Introduction to Solid State Electronics

Introduction to Solid State Electronics Semiconductors: These are the materials, which do not have free electrons to support the flow of electrical current through them at room temperature. However, valence electron may become free electrons if sufficient energy is induced into the material, for example, by heating the material. Solid State Devices: These are nonlinear devices (diodes, transistors, etc.), which are made by creating junction(s) of two types of semiconductor materials: (1) p-type materials and (2) n-type materials. Both p-type and n-type materials are created by adding impurities into two pure semiconductor elements: (1) Silicon and (2) Germanium. Here we shall discuss how p-type or n-type materials are created using Silicon, which undergoes through a process known as doping. The process of creating p-type or n-type materials using Germanium is essentially similar. Silicon-based p-type or n-type materials: Silicon atom has 14 protons and 14 electrons. Figure 1 shows the atomic structure of a Silicon atom. The electrons in the outer ring are called valence electrons. In pure silicon the atoms are held tightly together through what is known as covalent bond, in which the four valence electrons are shared with four neighboring atoms to form covalent bonds. Unlike conductors pure semiconductors do not have free electrons at room temperature to support the flow of electric current for any useful purpose. Figure 2 shows the crystal structure of pure Silicon. Figure 1: Atomic structure of the Silicon atom. Syed A. Rizvi 1

Doping: Figure 2: Crystal Structure of pure Silicon. It is the process of mixing an impurity with a pure semiconductor material. It is important to carefully choose impurity materials because impurities atoms should be able to fit into the crystal structure of the semiconductor material without disturbing the lattice. Two kinds of impurities are used: 1. The impurities with five valence electrons in the outer ring are called donors. The semiconductor material doped with a donor impurity is known as n-type semiconductor material. Phosphorous, Arsenic, and Antimony are examples of donor impurities. 2. The impurities with three valence electrons in the outer ring are called accepters. The semiconductor material doped with an accepter impurity is known as p-type semiconductor material. N-type Material: A Phosphorous atom has a total of 15 electrons, which leaves five electrons in the outer ring. When Phosphorous is added to Silicon as impurity one Syed A. Rizvi 2

Phosphorous atom makes covalent bonds with four Silicon atoms using four out of five of the electrons in the outer ring. This leaves the fifth phosphorous electron not being attached to any particular atom and thus can move around as a free electron. These free electrons support the flow of electrical current through the doped semiconductor material. The number of free electrons depends on the amount of impurity added. If a large amount of Phosphorous is mixed the semiconductor is known as heavily doped. Heavily doped n-type Silicon has more free electrons than a lightly doped n-type Silicon, in which a relatively small amount of impurity (phosphorous) is added. Figure 3 shows the crystal structure of n-type Silicon semiconductor. P-type Material: Figure 3: Crystal Structure of the n-type Silicon semiconductor. A Boron atom has a total of 5 electrons, which leaves three electrons in the outer ring. When Boron is added to Silicon as impurity one Boron atom makes covalent bonds with three Silicon atoms using the three electrons in the outer ring. This leaves the crystal structure with one missing covalent bond between the Boron and a Silicon atom. This missing covalent bond is represented as a hole in the crystal structure of the p-type material. The term hole implies that there is an Syed A. Rizvi 3

Figure 4: Crystal Structure of the p-type Silicon semiconductor. Figure 4: Crystal Structure of the p-type Silicon semiconductor after an electron fills a hole leaving behind a hole. Syed A. Rizvi 4

opportunity for an electron from the neighboring covalent bond to jump in and complete the missing covalent bond (filling the hole). Figure 4 shows the crystal structure of the p-type Silicon semiconductor. Note that when an electron jumps in and fills a hole to complete the missing covalent bond, it leaves a hole at its original location (the now broken covalent bond). Figure 5 shows the crystal structure of the p-type Silicon semiconductor after an electron jumps in to fill the hole (leaving a hole at its place). This phenomenon continues throughout the p- type semiconductor giving the perception of free holes analogous to free electrons in n-type semiconductor. Figure 6 depicts a representation of the p-type semiconductor with free holes and of the n-type semiconductor with free electrons. It is important to note that even though the p-type semiconductor has free holes and the n-type semiconductor has free electrons, both semiconductors are electrically neutral. P-N Junction: Figure 6: Representation of the p-type and n-type semiconductors. The p-type or n-type semiconductors are of little use by themselves. However, an interesting phenomenon takes place when a p-type semiconductor is placed next to an n-type semiconductor, thus forming a junction. At the junction some of the free electrons from the n-type semiconductor cross the junction and fill the holes. This movement of electrons across the junction leaves the region in n-type semiconductor adjacent to the junction with excess positive charge. The electrons filling the holes in the region adjacent to the junction on the p-type semiconductor create excess negative charge. Figure 7 shows the dynamics of a p-n junction. This oppositely charged region on both sides of the junction, known Syed A. Rizvi 5

