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Drain currents and their excess noise in triple gate bulk p-channel FinFETs of different geometry
Microelectronics Reliability 53 (2013) 394–399
Contents lists available at SciVerse ScienceDirect
Microelectronics Reliability journal homepage: www.elsevier.com/locate/microrel
Drain currents and their excess noise in triple gate bulk p-channel FinFETs of different geometry N. Lukyanchikova a, N. Garbar a, V. Kudina a,⇑, A. Smolanka a, E. Simoen b, C. Claeys b,c a
V. Lashkaryov Institute of Semiconductor Physics, Prospect Nauki 45, 03028 Kiev, Ukraine Imec, Kapeldreef 75, B-3001 Leuven, Belgium c KU Leuven, Kasteelpark Arenberg 10, B-3001 Leuven, Belgium b
a r t i c l e
i n f o
Article history: Received 8 December 2011 Received in revised form 17 October 2012 Accepted 17 October 2012 Available online 22 November 2012
a b s t r a c t The drain current I, spectral density of the low-frequency 1/f noise SI and transconductance gm of triple gate bulk p-channel field-effect transistors (FinFETs) fabricated on 200 mm diameter Cz silicon wafers have been studied in the standard (ST) and Dynamic Threshold Voltage (DT) modes of operation. For the ST regime, a sub-linear increase of the drain current I with increasing overdrive voltage |Vov| and practically no changes in the spectral density SI of the noise are observed at high values of |Vov|. The effect is attributed to a sub-linear increase of the free hole density in the channel, whereby the mobility does not change with increasing |Vov|. An increase of the values of I, SI and gm normalized for the device geometry with increasing Leff is found and is attributed to the decrease of the mobility degradation coefficient with increasing Leff. For the DT regime of operation, the decrease of the threshold voltage |Vth| is not accompanied by an increase of the drain current which decreases with increasing |VGF| due to the high leakage current passing through the forward biased drain and source junctions. However, that decrease of the drain current is not accompanied by changes in the value of SI. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Bulk FinFETs combine the good control of the short-channel effects with the ease of manufacturing on bulk silicon substrates [1]. The technology has reached a sufficient level of maturity to enable meaningful low-frequency (LF) noise measurements. Initial results have pointed out that for triple gate (trigate) bulk FinFETs with SiO2 or SiON gate dielectric, both 1/f noise and Generation– Recombination (GR) noise are present, whereby the 1/f noise in many cases is dominated by carrier trapping in the gate dielectric [2,3]. The GR noise was ascribed to traps both in the silicon fins and in the gate oxide, based on the gate-voltage dependence of the corner frequency fc. It was also noted that operation of n-channel bulk FinFETs in the dynamic threshold mode of operation [4–6], did not affect the LF spectral density, SI [7], while an improvement in the analog performance was observed [8]. Initial noise results on bulk p-MOSFETs with high-k/metal gate have also been reported [9]. Given the multiple gate nature of the devices, one of the obvious questions is whether the device geometry and in particular the fin width has an impact on the LF noise behavior. One should account for the fact that for narrow devices, most of the current is flowing along the (1 1 0) sidewalls, which have usually a different
⇑ Corresponding author. Tel.: +38 044 525 64 53; fax: +38 044 525 61 91. E-mail address: [email protected] (V. Kudina). 0026-2714/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.microrel.2012.10.011
orientation than for standard planar bulk transistors on (1 0 0) wafers. It turns out that for Silicon-on-Insulator (SOI) FinFETs, the device orientation has only a minor effect on the noise [10,11]. Another factor which can play a role is that in the case of narrow fins, the structure can be considered as fully depleted, i.e., the width of the fin is smaller than two times the depletion width at the sidewalls of the device. It is the aim to report here on detailed LF noise results of narrow high-k/metal gate bulk p-FinFETs with a fin height Hfin of 65 nm and various channel lengths. The noise will be studied both in standard operation (ST) and in the dynamic threshold (DT) mode with the substrate contacted to the gate. The dependences of the current noise spectral density will be correlated with the DC parameters, like the hole mobility. 2. Devices and experimental Bulk p-channel FinFETs with 10 fins (Nfin) of 65 nm height (Hfin) have been investigated. The devices have been processed on 200 mm Cz silicon wafers. The gate oxide consists of a 2.6 nm HfSiON-layer (40% Hf) on a 1 nm interfacial SiO2-layer. The Equivalent Oxide Thickness tEOT = 1.5 nm. A Selective Epitaxial Growth (SEG) in the source/drain regions is used to reduce the series resistance. Devices with a fin width Weff = 20 nm and Weff = 35 nm and a gate length Leff = 25–915 nm have been studied. The total width Z of the devices is calculated as Nfin(Weff + 2Hfin).
