Discussion

The summary of overstress results under three overstress conditions (DC, AC, and large-signal transition stresses) is listed in Table 3.2. The gate-oxide breakdown will degrade the transconductance (gm), output conductance (go), and threshold voltage (VTH) of MOSFET devices. After the overstress, the performances of the common-source amplifier with the non-stacked diode-connected active load structure under the DC, AC with DC offset, and large-signal transition stresses are seriously degraded with gate-oxide breakdown, and those of the common-source amplifier with stacked diode-connected active load structure are only slightly degraded under the large-signal transition stress. As a result, the performance degradation of the common-source amplifier with the non-stacked diode-connected active load structure is more seriously than that of the common-source amplifier with the stacked diode-connected active load structure. The small-signal performance of the common-source amplifier is very sensitivity to the DC operation point, so the gate-oxide breakdown will cause the gm VTH, and go degradations and extra gate-leakage current of the MOS transistor to induce the change of the DC operation point in the common-source amplifier. Considering the common-source amplifier with the non-stacked diode-connected active load structure, if the parameters, gm1 and gm2, are variable factor in the equation (3.1), the sensitivities of the equation (3.1) to the parameters, gm1 and gm2, are expressed as In the equations (3.10) and (3.11), the parameters go1 and go2 can be ignored, because they are small than 1. The parasitic capacitances CGD1 and CGS2 of the MOS transistors are not considered. The sensitivities of the equations (3.10) and (3.11) to the parameters gm1 and gm2, respectively, are approximate 1. Therefore, the gate-oxide breakdown of the MOS transistors has serious impact to the circuit performances of

analog circuits. As a result, the gate-oxide reliability is very important design issue in the nano-meter CMOS process. The gate-oxide reliability can be improved by the stacked structure in the common-source amplifier under small-signal input and output applications. The common-source amplifier with the stacked diode-connected active load structure can be worked in high supply voltage depended on the stacked number of transistor used to control the voltages (VGS, VGD, and VDS) across the transistor and to avoid the gate-oxide breakdown.

3.1.5. Effect of Hard and Soft Breakdowns on Performances of Common-Source Amplifiers

3.1.5.1. DC Stress

The measured dependence of power supply current IVDD in two amplifiers on stress time have been measured and recorded, as shown in Fig. 3.12, under the DC stress. Because the power supply current IVDD of the common-source amplifier with the stacked diode-connected active load structure is not degraded after the DC stress, the gate-oxide degradation of MOSFET is not occurred in this measurement. However, the power supply current IVDD of the common-source amplifier with the non-stacked diode-connected active load structure is degraded during the DC stress. Based on the prior proposed method [82], [91], the gate-oxide breakdown of MOSFET device can be modeled as resistance. Only the gate-to-diffusion (source or drain) breakdown was considered, since these represent the worst-case situation. Breakdown to the channel can be modeled as a superposition of two gate-to-diffusion events. Typical hard breakdown leakage has close-to-linear I-V behavior and an equivalent resistance of ~ 10³-10⁴ Ω, while typical soft breakdown paths have high non-linear, power law I-V behavior and equivalent resistance above 10⁵-10⁶ Ω [82]. The oxide breakdown is not occurred on gate-to-source side of M1 device in the common-source amplifier with the non-stacked diode-connected active load structure, because the voltage across gate-to-source side of M1 device is smaller than 1 V in the amplifier. The complete circuit of the common-source amplifier with the non-stacked diode-connected active load structure including gate-oxide breakdown model is shown in Fig. 3.13. The breakdown resistances of RBD1 and RBD2 can be used to simulate the impact of hard

and soft breakdowns on performances of the common-source amplifier with the non-stacked diode-connected active load structure. Comparing the measured results among Figs. 3.3, 3.5, 3.6, and 3.12, the dependence of power supply current IVDD

(non-stacked) on stress time in Fig. 3.12 can be separated by three regions (I, II, and III regions) due to the gate-oxide breakdown. This result has some differences between the impact of gate-oxide breakdown on performances of analog and digital circuits. When the performances of the common-source amplifier with the non-stacked diode-connected active load structure are degraded due to the gate-oxide breakdown, the power supply current IVDD is not increased immediately. The relationship between power supply current IVDD and gate-oxide breakdown occurred on M1 and M2 devices under three regions in the common-source amplifier with the non-stacked diode-connected active load structure can be modeled by

Region I: no gate-oxide breakdown occurred on M1 and M2 devices, Region II: hard breakdown occurred on M2 device, and

Region III: hard breakdown occurred on M1 and M2 devices.

