BPH 221 Lecture Series: Lecture 3 (I-V Characteristics of a diode)

To understand how we can make a useful application of a diode, we require the knowledge of its electrical characteristics. The characteristics of diode can be obtained by using a simple circuit like the one in figure 3.1.

Figure 3.1a:  Circuit diagram of diode in forward bias

In the circuit, we have a milli-ammeter and a protective resistor in series with the diode, the voltmeter V is connected to measure the voltage across the diode. Note that the positive pole of the voltage source is connected to the anode of the diode, meaning that it is in a forward bias connection.  Our objective is to study the current flow and voltage across the diode as the Voltage Vs increases.

 

Figure 3.1b:   Virtual implementation of circuit in figure 3.1a

To demonstrate the I-V characteristics of the diode, we implement the circuit in virtual laboratory, figure 3.1b shows the circuit implementation, the potentiometer P1 is used to vary the voltage output of the voltage source V1 across the diode D1. AM1 and VM1 measure the current and voltage across the diode respectively for every stepwise increase in P1 output.

Simulating the circuit we obtain the DC transfer characteristics of the diode, as shown in figure 3.2, bellow;

                                                                          (a)

                                (b)

Figure 3.2:  I-V characteristics curve of forward bias diode.

Figure 3.2(a) is showing the potentiometer output against current AM1 and voltage VM1 on different graphs, while figure 3.2(b) shows the VM1 (V) output against AM1 (I) output from the diode (I-V characteristic curve).

We can observe from the curves that, as the voltage VM1  across the diode increases, initially the corresponding current output is very low, unable to give any meaningful indication on the milli-ammeter, but when VM1 value gets to a certain level, 0.35V in our circuit example, you’ll begin to notice some increase in the level of current and at a point the current increases exponentially with respect to the voltage, VM1.

The explanation is that, current starts to flow in the circuit only when the voltage VM1 across the diode has been able to overcome the built-in voltage barrier of the diode, (see discussion in Lecture 1), the exponential increase in current occur at a voltage level a little above the voltage barrier, this is called the cut-in voltage.

We can also study the I-V characteristics of the diode in reverse bias condition. 

 

Figure 3.3a:  Reverse bias connection of the diode.

Figure 3.3b:   Virtual implementation of circuit in figure 3.3a

Here, we can observe that the polarity of V1 is reversed as against the circuit in figure 3.2, now the positive pole of the supply connects to the cathode and the negative pole to the anode of the diode, i.e. in reversed bias connection (see previous lecture). Simulating the circuit we obtain the DC transfer characteristics of the diode, as shown in figure 3.4, bellow;

(a)   Current AM1 and VM1 as they vary against potentiometer output

(b)   Voltage VM1 against Current AM1, I-V Characteristics curve

Figure 3.4: I-V characteristics of a diode in reverse bias connection.

From Figure 3.4(a) and (b), we can observe only a very small negative current bellow -40nA in AM1, compare to current flow in mA in the case of forward bias connection. The infinitesimal current flow is maintained at this same level even as voltage VM1 increases across its axis. The current is so small and unable to give any meaningful indication on the milli-ammeter so it is assumed as zero current (open circuit) with reverse biased connection of the diode.

We can combine the two characteristic curve i.e. reversed and forward biased in a single graph as shown in figure 3.5, bellow;

Figure 3.5: Combining the Forward and Reverse bias I-V Characteristics curve of a diode.

Types of Diodes:
1.  Light Emitting Diodes (LED):
LEDs are also a type of semiconductor diodes that glows when voltage is applied to it in a forward biased connection. This diode has many applications in electronics. Go to Light Emitting Diodes for discussion on the Construction, Electrical property and Applications of Light emitting diodes (LEDs). 
 2.  Photodiodes:
 Photodiodes are another type of semiconductor diodes, they a designed in such a way which, when exposed to light, generates a potential difference or change its electrical resistance. Go to Photo-diode for a brief discussion on operation and applications of photo-diode. 
3. Varactor Diodes:

A varactor , also known as tuning diode, a variable capacitance diode, a varicap diode or variable reactance diode, is a diode that exploit the principle of operation of semiconductor diode, to act or behave like a variable capacitor i.e. has variable capacitance, which is a function of the external voltage impressed on its terminals. Go to Varactor Diode for a brief discussion on construction and application of varactor diode. 


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I am Adeniran Adetunji, contact email: tunji4physics2@gmail.com

BPH 221 Lecture Series: Lecture 2 (Semiconductor Diode)

What is a diode?

A diode is a specialised electronic component with two electrodes called the anode and the cathode. The fundamental property of a diode is its tendency to conduct electric current in only one direction.

Vacuum Tube Diode

Originally the diode was in the form of a vacuum tube and we have what is called vacuum tube diodes. I will briefly introduce the construction and the operation of a vacuum tube diode. Figure 1 depicts a simplified diagram of a Vacuum Tube Diode.

Figure 2.1: Vacuum Tube Diode

In the diagram, the vacuum tube is represented by a circle; the anode A, the Cathode C, the anode and cathode plate, and the filament F. The cathode plate is heated by the filament when supplied with an AC current from another source. When the cathode plate gets heated up it starts to emit electrons i.e. thermionic emission, these electrons are collected by the anode plate A. In the external circuit, the anode is maintained positive and cathode negative, the electron will flow from the negative cathode to the positive plate A, thus current flows.

If on the other hand, the external circuit has made plate A negative and C positive, the electrons emitted by the cathode plate will be attracted by the positive C and repeled by negative A, electron will not migrate to the anode A and thus, current will not flow in the circuit. The is the unique property of a diode, i.e. only allow current to flow in one direction and not in the other direction, that is why it is called vacuum tube diode.

