A dynamic detection method of a graphene transistor gas sensor

Abstract

The application belongs to the technical field of gas sensors, and relates to a current dynamic model of a gas sensor, and specifically provides a dynamic detection method of a graphene transistor gas sensor, which is based on a graphene transistor direct current model, combines surface reaction kinetics to describe a reaction process of graphene and a detection gas, and simultaneously considers the effects of chemical adsorption and physical adsorption, so that the description of the reaction process is more accurate; further, the influence of a detection gas molecule adsorption amount on the electrical characteristics of graphene is introduced, a detection gas molecule adsorption amount kinetics model is combined with the graphene transistor direct current model, and finally, the dynamic detection model of the application is established, so that the model accuracy is effectively improved, and rapid and accurate gas concentration detection can be realized; in addition, the application can set the value of the detection gas molecule adsorption amount at an initial moment, is more in line with the actual application scenario of the gas sensor, and can meet the needs of continuous gas concentration detection of the gas sensor.

Description

Technical Field

[0001] This invention belongs to the field of gas sensor technology and relates to the dynamic current model of gas sensors, specifically providing a dynamic detection model for a graphene transistor gas sensor. Background Technology

[0002] Gas sensors, as a key type of sensing device, are widely used in environmental monitoring, industrial production, medical diagnostics, and other fields. Their basic principle is to achieve highly sensitive detection of target gas concentrations by detecting the interaction between gas molecules and the sensor material. With the continuous development of technology, graphene materials have attracted widespread attention in the field of gas sensors due to their unique electrical, thermal, and mechanical properties.

[0003] Graphene is a two-dimensional lattice structure composed of a single layer of carbon atoms, such as Figure 1 As shown, graphene possesses extremely high electron mobility, a large specific surface area, and excellent chemical stability, making it an ideal sensor material for detecting various gases, including but not limited to volatile organic compounds (VOCs) and nitrogen oxides (NOx). x Gases such as sulfur dioxide (SO2) can be emitted. Graphene can be used to create gas sensors. It can be made into a resistive gas sensor by adding metal electrodes to both ends of the graphene, or it can be made into a graphene transistor gas sensor by using graphene as the conductive channel material, following the structure of transistors commonly found in semiconductor integrated circuits. Compared to resistive sensors, transistor sensors can be controlled by gate voltage and have better electrical stability.

[0004] For graphene transistor gas sensors, taking back-gate graphene transistors as an example, such as... Figure 2 As shown, the back-gate graphene gas sensor comprises six parts: from bottom to top, a gate metal 1, a silicon substrate layer 2, a silicon dioxide layer 3, a graphene layer 4, a source metal 5, and a drain metal 6. The gas-sensitive material of this gas sensor is graphene. When the detected gas molecules react with the graphene, the electrical properties of the graphene are changed. When the electrical properties of the graphene change, the drain-source current also changes. The relevant information of the detected gas can be extracted from this electrical signal of the current change.

[0005] The reaction principle of the graphene transistor gas sensor with the detected gas is as follows:

[0006]

[0007] Here, Graphene represents the active sites on the surface of graphene, which can undergo adsorption reactions with the detection gas Gas, producing a product called Graphene·Gas; K a K is the adsorption rate constant.d The desorption rate constant;

[0008] Based on chemical reaction kinetics theory, assuming the reaction is simple, we can obtain the rate of change of the product's surface density over time:

[0009]

[0010] Wherein, [Gas], [Graphene], and [Graphene·Gas] represent the concentration of the detection gas, the surface density of the active sites on the graphene surface, and the surface density of the generated product, respectively;

[0011] Assuming the concentration of the detected gas is c, since in practical applications the molecular weight of the detected gas that graphene can adsorb is much smaller than the molecular weight of the detected gas in the gas environment, the concentration of the detected gas is always c; assuming the surface density of the active sites on the graphene surface before reacting with the detected gas is m, and the surface density of the product is x, then the surface density of the active sites on the graphene surface during the reaction is mx.