as the depletion region, creates a potential barrier, which is 0.7 volts for Silicon based semiconductor and 0.2 for Germanium based semiconductor. Figure 8: The p-n junction. The p-n junction forms a simple solid-state device known as the diode. Let s now examine the behavior of the p-n junction when a voltage source is connected across the device. If we connect the positive and negative terminals of a power supply to the p-type and n-type semiconductors, respectively, the junction is said to be forward-biased. Figure 9 shows the dynamics of the junction under this condition. When the potential applied across the p-n junction is sufficiently high Figure 9: A forward-biased p-n junction. Syed A. Rizvi 6

(greater than 0.7 volts for Silicon based semiconductor and greater than 0.2 volts for the germanium based semiconductor), the free electrons from the n-type material will be able to jump across the depletion region and go towards the positive terminal of the power supply. This causes the I D to flow through the p-n junction, from positive terminal to the negative terminal of the power supply. On the other hand, if we connect the positive and negative terminals of a power supply to the n-type and p-type semiconductors, respectively, the junction is said to be reverse-biased. Figure 10 shows the dynamics of the junction under this condition. When the potential applied across the p-n junction with this polarity, the free electrons in the n-type semiconductor are attracted towards the positive voltage and move away from depletion region. The holes on the p-type semiconductor are attracted to the negative terminal of the power supply. This, in effect, widens the depletion region and essentially makes it impossible to have a current flow from positive terminal to the negative terminal of the power supply. In this way, a p-n junction (diode) essentially acts like a valve, in which air can be pumped in one direction but cannot come out (flow) in the other direction. Figure 10: A reverse-biased p-n junction. The behavior of the p-n junction under forward -and reverse-biased conditions is very useful in several applications. Here, we ll consider one such application known as rectification. Rectification is a process of converting an AC signal to a DC signal. Figure 11 shows a simple circuit of a rectifier. This particular rectifier is called half-wave rectifier as it only produces the positive half cycle of the input signal at the output of the rectifier. Note that during the positive half cycle, the diode is forward biased and the current I D flows through the diode. During Syed A. Rizvi 7

the negative half cycle, however, the diode becomes reverse-biased and prevents the current flow through the diode. Figure 11: Half-wave rectifier. The average output voltage can be found as follows: The input voltage is a sine wave with a period T. The output is also a sine wave with a period T and a peak voltage of out max. However, the negative half of the sine wave is missing. Therefore, the average voltage at the output can be computed as: 1 2Πt = T T / 2 out_ max out_ max out_ av = out _max sin tdt sin dt 0. 318 T ω = = T T Π 0 0 out_ max Syed A. Rizvi 8

Diode operating characteristics: Applications of Diode As mentioned earlier, a silicon diode has potential barrier of 0.7 volts at the p-n junction. We ll refer to this potential barrier as ON. The diode will conduct electrical current if it is forward-biased and the applied voltage is greater than ON. If the diode is reversebiased, it will not conduct electrical current until the voltage is greater than what is know as breakdown voltage (referred to as peak reverse voltage on manufacturers data sheets). There is, however, a small amount of leakage current present while the diode is in reverse biased mode. At the breakdown voltage, a large amount of current flows through the device, which may permanently damage the device. The breakdown voltage for 1N4001 diode is 50 volts peak. Figure 1 shows the diode operating characteristics for the silicon-based devices. Note that the operating characteristics in the reverse-biased region are not drawn to the scale. Figure 1: Operating characteristics for a typical diode (Silicon). Syed A. Rizvi 9