However, there are some limitation of this vacuum diodes which are enumerate bellow;

i.                    It requires high voltage between plate (A) and cathode (C) up to about 100 to 200V for its operation.

ii.                  The filament requires separate power supply (6V) to generate electrons by Thermoionic emission.

iii.                It is too bulky and produces a lot of heat.

These limitations necessitate the search for another alternative which brought about the solid state device called Semiconductor Diodes.

Semiconductor Diodes

These diodes are semiconductor devices which might be described as passing current in one direction only. The have two leads like a resistor and allow current to flow through them depending upon the voltage between the leads. Though, they do not obey ohms law, meaning that the current flow is not directly proportional to the applied voltage.

 

Figure 2.2: Diode Symbol

The diode symbol in figure 2.2 above show the anode A, an arrow, a bar and cathode C, the arrow depicts the direction of current flow, that is the current flow from the anode to the cathode. 

Applications of Diodes

-          Diodes are used as rectifiers to convert AC to DC.

-          They are used as Switches in some applications.

-          They are used as Voltage regulators

The ordinary diodes used in electronics can be categorized into two types;

Signal diodes and rectifier diodes. Both diodes work the same way by allowing current to flow in one direction, the difference in the two diode is that;

Signal diodes have much lower power and current ratting, around 150mA, 500mW maximum compared to rectifier diodes, they function better in high frequency applications or in clipping and switching applications with short-duration pulse waveforms.

Rectifier diodes in the other hand are designed to handle much higher voltage and current and are typically found in power supplies.

In addition to the two diodes mentioned above, we have other diodes like the light emitting diodes LEDs and the Zener Diodes.

P-N Junction Diode

Understanding the operation of the semiconductor diode is the basis for an understanding of all semiconductor devices. One of the fundamental structures within semiconductor technology is the PN junction, it is the fundamental building block of semiconductor diodes and transistors and a number of other electronic components. PN junction is in essence the basic form a semiconductor diode.

The diode is actually manufactured as a single piece of material but to better understand its construction, we will imagine producing two separate pieces of N-type and P-type material (see figure 1) as discussed in our Lecture 1 and then “sticking” then together.

Figure 2.3: Separate Pieces of N-type and P-type Semiconductor material

Now imagine fusing these N-type and P-type semiconductor material together as in figure 2.4.

 

Figure 2.4: Fused N- and P- type Semiconductor material

When the fusing is done, the electron in the N-type will tend to migrate into the P-type and the holes in the P-type into the N-type  (due to attraction between unlike charges) these phenomenon tend to cause an even distribution of electron and holes throughout the semiconductor. As the electron from the N-type migrates across the junction into the P-type  they depletes the holes that are close to the junction through recombination, likewise the holes in the P-type depletes the electron near the junction in the N-type by recombining with them.

If we recall the process of producing the N-type and P-type material, for N-type the donor atom that is introduced into the intrinsic silicon crystal lattice has the same number of proton and electron in its atom. After doping, it combines with the silicon atom in a covalent bond to donate a free electron, this does not mean an extra electron is been produced the electron is just made to be free due to covalent bonding structure with the Silicon atoms. Mechanically, the total number of protons (positive charge) in the material is still equal to the number of electron (negative charge). Ditto the P-type material.

Now, back to our discussion on P-N junction, as the holes from the P-type  depletes the electron in the N-type it deposits immobile positive charge near the junction of the N-type , likewise the electron form the N-type material moving into the P-type depletes the holes near the junction and deposits immobile negative charges near the junction in the P-type side. (see figure 2.5).

Figure 2.5

The area near the junction of both the P- and N- type, where the mobile charge carrier has been depleted is known as the depletion layer. When this has occur, the positive charge deposit in the N-type near the junction will prevent further migration of the holes from the P-type into the N-type, since like charges repel, it will also attracts the electrons and keep them in the N-type.

Also the electron deposit in the P-type near the junction will debar the electron from the N-type material from further migration into it by repulsion; the electrons attract the holes and keep them in the material.

When this barrier imposed by the charge deposits at the depletion layer builds up to a certain level, it will completely halt the migration of charge carriers totally, this is barrier known as barrier voltage (i.e. the one sufficient to prevent any further migration). The voltage is about 0.6 to 0.7 for silicon and 0.2 to 0.3 for Germanium.

Forward bias Connection of a P-N junction diode

Figure 2.6: Forward bias connection

When we apply an external voltage source to a P-N junction, as in the connection in figure 2.6, the positive electrode of the voltage source is connected to the P-type side of the P-N junction and the negative electrode is connected to the N-type side of the P-N junction. The effect of this is that, the electrons in the N-type will be repelled by the negative electrode and the holes in the P-type will also be repelled by the positive electrode of the voltage source, both towards the junction thus narrowing the width of the depletion layer. When the applied voltage is more than the barrier voltage at the junction, the holes and electron will migrate across the junction and current will flow. This is known as forward biasing of the P-N junction diode.

Reverse biased connection of a P-N Junction 

Figure 2.7:  Reverse bias connection of a P-N junction

Here, the polarity of the voltage source is reversed compared to the forward bias connection described above. The positive electrode of the source is connected to the N-side of the P-N junction and the negative electrode is connected to the P-type. With this connection, the holes in the P-type will be attracted by the negative electrode while the electrons in the N-type are attracted by the positive electrode, this effect will make the depletion layer to be widened and thus disallow flow of electron and holes across the junction  i.e. current will not flow across the P-N junction and in the circuit. This connection is called reverse biasing of the diode. This phenomenon makes the P-N junction to function as a diode as it allow current to flow in only one direction.

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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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