A New Design of a CMOS Vertical Hall Sensor with a Low Offset

Abstract

Vertical Hall sensors (VHSs), compatible with complementary metal oxide semiconductor (CMOS) technology, are used to detect magnetic fields in the plane of the sensor. In previous studies, their performance was limited by a large offset. This paper reports on a novel CMOS seven-contact VHS (7CVHS), which is formed by adding two additional contacts to a traditional five-contact VHS (5CVHS) to alleviate the offset. The offset voltage and offset magnetic field of the 7CVHS are reduced by 90.20% and 88.31% of those of the 5CVHS, respectively, with a 16.16% current-related sensitivity loss. Moreover, the size and positions of the contacts are optimized in standard GLOBALFOUNDRIES 0.18 μm BCDlite^TM technology by scanning parameters using FEM simulations. The simulation data are analyzed in groups to study the influence of the size and contact positions on the current-related sensitivity, offset voltage, and offset magnetic field.

1. Introduction

Magnetic sensors have been widely used for applications in current sensing [1,2,3], biosensors [4], and consumer devices [5,6]. Hall effect sensors, which can be integrated into signal conditioning circuits using complementary metal oxide semiconductor (CMOS) technology, have the largest market share among all kinds of magnetic sensors [7]. Horizontal Hall sensors (HHSs), which are used to detect the magnetic field orthogonal to its surface, can meet the requirements of most application scenarios [8]. However, a three-dimensional (3D) Hall sensor is necessary in some applications, such as the measurement of a 3D magnetic field [9] and a space angle [10,11,12]. The most straightforward and promising way to implement 3D Hall sensors is to arrange multiple HHSs and vertical Hall sensors (VHSs) to detect magnetic fields orthogonal and parallel to the surface, respectively. VHSs with low sensitivity and especially large offsets are a weakness of the implementation of 3D Hall sensors [13,14,15].

After the development of the five-contact VHS (5CVHS) in [16], several variations have been proposed to improve the performance of VHSs, such as the four-contact VHS (4CVHS) [17,18], six-contact VHS (6CVHS) [19], and eight-contact circular vertical Hall devices (8CCVHD) [20]. The 5CVHS is a research hotspot to improve its performance [13,14,15], and variations have been proposed to reduce the offset by a large loss of sensitivity to accommodate low-voltage CMOS technology [21,22]. A symmetric four-folded and three-contact VHS (4F-3CVHS) has been proposed to reduce offset [23,24,25,26]. 4F-3CVHS, which has four active regions connected by additional wires, effectively improves VHS performance by increasing VHS complexity.

In this paper, we propose a new design for a seven-contact VHS (7CVHS) by adding two additional contacts in the body of a 5CVHS to reduce offset. The working principle of the 7CVHS and a contrastive analysis of the 5CVHS and 7CVHS are described in Section 2. The size and distances of contacts corresponding to the optimal performance of the 7CVHS are obtained by scanning parameters using FEM simulation, and the influence mechanism of the size and distances of contacts on the current-related sensitivity, offset voltage, and offset magnetic field are analyzed in detail in Section 3. Finally, Section 4 concludes this work.

2. From Five-Contact to Seven-Contact VHS

A 5CVHS, as shown in Figure 1, contains an N-type region in the p-substrate and five n⁺-diffusions serving as contacts from C1 to C5. The N-doped well, which works as an active region, largely determines the performance of 5CVHS. When the 5CVHS is working, the outer contacts, C1 and C5, are short-circuited, and a biasing current is applied between C3 and C1 (C5), as shown in Figure 1b. Obviously, the voltages of contacts C2 and C4 are equal because of the symmetry of the structure of 5CVHS. When the 5CVHS is placed in magnetic field B, the voltages of contacts C2 and C4 change because of the Hall effect. The Hall voltage is measured between C2 and C4. The Hall voltages of C2 and C4 have opposite directions, so the Hall voltage of the 5CVHS can be expressed as:

$$V_H(B\ne 0)=[V_{\mathrm{C}2}(B\ne 0)-V_{\mathrm{C}2}(B=0)]-[V_{\mathrm{C}4}(B\ne 0)-V_{\mathrm{C}4}(B=0)]$$

(1)

C2 and C4 serve as sensing contacts to obtain the Hall voltage of the 5CVHS. The voltage difference between them can be expressed as follows:

$$V_{out}(B\ne 0)=V_{\mathrm{C}2}(B\ne 0)-V_{\mathrm{C}4}(B\ne 0)$$

(2)

