Wei-Tai Gong(鞏偉泰), Yan Li(李閆), Ya-Bin Sun(孫亞賓), Yan-Ling Shi(石艷玲), and Xiao-Jin Li(李小進(jìn))

Shanghai Key Laboratory of Multidimensional Information Processing and the Department of Electrical Engineering,East China Normal University,Shanghai 200241,China

Keywords: negative bias temperature instability(NBTI),high-k metal gate(HKMG),threshold voltage shift,interface trap,gate oxide defect

1.Introduction

The physical mechanism of NBTI has been extensively investigated through comprehensive models established by several research groups.Commonly consistent results are achieved from the fact that three subcomponents contribute to the degradation of NBTI,i.e.,generated interface traps(?NIT),hole traps in pre-existing gate oxide defects(?NHT),and generated gate oxide traps (?NOT).[14-16]Note that they were treated as being uncoupled with each other.The generation of interface traps(?NIT)followed a power-law dependence on time in long-time NBTI stress and could be well described by using the double interface reaction-diffusion(RD)model.[17]For an HKMG device,the interface trap generation(?NIT)was ascribed to the breaking of Si-H bonds at the Si/interlayer(IL)interface and the diffusion of hydrogen molecular(H2)generated by the reaction of hydrogen atoms (H) withX-H bonds at the IL/high-Kinterface,with theXrepresenting oxygen or nitrogen-related gate oxide defect.The hole trapping in preexisting gate oxide defects(?NHT)was extremely sensitive to the gate nitriding process since the nitrogen could diffuse into gate oxide layer and thus creating original defects.[18-20]Note that it usually reached to a saturated state within a few seconds.The generation of gate oxide defects(?NOT)represents the contribution of hole trapping to overall degradation that occurs owing to fresh traps created in thicker gate oxide under higher stress.For most of HKMG devices with thinner oxide dielectric,?NOTmay be negligible.At the beginning of recovery,a fraction of electrons captured which are associated with interface traps[21]and holes detrapped in pre-existing gate oxide defects recover rapidly.After that,the long-time recovery process dominated the passivation of interface traps, induced by the back diffusion of H2molecules.[22,23]However,a fraction of H2molecules could not be recovered owing to being locked within the traps during stress.

In this work,we study the characteristics of NBTI degradation and recovery for 28-nm HKMG p-MOSFETs by using the experimental data and the comprehensive models.The NBTI parameters including power-law time exponent(n),temperature activation energy (EA), and oxide field acceleration factor (ΓE) are extracted.The influence of long-time NBTI stress biases(VG-STR)and temperatures(T)on device operating lifetime are accurately evaluated.Furthermore, the longtime recovery behaviors of devices are also analyzed by using comprehensive models.

2.Device and experiment

The p-MOSFETs used in this work were fabricated by the 28-nm HKMG process technology.The device had an equivalent oxide thickness(EOT)of 1.75 nm.In order to evaluate the influence of NBTI degradation, the values of threshold voltage(VT)were obtained under different values of stressVG-STR(1.4 V,1.5 V,and 1.6 V)and different values of temperatureT(80?C,100?C,and 125?C)at fixed stress timetSTR(3000 s).The fresh threshold voltage(VT0)of device has been extracted through the constant current method.The drain to source voltage ofVD=0.05 V was held to keep the device in linear region,with both source and substrate grounded.As the gate to source voltage (VG) increased until the drain current reaches 0.1 μA×W/L,VTcould be obtained byVG.Figure 1 shows the NBTI measurement setup of HKMG device through using the measure-stress-measure (MSM) method.Firstly, the transfer characteristic of fresh device was measured to extract theVT.Then,the stress was applied,and after that theVTwas measured periodically during the measurement.In this way,the dependence of threshold voltage shift (?VT) on thetSTRvariation could be obtained.

Fig.1.Schematic diagram of measurement setup to characterize NBTI stress.

