Advances in Materials Science and Engineering

Volume 2016 (2016), Article ID 6279162, 7 pages

http://dx.doi.org/10.1155/2016/6279162

## Main Parameters Characterization of Bulk CMOS Cross-Like Hall Structures

Electronics Laboratory, Institute of Electrical Engineering, School of Engineering, Ecole Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland

Received 1 February 2016; Accepted 11 May 2016

Academic Editor: Antonio Riveiro

Copyright © 2016 Maria-Alexandra Paun. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

A detailed analysis of the cross-like Hall cells integrated in regular bulk CMOS technological process is performed. To this purpose their main parameters have been evaluated. A three-dimensional physical model was employed in order to evaluate the structures. On this occasion, numerical information on the input resistance, Hall voltage, conduction current, and electrical potential distribution has been obtained. Experimental results for the absolute sensitivity, offset, and offset temperature drift have also been provided. A quadratic behavior of the residual offset with the temperature was obtained and the temperature points leading to the minimum offset for the three Hall cells were identified.

#### 1. Introduction

The Hall effect sensors have been used for a long time to detect the magnetic field, to measure the currents, in DC motors, and to serve different low-power applications in the industry [1, 2]. Their low cost integration and robustness make them ideal candidates for these applications. Nowadays, they have been largely optimized (from performance and cost-effectiveness perspectives) and are employed on a large scale. Both regular bulk [3] and Silicon on Insulator (SOI) [4, 5] CMOS technologies Hall sensors have been produced.

As presented by the author recently in various papers, the optimal choice of the device geometry and dimensions is crucial in the establishment of a high performance sensor [3, 5]. These sensors are affected by offset. An extensive study of the Hall cells offset is made by the author in [6].

The offset voltage is an unavoidable parasitic voltage that adds to the Hall voltage. The fabrication process of Hall effect sensors could result in nonzero offset, with values exceeding the accepted limit for specific applications.

If the voltage offset is not correctly assessed and minimized, it could impede the precision with which we can determine the Hall voltage. The most important generating causes for the offset are the imperfections in the fabrication process of the Hall device, such as any misalignment of the contacts or nonuniformity in material resistivity and thickness. The offset could be also produced by a combination of mechanical stress and piezoresistance effect [2]. In order to minimize the offset different techniques are used such as, one of the most used techniques nowadays, the connection-commutation or spinning-current technique [2].

Other works looked into different aspects of offset of Hall cells [6–10]. However, it is in the Ph.D. thesis of the author in 2013 that has served the purpose of an exhaustive analysis of the Hall cells offset and the proposal of various models to assess it.

The present paper is organized in five sections. Section 2 summarizes the basic definitions for Hall cells, while Section 3 focuses on the three-dimensional physical simulation methodology. In Section 4, the Hall cells model and their geometrical parameters of the studied devices, experimental results regarding their main parameters such as the input resistance, absolute sensitivity, and offset temperature drift are also provided at this point. The results are included and discussed in Section 5, with more experimental results regarding the single-phase and four-phase residual offset. A discussion of the temperature points for minimum offset is offered. The paper concludes and presents the future perspectives in Section 6.

#### 2. Definitions

This section summarizes the basic definitions for Hall devices behavior. A Hall effect device is characterized by the Hall voltage , given as follows:where is the geometrical correction factor, is the Hall scattering factor, is the biasing current, is the carrier density, is the elementary charge, is the thickness of the active region, and is the magnetic field induction [2]. In the case of silicon, is usually 1.15.

The sensitivity is one of the most important figures of merit related to a sensor. In general, the sensitivity is defined as the change in output resulting from a given change in input. Firstly, according to [2], the absolute sensitivity of a Hall magnetic sensor is given by the equation below:

It is worth noting that, for Hall cells fabricated in the same process, the geometrical correction factor (a number between 0 and 1) improves the absolute sensitivity [4]. At this moment, we can also note that, in order to increase the sensitivity of a Hall sensor, either a lower doping concentration in the active region should or a smaller depth of the active profile be used.

#### 3. On the Three-Dimensional Physical Simulations

In the optimization stages of the CMOS Hall devices, different geometries have been designed and integrated in both regular bulk and SOI technological processes. Three-dimensional physical simulations of magnetic field influence on the semiconductors were previously performed by the author in [5], in order to assess the device performance.

##### 3.1. Carrier Transport in Semiconductors

Assuming low injection, the classical carrier transport model for an n-type semiconductor [11] is based on the continuity equations: where is the elementary electronic charge, is the electron current density, is the hole current density, and , represent particle densities for electrons and holes, respectively. In the above equations, represents the generation rate of particle densities due to incident light. Logically, is the total current density. We mention here that for the case of p-type layer, in the equations above, the term passes into , while is the hole relaxation time and is the electron relaxation time.

In physics, the differential equations (4) describe the conservation of electric charge.

The particle densities expressions in terms of Fermi energy level and are as presented in the following relations:where denotes the electrostatic potential, is the intrinsic carrier concentration, is the absolute temperature, and is the Boltzmann constant.

For a complete description of semiconductor physical behavior, we also have to take into account the following equations:

Regarding the penultimate equation, is the space charge and is the charge density contributed by traps and fixed charges. In the common acceptation, the electric field induction , where is the electric field and is the electric permittivity of the material. In the last equation represents the electrostatic potential.

Replacing (6) in (5) and for a space charge specified as with denoting the fully ionized net impurity distribution, we get a partial differential equation of elliptic type:where is the concentration of ionized donors and is the ionized acceptors concentration. Finally we can say that the electrostatic potential is the solution of the Poisson equation in (7).

Using the Synopsys Sentaurus TCAD software [12] that is able to solve the Poisson equation, both electrons and holes continuity equations, three-dimensional physical simulations of Hall cells were performed.

#### 4. Hall Cells Model

This part includes the models developed for Hall cells behavior analysis, including offset modeling. Before entering the modeling approach, a few numerical values obtained through experimental measurements, for the main parameters of the integrated Hall cells in discussion, are presented.

More than dozen different Hall devices have been integrated in a 0.35 *μ*m XFAB CMOS technology. The present work is intended to emphasize a study on three Hall structures (basic, L, and XL). In Table 1 one could find the details on the considered cross-like Hall cells dimensions. The basic Hall cells are chosen as reference, while L and XL are scaled up dimensions of the first one.