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Comments on “numerical analysis of small-signal characteristics of a fully depleted SOI MOSFET”
~
Pergamon
Solid-State ElectronicsVol. 37, No. 7, pp. 1447-1448, 1994 Copyright © 1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0038-1101/94 $6.00+ 0.00
0038-1101(93)E0084-E
NOTE C O M M E N T S O N " N U M E R I C A L ANALYSIS O F S M A L L - S I G N A L C H A R A C T E R I S T I C S O F A FULLY D E P L E T E D S O l M O S F E T " (Received 13 July 1993)
l. INTRODUCTION In a recent paper[l], Yang and Li present an analysis of the small-signal intrinsic characteristics of thin-film fullydepleted SO1 MOSFETs. Two possible cases of full depletion are discussed, i.e. with the back interface (Si film/buried oxide) either in depletion or in accumulation. The present note points out several shortcomings in the discussion of the back accumulation case which may lead to incorrect interpretation of the capacitance curves. In particular, in the work[l], the front gate-to-source intrinsic capacitance (Cgfs) is predicted to be equal to 2/3 of the total gate oxide capacitance in the saturation regime, no matter the charge condition at the film back interface (accumulation or depletion). However from previous experimental and theoretical works dealing with partially-depleted SOl devices[2-4], it can rightfully be expected that in the back accumulation case, Ces~ should be larger than the conventional value. It is shown here that these results can indeed be extended to the case of full depletion with back accumulation, which questions the validity of the modelling presented in [I]. How this modelling should then be correctly interpreted and eventually modified is finally discussed. 2. CONFRONTATION OF YANG AND LI'S RESULTS WITH MEDICI SIMULATIONS Two-dimensional Medici simulations[5] have been performed on a device structure derived from the set of parameters specified in [1]. The front gate oxide, Si film and buried oxide thicknesses are 20, 200 and 400 nm respectively. The uniform film doping level is 10 ~6cm 3. The device length is 10/am. The front and back fiat-band voltages are both equal to 0 V. Default Medici values are used for the device width (1/am), the mobility, SRH generation-recombination processes and other general physical parameters. The validity of Medici to predict the intrinsic capacitances of SO1 MOSFETs is discussed into full detail in [4]. As in [1], Csf~ is extracted here from the simulation results using the quasi-static scheme: two steady-state bias points differing by a small incremental bias A Vs at the source are solved separately and C~fs is then computed from the gate charge difference AQg as -AQg/AV~. Figure 1 clearly shows that in saturation, the magnitude of Cgf~significantly depends on the charge condition at the film back interface. It is close to 2/3 of the total gate oxide capacitance under back depletion conditions and more than 10% larger under back accumulation, corroborating measurements previously realized on partially-depleted SOl devices[2,3]. Furthermore the simulations yield in subthreshold operation a non-zero and gate bias dependent C~-~. None of these unconventional behaviors are discussed in [1]. To understand the discrepancies between the results presented in [1] and these presented here, we analyze the
potential variation AW resulting from a source bias change by AVs, in a vertical cross-section of the SOI film at 1/am from the drain (i.e. in the pinch-off region). The potential variation at the front film interface is a direct image of the electric field variation in the gate oxide and hence of the charge change on the gate electrode. Figure 2 indicates that AW is strongly enhanced in back accumulation when compared to back depletion, thereby inducing the increase of Cgf~over 2/3 of the total gate oxide capacitance. The figure also shows that at the accumulated back interface, the potential variation is almost equal to AVs in quasi-static operation. This effect is not taken into account in [1]. 3. COMMENTS ON THE MODELLING IN Ill The discrepancies between the results presented in [1] and these presented here lie in the treatment of the floating substrate behavior. When Cr.fsis computed in [1], the floating body potential Vb is pinned to ground. In our simulations and measurements on the contrary, it is left floating and Fig. 2 demonstrated that Vb actually follows the source potential variations. The Cgf~ computed in [1] then only corresponds to a fraction of the total CCs we consider, i.e. the part corresponding to the partial derivative of the gate charge by the source voltage all other terminals including the body node kept constant. The remaining part of the actual CCs however appears in the small-signal equivalent circuit presented in Fig. l(b) of [I]. When the body node is
0.8
Off ~
0.6
Sat.
Triode
,.
~o.2 o
-. . . . . . . .
',t IIiS g I ~i C
Z
I
0.0
I
............. '
0
'
'
'
'
1 2 3 4 F r o n t gate-to-source V g f s voltage (V)
5
Fig. 1. Intrinsic front gate-to-source capacitance normalized to the total gate oxide capacitance for a drain-to-source bias equal to 1 V: (A,B) quasi-static simulation (AVs = 2.5 mV); (C) 1 MHz a.c. simulation; (A,C) back accumulation (back gate-to-source b i a s = - 2 0 V ) ; (B) back depletion (back gate-to-source bias = 0 V).