In Region I, the gate-oxide breakdown of MOSFET device is more likely to occur as the time-dependent dielectric breakdown (TDDB). In this region, the small-signal performance and power supply current IVDD of the common-source amplifier with the non-stacked diode-connected active load structure have very small variations on the stress time under DC stress. The gate-oxide breakdown is not occurred on M1 and M2 devices.

In Region II, the power supply current IVDD was not changed, but the small-signal performances of the common-source amplifier with the non-stacked diode-connected active load structure was seriously degraded. The reason, why the power supply current IVDD of the common-source amplifier is not changed, is due to the gate-oxide breakdown on M2 device. The simulated dependence of power supply current IVDD under different breakdown resistances RBD1 and RBD2 is shown in Fig.

3.14. The power supply current IVDD of the common-source amplifier with the non-stacked diode-connected active load structure is dominated by M1 device.

Because the gate-oxide breakdown on M1 device is not occurred, the power supply current IVDD of the common-source amplifier is limited under the DC stress. The simulated dependence of small-signal gain and output DC voltage level of the

common-source amplifier with the non-stacked diode-connected active load structure under different resistances RBD2 is shown in Fig. 3.15. Based on the prior proposed method [81], the impact of soft breakdown occurred on M2 device has less influence on circuit performances. The hard breakdown occurred on M2 device causes the serious degradations on performances of the common-source amplifier with the non-stacked diode-connected active load structure, but the power supply current IVDD

is not changed under the DC stress. These simulated results can be used to confirm and understand that the hard breakdown is only occurred on M2 device of the common-source amplifier with the non-stacked diode-connected active load structure during the DC stress in Region II.

In the Region III, the power supply current IVDD and small-signal performances of the common-source amplifier with the non-stacked diode-connected active load structure are seriously degraded under DC stress. The hard breakdown is occurred on both M1 and M2 devices under the DC stress in Region III.

Comparing the Regions I, II, and III under DC stress, the degradation on power supply current IVDD is dominated by gate-oxide breakdown on M1 device. The gate-oxide breakdown occurred on M2 device is a dominated factor to degrade the performances of the common-source amplifier with the non-stacked diode-connected active load structure. As a result, the hard breakdown has more serious impact on performances of the common-source amplifier.

3.1.5.2. Large-Signal Transition Stress

In order to investigate and understand the impact of hard and soft breakdowns on performances of the common-source amplifiers with the non-stacked and stacked diode-connected active load structures under large-signal transition stress, the complete circuits including the gate-oxide breakdown model are shown in Figs. 3.13 (non-stacked) and 3.16 (stacked), respectively. In these two amplifiers, the gate-oxide breakdown does not occur on gate-to-source sides of M1 (in Fig. 3.13) and M3 (in Fig.

3.16) devices under large-signal transition stress, because the voltages across gate-to-source sides of M1 and M3 devices are smaller than 1 V, respectively. The static and the dynamic currents in two amplifiers under digital operation are increased

after the gate-oxide breakdown [49]. The hard gate-oxide breakdown has been occurred on the common-source amplifier with non-stacked diode-connected active load structure after overstress. The soft gate-oxide breakdown has been occurred on common-source amplifier with stacked diode-connected active load structure after overstress. The simulated dependence of high and low output voltage levels (VH and VL) of the common-source amplifiers with the non-stacked diode-connected active load structures under the different resistances RBD1 and RBD2 is shown in Fig. 3.17.

The high output voltage level VH and low output voltage level VL of common-source amplifier with non-stacked diode-connected active load structure are degraded by oxide breakdown occurred on M1 and M2 devices, respectively. Comparing Figs. 3.10 and 3.17, the breakdown location in the common-source amplifier with the non-stacked diode-connected active load structure is occurred on M2 device after large-signal transition stress.

