d=10µm
9.E-08 7.E-08 d=25µm
5.E-08 3.E-08
1E-24 Vb (V) 0V 1E-27 6.0E-08
1.E-08 0
50
100 T ˚C
150
200
Fig. 4. Initial gate current measured during the SHH stress (Fig. 2) increases for a MOS–injector distance equal to 10 lm and is almost constant with temperature for a 25 lm distance, explained by the temperature dependence of the scattering.
8.0E-08 1/E (cm/V)
1.0E-07
thick oxide, d ¼ 10 lm, T ¼ 25 Fig. 5. Extraction (on a 50 A °C, Vinj Vb ¼ 2:1 V) of the barrier height in Fowler–Nordheim. A decrease (decrease of the slope) with bulk voltage (Vb ) is observed. This is induced by the bigger injected carrier energy at the interface than channel carrier one.
G. Ribes et al. / Microelectronic Engineering 72 (2004) 10–15 1.E-04
3 2.5 2 1.5
Ig (A)
Extracted Energy (eV)
13
y = 0.4344x
1
1.E-06 Vb=1 to 3V
0.5 0 0
2
4
6
8
1.E-08
Initial Energy (eV)
are considered. It is important to deeper characterize it, since if carrier–carrier scattering can be incriminated, the assumption that carrier energy (Vb ) and carrier density (Vinj Vb ) can be decorrelated with this structure is no more valid. Nevertheless, for different injected currents (Iinjected ), at fixed gate and bulk voltages the direct tunneling transparency (trapezoidal barrier) only depends of the carrier energy pffiffiffiffiffiffiffiffiffiffi ffi 3=2 3=2 4 2m q ½ðEÞ ðE þ V SiO2 Þ 3 h T ðEÞ ¼ exp F SiO2 ð2Þ [8], where E is the carrier energy, m is the effective carrier mass in the SiO2 , q is the electron charge, F SiO2 is the electric field in the oxide and V SiO2 is the potential in the oxide. Fig. 7 shows that the current injected dependence of the tunnel gate current can be well fitted by a linear relation ship: the slope belong only Vb dependent (Ig ¼ Iinjected T ðVb Þ). That means that the transparency (the slope of the characteristic) remains constant versus injected current. Thus, the carrier energy is clearly decorrelated with carrier current density. In order to check if the both measurement method are self-consistent one), we plot in Fig. 8 the trans(20 and 50 A gate oxide versus. parency extracted on 20 A 3=2 ðEextracted Þ ðEextracted þ V SiO2 Þ3=2 . By taking into account the scattering effect on hole energy ðEextracted ðeVÞ ¼ 0:43 Ei ðeVÞÞ mea-
2.E-02
6.E-02
6.E-02
8.E-02
Iinjected (A) Fig. 7. Gate-leakage current versus injected current measured at different bulk voltage and constant gate on nmos 20 A voltage (1 V) shows a good agreement with experience and a constant transparency versus injected current (constant energy versus injected current).
1.E-02
y = 8E-16e
1.E-03 T (E)
Fig. 6. Hole energy measured at the interface Si/SiO2 by extraction of the barrier height lowering of the FN gate current on SHH structures displays an extracted energy equal to 43% 50-A of the initial energy (Ei ðeVÞ ¼ Vb þ /np ).
3.E-03
11.079x
1.E-04 1.E-05
4
1.E-06 1.E-07
* 2m q
3 1.7
2
2.3
2.6
= 11 .11 FSio2
E^3/2-(E+VSio2)^3/2 Fig. 8. Extraction (using the energy extracted E ¼ Eextracted ¼ 0:57Ei on SHE structure with the method displayed in Fig. 5) at constant oxide field of the constant A showing a good agreement with the theoretic expression (2) and the self-consistence of both measurement methods.
sured with previous analysis (Fig. 6), the slope extracted is A ¼ 11:08 where the theoretical value is pffiffiffiffiffiffiffiffiffiffi ffi 4 2m q 3 h ¼ 11:11: ð3Þ A¼ F SiO2 (Note that A is extracted equal to 3.1 without introducing scattering impact.) Thus, the importance of scattering effect in the substrate is clearly high lighted and the consistence between 50 and 20 A SHH and SHE structure underlined. Besides, we have reproduced the same test for electron ðEextracted ðeVÞ ¼ 0:57 Ei ðeVÞÞ. The different behavior of electron and hole scattering
14
G. Ribes et al. / Microelectronic Engineering 72 (2004) 10–15
obtained can be well explained through the mean free path ratio [3]: Lrh Eextracted ðhÞ ScatðeÞ ¼ ¼ 0:72 Eextracted ðeÞ ScatðhÞ Lre 0:43 ¼ ¼ 0:75 : 0:57 This observation shows the consistence of the measurement for different oxide thickness (50 and and for both carriers (hole and electron). By 20 A) this way we are able to quantify the loss of energy in the substrate and the maximum energy of the injected carrier (electron or hole) at the interface.