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result, the value of the mobility lm corresponding to the maximum of the curve gm(Vov) also increases. Fig. 3b presents the dependence of lm on Leff for two different values of Weff. It is seen that lm increases not only with increasing Leff but also with decreasing Weff. It should be noted that the hole mobility is expected to be higher on the (1 1 0) sidewalls compared with the (1 0 0) standard plane [11]. As the sidewall contribution becomes more pronounced for the narrower fins, a higher mobility and maximum transconductance is thus expected. The mechanisms of both effects, namely the sub-linear increase of I with increasing |Vov| and the increase of lm with increasing Leff and decreasing Weff can be explained by the analysis of the drain current noise, as will be shown in the next section. 3.2. Drain current noise Fig. 1. Dependence of the threshold voltage and of the subthreshold slope of the curve I(VGF) on the effective length; Weff = 20 nm.
Fig. 1 presents the length dependence of the threshold voltage Vth and of the subthreshold slope S of the dependence I(VGF) under depletion conditions where I exp(b|VGF|), I and VGF are the drain current and gate voltage, respectively, b is the coefficient. It is seen that both values decrease at Leff P 40 nm (short channel effects). The drain current I and the spectral density SI of its noise have been measured at a drain voltage VDS = 25 mV in a wide range of gate voltages VGF. The noise spectra were measured in the frequency range f = 0.7 Hz to 100 kHz. The measurements have been carried out not only under standard biasing conditions (ST) but also in a Dynamic Threshold Voltage mode (DT) where the silicon substrate is short circuited with the gate.
The noise spectra measured for the devices studied are shown in Fig. 4. It is found that the noise spectra are 1/fc-like for the whole investigated gate biases irrespective of the value of gate length Leff, where c is close to unity (see Fig. 4a and b which correspond to the devices of Leff = 915 nm and Leff = 35 nm, respectively). Also in the case of the devices with Leff < 165 nm the Lorentzian components enter the noise spectra (see Fig. 4b). However in this paper we will confined to discussing the 1/fc noise behavior. The noise characteristics typical for the devices studied are presented in Fig. 5. Fig. 5a demonstrates the dependence of the normalized value of SI(Leff)3/Z for the spectral density of the drain current noise SI on Vov for devices of different Leff. As is seen, the value of SI practically stops to be dependent on Vov at sufficiently high |Vov| except for the samples of Leff = 915 nm. It is also seen that, like in the case of the normalized drain current, the value of
3. Results and discussion 3.1. Drain current Fig. 2 shows the dependences of the value of I(Leff/Z) on the overdrive voltage Vov measured for devices of different Leff. It is seen that in spite of the fact that the trivial influence of the values of Z and Leff is taken into account by multiplication of I by the value of (Leff/Z), the value of I(Leff/Z) measured at a given value of Vov, appears to depend on Leff, namely: the higher Leff, the higher I(Leff/Z). It is also seen from Fig. 2 that the increase of I(Leff/Z) with increasing |Vov| at sufficiently high |Vov| appears to become sub-linear. The dependence of gm(Leff/Z) on Vov for the devices of different Leff where gm is the transconductance is shown in Fig. 3a. It is seen that the normalized value of gm increases with increasing Leff. As a
Fig. 2. Dependence of the value of I(Leff/Z) on the overdrive voltage for devices with different Leff and Weff = 20 nm (the dependences for two devices of each length Leff are shown).
Fig. 3. Dependence of the value of gm(Leff/Z) on the overdrive voltage for devices of different Leff and Weff = 20 nm (the dependences for two devices of each length Leff are shown) (a) and of the mobility corresponding to the maximum in curves gm(Vov) on Leff for devices with Weff = 20 nm and 35 nm (b).
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Fig. 4. The noise spectra for devices of Leff = 915 nm (a) and Leff = 35 nm (b) with Weff = 20 nm.
Fig. 5. Dependence of the value of SI(Leff)3/Z (a) and of the value of SVGLeffZ (b) on the overdrive voltage for devices of different Leff and Weff = 20 nm.
the normalized drain current noise SI(Leff)3/Z increases with increasing Leff at a given value of Vov.
