4.1 Semiconductors

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4.1 SEMICONDUCTOR

4.1.1 Diodes

4.1.1.1 Semiconductor basic

Modern electronic devices are based on semiconductors. As its name implies, a semiconductor is a material that conducts current, but only partly. Most semiconductors are crystals made of certain materials, most commonly silicon. The electrons in an atom are organized in layers, these layers are called shells. Semiconductors typically have four electrons in their valence shell such as in silicon. 

The conductivity of a semiconductor is somewhere between that of an insulator, which has almost no conductivity, and a conductor, which has almost full conductivity. 

Pure silicon crystals are not that useful electronically. But if you introduce small amounts of other elements into a crystal, the crystal starts to conduct in an interesting way. The process of deliberately introducing other elements into a crystal is called doping. The element introduced by doping is called a dopant. By carefully controlling the doping process and the dopants that are used, silicon crystals can transform into one of two distinct types of conductors:

1. N type semiconductor
2. P type semiconductor

N-type semiconductor

N-type semiconductor is created when the dopant is an element that has five electrons in its valence layer. Phosphorus is commonly used for this purpose. Because the phosphorus atom has five electrons in its valence shell, but only four of them are bonded to adjacent atoms, the fifth valence electron is left hanging out with nothing to bond to. The extra valence electrons in the phosphorous atoms start to behave like the single valence electrons in a regular conductor such as copper. They are free to move about. Because this type of semiconductor has extra electrons, it's called an N-type semiconductor.

P-type semiconductor

P-type semiconductor is created when the dopant (such as boron) has only three electrons in the valence shell. When a small amount is incorporated into the crystal, the atom is able to bond with four silicon atoms, but since it has only three electrons to offer, a hole is created. The hole behaves like a positive charge.

When voltage is applied to either an N-type or a P-type semiconductor, current flows, for the same reason that it flows in a regular conductor: The negative side of the voltage pushes electrons, and the positive side pulls them. The result is that the random electron and hole movement that's always present in a semiconductor becomes organized in one direction, creating measurable electric current.

The newly doped N-type and P-type semiconductor materials do very little on their own as they are electrically neutral. However, if we join (or fuse) these two semiconductor materials together, to form a PN junction, they behave in a very different way.

4.1.1.2 The PN junction

It is possible to manufacture a single piece of a semiconductor material half of which is doped by P-type impurity and the other half by N-type impurity. 

The plane dividing the two zones is called junction. Theoretically, junction plane is assumed to lie where the density of donors and acceptors is equal. The P-N junction is fundamental to the operation of diodes, transistors and other solid-state devices.

Let us see if anything unusual happens at the junction. It is found that following three phenomena take place:

1. A thin depletion layer or region (also called space-charge region or transition region) is established on both sides of the junction and is so called because it is depleted of free charge carriers. Its thickness is about 10-6 m/ 1-micrometer.
2. A barrier / junction potential is developed across the junction.
3. The presence of depletion layer gives rise to junction and diffusion capacitances

4.1.1.3 Formation of Depletion Layer

Suppose that a junction has just been formed. At that instant, holes are still in the P-region and electrons in the N-region. However, there is greater concentration of holes in P-region than in N region (where they exist as minority carriers). Similarly, concentration of electrons is greater in N-region than in P-region (where they exist as minority carriers). This concentration differences establishes density gradient across the junction resulting in carrier diffusion. Holes diffuse from P to N-region and electrons from N-to P-region and terminate their existence by recombination.

This recombination of free and mobile electrons and holes produces the narrow region at the junction called depletion layer or potential hill. It is so named because this region is devoid of (or depleted of) free and mobile charge carriers like electrons and holes—there being present only positive ions which are not free to move.

It might seem from above that eventually all the holes from the P-side would diffuse to the N side and all the electrons from the N-side would diffuse to the P-side but this does not occur due to the formation of ions on the two sides of the junction. The impurity atoms which provide these migratory electrons and holes are left behind in an ionized state bearing a charge which is opposite to that of the departed carrier. Also, these impurity ions, just like germanium atoms, are fixed in their positions in the crystal lattice in the P- and N- regions of the diode, they form parallel rows or ‘plates’ of opposite charges facing each other across the depletion layer. 