Combining Equations (1) and (2), we can obtain the expression

$$V_{out}(B\ne 0)=V_H(B\ne 0)+[V_{\mathrm{C}2}(B=0)-V_{\mathrm{C}4}(B=0)]$$

(3)

The main component of V_out is the Hall voltage, from which the magnetic field can be calculated by their relationship, as follows:

$$V_H(B\ne 0)=S_I{I}_{in}B$$

(4)

where S_I is the current-related sensitivity of the 5CVHS, and I_in is the bias current applied between C3 and C1 (C5). The other part of V_out in Equation (3) is the voltage difference between C2 and C4 without a magnetic field, named the offset voltage V_off. The voltages of C2 and C4 should be equal in an ideal situation because of the symmetry structure of the 5CVHS on both sides of C3. However, offset voltage is unavoidable in engineering practice. The offset voltage can be converted to an offset magnetic field B_off, which is an important indicator of the sensor. B_off can be calculated using the following expression:

$$B_{off}=\frac{V_{off}}{S_I{I}_{in}}$$

(5)

The offset is caused by asymmetry on both sides of C3 due to mask misalignment, the junction field effect (JFE), and piezoresistive effects. The new VHS, named the 7CVHS, shown in Figure 2a,b, introduces two connections on either side of C3 to neutralize the asymmetry and to lower the offset. The connections from C1 to C5 and C7 to C3, no doubt, lead to a decrease in the effective current of forming the Hall voltage. Thus, current-related sensitivity is reduced. The 7CVHS in the five-contact mode (7CVHS in 5C) in Figure 2c has the same characteristics as a 5CVHS. We compare a 7CVHS with the same size in the modes shown in Figure 2a,c to determine the advantage of the new VHS. Because the 7CVHS design is based on 5CVHS, it uses the same regions of technology. Additionally, 7CVHS is completely compatible with CMOS technology and contains an N-type region in the p-substrate and seven n⁺-diffusions serving as contacts from C1 to C7. The N-doped well works as an active region. An MVNVT is an N-type region, which is the most suitable area to implement the active region of the 7CVHS in standard GLOBALFOUNDRIES 0.18 μm BCDlite^TM technology [27]. The doping concentration and depth of the MVNVT are 1.413 × 10¹⁷ cm⁻³ and 1.018 μm, respectively.

In the COMSOL model of 7CVHS, MVNVT is used as the active region. The models in COMSOL of two 7CVHS types and the voltage distributions on their surfaces are shown in Figure 3. The simulation setup parameters are given in

Table 1. Simulation setup parameters.

Symbol	Value	Description
q [C]	1.602 × 10−19	Electron charge
n [cm−3]	1.413 × 1017	Doping concentration
μ [cm2/Vsec]	1000	Electron mobility
B [T]	1	Magnetic field
t [m]	1.018 × 10−6	Depth of Hall sensor
w [m]	3 × 10−6	Width of Hall sensor
I [mA]	1	Bias current

. The size and performance comparisons of the model in Figure 2 are listed in

Table 2. Size and performance comparison of the model in Figure 2.

Type of VHS	l (μm)	d1 (μm)	d2 (μm)	d3 (μm)	SI (V/AT)	Voff (mV)	Boff (mT)
5CVHS	90	13	11	24	5.94	4.45 × 10−2	7.50
7CVHS					4.98	4.36 × 10−3	0.877
					−16.16%	−90.20%	−88.31%

. The offset magnetic field, expressed in Equation (5), is affected by the current-related sensitivity S_I and the offset voltage V_off. The large current-related sensitivity, another important performance indicator of a VHS, is beneficial for suppressing the offset magnetic field. The biasing current and the magnetic field are set to 1 mA and 1 T, respectively, in the simulations to obtain current-related sensitivity. First, d₁ changes to make C1 and C5 move away from C2 and C6 toward the left side of the 7CVHS when l, d₂ and d₃ remain the same to fix the positions of C2, C3, C4, C5, and C6. Second, d₂ changes to make C3 move away from C2 toward C4 and C5 move away from C6 toward C4. The first step is repeated in one of d₂. Third, d₃ changes to make C2 and C6 move away from C4 toward both sides of the 7CVHS, and the second step is repeated on d₃. Finally, l changes from 20 to 100 μm, and the third step is repeated on l. The offset is introduced by cutting C6 of 0.01 μm, and the size of the 7CVHS varies by l, d₁, d₂ and d₃ operated by the above four steps to obtain the offset voltage in different sizes. We choose the structure of 7CVHS with the smallest value of B_off and list it in Table 2. As illustrated in Table 2, the offset voltage and offset magnetic field of the 7CVHS are reduced by 90.20% and 88.31% of those of the 5CVHS, respectively, with a 16.16% current-related sensitivity loss. We also compare the 7CVHS with the design in [21]. As illustrated in