Fig. 5b shows the overdrive voltage dependence of the normalized equivalent gate voltage noise SVGLeffZ where SVG = SI/(gm)2. The observation of the plateau in the curve SVGLeffZ vs. Vov (at 0.15 V < |Vov| < 0.55 V for the devices of Leff = 165 nm and Leff = 40 nm and at 0.05 V < |Vov| < 0.35 V for the device of Leff = 65 nm) points to the fact that for the devices of Leff 6 165 nm the 1/f noise considered is of the McWhorter type [12]. Under the McWhorter model the 1/f noise is due to the fluctuations of the number of free charge carriers in the channel accompanying their exchange between the channel and the slow traps located in the gate dielectric at various distances from the Si/SiO2 interface. Observation of the pure 1/f noise points to the fact that the distribution of those traps over the distance into the gate dielectric is homogeneous. As to the devices of Leff = 915 nm, increasing of the value of SI(Leff)3/Z with increasing Vov and also the absence of a plateau in the dependence of SVGLeffZ on Vov suggests that the 1/f noise of these devices can be ascribed to the correlated DnDl fluctuations. The latter allow for number fluctuations due to the inversion layer carriers interaction with oxide traps and mobility fluctuations due to scattering by the trapped carriers [12,13]. The saturation of curves SI(Leff)3/Z for three different gate lengths is presented in Fig. 6a–c. It is seen that SI(Leff)3/Z decreases with decreasing Leff from 65 nm (a) to 35 nm (c). It should be noted that the analysis of the dependences of fSI/I2 on Vov [14] allows concluding that the 1/f noise measured for the FinFETs of Leff P 35 nm is not influenced by the series resistance noise, but is dominated by the channel resistance 1/f noise. One has to take into account that SI/Notl4 for the 1/f McWhorter noise and I/NSl where Not, l and NS are the trap concentration in the gate dielectric, the hole mobility and the free hole concentration in the channel, respectively, and that SI has to decrease with increasing |Vov| in the case where rch < Rser where rch and Rser are the channel and the series resistances, respectively [15]. For DnDl fluctuations one expects an increase in SI with increasing |Vov| [12], so that the plateau observed in the curves SI(Leff)3/Z vs. Vov for the devices of Leff = (165–35) nm means that in the region of sufficiently high values of |Vov| the following situation takes place [15]:
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Fig. 6. Dependence of SI(Leff)3/Z on the overdrive voltage for devices with Leff = 65 nm (a), 60 nm (b) and 35 nm (c).
(i) l is independent of Vov; (ii) the inequality rch Rser is fulfilled in the range of Vov considered; (iii) Not does not depend on Vov; (iv) the correlated DnDl mechanism of the 1/f noise does not manifest itself in the Vov range considered. By taking into account points (i) and (ii) the conclusion can be drawn that the sub-linear dependence of I on Vov observed at high |Vov| is not due to the decrease of l or to the increased influence of Rser in the source-drain resistance (equal to (rch + Rser)) but is due to the sub-linear increase of the free hole concentration NS with increasing |Vov|. These effects have been associated with the increasing value of |Vth| with increasing |VGF|, as for sufficiently high gate currents the sign of the increase of the charge in the traps located in the gate dielectric is the same as the sign of the minority carriers in the channel. It should be noted that the sub-linear increase of the free carrier concentration in the channel and the independence of l on Vov have been observed previously for the advanced n-channel MOS transistors of different types (planar SOI devices, FinFET devices with different gate stacks on strained and non-strained silicon films) [15,16]. Therefore the results described above are of a general nature for a wide class of state-of-the-art MOS transistors. Note also that it follows from points (iii) and (iv) that the increase of SVG observed at |Vov| > 0.55 V (Fig. 5b) is not due to the increase of Not with increasing |Vov| or to the increase of DnDl fluctuations. That increase of SVG is the result of the fact that SVG is determined as SVG = SI/(gm)2, where gm decreases due to the sub-linear increase of I with increasing |Vov|. In other words, that increase of SVG is not connected with some changes in the noise mechanism or its parameters.
Fig. 7 presents the dependences of I(Leff/Z) on SI(Leff)3/Z for devices of different Leff with Weff = 20 nm at the constant overdrive voltage Vov = 1 V. It is seen that
IðLeff =ZÞ / ½SI ðLeff Þ3 =Z1=4
ð1Þ
Note that the same relation has been found also for devices with Weff = 35 nm. It is also interesting to note that, as it is seen in Fig. 7, the point I(Leff/Z) on SI(Leff)3/Z for the devices of Leff = 915 nm, whose 1/f noise behavior is described in the framework of DnDl model, belongs to the curve I(Leff/Z)/[SI(Leff)3/Z]1/4 obtained for the devices of shorter lengths, for which 1/f noise of McWhorter type is typical. The reasons of such situation can be speculated
Fig. 7. The dependence of I(Leff/Z) on SI(Leff)3/Z measured at Vov = 1 V for devices with different values of Leff; Weff = 20 nm.
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Table 1 Threshold voltages in ST and DT regimes for devices with different Leff and Weff. Leff Weff (nm2)
190 35
165 35
65 35
915 20
165 20
Vth (V)
0.497 0.423
0.456 0.417
0.514 0.394
0.560 0.441
0.465 0.350
ST DT
Fig. 10. Dependence of the spectral density of the 1/f noise of the drain currents measured at f = 3 kHz in DT and ST regimes for a device with Leff = 65 nm and Weff = 35 nm.
Fig. 8. Drain current vs. gate voltage in DT and ST regimes for a device with Leff = 65 nm and Weff = 35 nm.