Obviously, row of fixed positive ions in the N-region is produced by the migration of electrons from the N- to P- region. Similarly, the row of fixed negative ions in the P-region is produced by the migration of holes from the P- to N-region.

If a majority carrier (either an electron or a hole) tries to cross into depletion layer, it can meet either of the following two facts:-

1. Either it can be trapped or captured by the row of fixed impurity ions of opposite sign which guard its own region. For example, a hole trying to approach the depletion layer may be neutralized by the row of fixed negative ions situated in the P-region itself at the edge of the depletion layer. So will be the case with the electron trying to approach the depletion layer from N-region.
2. It may succeed in entering the depletion layer where it will be repelled by the row of similarly-charged impurity ions guarding the other region. But its life will be cut short by recombination with a majority carrier of opposite sign which has similarly entered the depletion layer from the other half of the diode.

Ultimately, an equilibrium condition is reached when depletion layer has widened to such an extent that no electrons or holes can cross the P-N junction.

4.1.1.4 Junction or Barrier Voltage

Even though depletion layer is cleared of charge carriers, it has oppositely-charged fixed rows of ions on its two sides. Because of this charge separation, an electric potential difference VB is established across the junction even when the junction is externally isolated. It is known as junction or barrier potential. It stops further flow of carriers across the junction unless supplied by energy from an external source. At room temperature of 300ºK, VB is about 0.3 V for Ge and 0.7 V for Si. Barrier voltage depends on 

1. doping density, 
2. electronic charge and 
3. temperature. 

For a given junction, the first two factors are constant, thus making VB dependent on temperature. With increase in temperature, more minority charge carriers are produced, leading to their increased drift across the junction. As a result, equilibrium occurs at a lower barrier potential.

The strong field set up by VB causes drift of carriers through depletion layer. Under the influence of this field, holes drift from N-to P-region and electrons from Pto -N region. This drift current must be equal and opposite of the diffusion current because under condition of equilibrium and with no external supply, net current through the crystal is zero.

The processes involved in the formation of a P-N junction are:

1. Holes from the P-side diffuse into the N-side where they combine with free electrons.
2. Free electrons from the N-side diffuse into the P-side where they combine with holes.
3. The diffusion current (also known as recombination current) decays exponentially both with time and distance from the junction.
4. Due to the departure of free and mobile carriers from both sides of the junction, a depletion layer (centred around the junction) is formed. This layer contains only immobile or fixed (also called uncovered) ions of opposite polarity.
5. These uncovered but fixed ions set up a potential barrier across the junction.
6. This potential difference opposes the diffusion of free majority charge carriers from one side of the junction to the other till the process is completely stopped. (Incidentally this potential barrier aids in transfer of thermally generated minority charge carriers from one side of the junction to the other)
7. The width of depletion layer depends on the doping level. For heavy doping, depletion layer is physically thin because a diffusing charge carrier (either free electron or hole) has not to travel far across the junction for recombination (short lifetime). Opposite is the case if light doping is used.

4.1.1.4.1 Forward Biased P-N Junction

Suppose, positive battery terminal is connected to P-region of a semiconductor and the negative battery terminal to the N-region. In that case the junction is said to be biased in the forward direction because it permits easy flow of current across the junction. This current flow may be explained in the following two ways :

1. As soon as battery connection is made, holes are repelled by the positive battery terminal and electrons by the negative battery terminal with the result that both the electrons and the holes are driven towards the junction where they recombine. This masse movement of electrons to the left and that of holes to the right of the junction constitutes a large current flow through the semiconductor. Obviously, the junction offers low resistance in the forward direction.

As free electrons move to the left, new free electrons are injected by the negative battery terminal into the N-region of the semiconductor. Thus, a flow of electrons is set up in the wire connected to the negative battery terminal. As holes are driven towards the junction, more holes are created in the P-region by the breakage of covalent bonds. These newly-created holes are driven towards the junction to keep up a continuous supply. But the electrons so produced are attracted to the left by the positive battery terminal from where they go to the negative terminal and finally to the N region of the crystal. Incidentally, it may be noted that though there is movement of both electrons and holes inside the crystal, only free electrons move in the external circuit i.e. in the battery-connecting wires.

