Advanced compact model and processing circuit for integrated magnetic sensor systems

The generalized electric model of the Hall sensor, which is designed for circuit simulation, is taken into account the features of its design and used for manufacturing materials. The model of the Hall sensor is implemented in the language Verilog-A, has a simple structure and allows to accurately describe its performance characteristics.

ADVANCED COMPACT MODEL AND PROCESSING CIRCUIT FOR INTEGRATED MAGNETIC SENSOR SYSTEMS

Dao Dinh Ha1*, Tran Tuan Trung2

Abstract: The generalized electric model of the Hall sensor, which is designed

for circuit simulation, is taken into account the features of its design and used for manufacturing materials The model of the Hall sensor is implemented in the language Verilog-A, has a simple structure and allows to accurately describe its performance characteristics The equivalent circuit of the sensor is built on the basis of standard subcomponents and does not use complex equations to describe the physical processes in its structure A circuit and topological solution consisting

of Hall sensor, differential amplifier and 10-bit successive approximation register analog-to-digital converter and other components integrated on a single chip using the TSMC 0.18 μm CMOS MS/RF 1,8/3,3V PDK design library, allowing to receive and process data of sensor devices

Keywords: Hall sensor; Compact Model; Verilog-A; Signal processing circuit; Analog-to-digital converter

1 INTRODUCTION

In modern electronics sensors for measuring the induction of a magnetic field, contactless determination of mechanical and electrical influences is widely used This type of sensor is used in the automotive, mobile and consumer segments, medicine, aerospace and marine industries, power engineering – as sensors for cameras and displays, electronic compasses, etc [1] For practical applications, the Hall sensor (HS) is usually placed with a signal processing circuit on a single chip However, the constructive implementation of such a system remains a problem, because the sensor models are not included in the design library provided by the chip manufacturer Standard models for describing the electrical characteristics of

HS are too complex [2] or idealized [3] 2D or 3D physical models described by FEM simulators for integration with circuit simulation programs require significant computational costs [3], but are useful for analyzing the effect of geometric parameters on the behavior of a sensor To improve design efficiency and system performance, it is necessary to have an electrical (SPICE) model that adequately describes the characteristics of the sensor element Such a model describes the behavior of the sensor using a set of equations obtained by means of adequate assumptions and simplifications

Another important task in the field of sensor design is the development of systems that provide accurate processing of input data, as well as their conversion

to a digital signal The latter would greatly simplify the process of further analysis

of the results of measurements These tasks can be solved by sharing amplifiers and analog-to-digital converters, which enable the transition to a digital representation of the original analog signal with small amplitude

The paper presents the results of the development of a unified compact model of

a Hall sensor fabricated both by standard silicon technology and based on wide-gap semiconductors The model also provides the ability to account for the material and geometry of the integrated magnetic concentrator (IMC) designed to increase the sensitivity of the sensor A circuit-based solution consisting of a

low-noise amplifier and an analog-to-digital converter, which allows receiving and processing of sensor data, is developed and topologically realized

2 SIMULATION TOOLS, INVESTIGATED SENSOR CONSTRUCTIONS

AND COMPACT MODEL DESCRIPTION 2.1 Investigated Hall Sensor designs

In the calculations presented below, the simulation of the electric characteristics

of the Hall sensor was carried out in the Silvaco software environment [4], the IMC parameters were calculated in the FEMM program [5], the Verilog-A [6] language was used to develop the electrical model, and the compact model and circuit solutions were designed and tested using Cadence software [7]

Fig 1 shows the HS designs that are being investigated The design presented

on the left is a sensor manufactured using standard silicon technology [8], the design on the right is a sensor based on gallium nitride [9]

W

Sapphire (0001)

contact

Al x Ga 1-x N GaN AlN Ti/Al/Ni/Au

W

n-well

depletion layer

p-substrate

contact

oxide

Figure 1 Investigated Hall Sensors designs

1

2

2 3

θ

l d

D

4

Figure 2 Modeling determining the parameters of material sample by CST

Fig 2 shows the sensor system design, which includes an IMC It consists of four HS (2) and an IMC (3) formed on a silicon substrate (1) Four HS are perpendicular to each other along the edges of the IMC Between the IMC and the

HS there is a dielectric layer (4) of thickness d The IMC is a disk of a ferromagnetic material with a diameter D, a thickness l, and a deflection angle θ

Supermindur which has a high induction of magnetic saturation was used as the IMC material Earlier studies were carried out to optimize the design and technology, electrical and operational characteristics of presented sensors types within the device-technological simulation [8-10, 12]

2.2 Advanced compact model of the Hall Sensor

Fig 3 shows an equivalent circuit describing the HS compact For an ideal design (no technological discrepancy and mechanical stress in the system), the van der Pauw method is used to measure the surface resistance of the RS layer Since the device is symmetrical, it is necessary to determine the values of the two resistances between the contacts: RD for the resistance between the two opposite and RH for the two adjacent contacts [11] In comparison with the existing solutions [12], this scheme provides the possibility of taking into account the galvanomagnetic and temperature effects