[0012] Based on the above assumptions, the above formula can be written as:

[0013]

[0014] By solving the differential equation, we can obtain the functional relationship between the surface density of the generated product and the concentration of the detected gas and the reaction time:

[0015]

[0016] Where C0 is a constant generated during the integration process; at t=0, no surface products have been generated yet, so the value of C0 is obtained by x(0)=0; substituting it, we get:

[0017]

[0018] Furthermore, by normalizing the above equation, the time dynamics of the surface density of the generated product are obtained:

[0019]

[0020] Since the current is affected by the surface density of the generated products, and the variation law of the current is consistent with the variation law of the surface density of the generated products, the time dynamic model of the current is obtained as follows:

[0021]

[0022] Among them, I DS I represents the current of the graphene transistor at time t. DS0This represents the current in the graphene transistor at time t=0.

[0023] A gas sensor is a device that converts the concentration of a detected gas into an electrical signal. For a graphene transistor gas sensor, when the detected gas is introduced into its environment, its current changes and reaches a steady state after a certain period of time. Typically, the mapping relationship between the steady-state current of the gas sensor and the concentration of the detected gas is pre-established, and the concentration is determined based on the steady-state current. However, because the gas sensor requires a response time before the current reaches a steady state, the steady-state current method is no longer applicable in scenarios requiring rapid and accurate detection of gas concentration. This paper describes the current change process based on the aforementioned time-dynamic model, establishing a functional relationship between the current change, the detected gas concentration, and time, thereby achieving the goal of rapid and accurate gas concentration detection. However, the above time-dynamic model still has many problems: 1) It only considers one type of adsorption and does not consider both chemical adsorption and physical adsorption at the same time, so the model accuracy is low; 2) It does not consider the influence of the adsorption process of the detected gas molecules on the electrical properties of graphene, and does not consider the functional relationship between the amount of gas molecules adsorbed and the change in current. Instead, it simply equates the trend of the change in the amount of gas molecules adsorbed with the trend of the change in the current, resulting in an incomplete physical interpretation of the model; 3) The model assumes that x(0)=0, that is, the amount of gas molecules adsorbed at time 0 is 0. This is obviously not in line with the actual use scenario, resulting in a small applicability of the model. It can only be used for gas sensors that do not react with the detected gas and only perform concentration detection once. Summary of the Invention

[0024] The purpose of this invention is to provide a dynamic detection model for a graphene transistor gas sensor. Based on surface reaction kinetics, it considers both chemical and physical adsorption reactions, combines a DC model of the graphene transistor, and introduces the influence of the amount of adsorbed gas molecules on the electrical properties of graphene to establish the dynamic detection model of this invention. This model has high accuracy; by inputting any two of the following quantities—reaction time, gas concentration, and current—the value of the third quantity can be obtained, enabling rapid and accurate gas concentration detection.

[0025] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0026] A dynamic detection model for a graphene transistor gas sensor, characterized in that the dynamic detection model is expressed as:

[0027]

[0028] Among them, I D I represents the total current of the graphene transistor. Dn The current contributed by electrons, IDp The current contributed to the hole;

[0029]

[0030]

[0031] Where, μ n μ represents the electron mobility. p Q represents the hole mobility; W and L are the width and length of the graphene transistor, respectively. net,av,n and Q net,av,p These represent the average channel electron concentration and the average channel hole concentration, respectively, where e is the elementary charge and V is the average channel electron concentration and average channel hole concentration, respectively. DS N is the drain-source voltage. puddle v represents the remaining carrier concentration. sat,av,n and v sat,av,p These are the average saturation velocities of electrons and holes, respectively.

[0032] Furthermore, the electron mobility μ n With hole mobility μ p Specifically, it is expressed as follows:

[0033]

[0034]

[0035] Where, μ n0 and μ p0 These represent the electron and hole mobilities of graphene before the detection gas is introduced, respectively. 's' represents the influence of the amount of detection gas molecules adsorbed on the doping concentration and mobility, with a value of +1 or -1. β um β um,phy β up β up,phy m is the strength coefficient. a (t) represents the surface reaction kinetic equation, m a,phy (t) represents the physical adsorption kinetic equation, where t represents the time variable.