Table 3. Performance comparison with the design in [21].

Design	SI (V/AT)	Voff (mV)	Boff (mT)
[21]	8.75	1.93	197
7CVHS	4.98	4.36 × 10−3	0.877
	−43.09%	−99.77%	−99.56%

, the offset voltage and offset magnetic field of the 7CVHS are reduced by 99.77% and 99.56% of those of the 5CVHS, respectively, with a 43.09% current-related sensitivity loss.

3. 7CVHS Optimization

The current flows are illustrated in Figure 2a. The bias current I_in is divided into two currents to the left I_l and to the right I_r when passing contact C4. Then, I_l has two current branches, I_l1 from C4 to C3 and I_l2 from C4 to C2. I_l2 is the effective current for forming the Hall voltage of C3. I_l1 introduced by the connection between C3 and C4 is beneficial to the suppression of the offset voltage. However, I_l1, which has the same result as the short-circuit effect, reduces the effective current of the Hall voltage in C3. Thus, the introduction of I_l1 reduces the Hall voltage of C3. I_l1 flows from C3 to C7 through an external connection. Then, I_l1 flows from C7 to the left and into C6. The current I_r flowing to the right of C4 has the same characteristics. The Hall voltage measured between C1 (C5) and C7 (C3) is determined by the voltage variation caused by the Hall effect in contacts C1 to C7 and C3 to C5.

The current-related sensitivity S_I of the 7CVHS of various lengths l are shown in Figure 4a. The maximum and minimum values of S_I are extracted and shown in Figure 4b to clearly dictate the variation trend of S_I. The other parameters d₃, d₂ and d₁ corresponding to the maximum and minimum values of S_I are marked by (d₃, d₂, d₁) near the points in Figure 4b. The maximum value of S_I increases due to its large length. The study and analysis in [27] confirm that the large length is beneficial to the increase in current-related sensitivity of the 5CVHS. The sensitivity of the 7CVHS, derived from the 5CVHS, is mainly determined by the Hall voltages of C3 and C5, which serve as sensing contacts in the 5CVHS. Thus, a large length contributes to the increase in the Hall voltages of C3 and C5. Although the large value of d₃ makes the effective length of the 5CVHS in the 7CVHS containing C2, C3, C4, C5, and C6, the Hall voltages in C1 and C7 are weakened. However, the Hall voltage measured between C1 (C5) and C7 (C3) is determined by the voltage variation caused by the Hall effect in contacts C1 and C7, in addition to C3 and C5. Thus, the positions of C2 corresponding to the maximum values of S_I are center-right between C4 and the left side of the 7CVHS to increase the Hall voltage in C1, and C7 and C5 are placed in the symmetrical position of C2 at the right side of C4. Moreover, the maximum values of S_I correspond to the largest d₂ to make C3 near C4. C3 has the largest Hall voltage when placed close to C4, as does C5. The last parameter d₁ also should be the largest value to obtain the maximum values of S_I. The large value of d₁ makes C1 move away from C2 toward a lower I_l1. However, the decrease in I_l1 is beneficial to the increase in the Hall voltage in C5 and the measured Hall voltage. Moreover, I_r1 and I_l1 obtain large growth spaces with large lengths. The minimum values of S_I, as shown in Figure 4b with a red line, decrease with increasing length l of the 7CVHS. The values of d₃ corresponding to the minimum values of S_I are the largest to make C2 move away from C4. Meanwhile, there are few spaces to place C1, and d₁ has no other alternative but is set as 2 μm. Thus, the Hall voltages in C1 and C7 are suppressed to make the measurement low. Moreover, the values of d₂, which determine the locations of C3 and C5, have a large influence on the Hall voltage in C3 and C5. The large d₂ making C3 move toward C4 is beneficial to the original Hall voltage of C3 but causes a large I_r1 and I_l1 to lower the Hall voltage of C3. The values of d₂ corresponding to the minimum values of S_I make the C3 center-right balance the two above effects.