2. Another way to explain current flow in forward direction is to say that forward bias of V volts lowers the barrier potential to (V - VB) which now allows more current to flow across the junction.

Incidentally, it may be noted that forward bias reduces the thickness of the depletion layer. Energy band diagram for forward bias can be seen this reduction, conduction electrons in N-region are able to cross over to P-region. After reaching there, each electron falls into a hole (path A) and becomes a valence electron. In this way, it is able to continue its journey towards the left end of the crystal.

4.1.1.4.2 Forward V/I Characteristic

A typical V/I characteristic for a forward-biased P-N junction. It is seen that forward current rises exponentially with the applied forward voltage. However, at ordinary room temperature, a p.d. of about 0.3 V is required before a reasonable amount of forward current starts flowing in a germanium junction. This voltage is known as threshold voltage (Vth) or cut-in voltage or knee voltage VK. It is practically the same as barrier voltage VB. Its value for silicon junction is about 0.7 volt. For V < Vth, current flow is negligible. But as applied voltage increases beyond the threshold value, the forward current increases sharply. If forward voltage is increased beyond a certain safe value, it will produce an extremely large current which may destroy the junction due to overheating.

4.1.1.4.3 Reverse Biased P-N Junction

When battery connections to the semiconductor are made, the junction is said to reverse-biased. In this case, holes are attracted by the negative battery terminal and electrons by the positive terminal so that both holes and electrons move away from the junction and away from each other. Since there is no electron-hole combination, no current flows and the junction offer high resistance.

Another way of looking at the process is that in this case, the applied voltage increases the barrier potential to (V + VB), thereby blocking the flow of majority carriers.

Incidentally, it may be noted that under reverse bias condition, width of depletion layer is increased because of increased barrier potential. Although, in this case, there is practically no current due to majority carriers, yet there is a small amount of current (a few µA only) due to the flow of minority carriers across the junction.

Due to thermal energy, there are always generated some holes in the N-type region and some electrons in the P-type region of the semiconductor. The battery drives these minority carriers across the junction thereby producing a small current called reverse current or reverse saturation current I0 or IS. Since minority carriers are thermally-generated, I0 is extremely temperature dependent.

For the same reason, forward current is also temperature dependent but to a much less degree because minority current forms a very small percentage of the majority current. The name saturation has been used because we cannot get minority current more than what is produced by thermal energy. In other words, IS does not increase with increase in reverse bias.

IS is found to increase approximately 7 percent per 0ºC rise in temperature both for Ge and Si. Since, (1.07)10 = 2, it means that reverse current doubles for every 10ºC rise in temperature. It is worth noting that reverse saturation current is also referred to as leakage current of the P-N junction diode. With reverse bias, energy hill becomes too steep for majority carriers to go up the hill and cross over.

4.1.1.4.4 Reverse V/I Characteristic

As said earlier, the reverse saturation current is also referred to as leakage current of the P-N junction. V/I characteristics of a reverse-biased P-N junction, it is seen that as reverse voltage is increased from zero, the reverse current quickly rises to its maximum or saturation value. Keeping temperature constant as the reverse voltage is increased, I0 is found to increase only slightly. This slight increase is due to the impurities on the surface of the semiconductor which behaves as a resistor and hence obeys Ohm’s law. This gives rise to a very small current called surface leakage current. Unlike the main leakage (or saturation) current, this surface leakage current is independent of temperature but depends on the magnitude of the reverse voltage. A reverse-biased junction can be represented by a very large resistance.

4.1.1.5 Diode characteristics and properties

(a) Construction

It is a two-terminal device consisting of a P-N junction formed either in Ge or Si crystal. The Pand N-type regions are referred to as anode and cathode respectively. In Fig. 4.1.1.15(b), arrowhead indicates the conventional direction of current flow when forward-biased. It is the same direction in which hole flow takes place.