Like in the case of the DT MOS n-channel bulk devices described in [5], our devices in the DT regime are characterized by lower values of |Vth| than in the standard regime (Table 1). However, no increase of the drain current has been observed for the DT regime (Fig. 8). As it is seen from Fig. 8, even a decrease of I takes place at sufficiently high voltages |VG| (|VG| = |VGF| = |VGB| for the DT regime, where VGB is the substrate bias, and |VG| = |VGF| for the standard regime). High leakage currents flowing through the biased source and drain junctions in the DT regime seem to be the reason for such a behavior. Fig. 9 shows the dependences of the forward and reverse currents ID of the drain junction. It is seen that the forward current is rather high. Fig. 10 shows that the equality (SI)DT = (SI)ST is fulfilled where (SI)DT and (SI)ST are the spectral densities of the drain current in the Dynamic Threshold Voltage and standard voltage regimes, respectively. Therefore, in spite of the fact that the drain current decreases in the DT regime, its 1/f noise does not change. This can be explained by the fact that the leakage currents do not flow near the gate interface. 4. Conclusions
Fig. 9. Forward and reverse currents flowing through the drain junction for a device with Leff = 165 nm and Weff = 20 nm.
but it seems most obvious that the points (i)–(iii), which allow for the independence of l and Not on Vov, and fulfillment of the inequality rch Rser in the range of Vov considered, are also valid for the devices of Leff = 915 nm. If one uses for l the following well known formula valid for strong inversion regime [17]
l ¼ l0 =ð1 þ hjV ov jÞ
ð2Þ
where l0 is the low-field free carrier mobility and h is the coefficient characterizing the decrease of l with increasing |Vov| (the mobility degradation coefficient), then relation (1) indicates [15] that h decreases with increasing Leff while l0 does not depend on Leff. Therefore l increases with increasing Leff because of the corresponding decrease of h. 3.3. Current and noise in DT regime The results of the investigations of the drain currents and their 1/f noise in the Dynamic Threshold Voltage regime (DT) are the following.
The drain current in the p-channel FinFETs investigated manifests a sub-linear increase with increasing overdrive voltage |Vov| accompanied by a constant value of the drain current 1/f noise spectral density under conditions of high |Vov| values. The reason for such a behavior of I and SI is the sub-linear increase of the free hole concentration in the channel with increasing |VGF| and the independence of the mobility l on |Vov|. Both effects have been observed previously in other advanced MOSFETs and are attributed to the high gate current passing through the traps in the gate dielectric that prevents the increase of |Vov| with increasing |VGF|. The values of I, gm and SI normalized in accordance with their standard dependence on Leff and Weff increase with increasing Leff and decreasing Weff, in agreement with the observed behavior of l. The decrease of the coefficient h characterizing the decrease of l with increasing |Vov| is shown to be responsible for such a behavior of l. The increase of the equivalent input 1/f noise voltage with increasing |Vov| observed at high values of |Vov| is not due to some modification of the noise mechanism observed at low values of |Vov|. This has to be taken into account when trying to interpret such an increase frequently observed experimentally by manifestation of DnDl fluctuations. For the devices studied, the Dynamic Threshold Voltage regime decreases the threshold voltage |Vth| but doesn’t increase the drain current because of the high leakage currents passing through the drain and source junctions. The drain current 1/f noise doesn’t change in the DT regime.
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References [1] Park T, Choi S, Lee DH, Yoo JR, Lee BC, Kim JY, Lee CG. et al. Fabrication of bodytied FinFETs (Omega MOSFETs) using bulk Si wafers. In: VLSI technol symp tech dig; 2003. p. 135–6. [2] E. Simoen, M. Aoulaiche, N. Collaert, C. Claeys, Low-frequency noise in triplegate n-channel bulk FinFETs. In: Proc 21st Int conf on noise and fluctuations – ICNF 2011; 2011. p. 127–30. [3] Simoen E, Aoulaiche M, Collaert N, Claeys C. Low-frequency noise study of pchannel bulk MuGFETs. Trans Electrochem Soc 2011;39:53–60. [4] Colinge JP. An SOI voltage controlled bipolar MOS device. IEEE Trans Electron Devices 1987;44:845–9. [5] Andrade MGC, Martino JA. Analog performance in FinFETs: Bulk, DTMOS, BOI and SOI. In: Proc sixth workshop of the thematic network on silicon-oninsulator technology – EuroSOI; 2010. p. 67–8. [6] Andrade MGC, Martino JA. Analog performance at low temperatures in triplegate devices: Bulk, DTMOS, BOI and SOI. In: Proc 9th international workshop on low temperature, electronics – WOLTE9; 2010. pp. 45–7. [7] Andrade MGC, Martino JA, Simoen E, Claeys C. Comparison of the low-frequency noise of bulk triple-gate FinFETs with and without dynamic threshold operation. IEEE Electron Dev Lett 2011;32: 1597–9. [8] Andrade MGC, Martino JA, Aoulaiche M, Collaert N, Simoen E, Claeys C. Behavior of triple gate bulk FinFETs with and without DTMOS operation. SolidState Electron 2012;71:63–8.