Rectification: The behavior of the p-n junction under forward -and reverse-biased conditions is very useful in several applications. Here, we ll consider one such application known as rectification. Rectification is a process of converting an AC signal to a DC signal. Figure 2 shows a simple circuit of a rectifier. This particular rectifier is called half-wave rectifier as it only produces the positive half cycle of the input signal at the output of the rectifier. Note that during the positive half cycle, the diode is forward biased and the current I D flows through the diode. During the negative half cycle, however, the diode becomes reverse-biased and prevents the current flow through the diode. Figure 11: Half-wave rectifier. The average output voltage can be found as follows: The input voltage is a sine wave with a period T. The output is also a sine wave with a period T and a peak voltage of out max. However, the negative half of the sine wave is missing. Therefore, the average voltage at the output can be computed as: 1 2Πt = T T / 2 out _ max out _ max out _ av = out _ max sin tdt sin dt 0. 318 T ω = = T T Π 0 0 out _max Note that Syed A. Rizvi 10

2Π ω = 2Πf = T Half-wave rectification is not very efficient because the power from input to the output is transferred during only the positive half cycle. Another process, known as full-wave rectification, transfers the power from input to the output during both the positive and negative half cycles. Figures 3 and 4 show one possible way to perform full-wave rectification using a bridge rectifier. Figure 3: Bridge rectifier. The current flow is shown for the positive half cycle. Note that in Fig. 3, the diodes A and C are forward-biased and the diodes B and D (with dotted circle around them) are reverse-biased during the positive half cycle. Therefore, the current from the AC source passes through the diode A, leaves the bridge at the terminal marked + and then passes through the load resistor R L. The current then enters the bridge at the terminal marked, passes through the diode C and returns to the AC source. The output voltage at this point is the same as the input voltage during the positive half cycle. Figure 4 shows the current flow during the negative half cycle of the input voltage. During the negative half cycle the diodes B and D are forward-biased and the diodes A and C (with dotted circle around them) are reverse-biased. Therefore, the current from the AC source passes through the diode D, leaves Syed A. Rizvi 11

the bridge at the terminal marked + and then passes through the load resistor R L. The current then enters the bridge at the terminal marked, passes through the diode B and returns to the AC source. The output voltage still has the same polarity and, therefore, the same as the input voltage during the positive half cycle. That is, the negative half cycle has, in effect, revered at the output. In this way, we get power transferred from the input to the output of the circuit for both the positive and negative half cycles; however, the output voltage remains positive during both half cycles. Therefore, the average output voltage for the fullwave rectifier is twice of the average output voltage for the half-wave rectifier. Figure 4: Bridge rectifier. The current flow is shown for the negative half cycle. Note that the output voltage after rectification is unidirectional (DC). However, the amplitude of the output voltage is not constant. This phenomenon is known as the ripple effect. In the pulsating output voltage has the frequency equal to the input AC voltage in the case of half-wave rectification and the frequency twice that of the input AC voltage in the case of full-wave rectification. The difference between the maximum and the minimum output voltage of the unidirectional pulsating output voltage is known as ripple. In many applications requiring DC voltage it is highly desirable to have a relatively constant unidirectional voltage; that is, the output voltage should have minimum ripple. The ripple can be reduced by filtering the output of the rectifier. Syed A. Rizvi 12

Filtering: Figure 5 shows a half-wave rectifier with a filter. During the positive cycle the capacitor is charged to out_max. As the out decreases from out_max, the capacitor starts discharging through the load resistor R L. If the value of the capacitor is properly chosen, it can be made to discharge at a rate slower than the change in the output voltage. The idea is to discharge the capacitor such that it is not fully discharged before the next positive cycle starts. At the next positive cycle the capacitor is charged again to out_max. Figure 5: Half-wave rectifier with filter. Figure 6 shows the full-wave rectifier with filter. Note that output voltage is present during both the positive and negative half cycles of the input voltage. Therefore, the capacitor starts charging again after a relatively short period of time once it begins discharging when compared to half-wave rectifier. If R L and an acceptable value of ripple are known, the value of the capacitor can be found using the following approximate formula. Syed A. Rizvi 13

