Question

Inside your smartphone is a small integrated circuit called a "Hall sensor" that measures the magnetic field to fairly high precision. (It is actually made of three separate "Hal bars", to measure the field components in the r, y, and z directions). The Hall sensor acts like a compass for your phone, and assists in navigation and GPS apps. Let's assume each Hall bar is a strip that is 20 11m long, 5 ㎛ wide, and 1 μm thick. (a) Typically, the Hall bars in your phone are made of "doped" silicon a silicon crystal in which 0.1% of the silicon atoms are replaced with a boron atom. Each boron atom has one less valence electron than a silicon atom. The result is that each boron atom donates one positive "hole" (an electron vacancy that acts as a mobile positive charge carrier with charge +e). What is the density n of holes in the Hall bar? You can look up any relevant information about silicon on Wikipedia, etc... b) Let's assume that your smartphone is measuring Earth's magnetic field of B (2011Tji_ (50 μΤ)k, where 1 points magnetic north and k is up. A current of 5 mA is passed down the length of each Hall bar, in the +r, +y, +z direction respectively, and the Hall voltage is measured across its width. What is the Hall voltage (including sign) measured on each of the three Hall bars? The figure shows the geometry for the bar whose long axis is parallel to the x direction. The voltage reading is positive if the +y edge is at a higher potential than the -y edge.

Answer 1

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