Modeling and simulation of electrolyte pH change in conventional ISFET using commercial Silvaco TCAD

This paper proposes a numerical simulation approach to study the electrolyte pH change of ion-sensitive field effect transistor (ISFET) structures using Silvaco technology computer-aided design (TCAD) tools. This paper examines the ISFET device’s electrical response to electrolyte pH change. The modeling method is exploited by changing the potential surface charge depending on the electrolyte pH change and investigating how will it cause threshold voltage shift of ISFET device and other transfer characteristic parameters. The properties of a user-defined material offered by Silvaco are exploited to simulate the electrolyte behavior. The parameters of silicon semiconductor material (i.e., energy bandgap, permittivity, affinity, and density of states) are set to reconstruct an electrolyte solution. The electrostatic solution of the electrolyte area is investigated by giving a numerical solution for the semiconductor equation inside this area. Results show excellent agreement between theoretical model and self-consistency TCAD model. Additionally, transfer characteristics of a conventional ISFET device are simulated. The ID current as a function of the reference voltage VRef. and drain voltage VD for different pH scale and ID current as a function of VDS for different VRef. values for specific pH value are simulated. The proposed model allows accurate and efficient ISFET modeling by trying different designs and further optimization with commercial Silvaco TCAD tools rather than expensive fabrication.


Introduction
The last decade witnessed a tremendous convergence in CMOS-based microtechnology, which plays a crucial role in chemical sensing applications. This was enabled using solid-state sensors that can be implemented in planar form and fabricated using CMOS technology that is monolithically integrated on a single chip. This now provides an opportunity for chemical sensing platforms to leverage semiconductor technology that may offer advantages such as scalability, miniaturization, fabrication, and integration with intelligent instrumentation. Ion-sensitive field effect transistor (ISFET) is the most promising sensor for satisfying all these opportunities [1]. ISFET is the chemical sensor that has many advantages, as follows: 2nd International Conference on Sustainable Engineering Techniques (ICSET 2019) IOP Conf. Series: Materials Science and Engineering 518 (2019) 042020 IOP Publishing doi: 10.1088/1757-899X/518/4/042020 2 high integration capability, low cost, simple interface, and high productivity. Furthermore, the most promising property is the scalability in developing semiconductor fabrication, especially in its CMOS technology implementation. This property provides many enhancements for biomedical sensors via sensor minimization, which increases the speed of the sensor and requires few solutions [2].
Surface charge density that makes the ISFET sensitive to pH is caused by chemical reactions between the ISFET gate dielectric on one side and the electrolyte on the other side [3] [4]. In a conventional ISFET structure, the direct contact with solution is a sensing membrane called gate oxide. This area greatly influences the ISFET electrical behavior compared with the area of the entire sensor because of the existence of parasitic capacitance property, which degrades the ISFET sensitivity measurements. Protonation/Deprotonation reactions activate the surface charge potential (ψo) at the surface of ISFET. Coupling capacitance occurs between the surface and the float gate. This potential modulates the floating gate and shifts ISFET threshold voltage VT [5] [6]. The ISFET pH sensitivity is described and developed as a site-dissociation model by Yates [7].
Nevertheless, further research must examine more closely the links between IC design simulation and these models for more accurate analysis and further optimization; inopportunely, the famous commercial TCAD is not equipped with models, materials, and electrochemical processes that manage ISFET process and its operations [8]. Various approaches, such as experimental characterization, modeling [9] [10][3] [11], and simulation, have been used on ISFET research work [12] [13]. Until now, conventional ISFET has been modeled by different reports [14] [15]. A part of conventional ISFET from these reports assumed that the energy band gap of electrolyte is zero voltage. The non-zero band gap model has many advantages, such as convergence problem compensation, especially with high states of density, and high agreement with roll-off sensitivity phenomena in conventional ISFET.
In this paper, we propose a numerical simulation approach to study the electrolyte pH change of conventional ISFET structures using Silvaco TCAD tools [16]. Furthermore, we examine the ISFET device electrical response (transfer characteristics) to electrolyte pH change. The remaining sections present the model description in three parts, as reported in Section 2. The model result, validation, and discussion of the ISFET and its transfer characterization are introduced in Section 3. The conclusions and future work are summarized in Section 4.

