An Improved Method for DC Model of Liquid-Gated Graphene Field-Effect Transistor

Abstract

The present invention proposes an improved method for the DC model of a liquid-gated graphene field-effect transistor, which includes three steps: improving the traditional GFET model by combining electrochemical theory, introducing the direction of the concentration parameter variable for further improvement, and finally verifying. By introducing the electric double-layer capacitance, the present invention accurately describes the electrode physical effect in the liquid gate, first corrects the DC model of the traditional GFET, overcomes its disadvantage of not being applicable to LG-GFET, and combines the principle of chemical reaction equilibrium to deduce the influence of the analyte concentration on graphene doping. The relationship between the analyte concentration and the carrier mobility is fitted using the relaxation time function, and finally a concentration-related DC model of LG-GFET is established, improving the application scope of the model. At the same time, by introducing the analyte concentration as an independent variable, the concentration of the analyte can be directly obtained using this model while detecting the electrical signal, improving the detection efficiency in the field of biological detection.

Description

Technical Field

[0001] The present invention relates to the field of biological detection technologies, and in particular to a method for improving the DC model of a liquid-gated graphene field-effect transistor. Background Art

[0002] With the demand for more and more types of analytes and lower analyte concentrations, the requirements for biosensors are also getting higher and higher. Nano field-effect transistors are a new type of biosensor based on nanomaterials. Due to their unique physical and chemical properties, relatively high sensitivity, high selectivity, rapid detection, simple operation, and easy integration, etc., they have attracted extensive attention in the fields of life science and circuits. Graphene is a two-dimensional material with a large surface-to-body ratio, high electron mobility, excellent thermoelectric conductivity, and high mechanical strength. Because the high carrier mobility of graphene can enable the channel current to quickly respond to changes in the gate voltage (including the analyte-induced potential), the GFET (graphene field-effect transistor) is an ideal and rapid platform for monitoring biological reactions;

[0003] The DC model based on the GFET structure has derived a correct graphene channel charge model based on semiconductor physics and can well describe the physical effects of graphene. However, due to the limitation of the gate capacitance calculation method, this model can only be applied to GFETs and cannot correctly characterize LG-GFETs. Moreover, the DC model applicable to LG-GFETs also has higher requirements in other aspects. Therefore, this model needs to be further improved. The main reasons are as follows:

[0004] (1) In the DC model based on the GFET structure, the gate capacitance is calculated according to the simplest parallel-plate capacitance. Therefore, it can only be applied to the traditional GFET structure. Facing the LG-GFET structure that is increasingly widely used in biological detection today, this model cannot correctly describe its physical characteristics and cannot explain the influence of the gate probe insertion depth on the current, and its accuracy needs to be further improved;

[0005] (2) The DC model based on the GFET structure is completely related to electricity. The independent variables and some parameters in it are related to electricity and physics, lacking independent variables and parameters related to biochemistry. Therefore, it cannot be directly linked to biological detection. Using the current model for simulation can only obtain results related to electricity and cannot directly obtain the concentration parameter results that are very concerned about in biological detection. Therefore, the present invention proposes a method for improving the DC model of a liquid-gated graphene field-effect transistor to solve the problems existing in the prior art. Summary of the Invention

[0006] In view of the above problems, the object of the present invention is to propose an improved method for the DC model of a liquid-gated graphene field-effect transistor. This improved method for the DC model of a liquid-gated graphene field-effect transistor has the advantage of being able to obtain an electrical signal while directly obtaining the concentration of the analyte using this model, solving the problem in the prior art that the concentration parameter result, which is highly concerned in biological detection, cannot be directly obtained.

[0007] To achieve the object of the present invention, the present invention is realized through the following technical solutions: An improved method for the DC model of a liquid-gated graphene field-effect transistor, comprising the following steps:

[0008] Step 1: Obtain a traditional GFET model, and correct the obtained traditional GFET model in combination with electrochemical theory. Replace the gate capacitance formula in the traditional GFET model with the double-layer capacitance formula, that is, obtain a preliminarily improved DC model of LG-GFET.

[0009] Step 2: For the DC model of LG-GFET obtained in Step 1, introduce the direction of the concentration parameter variable for further improvement to obtain an improved LG-GFET model related to concentration. The direction of introducing the concentration parameter variable is divided into two types: the influence of the analyte concentration on the chemical equilibrium reaction and the influence of the analyte concentration on the carrier mobility of graphene.

[0010] Step 3: Verify the result of the improved LG-GFET model related to concentration obtained in Step 2. When the verification result is in line, it indicates that the improved LG-GFET model related to concentration has been obtained, and the improvement operation of the traditional GFET model is completed.