3.Results and discussion

3.1.Degradation characteristics

As mentioned above, the threshold voltage shift induced by the NBTI in HKMG device is composed of three parts caused by uncoupled physical mechanisms, i.e., ?NIT, ?NHT,and ?NOT,[16]and can be written as

whereqis the electronic charge,andCOXis the gate oxide capacitance.The degradation of the threshold voltage induced by the interface trap (?NIT) can be described by the double interface reaction diffusion model[24,25]as shown in Fig.2(a).The Si-H bonds are assumed to be located at the Si/IL interface,which is named the first interface of the HKMG device.TheX-H bonds are located at the second interface, which is defined at some distance away from the first interface.TheXrepresents oxygen or nitrogen-related defect.When the NBTI stress is applied,weak covalent Si-H bonds are easily broken by the collision under the stress, leading to the formation of unbonded Si or interfacial traps at the Si/IL interface.Owing to the concentration gradient, the H atoms released from the broken Si-H bond begin to diffuse towards the gate and can form H2molecules by reacting with theX-H bond at the IL/high-Kinterface.The ?NIThas a power-law dependence on time for long-time stress[22,26]and can be written as

whereEOXis the gate oxide field,EAITis the temperature activation,Ais the fitting parameter,kTis the thermal energy,nis the power-law time exponent,andΓITis the gate oxide field acceleration, which are all process-dependent and need modelling for the HKMG process.Moreover, the degradation of fresh threshold voltage is included in the degradation process by the calculation ofEOX.Using the iterative method, more accurate result can be obtained from the following equation:

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The temperature activation for interface trap(EAIT)consists of molecular H2diffusion(EADH2),forward breaking(EAKF)and reverse passivation (EAKR) of the Si-H bond.[27]Hence, it is written as

EAKRof 0.2 eV andEADH2of 0.58 eV are fixed in different HKMG devices,andEAKFis the only process-dependent factor and needs modelling according to the various experimental data.

Fig.2.Schematic diagram of (a) double interface reaction diffusion model and (b) hole trapping in pre-existing gate oxide defects during NBTI degradation.

The hole trapping model and detrapping model are another explanation for the NBTI.[25]As is well known,a great number of defects can be generated inside gate insulator in the manufacturing process.When gate stress bias is applied, the holes are trapped by the pre-existing gate oxide defects,which causes these defects to be positively charged,thereby leading the threshold voltage to shift as shown in Fig.2(b).The studies have confirmed that ?NHTis saturated and reaches a constant value for long-time stress,[22]and can be expressed as

where the parameterBand oxide field acceleration factorΓHTare related to the fabrication process.The temperature activation energy for ?NHT(EAHT) is fixed at a value of 0.052 eV for different processes.According to the generation mechanism of bulk gate oxide defects,the time evolution of ?NOTis represented by a stretched exponential form,[22]and it is expressed as

where the parameterβOT=0.33 is kept unchanged for various processes, andCis related to the fabrication process.It is important to remark that trap generation in gate insulator is negligible for HKMG devices owing to thinner EOT at lowerVG-STR.[16,28,29]In this work,?NOTis not considered for this low voltage core logic device.

Fig.3.Curves of measured(symbols)and model-calculated ?VT,?VIT,?VHT subcomponents (lines) at 125 ?C, VG-STR of -1.4 V (a) and-1.6 V(b),respectively.

