Silicon (50 g) has been doped with 27 mg of antimony (Sb). Determine the concentration of free charge carriers (carriers/cm3) at room temperature in this material.
Calculate the absorption edge of this material. Express your answer as a wavenumber in units of inverse meters.
a) 6.22*10^18
b)wavenumber= Eg / hc
Eg(Silicon band energy)= 1.11 eV (to joules)
h=6.6*10^-34
c=3*10^8
wavenumber= Eg*1.6*10^-19 / hc = 896969.69
To determine the concentration of free charge carriers in the silicon doped with antimony, we need to understand the doping process and the resulting charge carrier concentration.
1. Doping Process:
Doping is the intentional addition of impurities (dopants) to a pure semiconductor material to modify its electrical properties. In this case, antimony (Sb) is the dopant added to the silicon (Si) to create the desired electrical characteristics.
2. Concentration of Free Charge Carriers:
The concentration of free charge carriers in a doped semiconductor is determined by the dopant concentration and the type of doping (n-type or p-type). Since antimony is an n-type dopant, it adds extra electrons to the silicon crystal structure.
To calculate the concentration of free charge carriers, we can use the formula:
n = N * exp(-Eg / (2 * kt))
Where:
- n is the concentration of free charge carriers (carriers/cm^3)
- N is the concentration of dopant atoms (atoms/cm^3)
- Eg is the bandgap energy of silicon (eV)
- k is Boltzmann's constant (eV/K)
- T is the temperature in Kelvin
We are given:
- Silicon mass: 50 g
- Antimony mass: 27 mg (0.027 g)
- Silicon atomic weight: 28.086 g/mol
- Antimony atomic weight: 121.76 g/mol
To find the concentration of dopant atoms, we first need to convert the mass of antimony to the number of dopant atoms:
Number of dopant atoms = (Antimony mass / Antimony atomic weight) * Avogadro's number
Number of dopant atoms = (0.027 g / 121.76 g/mol) * 6.022 x 10^23 atoms/mol
Now, we can find the concentration of free charge carriers using the calculated dopant atom concentration and the other parameters:
n = (Number of dopant atoms / Silicon volume) * exp( -Eg / (2 * kt) )
However, to determine the silicon volume, we need to know the density of silicon.
Please provide the density of silicon, or if not available, we can use a typical value of 2.33 g/cm^3.
Once we have the silicon volume, we can calculate the concentration of free charge carriers at room temperature.