The offset voltages V_off of the 7CVHS of various lengths l are shown in Figure 4c. The maximum and minimum values of V_off are extracted and shown in Figure 4d to clearly reveal the variation trend of V_off. Almost all values of d₁ corresponding to the maximum V_off are 2 μm to locate C1 near C2 and C7 near C6. The effective lengths of the 7CVHS from C1 to C7 are shortened in the above condition. A small effective length causes a large offset voltage [28]. The values of d₂ and d₃ are almost proportional to lowering the current I_r1 and I_l1 and to enlarging the offset voltage V_off of the 7CVHS. The values of d₁ corresponding to the minimum of V_off are large to make C1 move away from C2 and C7 move away from C6 and increase the effective length of the 7CVHS, but they are not the largest because I_r1 and I_l1 decrease with increasing d₁. Meanwhile, the values of d₂ and d₃ are set to make the current I_r1 and I_l1 as large as possible.

The offset magnetic field B_off of the 7CVHS of various lengths l is shown in Figure 4e. The maximum and minimum values of B_off are extracted and shown in Figure 4f to clearly reveal the variation trend of B_off. V_off and B_off have almost the same relationship between the length of the 7CVHS l, and the values of d₁, d₂ and d₃ corresponding to the maximum and minimum of V_off and B_off are almost the same. The offset voltage V_off has a large effect on the offset magnetic field B_off from the above comparison. The inflection point of the black line indicates that the current-related sensitivity S_I of 7CVHS also affects the value of B_off. The smallest value of B_off is 0.8769 μT when the length of the 7CVHS is set to 90 μm.

The variations in S_I, V_off and B_off in Figure 4 depend not only on the variational values of l but also on the changes in d₁, d₂ and d₃. To concentrate on the impacts of the length l on S_I, V_off and B_off, the length l changes from 20 μm to 100 μm with the same ratio of values of l, d₁, d₂ and d₃ as 20:4:2:5. The values of S_I, V_off and B_off with l from 20 to 100 and the same ratio of values of l, d₁, d₂ and d₃ are illustrated in Figure 5. As shown in Figure 5a, the values of S_I increase with a large length. The same ratio of values of l, d₁, d₂ and d₃ keeps the current allocation unchanged. That is, the currents I_r1, I_r2, I_l1 and I_l2 largely remain the same. However, the large length causes the proportions of the contacts to decrease. This reduces the short-circuit effect. As shown in Figure 5b, the values of V_off increase with a large length. A large length leads to a large resistance. In our design, a current source is used to bias the Hall sensor. Therefore, the supply voltage increases with a larger length, leading to a higher offset voltage. The gradient of S_I is very small when compared with that of V_off. The impacts of the length on the offset magnetic field are basically in line with those on the offset voltage, as shown in Figure 5b.

When the length l of the 7CVHS is set to 90 μm, the current-related sensitivities S_I of various d₃ from 4 to 42 μm in different d₁ and d₂ are obtained, as shown in Figure 6a. The maximum and minimum of the current-related sensitivity S_Imax and S_Imin of each d₃ are extracted and shown in Figure 6b to study the relationship between S_I and d₃. The values of d₁ of S_Imax are always large enough to lower the current I_r1 and I_l1 to obtain the largest S_I in a fixed d₃. When d₃ is small enough, l_eff-C5, the effective length of the 5CVHS in the 7CVHS, as shown in Figure 6b, is reduced, so the Hall voltages in contacts C3 and C5 are suppressed. S_Imax achieves short growth with an increase in d₃ by enlarging l_eff-C5. However, S_Imax decreases as d₃ continues to increase. Meanwhile, the increases in I_r1 and I_l1 become the main factors that impact S_Imax and make S_Imax decrease with the increase in d₃. Moreover, S_Imin is obtained with the smallest value of d₁ to lower the currents I_r2 and I_l2. The large d₃ offers much space between C2 and C4 to place C3, and makes the current I_r2 and I_l2 decrease. The large d₃ causes a small S_Imax for this reason.