Figure 3 shows the time evolutions of measured and calculated ?VTas well as its subcomponents for HKMG devices atVG-STR= 1.4 V and 1.6 V, respectively.Note that the?NOTis negligible and the overall degradation only considers the ?NITand ?NHTsubcomponents.It can be seen that the experimental data are consistent with the calculations from the model for the NBTI degradation.The time evolution of?VTincreases rapidly at the onset of stress and shows the power-law dependence for long stress time.It can be observed that the ?NITdominates the majority of ?VTduring the NBTI stress,whereas the ?NHTis saturated in a few seconds and then keeps constant.The reason is that the contribution from the generated interface traps continuously increases for long stress time,however,the hole trapping in pre-existing bulk gate oxide defects is a fast process.The ?NITalso shows a power-law time dependence and increases as theVG-STRincreases.GiventSTR=3×103s, when theVG-STRreaches 1.4 V, the contribution from ?NITis 24.67 mV compared with 37.38 mV as theVG-STRbecomes 1.6 V.However, the contribution from the ?NHTchanges slightly as theVG-STRincreases, giving 5.2 mV@VG-STR=1.4 V,7.9 mV@VG-STR=1.6 V,respectively.Figure 4 shows the time evolutions of measured and calculated ?VTat different values ofVG-STRand temperature,demonstrating that the experimental data can be accurately predicted by the models.

Fig.4.Curves of measured(symbols),model-calculated ?VT(lines)for different values of VG-STR(a)and temperature(b),with identical model parameters used.The extracted parameters: (q/COX)×A = 4.2×10-9 (1/cm·s0.18), ΓIT (=ΓHT) = 0.24 (cm/MV), EAKF = 0.205 eV,n=0.18, (q/Cox)×B=9.32×10-10 (1/cm), C =0 (?VOT is negligible for HKMG devices at low stress bias).

Furthermore, the dependence of relative contributions from underlying ?NITand ?NHTon temperature andtSTRare analyzed.Figures 5(a)and 5(b)show the evolution of relative contributions from ?NITand ?NHTto the accumulated degradationversus Tat fixedVG-STR=1.5 V but differenttSTR,respectively.It can be seen that ?NIThas a strong dependence ontSTR, longertSTRlarger ?VIT.The relative contribution of?NITcan reach up to 90% for the longest stress time even at room temperature,as shown in Fig.5(a).?NITcontributes the most degradation and the impact of ?NHTweakens over longertSTR.On the contrary,whentSTRis short enough,the relative contribution from ?NHTis higher because the hole trapping in pre-existing gate insulator can be saturated in few seconds,as shown in Fig.5(b).

Fig.5.Relative contributions versus temperature for different values of?VIT/tSTR (a)and ?VHT/tSTR (b).

The dependence of NBTI degradation on channel length in HKMG p-MOSFETs is also studied.Taking the channel length into account,equation(1)can be revised as follows:

whereLis the channel length, andmis the fitting parameter.Figure 6 shows the time evolution of ?VTunder the fixedVG-STRandT, for the different channel lengths.The shorter the lengthL,the less the NBTI degradation is;as theLshrinks from 1000 nm to 30 nm,the NBTI degradation decreases from 36.9 mV to 12.7 mV attSTR=3000 s, correspondingly.The root cause is that in the post-gate high-temperature process steps in oxygen atmosphere,the oxygen diffuses into the highklayer at the corners of active-gate overlapping region and annihilates the positively charged oxygen vacancies.[6,30]This process reduces the average number of oxygen vacancies per gate area in narrow and short device,and thus the NBTI degradation is also alleviated.

Fig.6.Time evolutions of ?VT for different channel lengths at fixed VG-STR of -1.5 V at T = 125 ?C, and the extracted parameters:m=0.37 for different values of L.

From a practical point of view, it is essential to estimate the working lifetime of the device.The working lifetime of HKMG device is defined as the length of working time before its threshold voltage shift exceeds 50 mV.[31]Figure 7 illustrates the variations of operating lifetime withVG-STRat different values ofT,calculated from the model together with the extracted parameters.The model prediction shows that the higherVG-STRandTlead to the higher NBTI degradation.Consequently, the NBTI lifetime is significantly reduced as well.

Fig.7.Variations of NBTI lifetime with VG-STR for HKMG p-MOSFETs at different temperatures.

