# A Three-Axis Magnetic Field Microsensor Fabricated Utilizing a CMOS Process
## 2 The Design of Magnetic Field Sensors  
A magnetotransistor mechanism [PERSON] et al. (2019) was used to design this 3-axis MF microsensor. Figure 1a demonstrates the three-axis MF microsensor structure. Its structure is composed of a ring emitter, four bases, and eight collectors. The MF microsensor was constructed by an NPN magnetotransistor. As shown in Figure 1a, the STI oxide surrounds the emitter edge to counteract current moving. The STI oxide was also used to decrease the vertical p-n-junction effect and to eliminate the current from the surface of the magnetotransistor. Each electrode links a resistance, so the voltage difference of the bases in the \(x\)- and \(y\)-directions can be measured. A magnetotransistor depends on the Hall effect. Figure 1b presents a cross-sectional view of the MF microsensor. Carriers, giving a magnetic field in the \(x\)-direction, move from the emitter to the  
Figure 1: The MF microsensor structure: (**a**) tap view; (**b**) cross-sectional view. collectors and bases. On the right in Figure 1b, the path of the carriers is bent downward by Lorentz force when carriers move to the right collector, and they move across the right collector to the right base, leading to the right base current increment. On the left of Figure 1b, the path of the carriers is bent upward by Lorentz force when carriers move to the left collector, and they are difficult to move across the left collector to the left base, leading to the left base current decrement. Thereby, this action causes both the right and left bases in the \(y\)-direction to generate a voltage difference. Similarly, the bases in the \(x\)-direction produce a voltage difference when a magnetic field is given in the \(y\)-direction. In both collectors, the current causes an imbalance when a magnetic field is given in the \(z\)-direction, so both collectors generate a voltage difference. Figure 2 illustrates an equivalent circuit for the microsensor, where MT denotes the magnetotransistor, \(V_{\text{E}}\) is the bias voltage of the emitter, \(V_{\text{B1}}\), \(V_{\text{B2}}\), \(V_{\text{B3}}\), and \(V_{\text{B4}}\) are the voltages of the bases, \(V_{\text{C1}}\), \(V_{\text{C2}}\), \(V_{\text{C3}}\), \(V_{\text{C4}}\), \(V_{\text{C5}}\), \(V_{\text{C6}}\), \(V_{\text{C7}}\), and \(V_{\text{C8}}\) are the voltages of the collectors, \(R\) is the resister, and the symbol (4) represents the related circuit repeated four times. The resistor \(R\) is 1 k\(\Omega\). When the magnetic field in the \(x\)-direction applies to MT, we can measure a voltage difference between bases \(V_{\text{B2}}\) and \(V_{\text{B4}}\). Relatively, the magnetic field in the \(y\)-direction supplies to MT, and the voltage difference between bases \(V_{\text{B1}}\) and \(V_{\text{B3}}\) is then acquired. Finally, the voltage difference between collectors \(V_{\text{C1}}\) and \(V_{\text{C3}}\) (or \(V_{\text{C2}}/V_{\text{C4}}\)) is yielded when the magnetic field in the \(z\)-direction supplies to MT. Carrier motion in the MF microsensor was simulated using FEM (finite element method) software Sentaurus TCAD. The MF microsensor is a symmetrical structure, so only one-quarter of the MF microsensor is established to reduce model size and simulation time. The model is meshed using the Delaunay triangulation method, and the model has 4 \(\times\) 10\({}^{6}\) elements. The coupling effect of the electrical and magnetic fields is evaluated utilizing the Poisson electron hole approach. The carrier density of the MF microsensor model is computed by solving with the Bank/Rose approach. Figure 3 illustrates the computed results of the surface carrier density distribution for the MF microsensor model with the \(x\)-direction MF. The surface carrier density distribution of the MF microsensor without a magnetic field is presented in Figure 3a, and the surface carrier density distribution of the MF microsensor with 200 mT in the \(x\)-direction MF is presented in Figure 3b. In this computation, the emitter needs to supply a current and a bias voltage.