INPUT

CCVS1

CCVS4

CCVS3

CCVS2

-+

- +

-+

INPUT

OUTPUT OUTPUT

2

1

4

3

5

B

R

Figure 3 Equivalent circuit describing the basic HS compact model

The proposed equivalent circuit has 4 electrical outputs and one external source

as input (B) and includes the following components: 8 non-linear resistors designed to describe the dependences of the characteristics of the HS from the magnetic field and temperature; 4 current-controlled voltage sources, which allow estimating the contributions to the Hall voltage of currents flowing through nonlinear resistances; 4 interface blocks for the simulation of series resistances The parameters of the silicon-based HS compact model [11] are given in Table 1

The last two lines contain the parameters typical for the hall sensor made on the basis of wide-gap semiconductors The names of electrical model parameters used

in the text are shown in parentheses To simulate the magnetosensitive sensor with IMC, added the parameters presented in Table 2

Table 1 Silicon based hall sensor model parameters

NDNW (N D,NW) Concentration of charge carriers in

-3

1021–1023

NSUB (N SUB) Concentration of charge carriers in a

-3

5×1020–1021

DEFF (d eff) Effective depth of active area m (0.5–5)×10-6

MOBN (µ n) Mobility of electrons in the active

2/V∙s 0.072–0.141

MOBH (µ h) Mobility of holes in the active

2/V∙s 0.032–0.047

RSS (R S) Surface resistance of silicon Ohm 100–15×103

RDD (R D) Resistance between two opposite

3

RHH (R H) Resistance between two neighboring

3

BBR1 The first coefficient of resistance

-1

0–0.01 BBR2 The second coefficient of resistance

-2

-0.005–0 BBS1 The first coefficient of sensitivity

-1

0–0.01 BBS2 The second coefficient of sensitivity

-2

-0.005–0

RTC1 The first temperature coefficient of

-1

0–0.01

RTC2 The second temperature coefficient

-2

0–0.0005

ALPHA (α SI) Temperature coefficient of

-1

0–0.001

NSS (N S) Concentration of charge carriers in

-2

1016–1018

MOBN (µ S) Mobility of electrons in 2DEG m2/V∙s 0.01–1.0

Table 2 The compact model parameters of the magnetosensitive sensor with IMC

BSAT (B sat) Magnetic saturation induction Tesla 1–2.8

3 SIMULATION RESULTS 3.1 Device-technological vs Schematic simulation

Fig 4 and 5 show the results of a comparison between data of device-technological modeling in the software complex Silvaco and data of circuit simulation using the developed compact model a Hall sensor fabricated by standard silicon technology and based on wide-gap semiconductors, respectively

150 125 100 75 50 25 0

I , mA

V H

Device simulation

B = 0.25 T

B = 0.1 T

B = 0.5 T

Compact Model

B = 0.25 T

B = 0.1 T

B = 0.5 T

Figure 4 The simulated and modeled output Hall voltage V H versus

the biasing current at different magnetic field for Silicon Hall sensor

The analysis of the obtained results testifies to the high efficiency of the developed compact model The error in the data of device-technological and circuit simulation does not exceed 5%

0,2 0,4 0,6 0,8 1,0

40 35 30 25

10 5 0

I , mA

V H , 20

Device simulation

B = 0.1 T

B = 0.5 T

Compact Model

B = 0.1 T

B = 0.5 T

B = 0.25 T

B = 0.25 T

15

Figure 5 The simulated and modeled output Hall voltage V H versus

the biasing current at different magnetic field for GaN Hall sensor

3.2 Modeling of the sensor signal processing circuit

Currently widely used multi-functional integrated sensor systems that are realized by combining the sensor (often multiple) and processing circuitry on a single chip Such a system-on-chip (SoC) in which the data converter is integrated with the digital signal processing unit in one chip with integrated sensor may be a more effective solution In comparison with optional discrete chip ADC, this approach can significantly improve the compactness and reduce the cost of production, which is a critical consideration for the sensitive region, medical, mobile, automotive, and other applications

The processing of the sensor signal can be widely classified in terms of signal bandwidth (the rate of change of the measured physical quantity) and the resolution necessary to obtain meaningful information Typically, the required ADC can be built on the basis of one of two very efficient architectures: a sequential approximation register (SAR) and redundant discrete ADCs Sigma-Delta (SD) Used in our case SAR ADC allows to effectively handle signals with a different frequency range – from a few Hz to hundreds of kHz with a high enough accuracy – 6-8 bits to 20 bits and higher, and also provides high versatility and low power dissipation, making it ideal for these systems

Table 3 10-bit SAR ADC parameters

Min Typical Max

For this system, a topology which contains a system for receiving, amplifying, and sensory data processing based on the Hall sensor as an example on a single chip is developed using the TSMC 0.18 μm CMOS MS/RF 1.8/3.3V PDK The test circuit used a 10-bit, own designed SAR ADC implemented in silicon using TSMC 0.18 um CMOS MS/RF 1.8/3.3V technology The topological implementation of the Hall sensor, differential amplifier and ADC are presented in Fig 6

