A Graphene-Based Resistive Pressure Sensor with Record-High Sensitivity in a Wide Pressure Range

Pressure sensors are a key component in electronic skin (e-skin) sensing systems. Most reported resistive pressure sensors have a high sensitivity at low pressures (<5 kPa) to enable ultra-sensitive detection. However, the sensitivity drops significantly at high pressures (>5 kPa), which is inadequate for practical applications. For example, actions like a gentle touch and object manipulation have pressures below 10 kPa, and 10–100 kPa, respectively. Maintaining a high sensitivity in a wide pressure range is in great demand. Here, a flexible, wide range and ultra-sensitive resistive pressure sensor with a foam-like structure based on laser-scribed graphene (LSG) is demonstrated. Benefitting from the large spacing between graphene layers and the unique v-shaped microstructure of the LSG, the sensitivity of the pressure sensor is as high as 0.96 kPa−1 in a wide pressure range (0 ~ 50 kPa). Considering both sensitivity and pressure sensing range, the pressure sensor developed in this work is the best among all reported pressure sensors to date. A model of the LSG pressure sensor is also established, which agrees well with the experimental results. This work indicates that laser scribed flexible graphene pressure sensors could be widely used for artificial e-skin, medical-sensing, bio-sensing and many other areas.

I. LSG microstructure Figure S1. A 3D profile of the LSG morphology captured by a white light interference microscope.

II. The model of the LSG pressure sensor
Here we discuss the model formulated to interpret the relationship between pressure and conductivity in the LSG pressure sensor.
According to Figure 1a, the contact between two LSG layers can be modelled as a huge net of resistors containing N rows and N columns. The modelling contains two kinds of resistance (in-plane resistance and inter-plane resistance). The in-plane resistance can be referred to as the parallel resistance between two adjacent contacting points along the LSG in the same plane. The inter-plane resistance can be referred to the resistance perpendicular to the contact point of the resistors. For convenience, it is assumed that the pressure applied everywhere on the device is the same, therefore every inter-plane resistor has the same resistance. For the in-plane resistance, it is assumed that all have the same and unchangeable value p R .
SPICE is used to simulate the relationship between every inter-plane resistance and the total net resistance while C programming language is used to generate the huge simulation file. In Figure S2, the vertical axis represents the total in-plane resistance, LSG while the horizontal axis represents the each inter-plane resistance. The inter-plane resistance (ohm) The total resistance (ohm)

Figure S2. Theoretical results of the relationship between the inter-plane resistance and the total resistance
The relationship between the inter-plane resistance and the force applied on the device can be calculated as per the analysis shown below:

Pressure and displacement formula calculation：
The model is illustrated in Figure S3.

Figure S3. Geometrical modelling of the inter-plane contact
Consider the diagram in Fig. S3 as a cross-section of a single LSG trace. One-half of the base length (unit length) is labelled a, the total height before applying force is L, and the width of a given side is b (not displayed in the diagram). From the micro-structure, we can model this foam-like structure as an open-door foam, which satisfies the following formula: [S1] Where E and E * are the elastic modulus before and after applying pressure. The variables * and are the density of the foam hole. In order to simplify the model, we can use eq. (1) to obtain the dx as shown in Figure S3. Therefore we can get According to Young`s theorem where F is the force, S is the cross-sectional area, l is the total column length, and △l is the scratch length. In order to analyze the target structure, we first analyze the dx , and Combine these relations with equation (2), we obtain: Integrating the above equation yields an F vs ∆l relation.

 
When ∆L is very small, L − ∆L ≈ L , and 3L − ∆L ≈ 3L . Using these approximations, eq. (6) can be simplified as follows: 2. Inter-plane resistance vs. force In order to obtain the inter-plane resistance vs. force relationship, we must first obtain the displacement vs. resistance relation. The basic formula in eq. (8) can be used for this purpose: According to our model, we can rewrite eq. (8) as follows Therefore the relationship between R and ∆ has been obtained. Further, we combine eq. (9) and (6) to get the relationship between R and F .
3. According to ref. [S2], the electrical resistivity of the foam-like LSG obeys the following relationship: Where 0 /  is the relative electrical resistivity,  is the porosity, and K is the coefficient related to the geometric structure and other properties of foam-like materials.
When we apply force on the material, the air is squeezed-out of the pores. The volume and porosity prior to applying force is given by The formula can be re-written as follows: According to a geometrical relationship, can be rewritten as: Combining eq. (11) with eq. (12), we obtain: When a force is applied to the material, the structure and some properties of the material change. So K is the variable during the processing. The following model is supposed: Where 0 K and a is constant.
However if the L  is relatively large, then  becomes t  (a constant) i.e., the electrical resistivity doesn't change if the material is condensed enough.

Pressure (Pa)
Model LSG relationship between the applied force and total conductivity SUPPLEMENTARY TABLES