BPH 221 Lecture Series: Lecture 1 (Basics of Semiconductor Theory)

What is an Atom?

An atom is a fundamental piece of matter (matter is anything that can be touched physically). They are the extremely small particles of which we, and everything around us, are made.

An atom itself is made up of three tiny kinds of particles called subatomic particles: (i.) Protons, (ii.) Neutrons, and (iii.) Electrons.

An atom has a central positively charged nucleus orbited by negatively charged electrons; the positive charge of the nucleus is due to the positively charged protons it contains. In a normal (neutral) atom the number of protons and the number of electrons are equal. Therefore the atom is electrically neutral. The orbits of the electrons are arranged in shells. The first shell, closest to the nucleus, contains a maximum of two electrons. The next outer shell contains a maximum of eight electrons; the next shell also contains a maximum of eight electrons.

One way of differentiating atoms of different element is by the number of electrons in their outermost shell (called valence electrons). This number is used to group the element.

-          Atom with one electron in its outermost shell is called a group one element

-          Atom with two electron in its outermost shell is called a group two element

-          e.t.c.

Grp1          Grp 2            Grp 3              Grp4

The group an element belongs to represents their valence electron not the total number of electron in the atom of that element, the total number of electron in the atom can be greater, for example if the atoms have inner shells that also contain electrons. The number electrons in the outermost shell of many atoms are less that the maximum number of electrons the shell can contain, the shells can take maximum of eight electrons (if not the first shell, which takes only maximum of two electron). The outer shell of the atom is more stable when it is completely filled up.

Semiconductors are group 4 elements with four electrons in their outermost shell, the preceding discussions will be investigating the electrical properties of Semiconductors.

Intrinsic Semiconductor materials

The common naturally occurring semiconductors used in manufacturing of electronic materials are Silicon and Germanium.

 Pure Silicon

The atomic structure of pure silicon can be represented by the diagram in figure 1 below.

Figure 1: Atomic structure of pure silicon

Silicon and Germanium are both group four (4) elements that a commonly used in electronic device fabrication. In our further discussions we will refer to silicon but we should understand that the same thing is applicable to both.

Silicon as I mentioned earlier has have only four electrons in the outermost shell (i.e. 4 valence electrons). To achieve stability in the atom, it takes eight electrons to fill the outermost shell and to achieve this; the atoms share their valence electrons with neighbouring atoms so that each atom effectively contains eight electrons in the outermost shell. This sharing of valence electrons among neighbouring atoms forms what is called covalent bonds which binds the atoms together in the material. The result of the bonding is that each nuclei (along with the electron in the inner shells) are surrounded by eight outer electrons tightly bound in the atomic structure.

Energy levels and Energy band diagrams of Semiconductors

Energy band diagrams show the energy levels of the electrons in the semiconductor materials. For the fact that we are only interested in the electrical properties of semiconductors, our interest is in two of these bands, the conduction band and the valence band. The valence band is occupied by the electrons with the highest energy level of those which are still attached to their parent atoms, these refers to the valence electrons. The conduction band is occupied by electrons which are free from their parent atoms. These electrons are free to move through the material (when a voltage is applied, these electron drift to produce the electrical current experienced). In semiconductor, there is a gap between the valence and conduction bands, the gap called energy gap, reflects the amount of energy required to remove an electron from it’s parent atom (i.e. to transfer it from the valence to the conduction band).

 Figure 2: Energy band diagram of semiconductors

 Figure two is a simplified version of energy band model, indicating

-          bottom edge of the conduction band E_c

-          top edge of the valence band E_v

E_c and E_v are separated by the band gap energy E_g

Materials can be classified in-terms of their band gap

Filled bands and empty bands do not allow current flow, insulators have large E_G, Semiconductors have small E_G, and Metal has no band gap.

Intrinsic Semiconductor

There 2 types of mobile charge-carriers in Silicon;

-          Conduction electrons (negatively charged); these is produced by electrons that have been detached from their parent and has moved to the conduction band,

-           Holes this is produced by the movement of empty spaces in the valence band, created by electrons that has been exited to the conduction band or an incomplete valence band.

