Study of Different Parametric Variations of MOSFET Pressure Sensor

Received Jan 9, 2018 Revised Mar 2, 2018 Accepted Mar 18, 2018 There is a growing demand of miniaturization of the electronics world. A brief discussion for simulating and fabrication of the MOSFET based pressure sensor in nanoscale is being reviewed in this paper. Aim of this paper is to collect all the scaling challenges and their solutions together to make understanding the facts of the MOSFET based sensor. As the MOSFET move from micro scale to nanoscale the functioning changes dramatically. The Silicon oxide material fails when scale down to nano region. However, many issues such as electrical quality, thermodynamic stability, Kinetic stability, gate compatibility and process compatibility were being solved in the process of integration and implementation.


The Problem
Now the problem arises when we go for miniaturization of size of MOSFET. If we try to reduce the thickness below 2 nm in silicon oxide MOSFET there will be a free flow of drain current through the channel as reported by saeed et al [1]. The solution to this problem is also suggested by saeed et al [7] in the same literature that for obtaining a proper flow of drain current through channel we need to replace silica with a material having high k Value ( or high Di-electric constant). While exchange the oxide with a high di-electric material some factors has got to be thought of, these factors are: a. Material ought to be able to continue scaling to lower equivalent compound thickness. b. stop the gate threshold voltage instabilities caused by the high defect densities c. Limit the loss of carrier quality within the Si channel once mistreatment High-κ oxides d. Warrant dependability of the gate material.

The Proposed Solution
paper summarized the challenges and problems faced on scaling down the channel width of the MOSFET or ultimately scaling down the MOSFET size. Thus, they have suggested various insulating material for MOSFET having high dielectric constants which can be a replacement for the standard oxide layer along with their theoretical calculation. Some materials like group IIIA metal oxides such as aluminium oxide (Al2O3), group IVB Metal Oxides and silicates such as titanium oxide (TiO2), zirconium oxide (ZrO2), zirconium silicate (ZrSiO4), Hafnium oxide (HfO2), hafnium silicate (HfSixOy) etc are replacement of silicon.

LITERATURE SURVEY
Saeed Mohsenifar, M.H. Sharokhabadi, "Gate stack high-K materials for Si-based MOsfets Past, Present, and future", Microelectronics and solid state Electronics 2015, DOI:10.5923/j.msse.20150401.03 [1]. In this paper authors have discussed the challenges and problems faced on scaling down the channel width of the MOSFET or ultimately scaling down the MOSFET size. As from the paper it's been clear that Silicon material fail in standard CMOS technology (for nanoscale), due to the short channel effect and tunneling effect shown by silicon material. The working of the MOSFET changes when we move towards the nanoscale regime. In order to continue scaling the planar MOSFET without harmful SCE's, the effective channel length needs to be 40times the dielectric thickness so the dielectric thickness must be decreased along with the physical dimension of the device.
S.Suthram, J.C Zeiegert, T.Nishida, "Piezeoresistance coefficient of (100)Silicon nMOSFET measured at low and high (1.5GPa)channel stress", IEEE electron devices letters, Vol.28, NO.1, January 2007 [2]This paper gives a brief idea about the modeling of the highly stressed channel of the silicon MOSFET. In their experimental setup they have designed an unaxial channel stress; the wafer is allowed to  [3]. The piezeoresistance model have been commonly been used to describe mobility enhancement for low levels of process induced strain in CMOS technology. In this paper, a conversion between the change in conductivity and resistivity is developed such that a piezeoresistance model can be applied correctly to calculate the strain-induced mobility changes. They concluded that the linear piezeoresistance concept fails when the applied stress exceed the linear limit where nonlinear piezeoresistance effect occurs and showed that the correction to this i.e. the C-R conversion dramatically improves the accuracy over the commonly used formulation of piezeoresistance concept while maintaining its simplicity.
Jhong-Sheng Wang, William Po-Nien Chen, Chun-Hsing Shish,Chenhsin Lein,PinSu, "Mobility modeling and its extraction techniques for manufacturing starined-Si MOSFETs", IEEE electron letters, vol. 28, NO. 11 November 2007 [4]. In this letter, for a MOSFET channel thickness from 32nm to 73nm, a practical extraction method is integrated and proposed to decouple the parasitic parameters and to evaluate the mobility of short channel strained-Si devices. The extraction of parasitic source/drain resistance follows the improved Berkeley short channel IGFET model method to get an accurate drain current without parasitic drain resistance degradation for the current device. They concluded that, at a relatively high field, by assuming that a constant bulk piezeoresistance coefficient is applied for stress devices, their model can properly predict the mobility enhancement for the various strained-Si technologies and device dimensions by including the coulomb scattering corrections. A better description of tensile-stress mobility is achieved for nanoscale short channel devices.