Model description 2.1 Surface potential model:
Surface charge density that makes the ISFET sensitive to pH is caused by chemical reactions between the ISFET gate dielectric on one side and the electrolyte on the other side [14], [15], [29], [38]- [40]. As a first step toward the development of a general methodology, we will chemically and mathematically improve this relationship. Chemically, when we choose the insulator material as a sensing membrane, ions will rest on the surface membrane of the insulator according to the pH concentration. Therefore, the surface potential (ψo) is calculated by the hydrogen ion H + exchange between electrolyte solution and site binding of an insulator. The pH sensitivity of good insulator should cover wide range of pH scale besides liner response to this range [17]. Mathematically, for an FET device: where ܸ ீ is the gate voltage, ܸ ி is flatband voltage, q is electronic charge, NA is density of concentration, ‫ܥ‬ ை is the insulator capacitance per unit area calculated by ‫ܥ‬ ை = ߝ ௫ ‫ݐ‬ ௫ ൗ , and ܺ ௗ,் is the depletion layer width that can be found by the following: (1) as follows [18]: where ‫ܧ‬ , ߯ ௦ , Ǫ ௌ , and Ǫ ௫ are reference electrode potential, electrolyte-insulator interface dipole, work function of silicon, and charge located in the oxide, respectively. Ǫ ௌௌ and Cox are equivalent insulator-silicon interface charge and top-insulator capacitance per unit area, respectively. As mentioned in Section 1, the surface potential ߰ modulates the floating gate and shifts ISFET threshold voltage VT .Therefore, the Nernst equation control the proton activity at interface area that relates to potential is written as follows [19]: where q and k are elementary charge and Boltzmann constant, respectively. a is the proton activities in gate dielectric-electrolyte interface area and electrolyte. Therefore, we can conclude from (4) and (5) that the shift in threshold voltage for conventional ISFETs is given by the following: The site-dissociation model developed by Yates [7] describes the relationship between the change of potential with pH change, as follows: where where Nsil is the number of amphoteric silanol surface sites, and cHS is the surface H + concentration. Ka and Kb are the surface dissociation constants.

Electrolyte pH change model
As mentioned in Section 1, the major challenge is the electrolyte simulation in commercial TCAD because it is not equipped with models, materials, and electrochemical processes that manage ISFET process and its operations [8]. Therefore, our idea exploits the user-defined material property offered by Silvaco to  [16]. The properties of a user-defined material offered by Silvaco are exploited to simulate the electrolyte (solution) behavior. The parameters of silicon semiconductor material (i.e., energy bandgap, permittivity, affinity, and density of states) are reconstructed in an electrolyte solution. Therefore, electrostatic solution of the electrolyte area can be investigated by giving a numerical solution for the semiconductor equation inside this area. Three types of materials are available in Silvaco Atlas, namely, semiconductor, insulator, and conductor. The procedure of defining a new material in Atlas (user-defined) specifies the material name, the user group it belongs to, and the last known atlas about the default material. When these parameters are set in their correct places in the Silvaco input deck code, we can change and manipulate the material properties using MATERIAL statements (i.e., permittivity, energy bandgap, affinity, and density of states) as is typically done [16].
The most important parameters that bind the electrolyte solution physical properties with the intrinsic semiconductor electrical parameters are density of states, conduction band NC, and valence band NV. These parameters play key roles in the molar concentration of the solution based on the following methodology. At the chemical equilibrium, the dissociation of H2O is (H+ + OH−). Thus, the mass action law at 25 °C and pure water is introduced by the following [20]: Thus, The mass action law states that multiplying the free hole concentration p and the free electron n is equal to the square of the intrinsic carrier concentration ni under thermal equilibrium. The carrier concentration can be given as follows, based on Boltzmann statistics [12]: Therefore, (14) and (15) clearly demonstrate the relationship between pH change in electrolyte and the density of state for valence and conduction band.
The site-binding model side can be updated based on the relation that described from (9) to (15) by replacing each H + with its semiconductor counterpart. The mass action law in (9) is the same as the relation ݊ ଶ = ‫.݊‬ Therefore, we can rewrite (7) as follows: where the ni is a constant, and only p and n will change with pH.