Commercially available diodes usually have some means to indicate which lead is P and which lead is N.

Figure 4.1.1.15

A P-N junction diode is one-way device offering low resistance when forward-biased and behaving almost as an insulator when reverse-biased. Hence, such diodes are mostly used as rectifiers i.e. for converting alternating current into direct current.

4.1.1.5.1 V/I Characteristic

1. Forward Characteristic: when the diode is forward-biased and the applied voltage is increased

from zero, hardly any current flows through the device in the beginning. It is so because the

external voltage is being opposed by the internal barrier voltage VB whose value is 0.7 V for

Si and 0.3 V for Ge. As soon as VB is neutralized, current through the diode increases rapidly

with increasing applied battery voltage. It is found that as little a voltage as 1.0 V produces a

forward current of about 50 mA. A burnout is likely to occur if forward voltage is increased

beyond a certain safe limit.

2. Reverse Characteristic: When the diode is reverse-biased, majority carriers are blocked and

only a small current (due to minority carriers) flows through the diode. As the reverse voltage

is increased from zero, the reverse current very quickly reaches its maximum or saturation

value I0 which is also known as leakage current. It is of the order of nanoamperes (nA) for Si

and microamperes (µA) for Ge. The value of I0 (or Is ) is independent of the applied reverse

voltage but depends on (a) temperature, (b) degree of doping and (c) physical size of the

junction.
As seen from Figure 4.1.1.18, when reverse voltage exceeds a certain value called break-down voltage VBR (or Zener voltage Vz ), the leakage current suddenly and sharply increases, the curve indicating zero resistance at this point. Any further increase in voltage is likely to produce burnout unless protected by a current-limiting resistor.

4.1.1.5.2 Equation of the Static Characteristic

The volt-ampere characteristics described above are called static characteristics because they describe the d.c. behaviour of the diode. The forward and reverse characteristics have been combined into a single diagram of Fig. 4.1.1.18.

Figure 4.1.1.18

These characteristics can be described by the analytical equation called Boltzmann diode equation given below :

where I0 = diode reverse saturation current

V = voltage across junction (positive for forward and negative for reverse bias). k = Boltzmann constant = 1.38 × 10-23 J/ºK

T = crystal temperature in ºK

η = 1 – for germanium = 2 – for silicon
4.1.1.6 Special Diodes

4.1.1.6.1 Zener Diodes

It is a reverse-biased heavily-doped silicon (or germanium) P-N junction diode which is operated in the breakdown region where current is limited by both external resistance and power dissipation of the diode. Silicon is preferred to Ge because of its higher temperature and current capability.

when a diode breaks down, both Zener and avalanche effects are present although usually one or the other predominates depending on the value of reverse voltage. At reverse voltages less than 6 V, Zener effect predominates whereas above 6 V, avalanche effect is predominant. Strictly speaking, the first one should be called Zener diode and the second one as avalanche diode but the general practice is to call both types as Zener diodes.

Zener breakdown occurs due to breaking of covalent bonds by the strong electric field set up in the depletion region by the reverse voltage. It produces an extremely large number of electrons and holes which constitute the reverse saturation current (now called Zener current, Iz ) whose value is limited only by the external resistance in the circuit. It is independent of the applied voltage. Avalanche breakdown occurs at higher reverse voltages when thermally-generated electrons acquire sufficient energy to produce more carriers by collision.

Figure 4.1.1.19

(a) V/I Characteristic

A typical characteristic is shown by Fig. 4.1.1.19 in the negative quadrant. The forward characteristic is simply that of an ordinary forward-biased junction diode. The important points on the reverse characteristic are :

Vz = Zener breakdown voltage

Iz min = minimum current to sustain breakdown

Iz max = maximum Zener current limited by maximum power dissipation.

Since its reverse characteristic is not exactly vertical, the diode possesses some resistance called Zener dynamic impedance. However, we will neglect it assuming that the characteristic is truly
vertical. In other words, we will assume an ideal Zener diode for which voltage does not change once it goes into breakdown. It means that Vz remains constant even when Iz increases considerably.