[0036] Furthermore, the average channel electron concentration Q net,av,n and average channel hole concentration Q net,av,p Specifically, it is expressed as follows:

[0037]

[0038]

[0039]

[0040]

[0041]

[0042] Among them, C back V is the gate capacitance of the back gate. GS N is the gate-source voltage. f V represents the doping concentration. th The voltage is the equivalent threshold voltage, and π is the mathematical constant pi. To reduce Planck's constant, v f For Fermi velocity, Indicates variable symbol.

[0043] Furthermore, the doping concentration N f Specifically, it is expressed as follows:

[0044]

[0045] Where, N f0 The doping concentration of graphene before the detection gas is introduced is denoted by s, which represents the influence of the amount of detection gas molecules adsorbed on the doping concentration and mobility, with a value of +1 or -1. β Nf β Nf,phy m is the strength coefficient. a (t) represents the surface reaction kinetic equation, m a,phy (t) represents the physical adsorption kinetic equation, where t represents the time variable.

[0046] Furthermore, the surface reaction kinetic equation m a (t) is specifically represented as:

[0047]

[0048] Among them, K a With K d These are the adsorption rate constant and the desorption rate constant, respectively. This represents the saturated adsorption capacity of a graphene monolayer. c is the concentration of the gas being detected, α x The parameters are empirical, x = 0, 1, 2, 3.

[0049] Physical adsorption kinetic equation m a,phy (t) is specifically represented as:

[0050]

[0051] Among them, K a,phy and K d,phy c represents the adsorption rate constant and desorption rate constant of physical adsorption, respectively. eff,phy This represents the equivalent gas concentration due to physical adsorption. m represents the saturation adsorption capacity of gas molecules in a graphene monolayer due to physical adsorption. a,phy (0) represents the amount of gas molecules physically adsorbed at time t=0, where t represents the time variable.

[0052] Based on the above technical solution, the beneficial effects of the present invention are as follows:

[0053] This invention provides a dynamic detection model for a graphene transistor gas sensor, based on a graphene transistor DC model, supported by relevant semiconductor physics theories. Furthermore, it describes the reaction process between graphene and the detection gas by incorporating surface reaction kinetics, considering both chemisorption and physisorption, thus making the description of the reaction process more accurate. Further, it introduces the influence of the amount of gas molecules adsorbed on the electrical properties of graphene (carrier mobility, doping concentration). Based on the influence mechanism, it combines the gas molecule adsorption kinetic model with the graphene transistor DC model to finally establish the dynamic detection model of this invention, effectively improving model accuracy and enabling rapid and accurate gas concentration detection. In addition, the dynamic detection model of this invention allows setting the initial value of the amount of gas molecules adsorbed (not necessarily 0), which better matches the actual application scenarios of gas sensors and meets the needs of continuous gas concentration detection. Attached Figure Description

[0054] Figure 1 This is a schematic diagram of the existing graphene structure.

[0055] Figure 2 This is a schematic diagram of the structure of an existing back-grid graphene gas sensor.

[0056] Figure 3 This is a flowchart illustrating the modeling process of the dynamic detection model of the graphene transistor gas sensor in this invention.

[0057] Figure 4 This is a schematic diagram of a cross-section of an existing back-grid graphene gas sensor.

[0058] Figure 5 This is a state diagram of the surface reaction process at the solid-gas interface.

[0059] Figure 6 This is a schematic diagram of the dynamic detection model of the graphene transistor gas sensor in this invention.

[0060] Figure 7 This is a diagram showing the verification results of the dynamic detection model of the graphene transistor gas sensor in this invention. Detailed Implementation

[0061] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0062] This embodiment provides a dynamic detection model for a graphene transistor gas sensor, and its modeling process is as follows: Figure 3 As shown, the model consists of four parts: a DC model of graphene transistors, a reaction rate equation, a reaction kinetic equation, and a coupling equation. The four parts will be explained in detail below.

[0063] 1. Graphene transistor DC model

[0064] This invention is based on a DC model of graphene transistors. First, the DC model of graphene transistors is explained, taking a back-gate graphene transistor as an example. Figure 4 The image shown is a cross-sectional view of a back-gate graphene transistor, and its DC model.