TCAD model
Commercial TCAD allows users to introduce bias-dependent surface charges in the form of interface donor or acceptor traps. The challenge is simulating the updated surface charge density equation described by (16) in the electrolyte pH change model [14]. To introduce this equation to the simulator, interface trap statements are utilized to mimic the surface charge accurately, as follows [16]: "INTTRAP activates interface defect traps at discrete energy levels within the bandgap of the semiconductor and sets their parameter values. Device physics has established the existence of three different mechanisms, which add to the space charge term in Poisson's equation in addition to the ionized donor and acceptor impurities" [16]. Interface traps will add space charge directly into the right-hand side of Poisson's equation. To calculate the trapped charge in Poisson's equation, the total charge value is defined by the following: are the densities of ionized donor-like and acceptor-like traps, respectively. DENSITY and its probability of ionization are represented as FtA and FtD, respectively. For donor-like and acceptor-like traps, the ionized densities are calculated by the following equations: where FtA and FtD are given by the following equations: where SIGN is the carrier capture cross sections for electrons and SIGP holes. The thermal velocities for electrons and holes are ܸ and ܸ , respectively. For donor-like traps, the electron and hole emission rates, ݁ and ݁ , are defined by the following [16]: where Et and Ei are the trap energy level and the intrinsic Fermi level position, respectively. DEGEN.FAC is the degeneracy factor of the trap center. For acceptor traps, the electron and hole emission rates, ݁ and ݁ , are defined by the following [16]: Considering all equations mentioned above, we can rewrite the sit-binding model (7) based on TCAD model. We first assume that acceptor and donor traps exchange carriers only with the conduction and valence band of the semiconductor representing the electrolyte, respectively. Hence, we can rewrite (7) in terms of TCAD model as follows:

Validation of models
An ISFET device is simulated to check the suitability of the modeling procedure. The cross-section of the ISFET simulation structure is shown in  Figure 1. The parameters required for validation and simulation are easily derived from the literature data (Table (2) to fit with experimental [3]) for SiO2 gate dielectric to check the validity of our model and to show the agreement of models with the theoretical models and with experimental work. The first set of model validation examines the effect of changing pH on charge density in site-binding model. This is accomplished by comparing our models with the theoretical model developed by Yat [7] as shown in Error! Reference source not found.. Furthermore, the density of states NC and NV according to pH change values shown in Figure 3. We now turn to the experimental evidence on the comparison of the simulation of ISFET sensitivity with the standard real experimental that was done by ISFET developer Bergveld [3]. The results show good agreement between our model and the real experiment, as shown in Figure 4.  Table 2. Simulation Parameters of ISFET in Figure 1.    Figure 4: ISFET sensitivity validation

ISFET characterization
The electrostatic behavior (transfer characteristics) of a conventional ISFET device is simulated. Draining to source current Ids versus the reference gate voltage VRef. at various pH values for SiO2 gate oxide layer is shown in Error! Reference source not found.. The observed increase in threshold voltage could be attributed to the increase in pH values. Error! Reference source not found. shows that the lowest and the highest values of pH report less sensitivity compared with values in the range pH 5-9, which is consistent with the theories [3].
Another transfer characteristic is draining source voltage VDS for different pH scales in zero VRef. and ID current as a function of VDS for different VGS values for specific pH=7 value, as simulated and shown in Error! Reference source not found. and Figure 7, respectively.

Conclusion
A conventional ISFET, which uses simulation methods in addition to numerical modeling for pH sensing application, is proposed. The electrolyte pH change of ISFET device using Silvaco TCAD tools is investigated. The method exploits the properties of a user-defined material offered by Silvaco to simulate the electrolyte (solution) behavior. The parameters of silicon semiconductor material are set to reconstruct an electrolyte solution. Thus, the electrostatic solution of the electrolyte area can be investigated by giving a numerical solution for the semiconductor equation inside this area. The results show excellent agreement between theoretical model when comparing self-consistency TCAD model and real experimental work. Additionally, the transfer characteristics of a conventional ISFET device are simulated. The ID current as a function of the VRef. and VDS for different pH scale and ID current as a function of VDS for different VRef.   11 values for specific pH value are simulated. The proposed model paves the way for accurate and efficient ISFET modeling by trying different designs and further optimization with commercial Silvaco TCAD tools rather than expensive fabrication. As a future work, we plan to make more transfer characteristics to verify our model with different real experimental research work for model expandability issue.