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Microelectronics Tutorial: Extrinsic Semiconductors

Diagram of the conduction and valence bands in...

Image via Wikipedia

Concentrations of electrons and hole are small found in intrinsic semiconductors. As a result, the currents are small as well. We can increase these concentrations by adding some impurities to the semiconductor crystal. We’d like to have the impurity atom have a different number of valence electron than the semiconductor crystal.

N-doped Si

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Also, we want the impurity atom replace one of the semiconductor atoms. For silicon which has four valence electrons, then an impurity atom like  phosphorus with five valence electrons will replace a silicon atom in the silicon crystal.   The extra or fifth valence electron is loose bound to the phosphorus atom such that at room temperature, the electron has enough energy to break the bond.    These electrons are free to move about and contribute to the current in the semiconductor crystal. Using phosphorus as a the dopant material forms an n-type semiconductor material (for negatively charged electrons).  Also, phosphorus is known as a donor impurity since it donates an extra electron.

P-doped Si

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To get an p-type material (for positively charged holes), we’ll use either boron or aluminum which has three valence electrons.  Its three valence electrons are used to form three of the four covalent bonds nearest to the silicon atoms.  This leaves one bond position open easily filled by adjacent silicon valence electrons creating a hole and contributing to hole current.

The video below will help further explain the concept of doping as briefly discussed above.

Doping of semiconductors

This video describes the mechanism of current conduction inside of a p-type respectively n-type semiconductor. Using aluminum as a dopant for a silicon crystal creates holes inside of the crystal structure. Additional conduction electrons are provide…

Semiconductor materials containing impurity atoms are called extrinsic semiconductors.  They are also known as doped semiconductors.  By controlling this doping process, the concentrations will determine conductivity and currents associated with the semiconductor material.

At thermal equilibrium, we have a relationship between the electron and hole concentration

 {n_o}{p_o}=n_i^2                                                                             (Equation 1)

where

n_o is the thermal equilibrium of free electrons

n_p is the thermal equilibrium of hole electrons

and n_i is the intrinsic carrier concentration.

Suppose the donor concentration  N_d is much larger than the intrinsic concentration n_i. then

{n_o}{simeq}{N_d}                                                                             (Equation 2)

Using Equation 2, yield the hole concentration as

p_o=frac{n_i^2}{N_d}                                                                      (Equation 3)

Similarly, if the acceptor concentration    {N_a} is much larger than the intrinsic concentration n_i. then

{p_o}simeq{N_a}                                                                              (Equation 4)

Using Equation 4, yield the hole concentration as

n_o=frac{n_i^2}{N_a}                                                                      (Equation 5)

The above development assumes the concentrations are at room temperature.

For an n-type semiconductor, the majority carriers are the electrons since they outnumber the holes and are referred as minority carriers.  In p-type semiconductor, the holes are the majority carriers while the electrons are the minority carrier.

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