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How to Calculate Acceptor Doping Density

Almost every modern device or appliance that uses electricity contains semiconductors. Refrigerators, phones, flashlights -- all use semiconductors. Most semiconductors are made of base material doped with atoms that have extra electrons -- donors -- and atoms that have fewer electrons -- acceptors. The level of dopants changes all the properties of the material, so you can use a measurement of other semiconductor properties to calculate the acceptor doping density.

Things You'll Need

P-type semiconductor material
Resistance meter with microcontacts
Loupe or microscope

Instructions

- 1
  Measure the size of your semiconductor chip. As an example, assume you̵7;ve got a chip of boron-doped silicon that̵7;s 20 micrometers long, 5 micrometers tall and 10 micrometers wide.
- 2
  Measure the resistance of the material. For purposes of illustration, assume the resistance reading is 170 ohms.
- 3
  Calculate the resistivity of the material, which is given by resistivity = (area/length) x resistance. For the example, this is (50/20) x 10^-4 cm x 170 ohms = 0.043 ohm-cm.
- 4
  Convert the resistivity to conductivity, which is simply the inverse of resistivity. For the example problem, the conductivity = 1/0.043 = 23 per ohm-cm = 23 coulomb/cm-V-sec.
- 5
  Calculate the product of the acceptor density and the hole mobility, which is given by the conductivity divided by the charge of a hole. For the example, this means density x mobility = conductivity / hole charge = 23/(1.602 x 10^-19) 1/cm-V-sec = 1.4 x 10^20.
- 6
  Calculate a value for the acceptor density, find the mobility for that density and match the product to the value calculated in the previous step. With a computer or scientific calculator, you can calculate the product for a range of acceptor densities. For example, the mobility of holes in boron is given by mobility = 44.9 + (470.5 - 44.9)/(1 + (density/2.23 x 10^17)^.719) cm^2/V-sec. Plotting the product of density times mobility over the region from 10^17 to 10^20 per cm^3, you can find the point at which the product is 1.4 x 10^20 is at an acceptor density of 8.7 x 10^17 per cubic centimeter.

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