In pure Silicon, referred  to as intrinsic semiconductor  at room temperature, there is no electrons in the conduction band (i.e. no conduction electrons), and all the valence electron are packed in a completely filled covalent bond with neighbouring atoms (i.e. no hole present), therefore electrical resistivity is relatively high, meaning there is low conductivity.

At a certain temperature T, electron in the valence band of an intrinsic semiconductor acquire enough energy to break loose from the covalent bond and move to the conduction band. When an electron jumps from the valence band to the conduction band, it creates a hole in the valence band and a conduction electron becomes present in the conduction band. The concentration of electrons in the conduction band is equal to the concentration of holes in the valence band of an intrinsic semiconductor.

Let’s say;

n_i denotes intrinsic electron concentration

p_i denotes intrinsic hole concentration

However, n_i = p_i

We can simply say n_i, is the intrinsic carrier concentration which refers to either the intrinsic electron or hole concentration.

Commonly accepted values for n_i at T = 300⁰K

Silicon	1.5×1010cm-3
Germanium	2.4×1013cm-3

To increase conductivity of an intrinsic semiconductor, we aim at increasing the concentration of conduction electrons and holes in the semiconductor. This can be achieved in several ways:

1. By adding special impurity atoms (called dopants) into a pure silicon crystal (i.e. Intrinsic Semiconductor).
2. by application of an electric field
3. increase in temperature
4. by irradiation

Extrinsic Semiconductor

An extrinsic semiconductor is a semiconductor doped by a specific impurity which is able to deeply modify its electrical properties, making it suitable for electronic applications (diodes, transistors, etc.) or optoelectronic (light emitters and detectors).

To produce extrinsic semiconductor material specific amounts of impurity are added to the pure intrinsic semiconductor. This process is called doping and the impurity atoms are called donor or acceptor atoms. There are two types of extrinsic semiconductor, the P-type and the N-type semiconductor.

P-type Semiconductor

A P-type semiconductor is an extrinsic semiconductor (e.g. Si or Ge) doped with a group 3 element as an impurity acting as an acceptor (e.g. boron, aluminium or indium). These acceptors have atoms with three valence electrons (trivalent atoms). The three electrons will form covalent bonds with neighbouring silicon atoms. There will be shortage of one electron to form the fourth covalent bond. This creates a hole in the covalent bond structure, thus a hole in the valence band of the energy level diagram. Every impurity atom will produce a hole in the valence band. These holes will drift to produce an electrical current if a voltage is applied to the material and the P-type semiconductor is a much better conductor that the intrinsic pure silicon material.

Figure 3:  Extrinsic Semiconductor (P-Type)

Figure 4: Energy band for P-type Semiconductor

In figure 4 which depicts the energy band of a P-type semiconductor, you can see that the valence band contains holes due to the incomplete covalent bond around each donor atom. The conduction band is empty since there are not free electrons.

 N-Type Semiconductor

To produce an N-type semiconductor, the pure silicon is doped with a group 5 element such as phosphorus, antimony or arsenic called donors. These materials have atoms with five valence electrons (pentavalent atoms). Four of these electrons will form covalent bonds with neighbouring silicon atoms. As there are only four covalent bonds binding the donor atom to the neighbouring silicon atoms the fifth electron is not part of a covalent bond, and is therefore a free electron. Every impurity atom will produce a free electron in the conduction band. These electrons will drift to produce an electrical current if a voltage is applied to the material and the N-type semiconductor conducts electricity better that an intrinsic semiconductor.

 

Figure 4: Energy band for P-type Semiconductor

In figure 4 which depicts the energy band of a P-type semiconductor, you can see that the valence band contains holes due to the incomplete covalent bond around each donor atom. The conduction band is empty since there are not free electrons.