[0011] A further improvement lies in: In Step 1, compare and verify the obtained DC model of LG-GFET with the test results. If the comparison and verification result is in line, it indicates that an accurately described DC model of LG-GFET has been obtained. If the comparison and verification result is not in line, then correct the traditional GFET model again until it conforms to the test result.

[0012] A further improvement lies in: The test results are extracted based on the test results of LG-GFET detecting exosome solution.

[0013] A further improvement lies in: In the study of the influence of the analyte concentration on the chemical equilibrium reaction in Step 2, the detection results of exosomes are taken as the research object. The higher the exosome concentration, the more the amount combined with graphene.

[0014] A further improvement lies in that: in the research on the influence of the concentration of the detected substance on the carrier mobility of graphene in step two, different concentrations of exosome solutions are tested using an LG-GFET, and it is found that as the concentration increases, the carrier mobility decreases. Subsequently, the relationships between the hole and electron carrier mobilities and the concentration of the exosome solution are described by the formula:

[0015]

[0016]

[0017] In the formula, μ p0 and μ n0 represent the carrier mobilities of holes and electrons respectively. When the concentration approaches a high value, the carrier mobility basically stabilizes at a certain value. A p and A p represent the intensity coefficients of the change in carrier mobility with concentration, and represent the relaxation concentration.

[0018] A further improvement lies in that: in step three, when the verification result is not in line, it enters step two, and the obtained DC model of the LG-GFET is improved again.

[0019] A further improvement lies in that: in step three, the comparative verification is based on the comparison of the simulation data and the model calculation data at different concentrations.

[0020] A further improvement lies in that: during the improvement process, the model parameters are continuously adjusted and optimized.

[0021] The beneficial effects of the present invention are as follows: This method for improving the DC model of the liquid-gated graphene field-effect transistor combines electrochemical theory, introduces the electric double-layer capacitance to accurately describe the electrode physical effects in the liquid gate, first corrects the DC model of the traditional GFET, overcomes its drawbacks that are not applicable to the LG-GFET, and combines the principle of chemical reaction equilibrium to deduce the influence of the concentration of the detected substance on graphene doping. The relationship between the concentration of the detected substance and the carrier mobility is fitted using the relaxation time function. Finally, a concentration-related DC model of the LG-GFET is established, which improves the application range of the model. At the same time, by introducing the concentration of the detected substance as an independent variable, the concentration of the detected substance can be directly obtained using this model while detecting the electrical signal, improving the detection efficiency in the field of biological detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0023] Figure 1 It is a schematic diagram of the step flow of the present invention.

[0024] Figure 2 It is a schematic diagram of the formation of the electric double layer capacitance in the LG-GFET of the present invention.

[0025] Figure 3 It is a schematic diagram of the equivalent circuit after the electric double layer capacitance of the present invention.

[0026] Figure 4 It is a schematic diagram of the hole mobility model of the present invention.

[0027] Figure 5 It is a schematic diagram of the electron mobility model of the present invention.

[0028] Figure 6 It is a schematic diagram of the results of the concentration-related LG-GFET DC model of the present invention. Specific embodiments

[0029] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0030] According to Figures 1-6 shown, this embodiment proposes an improvement method for the DC model of a liquid-gated graphene field-effect transistor, including the following steps:

[0031] Step 1: Obtain a traditional GFET (graphene field-effect transistor) model, and correct the obtained traditional GFET model in combination with electrochemistry theory. Replace the gate capacitance formula in the traditional GFET model with the electric double layer capacitance formula, that is, obtain a preliminarily improved DC model of LG-GFET (liquid-gated graphene field-effect transistor), as Figure 2 and Figure 3 shown, when any two different phases come into contact, an electric potential will be generated between the two phases, which is caused by charge separation. Each of the two phases has an excess of charges, with equal amounts, opposite signs, attracting each other to form an electric double layer, and the calculation formula for the electric layer capacitance is:

[0032]

[0033] where ε0 and ε0 are the air permittivity and the relative permittivity of the solution respectively, and X D is the Debye length of the solution, which is obtained from the following formula, X S is the Stern layer thickness, generally the radius of the ion, taking 0.5 nm. The capacitance calculated therefrom is the capacitance per unit area, where:

[0034]

[0035] where R is the universal gas constant, F is the Faraday constant, T is the temperature, and I str_bulk is the ionic strength of the solution, and the ionic strength is calculated by the following formula:

[0036]

[0037] where zA and zX are the charge numbers of positive and negative ions respectively, and c bulk is the concentration of positive or negative ions. Since the capacitance per unit area requires integration when finally calculating the current, and the integration surface is the graphene layer, the capacitance at the DC needle needs to be mapped to the graphene layer one by one to complete the integration. Therefore, the double-layer capacitance at the equivalent gate probe is adopted, and its formula is expressed as:

[0038]

[0039] It can be seen from this that in this equivalent double-layer capacitance, the influence of the insertion depth of the gate probe on the drain current magnitude can be explained. Replacing the top-gate capacitance C in the traditional model with such a double-layer capacitance calculation formula top namely, the DC model applicable to LG-GFET is obtained;

[0040] Compare and verify the obtained DC model of LG-GFET with the test results. If the comparison and verification results are in line, it means that an accurately described DC model of LG-GFET is obtained. If the comparison and verification results are not in line, the traditional GFET model is corrected again until it conforms to the test results. The test results are extracted based on the test results of detecting exosome solution by LG-GFET;

[0041] Step 2: For the DC model of LG-GFET obtained in Step 1, introduce the direction of the concentration parameter variable and make a further improvement to obtain an improved concentration-related LG-GFET model. The direction of introducing the concentration parameter variable is divided into two types: the influence of the analyte concentration on the chemical equilibrium reaction and the influence of the analyte concentration on the graphene carrier mobility;

[0042] In the study of the effect of analyte concentration on chemical equilibrium reactions, the detection results of exosomes were used as the research object. The higher the exosome concentration, the more the amount of combination with graphene. This process of combination and decomposition is a chemical reaction, and its expression is:

[0043]

[0044] In the formula, EXO represents exosomes, EG represents the combination of exosomes and graphene, and K a and K d are the association constant and dissociation constant respectively. Let the initial concentration of exosomes be c, the density of the binding sites between graphene and exosomes at the beginning be m, and the concentration of EG generated at the final equilibrium be x. According to the equation, the concentration of EG generated finally can be deduced as:

[0045]

[0046] After obtaining the concentration of the combination of exosomes and graphene, it is necessary to convert it into the doping introduced by graphene. Therefore, in this embodiment, a correction factor is provided for this conversion process. The final doping amount N f,EXO introduced by the combination of exosomes and graphene is:

[0047] N f,EXO = a·c b ·x

[0048] In the formula, a and b are empirical parameters used to fit the trend of concentration and doping amount, and the Dirac point voltage can be obtained from the LG-GFET DC model:

[0049]

[0050] In the study of the effect of the concentration of the detected substance on the carrier mobility of graphene, exosome solutions with different concentrations were tested using an LG-GF ET. It was found that as the concentration increased, the carrier mobility decreased. The reason for the lower carrier mobility of graphene with higher exosome solution concentration is that the adsorption of exosomes on graphene leads to a decrease in graphene mobility. The higher the concentration, the more adsorption and the greater the decrease in mobility. Analyzing from the physical level: According to semiconductor physics theory, mobility is the average drift velocity of carriers generated under a unit electric field strength. Mobility represents the magnitude of the carrier conduction ability, and it and the carrier (electron or hole) concentration determine the conductivity of the semiconductor. Mobility is inversely proportional to the effective mass and scattering probability of the carrier. The effective mass of the carrier is related to the material, and electrons have different effective masses in different semiconductors. Therefore, the main factors affecting the carrier mobility in graphene are the scattering of interface defects and impurities. Interface defects are caused during device fabrication and are independent of the detected substance concentration. Therefore, the main factor affecting the carrier mobility of graphene by the detected substance concentration is the introduced scattering. Within a certain range, the higher the concentration, the more scattering is introduced, resulting in a greater decrease in carrier mobility. However, when a certain concentration is reached, it will inevitably saturate, that is, the carrier mobility decreases to a certain extent and then tends to be stable;

[0051] Subsequently, according to the law obtained from the above analysis, in this embodiment, the relationship between the mobility of holes and electrons and the concentration of the exosome solution is described by a formula. This formula is an expression similar to a relaxation time function and is:

[0052]

[0053]

[0054] In the formula, μ p0 and μ n0 represent the carrier mobilities when the concentration tends to a high value and is basically stable at a certain value. A p and A p represent the intensity coefficients of the carrier mobility change with concentration, and represent the relaxation concentrations, a parameter similar to the relaxation time. Finally, by adjusting the model parameters, the model effect can be seen, as shown in Figure 4 and Figure 5 ;

[0055] Step 3: Verify the results of the improved concentration-related LG-GFET model obtained in Step 2. When the verification result is in line, it means that the improved concentration-related LG-GFET model has been obtained, and the improvement of the traditional GFET model is completed. When the verification result is not in line, go back to Step 2 and improve the obtained LG-GFET DC model again;

[0056] Through the modification of the DC model of the traditional GFET and the research on concentration-related improvements, a concentration-related DC model of the LG-GFET was finally obtained, and the model expression is as follows:

[0057]

[0058] In the model, μ n,eff and μ p,eff are the effective mobilities of electrons and holes related to concentration respectively:

[0059]

[0060]

[0061] In the model, Q n,av and Q p,av are the average carrier concentrations of electrons and holes in the channel related to concentration respectively, that is:

[0062]

[0063]

[0064] In the model, v satn,av and v satp,av are the average saturation velocities of electrons and holes related to concentration respectively, that is:

[0065]

[0066]

[0067] The comparison and verification is based on the comparison of the simulation data and the model calculation data at different concentrations. That is, in this embodiment, by adjusting and optimizing the model parameters, it can finally fit well with the simulation data of four concentrations (0.001X, 0.01X, 0.1X, 1X), as Figure 6 shown.