3.2.Discussion on NBTI parameters

3.2.1.Power-law time exponent

The ?VTversus time shows a power-law dependence under long-time stress.The working lifetime can be significantly reduced as the time exponent(n)increases,hence it is essential to extract the time exponentnfor HKMG device.It is observed that the time evolution of ?VTshows a parallel relation to each other in log-log scale diagram with differentVG-STR.Then the value ofncan be extracted in the linear regression of measured?VTversus time evolution in a fixed range oftSTR=1000 s to 3000 s.Figure 8 shows the power law time exponent (n)as a function of variousVG-STRin HKMG p-MOSFET.It is crucial to find that the degradation shows a similar power-law time dependence withnof 0.18 for different values ofVG-STR.Moreover,it indicates that ?NITdominates the degradation under long-time NBTI stress.Note that the measured data are from the HKMG device with thinner EOT under lower stress conditions,hence ?NOTis neglected.

Fig.8.Extracted power-law time exponent n versus VG-STR,measured and fitted at T =125 ?C.

3.2.2.Temperature-activation energy

Figure 9 shows the measured ?VTas a function ofTat a fixedtSTRof 2000 s.It is clear that ?VTpresents the linear dependence ofTon a semi-log scale, and hence the temperature-activation energy(EA)which is close to 0.096 eV is extracted from Fig.9.It is important to remark that ?NITcontributes most of degradation, and theEAHT(0.052 eV) of?NHT[16]is lower than that of ?NIT.On the one hand,the time evolution of ?NITis mainly determined by the diffusion of molecular H2under long-time stress.TheEAKFfor forward breaking is close to theEAKRfor reverse passivation of the Si-H bond.It can be seen thatEAITof ?NITis similar to that ofEADH2/6 (about 0.1 eV), whereasEADH2is temperatureactivation of H2molecular diffusion.As a result,the extractedEA(0.096 eV) is slightly lower than 0.1 eV when the contribution of ?NHTis considered.

Fig.9.Measured ?VT as a function of temperature at fixed tSTR of 2000 s.

3.2.3.Field acceleration factor

As discussed above, the hole trapping in inverse layer leads Si-H bonds to break and defects to generate at the Si/IL interface,resulting in an increase in ?NIT.Similarly,the hole trapping in pre-existing gate oxide defects makes ?NHTaccumulate.?NITand ?NHThave the sameEOXdependence(ΓIT=ΓHT).Figure 10 shows the measured ?VTas a function ofEOXat given stress timetSTR=3000 s.The oxide field acceleration (ΓE) is also extracted from the slope of fitting line,giving a value of 0.231 cm/MV.

Fig.10.Measured and fitted ?VT as a function of stress EOX at fixed tSTR and T =125 ?C.

3.3.Recovery characteristics

Once the gate stress is removed,the energy of a fraction of?NITmay move below the Fermi level of substrate and recover rapidly by capturing electrons within a few seconds.Then,the remaining part of ?NITrecovers owing to the back diffusion of H2and H,which leads to the passivation of the broken bonds at the interface.It is important to remark that this is a slow process.The double interface reaction diffusion model can predict the physics process of slow recovery.At the beginning, the H2molecule reacts with the brokenX-bonds at the IL/high-Kinterface and generates H atoms.After that,the H atoms diffuse towards the Si/IL interface and passivate the broken Si bonds,resulting in the recovery of ?NIT.Of course,the probability of H2finding the interface defects decreases as the recovery time lapses, which can be expressed as the decrease of diffusion coefficient of H2with time.Note that a fraction of H species may be locked by the defects, resulting in a permanent degradation that cannot be recovered.[32]

Furthermore, the recovery of pre-existing and generated gate insulator defects is a fast process that is depicted by hole detrapping when the stress voltage is withdrawn.Because the trap generation in gate insulator is negligible for thinner EOT device and lowerVG-STR, the recovery due to ?NOTis also excluded during NBTI recovery.