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[9] E. Simoen, S. Put, P. Leroux, M. Van Uffelen, M. Jurczak, C. Claeys, Lowfrequency noise analysis of c-irradiated p-channel bulk MuGFETs. In: Proc 11th int conf ULIS; 2010. p 25–9. [10] Crupi F, Kaczer B, Degraeve R, Subramanian V, Srinivasan P, Simoen E, et al. Reliability comparison of triple-gate versus planar SOI FETs. IEEE Trans Electron Dev 2006;53:2351–7. [11] Put S, Harsh M, Collaert N, Van Uffelen M, Leroux P, Claeys C, et al. Effect of rotation, gate-dielectric and SEG on the noise behavior of advanced SOI MuGFETs. Solid State Electron 2010;54:178–84. [12] Simoen E, Claeys C. On the flicker noise in submicron silicon MOSFETs. Solid State Electron 1999;43:865–82. [13] Jayaraman R, Sodini CG. A 1/f noise technique to extract the oxide trap density near the conduction band edge of silicon. IEEE Trans Electron Dev 1989;36:1773–82. [14] Vandamme LKJ. Noise as a diagnostic tool for quality and reliability of electronic devices. IEEE Trans Electron Dev 1994;41:2176–87. [15] Lukyanchikova N, Garbar N, Kudina V, Smolanka A, Lokshin M, Simoen E, et al. High gate voltage drain current leveling off and its low-frequency noise in 65 nm fully-depleted strained and non-strained SOI nMOSFETs. Solid State Electron 2008;52:801–7. [16] Lukyanchikova N, Garbar N, Kudina V, Smolanka A, Simoen E, Claeys C. Lowfrequency noise in nFinFETs of different dimensions processed in strained and non-strained SOI wafers. Semicond Phys, Quantum Electron Optoelectron 2008;11:203–8. [17] Gibaudo G. New method for the extraction of MOSFET parameters. Electron Lett 1989;24:543–5.
Contents lists available at SciVerse ScienceDirect
Microelectronics Reliability journal homepage: www.elsevier.com/locate/microrel
Drain currents and their excess noise in triple gate bulk p-channel FinFETs of different geometry N. Lukyanchikova a, N. Garbar a, V. Kudina a,⇑, A. Smolanka a, E. Simoen b, C. Claeys b,c a
V. Lashkaryov Institute of Semiconductor Physics, Prospect Nauki 45, 03028 Kiev, Ukraine Imec, Kapeldreef 75, B-3001 Leuven, Belgium c KU Leuven, Kasteelpark Arenberg 10, B-3001 Leuven, Belgium b
a r t i c l e
i n f o
Article history: Received 8 December 2011 Received in revised form 17 October 2012 Accepted 17 October 2012 Available online 22 November 2012
a b s t r a c t The drain current I, spectral density of the low-frequency 1/f noise SI and transconductance gm of triple gate bulk p-channel field-effect transistors (FinFETs) fabricated on 200 mm diameter Cz silicon wafers have been studied in the standard (ST) and Dynamic Threshold Voltage (DT) modes of operation. For the ST regime, a sub-linear increase of the drain current I with increasing overdrive voltage |Vov| and practically no changes in the spectral density SI of the noise are observed at high values of |Vov|. The effect is attributed to a sub-linear increase of the free hole density in the channel, whereby the mobility does not change with increasing |Vov|. An increase of the values of I, SI and gm normalized for the device geometry with increasing Leff is found and is attributed to the decrease of the mobility degradation coefficient with increasing Leff. For the DT regime of operation, the decrease of the threshold voltage |Vth| is not accompanied by an increase of the drain current which decreases with increasing |VGF| due to the high leakage current passing through the forward biased drain and source junctions. However, that decrease of the drain current is not accompanied by changes in the value of SI. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Bulk FinFETs combine the good control of the short-channel effects with the ease of manufacturing on bulk silicon substrates [1]. The technology has reached a sufficient level of maturity to enable meaningful low-frequency (LF) noise measurements. Initial results have pointed out that for triple gate (trigate) bulk FinFETs with SiO2 or SiON gate dielectric, both 1/f noise and Generation– Recombination (GR) noise are present, whereby the 1/f noise in many cases is dominated by carrier trapping in the gate dielectric [2,3]. The GR noise was ascribed to traps both in the silicon fins and in the gate oxide, based on the gate-voltage dependence of the corner frequency fc. It was also noted that operation of n-channel bulk FinFETs in the dynamic threshold mode of operation [4–6], did not affect the LF spectral density, SI [7], while an improvement in the analog performance was observed [8]. Initial noise results on bulk p-MOSFETs with high-k/metal gate have also been reported [9]. Given the multiple gate nature of the devices, one of the obvious questions is whether the device geometry and in particular the fin width has an impact on the LF noise behavior. One should account for the fact that for narrow devices, most of the current is flowing along the (1 1 0) sidewalls, which have usually a different
⇑ Corresponding author. Tel.: +38 044 525 64 53; fax: +38 044 525 61 91. E-mail address: [email protected] (V. Kudina). 0026-2714/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.microrel.2012.10.011