The offset voltage V_off of the same length 90 μm with various d₃ from 4 to 42 μm in different d₁ and d₂ are obtained, as shown in Figure 6c. The maximum and minimum values of offset voltage V_offmax and V_offmin of each d₃ are extracted, as shown in Figure 6b, to study the relationship between V_off and d₃. The values of d₁ are largely set as 2 μm to lower the currents I_l1 and I_r1 and bring about the largest offset voltage V_offmax. V_offmax shows a rising trend overall with increasing d₃ because a large d₃ enlarges the bias voltage of the sensor. A large bias voltage increases the voltage of all parts of the sensor, including the offset voltages. Similar to the analysis in Figure 4c, almost all values of d₁ corresponding to the maximum of V_off are 2 μm to move C1 near C2 and C7 near C6. The effective lengths of the 7CVHS from C1 to C7 are shortened in this condition to obtain a large offset voltage. The minimum values of the offset voltages appear with a large d₁ to achieve a large effective length of 7CVHS.

The offset magnetic field B_off of the 7CVHS of various lengths d₃ is shown in Figure 6e. The maximum and minimum values of B_off are extracted and shown in Figure 6f to clearly reveal the variation trend of B_off. V_off and B_off have almost the same relationship between d₃, and the values of d₁ and d₂ corresponding to the maximum and minimum values of V_off and B_off are almost the same. The offset voltage V_off has a large effect on the offset magnetic field B_off from the above comparison. This point confirms the analysis and results shown in Figure 4.

To focus on the impacts of d₃ on S_I, V_off and B_off, we fix the distances of C3 to C4, C4 to C5, C1 to the left boundary, and C7 to the right boundary. In addition, the length of the 7CVHS is always set as 90 μm. Then, the value of d₃ varies from 4 μm to 40.5 μm to simulate the values of S_I, V_off and B_off. As shown in Figure 7a, the value of S_I decreases with a large value of d₃. With a large d₃, the currents I_r2 and I_l2 decrease because of the increase in their corresponding resistances. Thus, S_I decreases because of the reduction in the effective current of the Hall voltage. Moreover, the currents I_r1 and I_l1 increase because of the decrement of their corresponding resistances. Thus, the offset voltage decreases because of the large current needed to suppress the offset voltage, as shown in Figure 7b. The line of the offset magnetic field has a tendency similar to that of the offset voltage, as shown in Figure 7b. However, a small difference between them is derived from the variation in the value of S_I.

The relationship between the current-related sensitivity S_I and d₁ for various values of d₂ is shown in Figure 8a. When d₂ is unchanged, the growth of d₁ is beneficial to the increase in S_I by lowering the current I_r1 and I_l1. When d₁ is small enough, the small d₂ also leads to a large S_I by lowering the current I_r1 and I_l1. When d₁ becomes large, a large d₂ brings about a large S_I by making contacts C3 and C5 suitable to serve as sensing contacts with a large Hall voltage. The relationship between the offset voltage V_off with d₁ for various values of d₂ is shown in Figure 8b. When d₂ is small, V_off decreases first with increasing d₁ because a large d₁ leads to low currents I_l1 and I_r1. Then, the large d₁ brings about the large effective length of the 7CVHS to make V_off. increase. When d₂ is large, the increase in the effective length of the 7CVHS by enlarging the value of d₁ always plays a leading role and determines the decrease in V_off. The relationship between the offset magnetic field B_off and d₁ for various values of d₂ is shown in Figure 8c. The values of d₁ and d₂ have the same effect on V_off and B_off, as seen by comparing Figure 8b,c. This point confirms the analysis and results shown in Figure 4 and Figure 6.

4. Conclusions

We have proposed a new design for a vertical Hall magnetic sensor with a low offset named 7CVHS. Two additional contacts are added to balance the asymmetry of the traditional 5CVHS. Comparing the 7CVHS with the 5CVHS shows that the offset voltage and the offset magnetic field are reduced by 90.20% and 88.31% of those of the 5CVHS, respectively, by a loss of 16.16% of the current-related sensitivity. Moreover, the length and distances of the contacts are optimized by scanning within the total coverage. When l, d₃, d₂, and d₁ are set to 90, 13, 11, and 24 μm, respectively, the optimal performance of the 7CVHS is obtained, with the smallest offset magnetic field of 0.877 mT. In addition, the influence mechanisms of size and the distances of contacts on the current-related sensitivity, offset voltage, and offset magnetic field are studied by analyzing the data from different dimensions and perspectives.