[0068] In this embodiment, during the improvement process, the model parameters are continuously adjusted and optimized so that the model can fit well with the test results.

[0069] Compared with the traditional GFET DC model, the present invention uses an equivalent electric double-layer capacitance to accurately describe the physical effects of the liquid gate electrode. In addition, mathematical processing is performed on the electric double-layer capacitance at the gate probe, which is equivalent to two capacitors in series, enabling accurate description of the electrical characteristics of the LG-GFET, scientifically explaining the influence of the insertion depth of the gate probe on the magnitude of the drain current, and being not limited to the description of electrical signals compared with the traditional DC model. By introducing the concentration of the analyte as an independent variable, the electrical model is improved into an electro-chemical-physical related model. Using this model for simulation can obtain parameter results related to the concentration, and while detecting the electrical signal, the concentration of the analyte can also be directly calculated using this model.

[0070] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments. What is described in the above embodiments and the specification only illustrates the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed. The scope of protection claimed by the present invention is defined by the appended claims and their equivalents.

Claims

1. An improved method for the DC model of a liquid-gated graphene field-effect transistor, characterized in that: It includes the following steps: Step 1: Obtain a traditional GFET model, and correct the obtained traditional GFET model in combination with electrochemistry theory. Replace the gate capacitance formula in the traditional GFET model with the electric double layer capacitance formula, that is, obtain a preliminarily improved LG-GFET DC model. In Step 1, compare and verify the obtained LG-GFET DC model with the test results. If the comparison and verification results are in line, it means that an accurately described LG-GFET DC model has been obtained. If the comparison and verification results are not in line, correct the traditional GFET model again until it conforms to the test results; Step 2: For the LG-GFET DC model obtained in Step 1, introduce the direction of the concentration parameter variable for further improvement to obtain an improved concentration-related LG-GFET model. The direction of introducing the concentration parameter variable is divided into two types: the influence of the analyte concentration on the chemical equilibrium reaction and the influence of the analyte concentration on the carrier mobility of graphene; Step 3: Verify the results of the improved concentration-related LG-GFET model obtained in Step 2. When the verification results are in line, it means that an improved concentration-related LG-GFET model has been obtained, and the improvement of the traditional GFET model is completed.

2. The improvement method of the DC model of a liquid-gated graphene field-effect transistor according to claim 1, characterized in that: The test results are extracted based on the test results of LG-GFET for detecting exosome solution.

3. The improvement method of the DC model of a liquid-gated graphene field-effect transistor according to claim 1, wherein: In Step 2, in the study of the influence of the analyte concentration on the chemical equilibrium reaction, the detection results of exosomes are used as the research object. The higher the exosome concentration, the more the amount combined with graphene.

4. An improved method for the DC model of a liquid-gated graphene field-effect transistor according to claim 1, characterized in that: In Step 2, in the study of the influence of the analyte concentration on the carrier mobility of graphene, LG-GFET is used to test exosome solutions with different concentrations, and it is found that as the concentration increases, the carrier mobility decreases. Then, the relationship between the hole carrier mobility and the exosome solution concentration is described by the formula: The relationship between the electron carrier mobility and the exosome solution concentration, the formula is: where μ p0 and μ n0 respectively represent a value at which the mobilities of hole carriers and electron carriers are basically stable when approaching high concentrations. A p and A n respectively represent the intensity coefficients of the change in the mobilities of hole carriers and electron carriers with concentration. and respectively represent the relaxation concentrations of hole carriers and electron carriers, and C represents the concentration of the exosome solution.

5. The improvement method of the DC model of a liquid-gated graphene field-effect transistor according to claim 1, characterized in that: In Step 3, when the verification results are not in line, go to Step 2 and improve the obtained LG-GFET DC model again.

6. The improvement method of the DC model of a liquid-gated graphene field-effect transistor according to claim 1, characterized in that: In Step 3, the comparison and verification is based on the comparison of the simulation data and the model calculation data at different concentrations.

7. An improved method for the DC model of a liquid-gated graphene field-effect transistor according to claim 1, characterized in that: During the improvement process, the model parameters are continuously adjusted and optimized.

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