orientation than for standard planar bulk transistors on (1 0 0) wafers. It turns out that for Silicon-on-Insulator (SOI) FinFETs, the device orientation has only a minor effect on the noise [10,11]. Another factor which can play a role is that in the case of narrow fins, the structure can be considered as fully depleted, i.e., the width of the fin is smaller than two times the depletion width at the sidewalls of the device. It is the aim to report here on detailed LF noise results of narrow high-k/metal gate bulk p-FinFETs with a fin height Hfin of 65 nm and various channel lengths. The noise will be studied both in standard operation (ST) and in the dynamic threshold (DT) mode with the substrate contacted to the gate. The dependences of the current noise spectral density will be correlated with the DC parameters, like the hole mobility. 2. Devices and experimental Bulk p-channel FinFETs with 10 fins (Nfin) of 65 nm height (Hfin) have been investigated. The devices have been processed on 200 mm Cz silicon wafers. The gate oxide consists of a 2.6 nm HfSiON-layer (40% Hf) on a 1 nm interfacial SiO2-layer. The Equivalent Oxide Thickness tEOT = 1.5 nm. A Selective Epitaxial Growth (SEG) in the source/drain regions is used to reduce the series resistance. Devices with a fin width Weff = 20 nm and Weff = 35 nm and a gate length Leff = 25–915 nm have been studied. The total width Z of the devices is calculated as Nfin(Weff + 2Hfin).
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result, the value of the mobility lm corresponding to the maximum of the curve gm(Vov) also increases. Fig. 3b presents the dependence of lm on Leff for two different values of Weff. It is seen that lm increases not only with increasing Leff but also with decreasing Weff. It should be noted that the hole mobility is expected to be higher on the (1 1 0) sidewalls compared with the (1 0 0) standard plane [11]. As the sidewall contribution becomes more pronounced for the narrower fins, a higher mobility and maximum transconductance is thus expected. The mechanisms of both effects, namely the sub-linear increase of I with increasing |Vov| and the increase of lm with increasing Leff and decreasing Weff can be explained by the analysis of the drain current noise, as will be shown in the next section. 3.2. Drain current noise Fig. 1. Dependence of the threshold voltage and of the subthreshold slope of the curve I(VGF) on the effective length; Weff = 20 nm.
Fig. 1 presents the length dependence of the threshold voltage Vth and of the subthreshold slope S of the dependence I(VGF) under depletion conditions where I exp(b|VGF|), I and VGF are the drain current and gate voltage, respectively, b is the coefficient. It is seen that both values decrease at Leff P 40 nm (short channel effects). The drain current I and the spectral density SI of its noise have been measured at a drain voltage VDS = 25 mV in a wide range of gate voltages VGF. The noise spectra were measured in the frequency range f = 0.7 Hz to 100 kHz. The measurements have been carried out not only under standard biasing conditions (ST) but also in a Dynamic Threshold Voltage mode (DT) where the silicon substrate is short circuited with the gate.
The noise spectra measured for the devices studied are shown in Fig. 4. It is found that the noise spectra are 1/fc-like for the whole investigated gate biases irrespective of the value of gate length Leff, where c is close to unity (see Fig. 4a and b which correspond to the devices of Leff = 915 nm and Leff = 35 nm, respectively). Also in the case of the devices with Leff < 165 nm the Lorentzian components enter the noise spectra (see Fig. 4b). However in this paper we will confined to discussing the 1/fc noise behavior. The noise characteristics typical for the devices studied are presented in Fig. 5. Fig. 5a demonstrates the dependence of the normalized value of SI(Leff)3/Z for the spectral density of the drain current noise SI on Vov for devices of different Leff. As is seen, the value of SI practically stops to be dependent on Vov at sufficiently high |Vov| except for the samples of Leff = 915 nm. It is also seen that, like in the case of the normalized drain current, the value of
3. Results and discussion 3.1. Drain current Fig. 2 shows the dependences of the value of I(Leff/Z) on the overdrive voltage Vov measured for devices of different Leff. It is seen that in spite of the fact that the trivial influence of the values of Z and Leff is taken into account by multiplication of I by the value of (Leff/Z), the value of I(Leff/Z) measured at a given value of Vov, appears to depend on Leff, namely: the higher Leff, the higher I(Leff/Z). It is also seen from Fig. 2 that the increase of I(Leff/Z) with increasing |Vov| at sufficiently high |Vov| appears to become sub-linear. The dependence of gm(Leff/Z) on Vov for the devices of different Leff where gm is the transconductance is shown in Fig. 3a. It is seen that the normalized value of gm increases with increasing Leff. As a
Fig. 2. Dependence of the value of I(Leff/Z) on the overdrive voltage for devices with different Leff and Weff = 20 nm (the dependences for two devices of each length Leff are shown).