[0065]

[0066]

[0067]

[0068] Among them, I D I represents the total current of the graphene transistor. Dn The current contributed by electrons, I Dp The current contributed to holes; μ n μ represents the electron mobility. p Q represents the hole mobility; W and L are the width and length of the graphene transistor, respectively. net,av,n and Q net,av,p These represent the average channel electron concentration and the average channel hole concentration, respectively, where e is the elementary charge and V is the average channel electron concentration and average channel hole concentration, respectively. DS N is the drain-source voltage. puddle v represents the remaining carrier concentration. sat,av,p The average saturation velocity;

[0069] Further expand the formula for calculating current;

[0070]

[0071]

[0072]

[0073]

[0074]

[0075]

[0076] Among them, C back ε0 is the gate capacitance of the back gate, ε0 is the absolute dielectric constant, and ε0 is the gate capacitance of the back gate. back t is the relative permittivity of the back-gate dielectric. back V represents the thickness of the back-gate dielectric; GS N is the gate-source voltage. f V represents the doping concentration. th The voltage is the equivalent threshold voltage, and π is the mathematical constant pi. To reduce Planck's constant, v f It is the Fermi velocity.

[0077] 2. Reaction rate equation

[0078] This invention relates to adsorption at the solid-gas interface, which can be divided into two types: chemical adsorption and physical adsorption. The surface reaction process is divided into three states:

[0079] State 1: Solid surface that has not undergone adsorption with gas molecules;

[0080] State 2: Gas molecules diffuse from the gas phase space to the solid surface and adsorb onto the active sites on the solid surface to generate product molecules;

[0081] State 3: The adsorbed gas molecules desorb and diffuse away from the solid surface into the gas phase space;

[0082] In actual graphene reactions with gas molecules, the three states on the graphene surface coexist and eventually reach dynamic equilibrium.

[0083] like Figure 5 The diagram shows the state of the surface reaction process at the solid-gas interface. The derivation of chemisorption is presented below based on surface reaction kinetics; the adsorption rate on the bare surface can be expressed as:

[0084]

[0085] Where c is the concentration of the detected gas, Z is the collision rate of the detected gas molecules on a unit graphene surface at a unit concentration, and p is the collision efficiency, calculated using the following formula:

[0086]

[0087] Among them, E a , where is the height of the activation barrier or the activation energy, B is a constant determined by the mobility of the adsorption transition state on the surface and the number of adsorption centers per unit surface of graphene, R is the universal gas constant, and T is the absolute temperature.

[0088] The adsorption rate on a partially covered surface (coverage refers to the detection gas molecules occupying the active centers on the graphene surface) can be expressed as:

[0089]

[0090] Among them, A a f is the product of Z and B. a (θ) represents the probability of a detected gas molecule colliding with an uncovered surface, and is a function of the coverage θ; considering that a detected gas molecule occupies only one active site on the graphene surface, i.e., unit adsorption, f a (θ) represents the fraction of the surface that is not covered;

[0091]

[0092] For the desorption process, the desorption rate depends on the coverage of the graphene surface and is independent of the concentration of the detection gas; similarly, by discussing the adsorption rate, we can derive the equation for the desorption rate:

[0093]

[0094] Among them, A d It is an empirical parameter, f d (θ) represents the probability of the covered surface being allowed to desorb, E d f represents the desorption activation energy; for unit adsorption, f d (θ) is:

[0095]

[0096] Based on the above derivation, the reaction rate equations for the adsorption and desorption rates on the graphene surface are as follows:

[0097]

[0098]

[0099]

[0100]

[0101] Among them, K a and K d These are the adsorption rate constant and the desorption rate constant, respectively, which are constants determined by temperature and independent of coverage and the concentration of the detected gas;

[0102] According to the law of mass action, the reaction rate of an elementary reaction is proportional to the product of the powers of the concentrations of each reactant. Therefore, the adsorption rate equation can be further modified as follows:

[0103]

[0104] Where, α x The parameters are empirical, x=0,1,2,3, which include the uncertainty of the reaction rate equation and the inaccuracy of the gas concentration introduced.

