Electronics I Dr. Emad Aljaberi Department of Physics College of Science Fall Semester 2022/2023 PN Junction Diode A PN-junction diode might be made, when an n-type and a p-type semiconductor are joined together. The electric leads of the diode are usually formed from metallic contacts, as shown in Fig. 3.1. ممنوع تداولها في مكاتب االستنساخ Fig. 3.1. Construction of Si layers PN-junction diode. As illustrated in Fig. 3.2, since the positive and negative charge densities are different in these two regions, the charges would be forced to diffuse in the opposite directions due to thermal energy. ➢ In the N-type region, positive charges could be available near the junction ➢ In the P-type region, negative charges would be in the P-type region. Fig. 3.1. Depletion region of PN-junction diode. In the electronic circuits of the P-type region and the N- type regions are called anode and cathode, respectively. 1 Electronics I Dr. Emad Aljaberi Department of Physics College of Science Fall Semester 2022/2023 The electronic symbol and different types of a PN-junction diode are shown in Fig. 3.3. (b) Fig. 3.3. Electronic symbol of a PN-junction diode. (b) Some types of PN-junction diodes used in electronic circuits. ممنوع تداولها في مكاتب االستنساخ (a) Biasing a PN Junction Diode ➢ The depletion region might be gotten smaller or expanded depending on the polarity and value of the applied potential. ➢ A diode made of the same semiconductor materials is called homojunction likes (P-Si/N-Si). ➢ A diode made of different types of semiconductor materials, is called heterojunction likes (P-Si/N-Ge). 1- No Bias ▪ There is No an external potential applied to the junction, different components of charge carriers could be transported in both regions. ▪ Two types of the majority carriers are available in the junction: electrons in the N-type region and holes in the P-type region. ▪ The minority carriers in the P-type and N-type regions are electrons and holes, respectively. 2 Electronics I Dr. Emad Aljaberi Department of Physics College of Science Fall Semester 2022/2023 ▪ Due to gradient in the carrier concentrations, the majority carriers will diffuse in the opposite direction, and ▪ The process is called diffusion. ▪ The minority carriers will drift towards the P-type region and N-type region. ▪ This process continues until thermal equilibrium occurs in both sides of the junction. ▪ A depletion region is formed, which is fundamentally free of charges. ▪ An electric field occurs in the interface between them. ▪ In this region, due to the electric field, a voltage would grow up across the junction and called built-in-potential (𝑉𝑏 ). 2- Forward Bias ممنوع تداولها في مكاتب االستنساخ (a) Electronic circuit. (b) Junction structure. (b) Fig. 3.4. Forward-biased PN junction diode representation. a) The PN-junction is forward biased: I. A positive-voltage terminal is connected to the P-type region. II. A negative -voltage terminal is connected to the N-type region. 3 Electronics I Dr. Emad Aljaberi Department of Physics College of Science Fall Semester 2022/2023 b) The depletion region is narrowed because the majority carries, which are electrons in the N-type and holes in the P-type, are forced to diffuse in the opposite directions. c) When the applied potential is more than the built-in-potential, a forward current can pass through the circuit. ممنوع تداولها في مكاتب االستنساخ 3- Reverse Bias (a) Electronic circuit. (b) Junction structure. Fig. 3.4. Forward-biased PN junction diode representation. a) The PN-junction is reversed biased: I. A negative -voltage terminal is connected to the P-type region. II. A positive-voltage terminal is connected to the N-type region. b) The applied potential is less than the built-in-potential (𝑉𝑏 ). c) The minority carriers will be drifted towards the P-type region and N-type region. d) This process continues until thermal equilibrium occurs in both sides of the junction. 