The schematic symbol of a Zener diode and its equivalent circuit are shown in Fig. 4.1.1.20(a). The complete equivalent circuit is shown in Fig. 4.1.1.20 (b) and the approximate one in Fig.

4.1.1.20 (c) where it looks like a battery of Vz volts.

The schematic symbol of Fig. 4.1.1.20 (a) is similar to that of a normal diode except that the line representing the cathode is bent at both ends. With a little mental effort, the cathode symbol can be imagined to look like the letter Z for Zener.

Figure 4.1.1.20

(b) Zener Voltages

Zener diodes are available having Zener voltages of 2.4 V to 200 V. This voltage is temperature dependent. Their power dissipation is given by the product Vz Iz... maximum ratings vary from 150mW to 50 W.

(c) Zener Biasing

For proper working of a Zener diode in any circuit, it is essential that it must 1. be reverse-biased;

2. have voltage across it greater than Vz;
(d) Diode Identification

Physically, a Zener diode looks like any other diode and is recognized by its IN number such as IN 750 (10 W power) or IN 4000 (high power).

(e) Uses

Zener diodes find numerous applications in transistor circuitry. Some of their common uses are :

1. as voltage regulators;

2. as a fixed reference voltage in a network for biasing and comparison purposes and for

calibrating voltmeters;

3. as peak clippers or voltage limiters;

4. for metre protection against damage from accidental application of excessive voltage;

5. for reshaping a waveform.

4.1.1.6.2 Varactor Diode

The varactor diode is a semiconductor, voltage-dependent variable capacitor alternatively known as varicap or voltacap or voltage-variable capacitor (VVC) diode. Basically, it is just a reversebiased junction diode whose mode of operation depends on its transition capacitance (CT). Reverse-biased junctions behave like capacitors whose capacitance is ∝ 1/VRn where n varies from 1/3 to 1/2. As reverse voltage VR is increased, depletion layer widens thereby decreasing the junction capacitance. Hence, we can change diode capacitance by simply changing VR. Silicon diodes which are optimised for this variable capacitance effect are called varactors.

Figure 4.1.1.22

Applications

Since the junction capacitance of a varactor is in the pF range, it is suitable for use in highfrequency circuits. Its main applications are as

1. automatic frequency control device, 2. FM modulator,

3. adjustable band-pass filter, 4. Parametric amplifier.
4.1.1.6.3 Schottky Diode

It is also called Schottky barrier diode or hot-carrier diode. It is mainly used as a rectifier at signal frequencies exceeding 300 MHz. It has more uniform junction region and is more rugged than PIN diode - its main rival.

(a) Construction

It is a metal-semiconductor junction diode with no depletion layer. It uses a metal (like gold, silver, platinum, tungsten etc.) on the side of the junction and usually an N-type doped silicon semiconductor on the other side. The diode and its schematic symbol are shown in Fig. 4.1.1.23.

(b) Operation

When the diode is unbiased, electrons on the N-side have lower energy levels than electrons in the metal. Hence, they cannot surmount the junction barrier (called Schottky barrier) for going over to the metal.

When the diode is forward-biased, conduction electrons on N-side gain enough energy to cross the junction and enter the metal. Since these electrons plunge into the metal with very large energy, they are commonly called ‘hot-carriers’. That is why this diode is often referred to as hotcarrier diode.

(c) Applications

This diode possesses two unique features as compared to an ordinary P-N junction diode:

1. It is a unipolar device because it has electrons as majority carriers on both sides of the

junction. An ordinary P-N junction diode is a bipolar device because it has both electrons and

holes as majority carriers;

2. Since no holes are available in metal, there is no depletion layer or stored charges to worry

about. Hence, Schottky diode can switch OFF faster than a bipolar diode.

Because of these qualities, Schottky diode can easily rectify signals of frequencies exceeding 300 MHz. As shown in Fig. 4.1.1.24, it can produce an almost perfect half-wave rectified output.

The present maximum current rating of the device is about 100 A. It is commonly used in switching power supplies that operate at frequencies of 20 GHz. Another big advantage of this diode is its low noise figure which is extremely important in communication receivers and radar units etc.