[0105] 3. Reaction kinetic equations

[0106] Assuming the detected gas is Gas and the graphene is Gr, the chemical reaction equation can be obtained as follows:

[0107]

[0108] Wherein, [···] represents the chemical bonds formed between functional groups or other chemically active sites on graphene and the detection gas; further consideration is given to the rate of change of the amount of detection gas molecules adsorbed over time;

[0109]

[0110]

[0111] Where, m a To detect the amount of gas molecules adsorbed, This represents the saturated adsorption capacity of a graphene monolayer; the value of the coverage multiplied by the saturated adsorption capacity of a monolayer is the amount of gas molecules adsorbed.

[0112] The surface reaction kinetic equations will be derived below:

[0113]

[0114]

[0115]

[0116]

[0117] Where C0 is a constant generated during the integration process, the function of the change in the amount of gas molecules adsorbed over time can be further obtained:

[0118]

[0119] The specific value of C0 is derived below:

[0120]

[0121]

[0122] Substituting the derived C0 back into the original equation yields the final surface reaction kinetic equation, which describes the functional relationship between the amount of detector gas molecules adsorbed and the reaction time under different concentrations of detector gas and different initial values ​​of detector gas molecule adsorption:

[0123]

[0124] The above is the derivation process for chemisorption. For physisorption, gas molecules are adsorbed through van der Waals forces interacting with carbon atoms on the graphene surface. Because graphene has a large specific surface area, it provides a large number of adsorption sites and contact area, so the influence of physisorption also needs to be considered. Similar to chemisorption, the kinetic equation for physisorption can be obtained as follows:

[0125]

[0126] Among them, K a,phy and K d,phy c represents the adsorption rate constant and desorption rate constant of physical adsorption, respectively. eff,phy This represents the equivalent gas concentration due to physical adsorption. m represents the saturation adsorption capacity of gas molecules in a graphene monolayer due to physical adsorption. a,phy (0) represents the amount of gas molecules physically adsorbed at time t=0, where t represents the time variable;

[0127] 4. Coupling equations

[0128] When detecting gas molecule adsorption on graphene, three important indicators are: adsorption energy, charge transfer, and adsorption distance. A higher adsorption energy indicates more stable adsorption; a larger charge transfer indicates a greater influence of gas adsorption; and a shorter adsorption distance indicates more stable adsorption. Compared to physical adsorption, chemisorption has a higher adsorption energy, a larger charge transfer, and a shorter adsorption distance. When gas molecules adsorb onto graphene, they significantly affect two electrical properties of graphene: mobility and doping concentration. Charge carriers in graphene are disturbed by adsorbed gas molecules during movement, causing scattering and resulting in a decrease in mobility. However, the charge transfer during gas molecule adsorption reduces the charge carrier concentration in graphene, leading to weakened Coulomb scattering. The combined effect of this and the scattering caused by gas molecules manifests as an increase in mobility. The trend is upward; the change in doping concentration is due to the charge transferred during the adsorption of gas molecules. Assuming that the gas molecules do not affect each other, the charge transferred per unit of gas molecule adsorption is equal, so the relationship between doping concentration and the amount of gas molecules adsorbed is linear. Graphene contains N-type or P-type doping, and the charge transferred during the adsorption of gas molecules may be positive or negative. Therefore, the relationship between doping concentration and the amount of gas molecules adsorbed is determined by both the type of doping and the type of charge transferred during gas molecule adsorption. The relationship between mobility and the amount of gas molecules adsorbed is much more complex, but after parameter extraction, it was found that gas adsorption mainly affects the doping concentration rather than the mobility. Therefore, the relationship between mobility and the amount of gas molecules adsorbed can also be considered linear.

[0129] The final relationship between the amount of gas molecules adsorbed and the DC model is as follows:

[0130]

[0131]

[0132]

[0133] Where, N f0 The doping concentration of graphene before the detection gas is introduced is β; s represents the direction of the effect of the amount of detection gas molecules adsorbed on the doping concentration and mobility, with a value of +1 or -1; Nf β Nf,phy β um β um,phy β up β up,phy The intensity coefficient represents the strength of the effect of the amount of gas molecules adsorbed on the doping concentration and mobility; μ n0 and μ p0 The values ​​represent the electron mobility and hole mobility of graphene before the detection gas was introduced.

