In this section, we introduce an analytical sensitivity model for long channel Si-NW biosensors with antenna operated in subthreshold region. Fig. 4-6 shows the Si-NW structure studied in this work [4.4]. In the subthreshold regime, we assume that the Si-channel is fully depleted with negligible mobile carriers, and the nanowire is a device with negligible potential change along the Y-direction. Therefore, the potential distribution satisfies the following Poisson’s equation:
, (4-3)
where N is the channel doping concentration, and is the dielectric constant for silicon. The boundary conditions are shown as below:
,
(4-4a)
·
,
(4-4b)
·
where D and ti are the channel diameter and thickness of gate insulator, respectively.
VGS is the surface potential on the sensing region, and Vfb is the flat-band voltage. Ci
is the capacitance per unit length for an infinitely long cylindrical capacitor, which neglects the fringing effect of the field near the edges of the capacitor [4.13]. Solving the boundary value problem in the cylindrical coordinate, the solution can be expressed as [4.4]:
(4-5)
Using the channel potential solution, the subthreshold drain current can be calculated as [4.4]:
·
·
(4-6)
where q is the elementary charge, is the carrier mobility, ni is the intrinsic carrier density, is the effective channel length, is the Boltzmann constant, and is the absolute temperature. The sensitivity model of the Si-NW biosensors can be further derived from the drain current equation as:
∆
(4-7)
Fig. 4-7(a) and Fig. 4-7(b) show that the subthreshold current model agrees well with the 3-D device simulation. However, it should be noted that the assumption of negligible mobile carriers in the model derivation has set constraints on the channel doping concentration of Si-NW biosensors.
Fig. 4-8 shows that the analytical sensitivity model agrees well with the device simulation results for various doping concentrations. Fig. 4-9 shows that the analytical sensitivity model agrees well with the device simulation results for various channel diameters. It can be seen that the sensitivity of Si-NW biosensors with antenna is insensitive to the channel diameters and doping concentration. This is because the nanowire structure has a superior gate control ability to keep the subthresohld swing near the ideal value, 60mv/dec, at room temperature.
In addition, we can relate the sensitivity of Si-NW biosensors with antenna with the device subthreshold swing as below:
∆
, ∆ ,
∆
, ∆ , , ∆
,
, ∆
, . ∆
(4-8)
We can rewrite the sensitivity expression in equation (4-8) as below:, ∆ ,
,
, ∆
,
. ∆
(4-9)
From equation (4-9), we can see that the sensitivity is exponentially dependent on the inverse subthreshold swing. Fig. 4-10 shows the corresponding sensitivity for various subthreshold swings, and it is verified by 3-D device simulation. When the subthresholod swing is ~60mV/dec, the corresponding sensitivity is ~5.9. It is consistent with our previous simulation results in Fig. 4-4. Moreover, equation (4-9) indicates that Si-NW biosensors with antenna has ~3X enhancement in sensitivity compared with the traditional ISFET (bulk) if the subthreshold swing is improved from 100mv/dec (bulk) to 60mv/dec (Si-NW).
4-9
Conclusions
Our conclusions for this chapter are summarized as follows:
(7) The simulation flow of Si-NW biosensors with antenna has been demonstrated.
(8) The Si-NW biosensor with antenna operating in the subthreshold region has a better sensitivity than in the superthreshold region.
(9) The sensitivity is insensitive with diameter and doping concentration. It implies that the proposed structure [4.3] has the potential to suppress the process variations.
(10) An analytical sensitivity model for Si-NW biosensors with antenna operating in subthreshold regime has been demonstrated.
(11) We have demonstrated the correlation between the sensitivity and the subthreshold swing. Compared with ISFETs, the Si-NW biosensors with antenna have ~3X sensitivity gain if the subthreshold swing is improved from 100mv/dec (bulk) to 60mv/dec (Si-NW).
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Thermal oxide
Debye length 0.304 λ ~ [nm]
NaCl
Fig. 4-1. (a) The proposed biomolecules detecting system [4.3] which can be separated to (b) the sensing region, and (c) the semiconductor region.