# A Three-Axis Magnetic Field Microsensor Fabricated Utilizing a CMOS Process
## 2 The Design of Magnetic Field Sensors
The current and bias voltage for the emitter are 4 mA and 1.8 V, respectively. As shown in Figure 3a,b, we know that the base current increases by 930 nA at 200 mT in the \(x\)-direction MF by comparison of the computations. Figure 2: Equivalent circuit of the MF microsensor. With the same computation method, surface carrier density distribution in the \(z\)-direction MF for the microsensor was evaluated. The emitter requires a bias voltage and a current. The bias voltage and current applied to the emitter were 1.8 V and 4 mA, respectively. Figure 4 illustrates the evaluated results of the surface carrier density distribution for the MF microsensor in the \(z\)-direction MF. The surface carrier density distribution of the MF microsensor without a magnetic field is illustrated in Figure 4a, and the surface carrier density distribution of the MF microsensor with 200 mT in the \(z\)-direction MF in Figure 4b. As shown in Figure 4a,b, the current of the left collector increases by 90 nA at 200 mT in the \(z\)-direction MF. To characterize the relation between the output signal and the magnetic field, the output voltage of the bases in the \(x\)-direction MF was evaluated using TCAD. The bias voltage and current applied to the emitter in this evaluation were 1.8 V and 4 mA, respectively. The magnetic field changed from \(-\)200 to 200 mT in the \(x\)-direction. Figure 5 shows the evaluated voltage difference of the bases in the \(x\)-direction MF. As shown in Figure 5, the voltage difference of the bases was \(-\)1.3 mV at \(-\)200 mT, and this value changed to 1.3 mV at 200 mT. The slope of the curve in Figure 5 is 6.5 mV/T. Because the MF microsensor is a symmetric structure, the voltage difference of the bases in the \(y\)-direction MF is the same as that in the \(x\)-direction MF. Figure 4: Carrier density of the MF microsensor with (**a**) 0 mT and (**b**) 200 mT in the \(z\)-direction MF. Figure 3: MF microsensor carrier density with (**a**) 0 mT and (**b**) 200 mT in the \(x\)-direction MF. To understand the MF microsensor performance in the \(z\)-direction MF, it was analyzed with the same method. The evaluation of voltage difference for collectors in the \(z\)-direction magnetic field is presented in Figure 6. The results depict that the voltage difference of the collector was \(-0.08\) mV at \(-200\) mT, and the value increased to \(0.08\) mV at \(200\) mT. The slope of the curve in Figure 6 is \(0.4\) mV/T. As shown in Figures 5 and 6, the slope of the curve (Figure 5) is \(6.5\) mV/T, and the slope value (Figure 6) is \(0.4\) mV/T. Therefore, the output signals of the bases and collectors in the MF microsensor were not large. To magnify the output signal of the MF microsensor, an amplifier circuitry was utilized to enlarge the output signal of the MF microsensor. Figure 7 shows the amplifier circuitry of the MF microsensor, where V\({}_{in}\) denotes the MF sensor voltage difference, and \(V_{0}\) is the amplifier circuitry output voltage. The amplifier circuitry contains six resistors and two amplifiers. The first stage amplifier of \(A_{1}\) enlarges the voltage difference of V\({}_{in}\) and eliminates the initial offset of the sensor. Then, the second stage amplifier of \(A_{2}\) strengthens the amplifier \(A_{1}\) output voltage. The output voltage of the amplifier circuitry can be expressed as [29]  
\[V_{0}=\left(\frac{R_{b}\times R_{d}}{R_{a}\times R_{c}}\right)V_{in} \tag{1}\]  
where \(R_{a}\), \(R_{b}\), \(R_{c}\), and \(R_{d}\) denote resistors as shown in Figure 7. According to Equation (1), we can match the resistors to obtain an ideal magnification effect. Figure 5: Voltage difference of bases in \(x\)-direction MF. Figure 6: Voltage difference of collectors in the \(z\)-direction MF. Figure 7: Amplifier circuitry. The resistors \(R_{a}\), \(R_{b}\), \(R_{c}\) and \(R_{d}\) in this evaluation are 1, 50, 5 and 25 k\(\Omega\), respectively. Substituting the resister values into Equation (1), we know that the gain of circuitry is 250.