[0134] like Figure 6The diagram illustrates the operation of this invention. For example, by inputting the reaction time and the concentration of the detected gas, the model can be applied to obtain the current magnitude; by inputting the current and the reaction time, the model can be applied to obtain the concentration of the detected gas. Figure 7 The figure shown is a verification result diagram of the dynamic detection model of the present invention. As can be seen from the figure, the model has high accuracy and can achieve rapid and accurate gas concentration detection. When medium and high concentration gases are introduced, the value of the amount of gas molecules adsorbed does not have to be 0, which is consistent with the actual application scenario of gas sensors and can meet the needs of gas sensors for continuous gas concentration detection.

[0135] The above description is merely a specific embodiment of the present invention. Any feature disclosed in this specification may be replaced by other equivalent or similar features unless otherwise specified. All disclosed features, or steps in all methods or processes, may be combined in any way except for mutually exclusive features and / or steps.

Claims

1. A dynamic detection method for a graphene transistor gas sensor, characterized in that, Establish a dynamic detection model, represented as follows: where I D is the total current of the graphene transistor, I Dn is the current contributed by the electrons, I Dp is the current contributed by the holes; Where, μ n μ represents the electron mobility. p Q represents the hole mobility; W and L are the width and length of the graphene transistor, respectively. net,av,n and Q net,av,p These represent the average channel electron concentration and the average channel hole concentration, respectively, where e is the elementary charge and V is the average channel electron concentration and average channel hole concentration, respectively. DS n is the drain-source voltage. puddle v represents the remaining carrier concentration. sat,av,n and v sat,av,p These are the average saturation velocities of electrons and holes, respectively; electron mobility μ n With hole mobility μ p Specifically, it is expressed as follows: Where, μ n0 and μ p0 These represent the electron and hole mobilities of graphene before the detection gas is introduced, respectively. 's' represents the influence of the amount of detection gas molecules adsorbed on the doping concentration and mobility, with a value of +1 or -1. β um β um,phy β up β up,phy m is the strength coefficient. a (t) represents the surface reaction kinetic equation, m a,phy (t) represents the physical adsorption kinetic equation, where t represents the time variable; Surface reaction kinetic equation m a (t) is specifically represented as: Among them, K a With K d These are the adsorption rate constant and the desorption rate constant, respectively. This represents the saturated adsorption capacity of a graphene monolayer. c is the concentration of the gas being detected, α x For empirical parameters, x = 0, 1, 2, 3; Physical adsorption kinetic equation m a,phy (t) is specifically represented as: Among them, K a,phy and K d,phy c represents the adsorption rate constant and desorption rate constant of physical adsorption, respectively. eff,phy This represents the equivalent gas concentration due to physical adsorption. m represents the saturation adsorption capacity of gas molecules in a graphene monolayer due to physical adsorption. a,phy (0) represents the amount of gas molecules physically adsorbed at time t=0, where t represents the time variable; By inputting the current and the reaction time, the concentration of the detected gas is obtained using the dynamic detection model.

2. The dynamic detection method of the graphene transistor gas sensor according to claim 1, characterized in that, Average channel electron concentration Q net,av,n and average channel hole concentration Q net,av,p Specifically, it is expressed as follows: Among them, C back V is the gate capacitance of the back gate. GS N is the gate-source voltage. f V represents the doping concentration. th The voltage is the equivalent threshold voltage, and π is the mathematical constant pi. To reduce Planck's constant, v f For Fermi velocity, Indicates variable symbol.

3. The dynamic detection method of the graphene transistor gas sensor according to claim 2, characterized in that, Doping concentration N f Specifically, it is expressed as follows: Where, N f0 The doping concentration of graphene before the detection gas is introduced is denoted by s, which represents the influence of the amount of detection gas molecules adsorbed on the doping concentration and mobility, with a value of +1 or -1. β Nf β Nf,phy m is the strength coefficient. a (t) represents the surface reaction kinetic equation, m a,phy (t) represents the physical adsorption kinetic equation, where t represents the time variable.

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