As a result,the overall recovery of threshold voltage shift consists of fast electron capturing(?VIT1),slow recovery of interface traps (?VIT2), and fast hole detrapping of pre-existing gate insulator traps (?VHT).The total recovery can be expressed as

whereFFASTdenotes the fast recovery component of ?NIT,αis the scaling factor of non-recoverable component due to H species locked in the trap,andξrepresents the decrease of H2diffusion with time going by.Note that the parameterξcan be approximately treated as a constant whentREC

whereτECis the electron capture time constant, andτRECis the hole detrapping time constant.The stretched-exponential form is used to describe the time constant dispersion with the parametersβECandβREC,and ?VHT0is also obtained from the NBTI stress model discussed above.

Fig.11.Measured and calculated ?VT as well as its underlying subcomponents recovery(?VIT1,?VIT2,and ?VHT)as a function of recovery time after different values of NBTI VG-STR and temperature during VG-REC =0 V.And the extracted parameters: (1-FFAST)(1-α)ξ1/2=0.3,FFAST=0.02,τEC=0.82,βEC=0.36,τREC=0.5,and βREC=0.23.

Figure 11 plots the time evolution of measured and calculated ?VTrecovery under stress for different values ofVG-STRandT, in which the underlying three subcomponents calculated by the models are also shown.It is clear that the process of electron capturing and hole detrapping recover fast.The long-time recovery occurs based on the trap passivation induced by the slow back diffusion of H2.

Fig.12.Time kinetics of relative contribution from ?VIT1,?VIT2,and ?VHT to the remaining overall degradation at tSTR=100 s(a),300 s(b),and 106 s(c),and the time kinetics of relative contribution from ?VIT1, ?VIT2, ?VHT, and ?VT to the initial degradation before recovery at tSTR =100 s(d), 300 s(e), and 106 s(f),with VG-STR=-1.5 V,VG-REC=0 V,and T =125 ?C.

Figure 12 shows the time evolution of the calculated ?VTand underlying ?VIT1, ?VIT2, and ?VHTby using the comprehensive model and extracted parameters.It is observed that as the stress time decreases, the contribution of ?VHTincreases.Consequently, the overall recovery turns out to be faster.For the stress times such as 100 s, 3000 s, and 106s, shown in Figs.12(a)-12(c), the recovery times for ?VIT2which contributes to 99% of the remaining degradation are 200 s, 60 s,and 20 s,respectively,demonstrating that ?VIT2dominates the slow process through H2back diffusion during long-time recovery.

Figure 13 shows the time evolution of the measured and the calculated ?VT, and its underlying subcomponents at different values of NBTIVG-STRandTfor the p-MOSFETs.The comprehensive models fit the measured data well.It is noteworthy that about 34%of overall degradation for these devices recovers at 2000 s.For the stress voltage of 1.4 V,1.5 V,and 1.6 V, the recovery at 125?C after 2000 s reaches to 31.4%,34.9%, and 34.7%, respectively.ForVG-STR= 1.5 V andT=80?C,the recovery also arrives at 35.8%.

Fig.13.Time evolution of measured and calculated ?VT recovery for different values of NBTI VG-STR and temperature.

4.Conclusions

In summary,the NBTI characteristics of degradation and recovery are studied for 28-nm HKMG p-MOSFETs by using comprehensive models.It is shown that the extracted parameters reflect the long-time NBTI characteristics well.The contribution of the independent underlying subcomponents ?VITand ?VHTto overall degradation is calculated, and the results indicate that the ?VITdominated the NBTI degradation during stress experiments.The reason behind this behavior is that the?VITshows power-law time dependence ofn=0.18 at longtime degradation, while ?VHTis saturated in a few seconds.Meanwhile, NBTI parameters including the power-law time exponent of 0.18, temperature activation energy of 0.096 eV,and gate oxide field acceleration factor of 0.231 cm/MV are all extracted based on experimental data.The results in this work also provide a reference for reliable design by discussing the dependence of lifetime on stress,voltage and temperature.The main physical mechanism for recovery process of threshold voltage degradation after NBTI stress is confirmed to be the passivation of interface traps due to back diffusion of H2.