Fig. 3. Dependence of the value of gm(Leff/Z) on the overdrive voltage for devices of different Leff and Weff = 20 nm (the dependences for two devices of each length Leff are shown) (a) and of the mobility corresponding to the maximum in curves gm(Vov) on Leff for devices with Weff = 20 nm and 35 nm (b).
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Fig. 4. The noise spectra for devices of Leff = 915 nm (a) and Leff = 35 nm (b) with Weff = 20 nm.
Fig. 5. Dependence of the value of SI(Leff)3/Z (a) and of the value of SVGLeffZ (b) on the overdrive voltage for devices of different Leff and Weff = 20 nm.
the normalized drain current noise SI(Leff)3/Z increases with increasing Leff at a given value of Vov.
Fig. 5b shows the overdrive voltage dependence of the normalized equivalent gate voltage noise SVGLeffZ where SVG = SI/(gm)2. The observation of the plateau in the curve SVGLeffZ vs. Vov (at 0.15 V < |Vov| < 0.55 V for the devices of Leff = 165 nm and Leff = 40 nm and at 0.05 V < |Vov| < 0.35 V for the device of Leff = 65 nm) points to the fact that for the devices of Leff 6 165 nm the 1/f noise considered is of the McWhorter type [12]. Under the McWhorter model the 1/f noise is due to the fluctuations of the number of free charge carriers in the channel accompanying their exchange between the channel and the slow traps located in the gate dielectric at various distances from the Si/SiO2 interface. Observation of the pure 1/f noise points to the fact that the distribution of those traps over the distance into the gate dielectric is homogeneous. As to the devices of Leff = 915 nm, increasing of the value of SI(Leff)3/Z with increasing Vov and also the absence of a plateau in the dependence of SVGLeffZ on Vov suggests that the 1/f noise of these devices can be ascribed to the correlated DnDl fluctuations. The latter allow for number fluctuations due to the inversion layer carriers interaction with oxide traps and mobility fluctuations due to scattering by the trapped carriers [12,13]. The saturation of curves SI(Leff)3/Z for three different gate lengths is presented in Fig. 6a–c. It is seen that SI(Leff)3/Z decreases with decreasing Leff from 65 nm (a) to 35 nm (c). It should be noted that the analysis of the dependences of fSI/I2 on Vov [14] allows concluding that the 1/f noise measured for the FinFETs of Leff P 35 nm is not influenced by the series resistance noise, but is dominated by the channel resistance 1/f noise. One has to take into account that SI/Notl4 for the 1/f McWhorter noise and I/NSl where Not, l and NS are the trap concentration in the gate dielectric, the hole mobility and the free hole concentration in the channel, respectively, and that SI has to decrease with increasing |Vov| in the case where rch < Rser where rch and Rser are the channel and the series resistances, respectively [15]. For DnDl fluctuations one expects an increase in SI with increasing |Vov| [12], so that the plateau observed in the curves SI(Leff)3/Z vs. Vov for the devices of Leff = (165–35) nm means that in the region of sufficiently high values of |Vov| the following situation takes place [15]:
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Fig. 6. Dependence of SI(Leff)3/Z on the overdrive voltage for devices with Leff = 65 nm (a), 60 nm (b) and 35 nm (c).
(i) l is independent of Vov; (ii) the inequality rch Rser is fulfilled in the range of Vov considered; (iii) Not does not depend on Vov; (iv) the correlated DnDl mechanism of the 1/f noise does not manifest itself in the Vov range considered. By taking into account points (i) and (ii) the conclusion can be drawn that the sub-linear dependence of I on Vov observed at high |Vov| is not due to the decrease of l or to the increased influence of Rser in the source-drain resistance (equal to (rch + Rser)) but is due to the sub-linear increase of the free hole concentration NS with increasing |Vov|. These effects have been associated with the increasing value of |Vth| with increasing |VGF|, as for sufficiently high gate currents the sign of the increase of the charge in the traps located in the gate dielectric is the same as the sign of the minority carriers in the channel. It should be noted that the sub-linear increase of the free carrier concentration in the channel and the independence of l on Vov have been observed previously for the advanced n-channel MOS transistors of different types (planar SOI devices, FinFET devices with different gate stacks on strained and non-strained silicon films) [15,16]. Therefore the results described above are of a general nature for a wide class of state-of-the-art MOS transistors. Note also that it follows from points (iii) and (iv) that the increase of SVG observed at |Vov| > 0.55 V (Fig. 5b) is not due to the increase of Not with increasing |Vov| or to the increase of DnDl fluctuations. That increase of SVG is the result of the fact that SVG is determined as SVG = SI/(gm)2, where gm decreases due to the sub-linear increase of I with increasing |Vov|. In other words, that increase of SVG is not connected with some changes in the noise mechanism or its parameters.