Zener Diode Zener diode is a special diode that is fabricated in such a way as to make the breakdown characteristics very steep. Furthermore, the device is made to work in the reverse breakdown region. Figure 7 shows the operating characteristics of Zener diode. Note that when the reverse biased voltage reaches Z there is a sharp increase in the reverse biased current (I Z ). It is important to limit the current through Zener diode to I Zmax to avoid permanent damage to the device. Figure 7: Operating characteristics of the Zener diode. Zener diode is used to build voltage regulators. A voltage regulator provides a constant voltage to the load under varying source voltage or varying load condition. Figure 8 shows a simple circuit for a voltage regulator using Zener diode. The current through Zener diode I Z can be found as follows: I = I + I also, I I R Z L S Z R =, therefore, Ri S Z Z = IL. (2) Ri Note that, Syed A. Rizvi 14

R S Z S Z i = =. (3) I I + I R Z L Let s now examine the conditions under which the current through Zener diode is minimum or maximum. It can be seen from Eq. 2 that I Z is a minimum when S is a minimum and I L is maximum. That is, I Z min Smin Z = IL max. (4) Ri Also, I Z is a maximum when S is a maximum and I L is minimum. That is, I Z max Smax Z = IL min. (5) Ri Note that the I Zmin given by Eq. 3 must be greater than the minimum required current in the breakdown region specified by the manufacturer of the Zener diode. Similarly, I Zmax given by Eq. 4 must be less than the maximum allowed current in the breakdown region specified by the manufacturer of the Zener diode. As a rule of thumb, I Zmin should be not less than 10% of I Zmax to assure that the diode operates in the constant breakdown voltage region. That is, I Zmin = 0.1 I Zmax. (6) From Eqs. 4, 5, and 6 I Zmax is given by I Z max I ( ) + I ( 0.9 0.1 Lmin Z S min Lmax S max Z =. (7) Smin Z Smax ) Figure 8: Zener voltage regulator. Syed A. Rizvi 15

Design Example 1: Design a full wave rectifier for the following conditions: 1. The minimum output voltage should be at least 90% of the maximum output voltage. 2. The load resistance may vary from 1.5 KO to 2.0 KO. Assume ideal diodes are used. The peak input voltage is 100. Solution: We ll use the full wave bridge rectifier. Since we are assuming that ideal diodes are used, the maximum output voltage Omax is the same as input peak voltage. That is, Omax = 100. The minimum output voltage should be atleast 0.9x Omax. Therefore, Omin = 0.9 x 100 = 90. The value of the capacitor can be found using the following Eq. C = f O max p R L Syed A. Rizvi 16

Where,? = Omax - Omin = 100 90 = 10. Omax = 100 f P = 120 (Note that f P = 120 for full wave rectifier and f P = 60 for the half wave rectifier). R L = 1.5 KO (Note that we must choose smallest value of R L if we are given a range of values for R L ). 100 10 3 10x120x1.5x10 6 C = = 55.6x = 55.6 µf Design Example 2: Design a 10 Zener regulator for the following conditions: 1. The load current I L ranges from 100 ma to 200 ma. 2. The source voltage ranges from 14 to 20. Solution: Form condition 1 we have: I Lmin = 100 ma and I Lmax = 200 ma Form condition 2 we have: Smin = 14 and Smax = 20 We can find I Zmax using Eq. 7. That is, I Z max I = Lmin ( Z S min) + ILmax ( 0.9 0.1 Smin Z S max Smax Z ) Syed A. Rizvi 17

3 3 100x10 (10 14) + 200x10 (20 10) I Z max = = 0. 53A 14 9 2 We ll use Eq. 5 to calculate R i (given below). I Z max Smax Z = IL min. This equation can be rearranged as: Ri Ri S max Z 20 10 = = = 15. 9Ω I + I 0.53 + 0.1 Zmax Lmin Note that I Lmin = 100 ma = 100x10-3 A = 0.1 A. Now we ll calculate power ratings for the resister and Zener diode. Power can be calculated as: Power = x I = I 2 x R = 2 / R. Power rating for Zener diode: the voltage across the Zener diode is Z = 10. The maximum current through the Zener diode is I Zmax = 0.53A. Therefore, the power rating for the Zener diode is: P = 10 X 0.53 = 5.3 Watts Power rating for Resistor R i : The current through the resistor R i is given by I R = I Zmax + I Lmin = 0.53 + 0.1 = 0.63 A. The maximum voltage across R i is given by = Smax Z = 20 10 = 10 Therefore, the power rating of R i is: 10 X 0.63 = 6.3 Watts. This completes the design of the voltage regulator. Syed A. Rizvi 18