The impact of gate-oxide breakdown on performance of the common-source amplifier with the stacked diode-connected active load structure can be simulated and investigated by the same method to find breakdown location. Fig. 3.18 shows the simulated dependence of the high and low output voltage levels (VH and VL) of the common-source amplifier with the stacked diode-connected active load structure under the different resistances of RBD3, RBD4, RBD5, and RBD6, respectively. The different breakdown locations cause different performance degradations of the common-source amplifier with the stacked diode-connected active load structure under large-signal transition stress. Comparing Figs. 3.10 and 3.18, the breakdown location in the common-source amplifier with the stacked diode-connected active load structure is occurred on M5 or M6 device under large-signal transition stress. The high and low output voltage levels (VH and VL) of the common-source amplifier with the stacked diode-connected active load structure are increased, when the stress time is increased. The common-source amplifier with the stacked diode-connected active load structure has slow degradation rate, because the voltage across MOSFET device is smaller than that of common-source amplifier with the non-stacked diode-connected active load structure. The hard breakdown has more serious impact on performances of common-source amplifier with non-stacked diode-connected active load structure. The stacked structure can be used to improve the reliability of analog circuits in nanoscale CMOS technology.

3.1.5. Summary

The impact of gate-oxide reliability on CMOS common-source amplifiers with the non-stacked and stacked diode-connected active load structures has been investigated and analyzed under the DC stress, AC stress with DC offset, and large-signal transition stress. The small-signal parameters of the common-source amplifier with the non-stacked diode-connected active load structure are seriously degraded than that with stacked diode-connected active load structure by gate-oxide breakdown under DC, AC, and large-signal transition stresses. The stacked structure can be used to improve the reliability of analog circuit in nanoscale CMOS process.

The impact of soft breakdown, hard breakdown, and breakdown location on circuit performances of the common-source amplifiers with the non-stacked and stacked diode-connected active load structures has been investigated and analyzed. The hard gate-oxide breakdown has more serious impact on performances of the common-source amplifier with the diode-connected active load.

3.2. Operational Amplifier

3.2.1. Background

The reduction of power consumption has become increasingly important to portable products, such as mobile phone, notebook, and flash memory. In general, the most common and efficient way to reduce the power consumption in CMOS very large scale integrated circuits (VLSI) is to reduce the power-supply voltage. To reduce the power consumption in CMOS VLSI systems, the standard supply voltage trends to scale down from 5 to 1 V. Thus the gate-oxide thickness of the MOS transistor will be become thin to reduce nominal operation voltage (power-supply voltage). In general, the VLSI productions have lifetime more than 10 years, but the thin gate oxide of the MOS transistor has many problems, such as gate-oxide breakdown, tunneling current and hot carrier effect, that will degrade the lifetime of the MOS transistor. Therefore, to improve the gate-oxide reliability of MOS transistor and to investigate the effect of gate-oxide breakdown on CMOS circuit performances will become more important in the nanometer CMOS technology.

The occurrence of gate-oxide breakdown during the lifetime of CMOS circuits cannot be completely ruled out. The exact extrapolation of time-to-breakdown at circuit operating conditions is still difficult, since the physical mechanism governing the MOSFET gate dielectric breakdown is not yet fully modeled. It was less of a problem for old CMOS technologies, which have the thick gate oxide. However, because the probability of gate-oxide reliability strongly increases with the decrease of gate-oxide thickness [1], the CMOS circuits in nano-scale technologies could be insufficiently reliable.

The defect generation leading to gate-oxide breakdown and the nature of the conduction after gate-oxide breakdown has been investigated [49]-[52], [79]-[82], [80], [92], [93], which point out that the gate-oxide breakdown will degraded the small-signal parameters of the MOS transistor, such as tranconductance gm and threshold voltage VTH. Recently, some studies on the impact of MOSFET gate-oxide breakdown on circuits have been reported [49]-[52], [78], [79]. In [49], it was demonstrated that the digital complementary logic circuits would remain functional beyond the first gate-oxide hard breakdown. A soft gate-oxide breakdown event in the CMOS digital dynamic logic circuits relying on the uncorrected soft nodes may result in the failure of the circuit [50]. The gate-oxide breakdown on RF circuits was also studied [51]. The impact of gate-oxide breakdown on CMOS differential amplifier and digital complementary logic circuits had been simulated [89]. Some designs of analog circuits [84], [85] and the mixed-voltage I/O interface [86], [87] indicate that gate-oxide reliability is a very import design consideration in CMOS circuits.

However, the impact of MOSFET gate-oxide breakdown on the CMOS operational amplifier circuits is still not well studied and really verified in a silicon chip. The CMOS analog circuits are very sensitive to the small-signal parameters of MOSFET, such as tranconductance gm and threshold voltage VTH. Therefore, the gate-oxide breakdown is expected to have severe impact on the circuit performances of analog circuits.