The results of computer simulation in the Cadence software package using the proposed signal processing circuit are presented in Fig 7 and Table 3 During the simulation, developed and described above compact model was used to simulate

the HS electrical characteristics In Fig 7 shows: B - magnetic field, V H+ , V H- - hall

voltage, code - DAC output signal, out - 10-bit ADC output signal

1 – Hall sensor

2 – Differential amplifier

3 – Voltage reference

4 – ADC

4

3 1

2

1168 um

Figure 6 Topological implementation of Hall sensor,

differential amplifier and ADC

0

500 0

В

1,8 0,9

730

770 750

0

1,5 0,8 refp refn vcm

data <9:0>

1,8 0 0,9 code

0,5 0

out

1,0 0,5

1,0

Time, us

Figure 7 The «Hall Sensor – processing circuit» system simulation results

4 CONCLUSION

The advanced compact model of Hall sensor presented in this paper has a simple structure which leads to fast simulations while allowing an accurate description of the behavior of the device It is made of simple sub-components and does not involve any complex equation The revision and expending of the model, primarily the mobility, provide the possibility of its use for simulation of Hall sensor based on other materials, for example wide-gap semiconductors and consider the impact of

an integrated magnetic concentrator The results of simulation of the "Hall sensor – processing scheme" system using the developed compact model and signal processing circuit demonstrate the high efficiency of the proposed solutions

REFERENCES

[1] R Popovic, "Hall Effect Devices" Institute of Physics Publising Second

Edition 420 p (2004)

[2] E Jovanovic, T Pesic and D Pantic, "3D simulation of cross-shaped Hall sensor and its equivalent circuit model" Proceedings of the 24th International

Conference on Microelectronics, pp 235-238 (2004)

[3] A Rossini, F Borghetti, P Malcovati, "Behavioral model of magnetic sensors for SPICE simulations", ICECS, pp 1-4 (2005)

[4] https://www.silvaco.com

[5] http://www.femm.info/wiki/HomePage

[6] K Kundert, "The Designer's Guide to Verilog-AMS" Kluwert Academic

Publishers, Boston (2004)

[7] https://www.cadence.com

[8] H Dao, A Belous, V Saladukha, "Optimization of structural and technological parameters of the field effect Hall sensor" ATC, Vietnam, pp 642–644 (2015) [9] V Stempitsky, Dao Dinh Ha, Tran Tuan Trung "Suppression of the Self-Heating Effect in AlGaN/GaN High Electron Mobility Transistor by Diamond Heat Sink Layers" ATC, Vietnam, pp 264–267 (2016)

[10] Dao Dinh Ha, V Stempitsky, "Investigation of the Hall Sensor Characteristics with Various Geometry of the Active Area", Nano- i

Mikrosistemnaya Tekhnika, vol.20, no.3, pp 174-186 (2018)

[11] Y Xu and H Pan, "An Improved Equivalent Simulation Model for CMOS Integrated Hall Plates" Sensors, vol 11, pp 6284-6296 (2011)

[12] Dao Dinh Ha, V Stempitsky, Tran Tuan Trung, "Verilog-A compact model of the silicon Hall element" ICDV Vietnam, pp 41-46 (2017)

TÓM TẮT

MÔ HÌNH TỔNG QUÁT TIÊN TIẾN VÀ MẠCH XỬ LÝ TÍN HIỆU CHO HỆ THỐNG CẢM BIẾN TỪ TRƯỜNG TÍCH HỢP

Đề xuất mô hình điện tổng quát của cảm biến Hall, được thiết kế cho mô phỏng mạch, có tính đến các tham số thiết kế và vật liệu sử dụng Mô hình cảm biến được triển khai theo ngôn ngữ Verilog-A có cấu trúc đơn giản và cho phép mô tả chính xác các đặc tính của cảm biến Mô hình tương đương được mô tả dựa trên các thành phần mạch điện tiêu chuẩn và không sử dụng các phương trình phức tạp để mô tả các quá trình vật lý diễn ra trong cấu trúc cảm biến Thiết kế một cấu trúc mạch bao gồm cảm biến Hall, mạch khuếch đại và mạch chuyển đổi tín hiệu tương tự-số 10 bit tích hợp trên chip

sử dụng thư viện thiết kế TSMC 0.18 um CMOS MS/RF 1,8/3,3V PDK cho phép nhận và xử lý tín hiệu của các thiết bị cảm biến

Từ khóa: Cảm biến Hall, Mô hình nhỏ gọn; Verilog-A; Mạch xử lý tín hiệu; Mạch chuyển đổi tương tự-số

Received 20 th April 2020 Revised 21 th August 2020 Published 28 th August 2020

Author affiliations:

1 Le Quy Don Technical University;

2

Academy of Military Science and Technology

*Corresponding author: havixuly@gmail.com