1447
1448
Note .
.
.
.
l
.
.
.
.
.
~o l-J
B o
0 '0.i0 '0.20 Depth in Si film, x (Microns) Fig. 2. Potential variation from film front interface (x = 0) to back interface (x = 0.2 #m) at I # m of the drain for a front gate-to-source bias equal to 2 V and a drain-tosource bias equal to 1 V: (A,B) quasi-static simulation (AV~ = 2.5 mV); (C) transient simulation (AV~ = 2.5 mV applied as a linear ramp of 0.1 #s of duration); (A,C) back accumulation (back gate-to-source bias = - 2 0 V); (B) back depletion (back gate-to-source bias = 0 V). floating, the additional part of Cgfs derives from the series combination of the body-to-source C~ and gate-to-body C ~ capacitances. Estimating this contribution from the values of C~ and C ~ in saturation indicated in Fig. 7 of[I], we indeed found a value approximately close to the difference between our Csfs and the 2/3 of the total oxide capacitance. Nevertheless, the discrepancy between Yang and Li's results and ours does not only lie in the use of different definitions for C¢~.. More fundamentally, under back accumulation condttions the source and body nodes are not only connected by a capacitor as defined in [1], especially in quasi-static operation. Vb is indeed the potential of an accumulation layer whose carriers can only be provided and removed by the source junction as long as no body contact is present. In that case and in quasi-static operation, Vb is strictly equal to Vs and AVb to AVs, as clearly observed in Fig. 2. This is not stated in [1] and explains the discrepancy between Yang and Li's subthreshold C~rscharacteristics and ours (Fig. 1). In [1] C~ falls to zero in subthreshold operation suppressing any body-to-source connection. If we take into account in Yang and Li's equivalent circuit (Fig. l(b) in [1]) that Vb is tied to V~, we find that the actual gate-to-source capacitance is then equal to C ~ and we may indeed verify that the magnitude of our Csf~(Fig. 1) is similar to Yang and Li's C ~ (Fig. 7 in [1]). To be complete, we have also analyzed the non-quasistatic Csf, characteristics with the small-signal computation scheme of Medici applying at the source contact a 1 MHz sine voltage variation of 2.5 mV in amplitude. The results show a dramatic decrease of C~f, to almost zero conventional values in subthreshold operation and a slight reduction of Csfs in saturation (Fig. I). The reason lies again in the
intensity of the source-to-body connection. In transient or high-frequency small-signal operation, AVb is not strictly equal to AVs as a result of the time constants of the generation/recombination processes through the source junction (Fig. 2, curve C). In order to reproduce the complex small-signal characteristics we have observed in the case of full depletion with back accumulation, a correct modelling of the source-tobody junction response is required. The model presented in [1] should hence incorporate in addition to Cb~, a non-zero conductance between the source and body nodes in order to impose Vb equal to V~in quasi-static operation and take into account the frequency dependence of the AVb to AVs ratio. Finally it is important to note that impact ionization effects are not considered in [1] nor in the present discussion and could further alter the small-signal characteristics of SOl MOSFETs as shown in [2-4]. 4. CONCLUSION The discrepancies existing between a recent paper by Yang and Li[1] and other results[2-4] have been clarified. Yang and Li's small-signal model for fully-depleted SOl MOSFETs is finally found to be consistent with highfrequency measurements previously published[2-4] provided that the correct interpretation of the back accumulation case is given and impact ionization effects are not considered. This discussion clearly lacked in the initial paper[l]. Nevertheless to fully reproduce the complex and frequencydependent small-signal behavior of the SOl MOSFET with back accumulation, Yang and Li's model has to be corrected by taking into account the non zero conductance of the source-to-floating body junction. Acknowledgements--The author wished to thank TMA for providing Medici under its University Partners Program and Professor J.-P. Colinge for critically reviewing the manuscript. Denis Flandre is Research Associate of the National Fund for Scientific Research (Belgium). Laboratoire de MicroFlectronique UniversitF Catholique de Louvain Place du Levant 3 B- 1348 Louvain -la-Neuve Belgium
D. FLANDRE
REFERENCES 1. P. C. Yang and S. S. Li, Solid St. Electron. 36, 939 (1993). 2. D. Flandre, F. Van de Wiele, P. G. A. Jespers and M. Haond, Proc. 20th European Solid State Device Research Conf. (ESSDERC), Nottingham, England, p. 437. lOP Publishing (1990). 3. D. Flandre, Electron. Lett. 28, 967 (1992). 4. D. Flandre, IEEE Trans. Electron Devices 40, 1785 (1993). 5. TMA MEDICI: Two-dimensional device simulation program, Version 1. Technology Modeling Associates Inc., Palo Alto, Calif. (1992).