In this work, the effect of MOSFET gate-oxide reliability on the operational amplifiers with the two-stage (non-stacked) and folded-cascode (stacked) structures is investigated in a 130-nm low-voltage CMOS process [88]. The small-signal gain, phase margin, unity-gain frequency, and power supply rejection ratio (PSRR) of these

operational amplifiers with different configurations are measured and compared after different stresses.

3.2.2. Operational Amplifiers

The operational amplifier is a basic unit in many analog circuits and systems, such as output buffer, sample-and-hold circuit, and analog-to-digital converter. The operational amplifiers with the two-stage and folded-cascode structures are selected to verify the impact of MOSFET gate-oxide reliability on analog circuits. The complete circuits of the operational amplifiers are shown in Figs. 3.19(a) and 3.19(b). The operational amplifier with the two-stage structure comprises the differential amplifier (M1-M5), common-source amplifier (M6-M7), and source follower (M8-M9). The operational amplifiers with the two-stage and folded-cascode structures have been fabricated in a 130-nm low-voltage CMOS process. The normal operating voltage and the gate-oxide thickness (tox) of all MOSFET devices in these operational amplifiers are 1 V and 2.5 nm, respectively, in a 130-nm low-voltage CMOS process. The channel length of NMOS and PMOS transistor in the two operational amplifiers is set to 0.5 μm or 1 μm to avoid the short channel effect, such as threshold variation, drain-induced barrier lowering (DIBL) effect, hot-carrier effect, velocity saturation, and mobility degradation effect. The body terminals of the all NMOS and PMOS transistors are connected to ground and power supply voltage, respectively. The device dimensions of two amplifiers are shown in Table 3.3. This design approach is usually used to design the operational amplifier in analog integrated circuit applications.

In signal MOSFET device, if the critical terminal voltage of the device, such as gate-to-source voltage (VGS), gate-to-drain voltage (VGD), and drain-to-source voltage (VDS), is kept within the normal operating voltage VDD of the technology, the electric fields across the MOS device will not cause the damage on the gate oxide. Therefore, the bias circuit of the operational amplifiers is designed with stacked structure to avoid the gate-oxide breakdown. The Miller compensated capacitance CC of the two-stage operational amplifier in Fig. 3.19(a) is realized by the metal-insulator-metal (MIM) structure, which has no gate-oxide reliability problem. The impact of

MOSFET gate-oxide reliability on the operational amplifiers with the two-stage and folded-cascode structures is verified by using continuous stress with supply voltage of 2.5 V. The input common-mode voltage of the operational amplifiers is set to 1.25 V, respectively. Simulated by HSPICE, the open-loop gain and phase margin of the operational amplifier with the two-stage structure are 64.7 dB and 47.8 degree, respectively, under output capacitive load of 10 pF. The open-loop gain and phase margin of another operational amplifier with the folded-cascode structure are 61.9 dB and 89 degree, respectively, under output capacitive load of 10 pF. The open-loop small-signal gain (AV_two-stage) of the operational amplifier with the two-stage structure is given by where the go and gm are the output conductance and transconductance of the corresponding MOSFET in the operational amplifiers. The gox, goy, and goz equal to go5+go2, go6+go7, and go8+go9, respectively. The open-loop small-signal gain (AV_folded-cascode) of the operational amplifier with the folded-cascode structure is also written as

where the ro is the output resistance of the corresponding MOSFET in the operational amplifiers. The short-channel effect, body effect, and parasitic capacitance of MOS transistors in the two operational amplifiers are ignored in the equations (3.12), (3.13), and (3.14). The capacitances CL and CC are the output capacitive load and Miller compensated capacitance, respectively, in the two operational amplifiers.

3.2.3. Overstress Test

The operational amplifiers with the close-loop (unity-gain buffer) and open-loop (comparator) configurations are selected to verify the impact of MOSFET gate-oxide

reliability on the circuit performances of the operational amplifiers with the two-stage and folded-cascode structures in a 130-nm low-voltage CMOS process. The small-signal gain, phase margin, output-signal swing, PSRR, and rise and fall times of the operational amplifiers varied with gate-oxide breakdown will be measured and analyzed. Because the MOSFET devices in analog circuits usually work in the

reliability on the circuit performances of the operational amplifiers with the two-stage and folded-cascode structures in a 130-nm low-voltage CMOS process. The small-signal gain, phase margin, output-signal swing, PSRR, and rise and fall times of the operational amplifiers varied with gate-oxide breakdown will be measured and analyzed. Because the MOSFET devices in analog circuits usually work in the