# A High-Resolution Magnetic Field Imaging System Based on the Unpackaged Hall Element Array
## 2 Materials and Methods  
### Fabrication of Unpackaged Hall Element Array  
Currently, the vast majority of magnetic field imaging systems are designed using arrays of packaged Hall sensors, but the enclosures of these sensors limit the spacing of neighboring sensors and also result in the presence of positional offsets of the Hall elements, as shown in Figure 1. The distance \(h_{1}\) between the sensors is limited by the enclosure size to millimeters, making it difficult to further improve the spatial resolution of the system. In addition, the presence of the enclosure interferes with the soldering process, causing the sensors to shift their position, as shown in Figure 1b. Assuming no offset error for the first sensor, the ideal spacing of the sensors is \(y_{0}\). For the second and third sensors, their offsets in the x-direction are \(x_{1}\) and \(x_{2}\), and in the y-direction, they are \(y_{1}-y_{0}\) and \(y_{2}-y_{0}\), respectively. Figure 1c illustrates the positional offset caused by the placement of the Hall elements inside the package enclosure. The limited alignment accuracy of the die bonder makes it difficult for two Hall elements to be located at the same position inside the enclosure. In order to overcome the above problems, we designed the magnetic sensing probe of the system using unpackaged Hall elements.  
Figure 2 demonstrates the alignment design of the unpackaged Hall elements. These elements all come from the same wafer, which is diced in segments by the wafer dicing to form multiple segments of unseparated Hall elements. Since the wafers are fabricated using a photolithography process, which has micron-level manufacturing accuracy, the offset error of the unseparated Hall elements is effectively reduced. In addition, the width of the dicing channel between the Hall elements is only retained, which is typically a few tens of micrometers, significantly reducing the pixel center distance between the elements and improving the spatial resolution of the system.  
In this study, the unpackaged Hall linear array using 256 Hall elements is designed to extend the detection area of the system. These Hall elements are made of GaAs, model MG1A01, which provide more than eight times the sensitivity of silicon-based elements and have good linearity. The performance parameters of the GaAs Hall element are shown in Table 1.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Offset Voltage** & **Input Resistance** & **Output Resistance** & **Sensitivity** & **Linearity** \\ \hline \(<\)2 mV & 750 \(\Omega\) & 750 \(\Omega\) & 1.4 mV/mT@5 V & 0.5\% (\(<\)500 mT) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Performance parameters of MG1A01 Hall element.  
Figure 1: Impact of package enclosure on Hall sensors: (**a**) limited spacing of adjacent sensors; (**b**) PCB soldering shifts the position of sensors; (**c**) placing Hall elements inside the enclosure shifts their position.  
Figure 2: Alignment design of the unpackaged Hall linear array.  
Since the performance of Hall elements on different wafers varies slightly, the 256 Hall elements used in this paper all come from the same wafer to eliminate this effect. Figure 3 presents a designed unpackaged Hall linear array board. The electrode sections of each Hall element attach to the output pads via metal leads, requiring a total of 512 pads, which are aligned on both sides of the array. In addition, arranging the VCC and GND pads provides voltage bias to the array. Each Hall element has dimensions of 200 \(\upmu\)m \(\times\) 200 \(\upmu\)m \(\times\) 200 \(\upmu\)m and the spacing between the centers of adjacent elements is 255 \(\upmu\)m. There is an absence of gaps between the adjacent Hall elements, retaining a dicing channel width of only 55 \(\upmu\)m. The unpackaged Hall linear array is 6.53 cm in length and the entire PCB measures 7.95 cm \(\times\) 7.59 cm.