# Outline of semiconductor magnetoresistive element

1. What is a semiconductor magnetoresistive element?

■ The resistance value changes depending on the magnetic flux density applied to a semiconductor film in vertical direction.
■ The resistance value changes in the same manner when either magnetic field (the north or south polarity) is applied.
■ By combining multiple elements, the resistance change can be taken out as a voltage change.
■ Materials in use require high electron mobility. (Generally, InSb with high mobility is used.)

2. Modeling of semiconductor magnetoresistive effect

 As shown in the figure at the right, if no magnetic field (magnetic flux density) is applied to a semiconductor film, the carriers (electrons) move straight in the semiconductor toward the electric field direction by the force qE generated by the applied electric field. However, if a magnetic field is applied, the Lorentz force qvB forces to bend the moving direction of the carriers. Where, q represents elementary charge, E represents strength of electric field, v represents electron speed, and B represents magnetic flux density. As the moving distance is longer, the resistance value increases.

3. Magnetoresistive effect of semiconductor film

In the low magnetic field (approx. 0.4T or less), the rate of magnetoresistive change D R/R0 is proportional to the square

root of the product of the semiconductor film electron mobility m and magnetic flux density B that is vertically applied to

the semiconductor film, and in the high magnetic field range (approx. 0.4T or more) it is proportional to μ and B.

■ Definition of rate of magnetoresistive change

RB: Resistance value in magnetic field
R0: Resistance value in non-magnetic field

■ Rate of magnetoresistive change in low magnetic field range (0.4T or less)

 RB: Resistance value in magnetic field      R0: Resistance value in non-magnetic field       μ : Electron mobility        B: Magnetic flux density

■ Rate of magnetoresistive change in high magnetic field range (0.4T or more)

 RB: Resistance value in magnetic field     R0: Resistance value in non-magnetic field      μ : Electron mobility      B: Magnetic flux density

* The higher the electron mobility in the semiconductor becomes, the larger the magnetoresistive effect is.

4. Materials for semiconductor magnetoresistive element

 As shown above, the semiconductor magnetoresistive effect depends on the electron mobility m of the material. In other words, the higher the electron mobility of the material, the larger the magnetoresistive effect is. Therefore, InSb is used as a material for the semiconductor magnetoresistive element, because it has the highest electron mobility among the III-V compound semiconductors that have larger electron mobility. Since InSb has the highest electron mobility of 78000 (cm2/Vsec) among the semiconductors, it is a suitable material for semiconductor magnetoresistive element. [Electron mobility of III-V compound semiconductor single crystal]