5. The injected current dependence of charge to breakdown Previously, we have verified the assumption that in SHH and SHE stress the carrier energy and density is really decorrelated. This enables indubitably us to show that the charge to breakdown is dependent of the injected current on SHE and SHH structures (Fig. 9). In the hypothesis of percolation model [9,10], it means that the total number of defects at breakdown (Nbd ) and/or the defect generation rate (Pg ) in SHH or SHE stress is dependent of the injected current for low energy stress (less than 5 eV Vbnmos ¼ 8 V, Vbnmos ¼ 10 V). Indeed, for higher energy stress (>5 eV) this behavior was not observed 10000
Qbd@50% (C/cm2)
SHE Vb=-4V~2.9eV @ 25˚C
1000
y = 3E-12x-13.95
SHH Vb=5V~2.5eV @125˚C
100
10
1 0.02
y = 4E-12x-10.042
0.04
0.06
0.08
0.1
0.12
[2,4,7]. In the hypothesis of hydrogen release model [4], it is interesting to note that a similar result has been observed on the desorption yield (atoms/ electrons) of hydrogen atoms by a scanning tunneling microscope (STM) tip [5,6]. This current dependence is explained by the multi-vibrational excitation of the Si–H bond. Under the threshold of 5 eV one carrier is not able to break the bond alone and a need of carrier impact frequency is required (current). Thus, a similar behavior between breakdown in SHH–SHE stress and hydrogen desorption is observed. Indeed, defect generation rate has not only a bulk bias dependence (electron energy), but it is also a strong function of the tunneling current (Fig. 9), suggesting that many electrons must cooperate to create a defect, which has the same threshold than the Si–H bond. This observation leads to conclude that the responsible defect of breakdown path has the same behavior that hydrogen desorption and so it is one more argument in favor of the role of hydrogen species in the creation of a percolation path leading to breakdown. 6. Conclusion Using a deeper characterization of the SHH and SHE stress, we explain the low temperature dependence of the SHH stress by a scattering effect. In showing the importance of scattering impact on the understanding of the SHH and SHE results, we verify the good decorelation between carrier energy and density. This enables indubitably us to report a current dependence of the defect generation rate for low carrier energy. Furthermore, we explain this behavior with multiple vibrational state of the Si–H bound. Hence, we demonstrate for the first time a current dependence of the defect generation rate leading us to a better understanding of the oxide and interface degradation.
Iinjected (A) nmos SHE Fig. 9. The charge to breakdown measured on 20 A structure at Vgate ¼ 1 V, Vbulk ¼ 4 V (2.9 eV) and pmos SHH structure at Vgate ¼ 1 V, Vb ¼ 5 V (2.5 eV) at different injected current displays an injected current dependence.
References [1] J.H. Stathis, D.J. Dimaria, Tech. Dig. Int Electron Dev. Meeting 44 (1998) 167.
G. Ribes et al. / Microelectronic Engineering 72 (2004) 10–15 [2] E.M. Vogel, M.D. Edelstein, J.S. Suehle, J. Appl. Phys. 90 (5) (2001). [3] Cromwell, Sze, Appl. Phys. Lett. 9 (1966) 242. [4] D.J. DiMaria, J. Appl. Phys. 86 (4) (1999). [5] Ph. Avouris, R. Walkup, A.R. Rossi, H.C. Akpati, P. Nordlander, T.-C. Shen, G.C. Abeln, J.W. Lyding, Surf. Sci. (1996) 368–377. [6] T.C. Shen, C. Wang, G. Abeln, J.R. Tucker, J.W. Lyding, Ph. Avouris, R. Walkup, Science 268 (1995) 1590.
15
[7] H. Satake, S. Takagi, A. Toriumi, in: Proceedings of International Reliability Physics Symposium, Denver, CO, IEEE, NJ, 1997, p. 156. [8] M. Depas, B. Vermeire, P.W. Mertens, R.L. Van Meirhaeghe, M.M. Heyns, Solid-State Electron. 38 (1995) 1465. [9] D.J. Dumin, S.K. Mopuri, S. Vanchinathan, R.S. Scott, R. Subamoniam, T.G. Lewis, IEEE Trans. Electron Dev. 42 (4) (1995). [10] J.H. Stathis, J. Appl. Phys. 86 (10) (1999).