Fig. 7 presents the dependences of I(Leff/Z) on SI(Leff)3/Z for devices of different Leff with Weff = 20 nm at the constant overdrive voltage Vov = 1 V. It is seen that
IðLeff =ZÞ / ½SI ðLeff Þ3 =Z1=4
ð1Þ
Note that the same relation has been found also for devices with Weff = 35 nm. It is also interesting to note that, as it is seen in Fig. 7, the point I(Leff/Z) on SI(Leff)3/Z for the devices of Leff = 915 nm, whose 1/f noise behavior is described in the framework of DnDl model, belongs to the curve I(Leff/Z)/[SI(Leff)3/Z]1/4 obtained for the devices of shorter lengths, for which 1/f noise of McWhorter type is typical. The reasons of such situation can be speculated
Fig. 7. The dependence of I(Leff/Z) on SI(Leff)3/Z measured at Vov = 1 V for devices with different values of Leff; Weff = 20 nm.
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Table 1 Threshold voltages in ST and DT regimes for devices with different Leff and Weff. Leff Weff (nm2)
190 35
165 35
65 35
915 20
165 20
Vth (V)
0.497 0.423
0.456 0.417
0.514 0.394
0.560 0.441
0.465 0.350
ST DT
Fig. 10. Dependence of the spectral density of the 1/f noise of the drain currents measured at f = 3 kHz in DT and ST regimes for a device with Leff = 65 nm and Weff = 35 nm.
Fig. 8. Drain current vs. gate voltage in DT and ST regimes for a device with Leff = 65 nm and Weff = 35 nm.
Like in the case of the DT MOS n-channel bulk devices described in [5], our devices in the DT regime are characterized by lower values of |Vth| than in the standard regime (Table 1). However, no increase of the drain current has been observed for the DT regime (Fig. 8). As it is seen from Fig. 8, even a decrease of I takes place at sufficiently high voltages |VG| (|VG| = |VGF| = |VGB| for the DT regime, where VGB is the substrate bias, and |VG| = |VGF| for the standard regime). High leakage currents flowing through the biased source and drain junctions in the DT regime seem to be the reason for such a behavior. Fig. 9 shows the dependences of the forward and reverse currents ID of the drain junction. It is seen that the forward current is rather high. Fig. 10 shows that the equality (SI)DT = (SI)ST is fulfilled where (SI)DT and (SI)ST are the spectral densities of the drain current in the Dynamic Threshold Voltage and standard voltage regimes, respectively. Therefore, in spite of the fact that the drain current decreases in the DT regime, its 1/f noise does not change. This can be explained by the fact that the leakage currents do not flow near the gate interface. 4. Conclusions
Fig. 9. Forward and reverse currents flowing through the drain junction for a device with Leff = 165 nm and Weff = 20 nm.
but it seems most obvious that the points (i)–(iii), which allow for the independence of l and Not on Vov, and fulfillment of the inequality rch Rser in the range of Vov considered, are also valid for the devices of Leff = 915 nm. If one uses for l the following well known formula valid for strong inversion regime [17]
l ¼ l0 =ð1 þ hjV ov jÞ
ð2Þ
where l0 is the low-field free carrier mobility and h is the coefficient characterizing the decrease of l with increasing |Vov| (the mobility degradation coefficient), then relation (1) indicates [15] that h decreases with increasing Leff while l0 does not depend on Leff. Therefore l increases with increasing Leff because of the corresponding decrease of h. 3.3. Current and noise in DT regime The results of the investigations of the drain currents and their 1/f noise in the Dynamic Threshold Voltage regime (DT) are the following.
The drain current in the p-channel FinFETs investigated manifests a sub-linear increase with increasing overdrive voltage |Vov| accompanied by a constant value of the drain current 1/f noise spectral density under conditions of high |Vov| values. The reason for such a behavior of I and SI is the sub-linear increase of the free hole concentration in the channel with increasing |VGF| and the independence of the mobility l on |Vov|. Both effects have been observed previously in other advanced MOSFETs and are attributed to the high gate current passing through the traps in the gate dielectric that prevents the increase of |Vov| with increasing |VGF|. The values of I, gm and SI normalized in accordance with their standard dependence on Leff and Weff increase with increasing Leff and decreasing Weff, in agreement with the observed behavior of l. The decrease of the coefficient h characterizing the decrease of l with increasing |Vov| is shown to be responsible for such a behavior of l. The increase of the equivalent input 1/f noise voltage with increasing |Vov| observed at high values of |Vov| is not due to some modification of the noise mechanism observed at low values of |Vov|. This has to be taken into account when trying to interpret such an increase frequently observed experimentally by manifestation of DnDl fluctuations. For the devices studied, the Dynamic Threshold Voltage regime decreases the threshold voltage |Vth| but doesn’t increase the drain current because of the high leakage currents passing through the drain and source junctions. The drain current 1/f noise doesn’t change in the DT regime.
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