Pergamon
Solid-State ElectronicsVol. 37, No. 7, pp. 1447-1448, 1994 Copyright © 1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0038-1101/94 $6.00+ 0.00
0038-1101(93)E0084-E
NOTE C O M M E N T S O N " N U M E R I C A L ANALYSIS O F S M A L L - S I G N A L C H A R A C T E R I S T I C S O F A FULLY D E P L E T E D S O l M O S F E T " (Received 13 July 1993)
l. INTRODUCTION In a recent paper[l], Yang and Li present an analysis of the small-signal intrinsic characteristics of thin-film fullydepleted SO1 MOSFETs. Two possible cases of full depletion are discussed, i.e. with the back interface (Si film/buried oxide) either in depletion or in accumulation. The present note points out several shortcomings in the discussion of the back accumulation case which may lead to incorrect interpretation of the capacitance curves. In particular, in the work[l], the front gate-to-source intrinsic capacitance (Cgfs) is predicted to be equal to 2/3 of the total gate oxide capacitance in the saturation regime, no matter the charge condition at the film back interface (accumulation or depletion). However from previous experimental and theoretical works dealing with partially-depleted SOl devices[2-4], it can rightfully be expected that in the back accumulation case, Ces~ should be larger than the conventional value. It is shown here that these results can indeed be extended to the case of full depletion with back accumulation, which questions the validity of the modelling presented in [I]. How this modelling should then be correctly interpreted and eventually modified is finally discussed. 2. CONFRONTATION OF YANG AND LI'S RESULTS WITH MEDICI SIMULATIONS Two-dimensional Medici simulations[5] have been performed on a device structure derived from the set of parameters specified in [1]. The front gate oxide, Si film and buried oxide thicknesses are 20, 200 and 400 nm respectively. The uniform film doping level is 10 ~6cm 3. The device length is 10/am. The front and back fiat-band voltages are both equal to 0 V. Default Medici values are used for the device width (1/am), the mobility, SRH generation-recombination processes and other general physical parameters. The validity of Medici to predict the intrinsic capacitances of SO1 MOSFETs is discussed into full detail in [4]. As in [1], Csf~ is extracted here from the simulation results using the quasi-static scheme: two steady-state bias points differing by a small incremental bias A Vs at the source are solved separately and C~fs is then computed from the gate charge difference AQg as -AQg/AV~. Figure 1 clearly shows that in saturation, the magnitude of Cgf~significantly depends on the charge condition at the film back interface. It is close to 2/3 of the total gate oxide capacitance under back depletion conditions and more than 10% larger under back accumulation, corroborating measurements previously realized on partially-depleted SOl devices[2,3]. Furthermore the simulations yield in subthreshold operation a non-zero and gate bias dependent C~-~. None of these unconventional behaviors are discussed in [1]. To understand the discrepancies between the results presented in [1] and these presented here, we analyze the
potential variation AW resulting from a source bias change by AVs, in a vertical cross-section of the SOI film at 1/am from the drain (i.e. in the pinch-off region). The potential variation at the front film interface is a direct image of the electric field variation in the gate oxide and hence of the charge change on the gate electrode. Figure 2 indicates that AW is strongly enhanced in back accumulation when compared to back depletion, thereby inducing the increase of Cgf~over 2/3 of the total gate oxide capacitance. The figure also shows that at the accumulated back interface, the potential variation is almost equal to AVs in quasi-static operation. This effect is not taken into account in [1]. 3. COMMENTS ON THE MODELLING IN Ill The discrepancies between the results presented in [1] and these presented here lie in the treatment of the floating substrate behavior. When Cr.fsis computed in [1], the floating body potential Vb is pinned to ground. In our simulations and measurements on the contrary, it is left floating and Fig. 2 demonstrated that Vb actually follows the source potential variations. The Cgf~ computed in [1] then only corresponds to a fraction of the total CCs we consider, i.e. the part corresponding to the partial derivative of the gate charge by the source voltage all other terminals including the body node kept constant. The remaining part of the actual CCs however appears in the small-signal equivalent circuit presented in Fig. l(b) of [I]. When the body node is
0.8
Off ~
0.6
Sat.
Triode
,.
~o.2 o
-. . . . . . . .
',t IIiS g I ~i C
Z
I
0.0
I
............. '
0
'
'
'
'
1 2 3 4 F r o n t gate-to-source V g f s voltage (V)
5
Fig. 1. Intrinsic front gate-to-source capacitance normalized to the total gate oxide capacitance for a drain-to-source bias equal to 1 V: (A,B) quasi-static simulation (AVs = 2.5 mV); (C) 1 MHz a.c. simulation; (A,C) back accumulation (back gate-to-source b i a s = - 2 0 V ) ; (B) back depletion (back gate-to-source bias = 0 V).