METHODOLOGY
The question arises here is that how the thickness of channel will affect the sensitivity of MOSFET pressure sensor. There are many literatures in which it is reported that with the decrease in the channel width the drain current increases, which therefore increases the sensitivity of the device [9]. In this section we will discuss about the dependency of sensitivity of device with channel thickness and also the various literatures which reported about the same problem.
Various parameters used to design and simulate MOSFET embedded pressure sensor a. Diaphragm shape, size and material-Square, 100µm x 100 µm x 5 µm, Silicon b. using 5 µm CMOS technology for n-MOSFET piezoresistor c. Dimension of n-MOSFET = 1.5 µm x 1.25 µm x1 µm d. Drain current ID(sat) = 2 µA e. Source to drain voltage= .5V f. Output resistance = VSD/ ID(sat) = .25MΩ g. Resistance of n-MOSFET equivalent piezoresitor= R= ro = 2MΩ h. Resistivity of n-MOSFET piezoresistor=, ρ= 25 Ωm i. Reference Temperature To = 300 K Operating principle of the MOSFET pressure sensor is presented by zhao hua zhang et al [5]. Based on the stress sensitive effect of MOSFET, a new MOSFET-bridge-circuit structure is designed, as shown in As a result, the sensor output signal Vout is zero. When a pressure is forced on the membrane, the current and piezo-resistance in each bridge arm are changed. The variation of the PMOSFET current is proportional to the change of channel mobility Δµp, computed as [6]: ∆ IDS / IDS = ∆µ /µo = πl .σl + πt .σt (2) Where, 1 and 2 are the parallel and vertical stress in the channel; 1 and 2 are the parallel and vertical channel piezoresistive coefficient, respectively. The change of piezoresistance is also proportional to the resistor mobility change ΔR, which can be expressed using a similar formula, as: ∆ R/ RO = ∆ µR / µRO = πl .σl + πt .σt Where, 1 and 2 are the parallel and vertical stress in the resistor bar, 1 and 2 are the parallel and vertical piezoresistive coefficient, respectively.
According to the different current direction placing, the bridge becomes unbalance. The µP of M1 and the µR of R2 get increased with the stress, in opposition, the µP of M2 and the µR of R1 are decreased. Then the two arms outputs become as [6]: Therefore, the sensor output is obtained as [6]: Formula (5) shows that, Vout is proportional to the stress as well as the forced pressure. This is the operating principle of the novel MOSFET-bridge-circuit pressure micro sensor.
Several literatures has been reported the sensitivity of this pressure sensor to be increasing upto 100 micrometer of channel thickness concluded that the sensitivity of the MOSFET sensor will also increase with reduction in channel thickness with the increase in drain current [4], [5]. There are also some literatures has reported that the drain current of MOSFET increases with reduction in thickness of channel [9]. With above formulas and the literature mentioned above we can conclude that the sensitivity of the MOSFET pressure sensor should increase if we go below 130 nm thickness of channel. In this paper we will present the comparison of sensitivity of MOSFET pressure sensor having thickness from 130 nm to 20 nm.

RESULT AND DISCUSSION
After simulating MOSFET for various thicknesses and applying a force of 2 bar we have obtained the I-V curve i.e. the drain current and drain voltage curve ( Figure 1) and plotted the thickness versus resistance curve.  The theoretical calculation for increasing the sensitivity of the sensor we can relate the sensitivity of the sensor to the resistance, lower the resistance in the channel greater the mobility of the carrier and hence the sensitivity increases as the variation in the current will be sensible. Thus the equation below defines the resistance of the channel R = (VDD -VGS) / IG (6) Where, VDD is drain voltage, VGS is gate to source voltage, IG is gate current. After simulating MOSFET in 2 Dimensional structure for various thicknesses obtained the I-V curve i.e the drain current and drain voltage curve ( Figure. Thus from figure it's been visible that when we move from 200nm towards 10nm the resistance initially increases till 130nm but below it the resistivity decreases hence the sensitivity increases for the channel thickness of MOSFET below 130nm to 10nm for the conventional silicon material.

COMPARATIVE ANALYSIS
Curve below 2nm has been plotted for the three different materials that is for Zirconium Oxide (Zr 2 O 3 ), Lanthanum Oxide (La 2 O 3 ) and Hafnium Oxide (HfO 2 ). In order to compare these materials in this section a comparative I-V curves has been drawn below 2nm for analysis of the best material among the respective three.   It can be observed that a small amount of Current is drawn from the circuit about few milli Amperes

CONCLUSION
Thus, after studying all the views from the various authors the MOSFET based pressure sensors sensor have been studied for its optimised performance and enhancing the sensitivity of the sensors while decreasing the size of them. The materials with higher k value can be used to overcome all the challenges in scaling down the MOSFET. These MOSFET based sensors which are smaller enough can be used in various applications in the field of medical science and technology according to the need and availability.
The sensitivity of the MOSFET pressure sensor is found to be increasing as the thickness of channel is reducing, this result occurs due to high drain current at lower thickness. Further it is reported in some literature that further reduction in the thickness of channel will allow the free flow of electron through the MOSFET. So it is suggested to use the material having high dielectric constant such as HfO2, if more size miniaturisation is required.