It is also used in clipping and clamping circuits, computer gating, mixing and detecting networks used is communication systems.
4.1.1.7 Diodes Symbols

Figure 4.1.1.25 represents the symbols for different type of diodes.

Figure 4.1.1.25: Some diode symbols.

4.1.1.8 Diodes in Series and Parallel

4.1.1.8.1 Series Diode Configurations

For all the analysis to follow, it is assumed that

The forward resistance of the diode is usually so small compared to the other series elements of the network that it can be ignored.

This is a valid approximation for the vast majority of applications that employ diodes. Using this fact will result in the approximate equivalents for a silicon diode and an ideal diode that appear in Table 4.1. For the conduction region the only difference between the silicon diode and the ideal diode is the vertical shift in the characteristics, which is accounted for in the equivalent model by a dc supply of 0.7 V opposing the direction of forward current through the device. For voltages
less than 0.7 V for a silicon diode and 0 V for the ideal diode the resistance is so high compared to other elements of the network that its equivalent is the open circuit.

TABLE 4.1: Approximate and Ideal Semiconductor Diode Models.

For each configuration the state of each diode must first be determined. Which diodes are "on" and which are "off"? Once determined, the appropriate equivalent can be substituted and the remaining parameters of the network determined.

In general, a diode is in the "on" state if the current established by the applied sources is such that its direction matches that of the arrow in the diode symbol, and VD ≥ 0.7 V for silicon, VD ≥ 0.3 V for germanium, and VD ≥ 1.2 V for gallium arsenide.

Figure 4.1.1.26: Series diode configuration.

For each configuration, mentally replace the diodes with resistive elements and note the resulting current direction as established by the applied voltages ("pressure"). If the resulting direction is a "match" with the arrow in the diode symbol, conduction through the diode will occur and the
device is in the "on" state. The description above is, of course, contingent on the supply having a voltage greater than the "turn-on" voltage (VK) of each diode.

If a diode is in the "on" state, one can either place a 0.7-V drop across the element or redraw the network with the VK equivalent circuit as defined in Table 4.1. In time the preference will probably simply be to include the 0.7 V drop across each "on" diode and draw an open line through each diode in the "off" state.

The state of the diode is first determined by mentally replacing the diode with a resistive element as shown in Figure 4.1.1.27(a). The resulting direction of I is a match with the arrow in the diode symbol, and since E > VK, the diode is in the "on" state. The network is then redrawn as shown in Figure 4.1.1.27(b) with the appropriate equivalent model for the forward-biased silicon diode. Note for future reference that the polarity of VD is the same as would result if in fact the diode were a resistive element. The resulting voltage and current levels are the following:

VD = VK VR = E - VK ID = IR = VR/R

(4)(5)(6)

Figure 4.1.1.27: (a) Determining the state of the diode of Figure 4.1.1.26; (b) substituting the equivalent model for the "on" diode of Figure 4.1.1.27a.

Figure 4.1.1.28: Reversing the diode of Figure 4.1.1.26

In Figure 4.1.1.28 the diode of Figure 4.1.1.26 has been reversed. Mentally replacing the diode with a resistive element as shown in will reveal that the resulting current direction does not match the arrow in the diode symbol. The diode is in the "off" state, resulting in the equivalent circuit of
Figure 4.1.1.28. Due to the open circuit, the diode current is 0 A and the voltage across the resistor R is the following:

VR = IRR = IDR = (0 A) R = 0 V

4.1.1.8.2 Parallel and Series-Parallel Configurations

The methods applied previously can be extended to the analysis of parallel and series-parallel configurations. For each area of application, simply match the sequential series of steps applied to series diode configurations.

Example: Determine V0, I1, ID1, ID2

Figure 4.1.1.29

Figure 4.1.1.30

For the applied voltage the 'pressure' of the source acts to establish a current through each diode in the same direction of the diode symbol. As the applied voltage is greater than 0.7 V, both

diodes are in the 'on' state, the voltage across parallel elements is always the same. V0= 0.7V

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