In this chapter, we have presented a standard MOSFET fabrication process and physical model of device simulation. The characterization approach for random dopants fluctua-tion which dominates the Vth fluctuation in NMOSFETs was then introduced. Based on the large-scale statistical approach, the fluctuation of explored transistors, such as control, LAC, inLAC, DMG and inDMG devices could be calculated by solving the device transport equations. The accuracy of control device has been confirmed by experimentally measured data for ensuring the best accuracy.
Chapter 3
RDF Effects in Planar MOSFET and Analog Circuits
I
n this chapter, the DC characteristics, AC characteristics, and analog circuit charac-teristics induced by RDF are investigated, such as the electrostatic potential, ID− VG characteristics, CG−VGcharacteristics, current mismatch of current mirror circuit, and dy-namic characteristics of common source amplifier. The random-dopant-induced Vth, Ion, Ioff , gm, ro are further discussed in 16-nm-gate planar MOSFETs, respectively. The cur-rent mismatch, circuit gain, 3dB bandwidth, and unity-gain bandwidth of analog circuits (current mirror and common source amplifier) are also discussed.45
3.1 DC Characteristic Fluctuations
Both the randomness of dopants in the channel and source/drain (S/D) regions may in-duce the Vth fluctuation in a control device. In order to verify the importance of the RDF in the channel region, the RDF in source and drain regions is also investigated. An exam-ple of a 16-nm-gate control device with atomistic doping profiles both in the channel and source/drain regions is shown in Fig. 3.1. The actual location of random discrete dopants and the electrostatic potential are illustrated in Fig. 3.1(a). Note that the atomistic doping in the source/drain of device will not only introduce the electrostatic potential fluctuation but also the variations in the effective length of the channel as shown in Fig. 3.1(b). Fig-ure 3.2 shows the comparison of RDF effect in channel versus source/drain region. The Vth fluctuations are 42.8 mV and 20 mV in channel and source/drain RDF only devices, respectively. Moreover, the fluctuation is only 47.1 mV for both channel and source/drain RDF devices. It can be seen that the influence of channel RDF on Vthfluctuation is around 90%, which means the Vth fluctuation in our control device is dominated by the random-ness of dopants in the channel rather than the source/drain region. Therefore, RDF in the source/drain region can be neglected and won’t be considered in the following study.
Figure 3.3 shows the ID − VG characteristic fluctuations of the discrete-dopant fluctu-ated control devices, where the solid line shows the nominal device, whose channel doping
3.1 : DC Characteristic Fluctuations 47
profile is continuously doped with 1.5×1018cm−3, and the dashed lines are random-dopant-fluctuated devices. From the random-dopant-number point of view, the equivalent channel doping concentration is increased when the dopant number increases, which substantially alters the ID − VG characteristic, threshold voltage (Vth), on-state currents (Ion), off-state currents (Ioff) and transconductance (gm) as shown in Figs. 3.4. The threshold voltage is determined from a current criterion that the drain current larger than 10−7 (W/L) ampere, as marked in Fig 3.3. As the number of dopants in channel is increased, the device’s Vth is increased and thus decreases the on- and off-state current, as disclosed in Figs. 3.4(a)-(c).
The transconductance (gm) is the change in the drain-source current (Ion) divided by the change in the gate-source voltage (VGS) with a constant drain-source voltage (VDS), which is defined by
gm = ∂Ion
∂Vg ∝ VGS− Vth. (3.1)
When the dopant number is increased, according to the definition of gm, Vth will increase and so let gm decrease, as shown in Fig. 3.4(d). The fluctuation of Vth is 42.8 mV in our control devices. Compared Vth fluctuation of 31 mV which calculated by analytical formula shown in [15].
σVth,RDF = 3.19 × 10−8 toxNA0.4
LeffWeff
, (3.2)
where the tox is the thickness of gate oxide; W and L are the width and length of the transistor. However, the analytical formula can only consider the random dopant concen-tration but the random dopant position. The position of random dopants induced different fluctuation of characteristics in spite of the same number of dopants. The physical mecha-nism can be briefly described by band profile. Figures 3.5(a) and 3.5(c) show the extracted band profile for the same discrete dopants with different discrete-dopant-location devices from Fig. 3.5(b), respectively. In Fig 3.5(a), the band profile is smooth due to the discrete dopants located below surface. However, there are several potential barriers in the discrete dopant located in surface, as shown in Fig. 3.5(c). These potential barriers are induced by the corresponding dopants in device’s channel and therefore change the threshold voltage.
Finally, the normalized Vth, Ion, Ioff, and gmvariations (the standard deviation divided by the mean value of DC characteristics) in the control device are 16.4%, 10.7%, 73.8%, and 2.6%, respectively.
3.1 : DC Characteristic Fluctuations 49
D
E D
E
Figure 3.1: Example of a 16-nm planar MOSFET with atomistic doping profiles both in the channel and S/D regions. (a) The actual locations of random discrete dopants and (b) the fluctuation in electrostatic potential are illustrated. There are 7 and 358 dopants located in channel region and S/D region,
respectively.
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Figure 3.2: Comparison of RDF effect in channel versus S/D region ofa planar MOSFET. The Vthfluctuations are 42.8 mV and 20 mV for channel and S/D RDF only cases, respectively. The Vthfluctuation is 47.1 mV for both channel and S/D RDF cases. Note that the channel RDF introduced around 90% of Vthfluctuation.
3.1 : DC Characteristic Fluctuations 51 Figure 3.3: DC characteristic fluctuations of ID− VG characteristics,
where the solid line shows the nominal device, whose channel doping profile is continuously doped with 1.5×1018 cm−3, and the dashed lines are random-dopant-fluctuated devices. The threshold voltage is determined from a current criterion that the drain current larger than 10−7A. Ion is determined at VG= 0.8 V and Ioff is determined at VG = 0 V.
'RSDQW1XPEHU and (d) gmcharacteristics. As the number of dopants in channel is increased, the devices Vth is increased and thus decreases the on- and off-state current and
transconductance. The magnitude of the spread
characteristics increases as the number of dopants increase.
Furthermore, the position of random dopants induced different fluctuation of characteristics in spite of the same number of dopants.
3.1 : DC Characteristic Fluctuations 53
Figure 3.5: Extracted band profile for (a) discrete dopant-located below surface and (c) discrete-dopant-located in the surface devices. Several potential barriers in the
discrete-dopant-located in the surface device are induced by the corresponding dopants in devices channel and therefore change the threshold voltage. (b) Discrete dopants
randomly distributed in the (96 nm)3 cube with the average concentration of 1.5×1018cm−3.