1447
1448
Note .
.
.
.
l
.
.
.
.
.
~o l-J
B o
0 '0.i0 '0.20 Depth in Si film, x (Microns) Fig. 2. Potential variation from film front interface (x = 0) to back interface (x = 0.2 #m) at I # m of the drain for a front gate-to-source bias equal to 2 V and a drain-tosource bias equal to 1 V: (A,B) quasi-static simulation (AV~ = 2.5 mV); (C) transient simulation (AV~ = 2.5 mV applied as a linear ramp of 0.1 #s of duration); (A,C) back accumulation (back gate-to-source bias = - 2 0 V); (B) back depletion (back gate-to-source bias = 0 V). floating, the additional part of Cgfs derives from the series combination of the body-to-source C~ and gate-to-body C ~ capacitances. Estimating this contribution from the values of C~ and C ~ in saturation indicated in Fig. 7 of[I], we indeed found a value approximately close to the difference between our Csfs and the 2/3 of the total oxide capacitance. Nevertheless, the discrepancy between Yang and Li's results and ours does not only lie in the use of different definitions for C¢~.. More fundamentally, under back accumulation condttions the source and body nodes are not only connected by a capacitor as defined in [1], especially in quasi-static operation. Vb is indeed the potential of an accumulation layer whose carriers can only be provided and removed by the source junction as long as no body contact is present. In that case and in quasi-static operation, Vb is strictly equal to Vs and AVb to AVs, as clearly observed in Fig. 2. This is not stated in [1] and explains the discrepancy between Yang and Li's subthreshold C~rscharacteristics and ours (Fig. 1). In [1] C~ falls to zero in subthreshold operation suppressing any body-to-source connection. If we take into account in Yang and Li's equivalent circuit (Fig. l(b) in [1]) that Vb is tied to V~, we find that the actual gate-to-source capacitance is then equal to C ~ and we may indeed verify that the magnitude of our Csf~(Fig. 1) is similar to Yang and Li's C ~ (Fig. 7 in [1]). To be complete, we have also analyzed the non-quasistatic Csf, characteristics with the small-signal computation scheme of Medici applying at the source contact a 1 MHz sine voltage variation of 2.5 mV in amplitude. The results show a dramatic decrease of C~f, to almost zero conventional values in subthreshold operation and a slight reduction of Csfs in saturation (Fig. I). The reason lies again in the
intensity of the source-to-body connection. In transient or high-frequency small-signal operation, AVb is not strictly equal to AVs as a result of the time constants of the generation/recombination processes through the source junction (Fig. 2, curve C). In order to reproduce the complex small-signal characteristics we have observed in the case of full depletion with back accumulation, a correct modelling of the source-tobody junction response is required. The model presented in [1] should hence incorporate in addition to Cb~, a non-zero conductance between the source and body nodes in order to impose Vb equal to V~in quasi-static operation and take into account the frequency dependence of the AVb to AVs ratio. Finally it is important to note that impact ionization effects are not considered in [1] nor in the present discussion and could further alter the small-signal characteristics of SOl MOSFETs as shown in [2-4]. 4. CONCLUSION The discrepancies existing between a recent paper by Yang and Li[1] and other results[2-4] have been clarified. Yang and Li's small-signal model for fully-depleted SOl MOSFETs is finally found to be consistent with highfrequency measurements previously published[2-4] provided that the correct interpretation of the back accumulation case is given and impact ionization effects are not considered. This discussion clearly lacked in the initial paper[l]. Nevertheless to fully reproduce the complex and frequencydependent small-signal behavior of the SOl MOSFET with back accumulation, Yang and Li's model has to be corrected by taking into account the non zero conductance of the source-to-floating body junction. Acknowledgements--The author wished to thank TMA for providing Medici under its University Partners Program and Professor J.-P. Colinge for critically reviewing the manuscript. Denis Flandre is Research Associate of the National Fund for Scientific Research (Belgium). Laboratoire de MicroFlectronique UniversitF Catholique de Louvain Place du Levant 3 B- 1348 Louvain -la-Neuve Belgium
D. FLANDRE
REFERENCES 1. P. C. Yang and S. S. Li, Solid St. Electron. 36, 939 (1993). 2. D. Flandre, F. Van de Wiele, P. G. A. Jespers and M. Haond, Proc. 20th European Solid State Device Research Conf. (ESSDERC), Nottingham, England, p. 437. lOP Publishing (1990). 3. D. Flandre, Electron. Lett. 28, 967 (1992). 4. D. Flandre, IEEE Trans. Electron Devices 40, 1785 (1993). 5. TMA MEDICI: Two-dimensional device simulation program, Version 1. Technology Modeling Associates Inc., Palo Alto, Calif. (1992).