N-Type Semiconductor

To produce an N-type semiconductor, the pure silicon is doped with a group 5 element such as phosphorus, antimony or arsenic called donors. These materials have atoms with five valence electrons (pentavalent atoms). Four of these electrons will form covalent bonds with neighbouring silicon atoms. As there are only four covalent bonds binding the donor atom to the neighbouring silicon atoms the fifth electron is not part of a covalent bond, and is therefore a free electron. Every impurity atom will produce a free electron in the conduction band. These electrons will drift to produce an electrical current if a voltage is applied to the material and the N-type semiconductor conducts electricity better that an intrinsic semiconductor.

Figure 5:  Extrinsic Semiconductor (N-type)

  

Figure 6:  Energy band diagram for N-type Semiconductor

 

Carrier (Electrons and Holes) Density in Semiconductor Materials

Intrinsic Material:

Although currents may be induced in pure or intrinsic semiconductor crystal, due to the movement of free charges (the electron-hole pairs), these currents are too small to be of real use. The intrinsic concentration n_i, is a function of bandgap, temperature, and physical constants of material.

 In intrinsic material, the number of electrons and holes must be equal because they are generated in pairs. In an extrinsic semiconductor the increase in one type of carrier (n or p) reduces the concentration of the other through recombination so that the product of the two (n and p) is a constant at any given temperature. The carriers whose concentration in extrinsic semiconductors is the larger are designated the majority carriers and those whose concentration is the smaller the minority carriers.

At equilibrium, with not external influences such as light sources or applied voltages, the concentrations of electron, n₀, and the concentration of holes, p₀, are related by;

            n₀×p₀=n_i²          … … (eq 1)

n_i denotes the carrier concentration in intrinsic semiconductor e.g. silicon.

In n-type semiconductor material, the concentration of the donor in the host material, (e.g. silicon) is designated by N_D. When the donor electrons move from their parent atoms, they leave behind a positively charged ion. These ions are fixed in the semiconductor lattice so they cannot contribute to current.

So also for p-type semiconductor, N_A denotes the concentration of the acceptors in the semiconductor host material. When the acceptor atoms “picks up the fourth,” electron it becomes a negatively charged ion, that is fixed and does not contribute to current, these immobile charged atoms in the two cases (N-type and P-type) has an effect that will be discussed latter.

It should be noted that doping does not change the electrical neutrality of the semiconductor material because the number of positive and negative charges are algebraically equal. Doping conventionally does not change the chemical and mechanical properties of a semiconductor, but the electrical properties.

Because of this charge neutrality, we can write;

n₀ which is the electron concentration and the ionized acceptor are the contributors to the negative charge in the semiconductor, while p₀, which is the hole concentration and the ionized donor atoms, are the contributors to the positive charge in the same. If the semiconductor is to be electrically neutral the equation (i) above holds.

In n-type semiconductor there are typically only donor impurities and the donor concentration is much greater than the intrinsic carrier concentration, N_A=0, and N_D>> n_i.

Under these conditions we can write n₀≈N_D.

Where n₀ is the free electron concentration in the n-type material and N_D is the donor concentration (number of added impurity atoms/cm³).

Since there are many extra electrons in n-type material due to donor impurities, the number of holes will be much less that in intrinsic silicon and is given by;

Where p₀ is the holes concentration in an ­n-type material and n_i is the intrinsic carrier concentration in silicon.

Similarly, in the p-type regions we can generally assume that N_D=0 and N_A>>n_i. In p-type regions, the concentration of positive carriers (holes), p0, will be approximately equal to the acceptor concentration, N_A.

            P₀=N_A

and the number of negative carriers in the p-type material, n₀, is given by

            n₀ = n_i²/N_A

The above equations are valid when N_D or N_A is >>n_i, which will always bet the case in the problems related to electronic device design.

Conductivity of a semiconductor type can be calculated by the relation;

While resistivity is the reciprocal of conductivity and is given by;

q  -  electronic charge (1.6×10¹⁹)

μ_n – electron mobility

μ_n – holes mobility

n  - electron concentration  (negative charge)

p  -  holes concentration (positive charge)

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