4 Electronics I Dr. Emad Aljaberi Department of Physics College of Science Fall Semester 2022/2023 e) This bias gives rise to increase thickness of the depletion region. f) A very small current can pass from the N-Type region to the P-type region, which is referred to as a reverse current (𝐼𝑅 ). Space Charge Region (SCR) • The diode is assumed to have an abrupt transition from a p-type to a n-type semiconductor. • The charges in this region would be distributed as −𝑥𝑝 < 𝑥 < 0 → 𝜌𝑝 = −𝑞𝑁𝐴 , and ممنوع تداولها في مكاتب االستنساخ 0 < 𝑥 < 𝑥𝑛 → 𝜌𝑛 = 𝑞𝑁𝐷 . • In SCR the net charge is expressed by 𝜌 = 𝑞(𝑁𝐷 − 𝑁𝐴 ) Fig. 3.6. Space charge region of a 𝒑𝒏 junction. 5 Electronics I Dr. Emad Aljaberi Department of Physics College of Science Fall Semester 2022/2023 ➢ The junction is neutral: ▪ The net charge is zero, the charges per unit area in both regions are zero. 𝑥𝑝 𝑁𝐴 = 𝑥𝑛 𝑁𝐷 ممنوع تداولها في مكاتب االستنساخ ▪ The overall width (𝑤) of the space charge region is given by 𝑤 = 𝑥𝑝 + 𝑥𝑛 or in term of 𝑉𝑏 : 𝑤 =√ 2𝜀𝑠 𝑁𝐴 + 𝑁𝐷 𝑉𝑏 ( ) 𝑞 𝑁𝐴 𝑁𝐷 𝜀𝑠 is the electric permittivity of semiconductor. ✓ This equation is valid only for zero bias, otherwise the depletion layer thickness decreases or increases. Energy Band Alignment Consider a PN-junction diode Fig. 3.7. (a) Energy band structure of separated 𝒑-type and 𝒏-type semiconductors. (b) Energy band structure of a 𝒑𝒏-homojunction diode. 6 Electronics I Dr. Emad Aljaberi Department of Physics College of Science Fall Semester 2022/2023 • The Fermi levels in the forbidden gap of the separated semiconductors have different positions. • The Fermi level is line-up in the 𝑝𝑛 junction: ➢ The edge of both the conduction and valence bands of the n-type semiconductors will bend up. ➢ The edge of both the conduction and valence bands of the p-type semiconductors will bend down. ➢ The conduction bands of both types will coincide and the valence bands will coincide too. • Thermal equilibrium in a 𝑝𝑛 junction: ➢ No temperature gradient throughout sample. ➢ Excitation of carriers is unavailable. • No current might flow in the 𝑝𝑛-junction, ➢ The net current is equal to zero. That is 𝑗𝑛 = 0, or 𝑑𝑟𝑖𝑓𝑡 𝑗𝑛 𝑑𝑖𝑓𝑓 = −𝑗𝑛 and 𝑗𝑝 = 0 7 ممنوع تداولها في مكاتب االستنساخ • drift current caused by the electric field = diffusion current due to thermal gradient. Electronics I Dr. Emad Aljaberi Department of Physics College of Science 𝑑𝑟𝑖𝑓𝑡 𝑗𝑝 Fall Semester 2022/2023 𝑑𝑖𝑓𝑓 = −𝑗𝑝 ممنوع تداولها في مكاتب االستنساخ n-type 𝑛 ≊ 𝑁𝐷 𝑛𝑖2 𝑝𝑜 = 𝑁𝐷 p-type 𝑝 ≊ 𝑁𝐴 𝑛𝑖2 𝑛𝑜 = 𝑁𝐴 • In the 𝑝-type region the concentration of holes that are majority is much higher than that of electrons, which are minority carriers. • In the 𝑛-type region the concentration of electrons is much larger than that of holes. Fig. 3.8. Charge-carrier distribution in 𝒑-type and 𝒏-type semiconductors. In the forward bias, the difference between the Fermi levels of the junction can be expressed by 8 Electronics I Dr. Emad Aljaberi Department of Physics College of Science Fall Semester 2022/2023 𝑞𝑉𝑏 = 𝐸𝑓𝑛 − 𝐸𝑓𝑝 ممنوع تداولها في مكاتب االستنساخ (a) (b) Fig. 3.9. Band structure of a PN junction in (a) forward bias and (b) reverse bias. Shockley equation In Shockley model of PN junction: • The junction is assumed to be an abrupt, whereas the region out of the space charge region is neutral. • The carrier densities at the boundaries are related to the potential distribution. • The injected minority carrier density is small in comparison to the majority carrier density. • The depletion region is free of charge, and so generation or recombination cannot occur. The current density passing through an ideal 𝑝𝑛-junction diode due to applying a voltage (𝑉) is described by the Shockley equation 9 Electronics I Dr. Emad Aljaberi Department of Physics College of Science 𝐼 = 𝑞𝐴𝑛𝑖2 . ( Fall Semester 2022/2023 𝐷ℎ 𝐷𝑒 𝑉 + ) [exp ( ) − 1] 𝐿ℎ 𝑁𝐷 𝐿𝑒 𝑁𝐴 𝑉𝑇 𝑞 : electron charge, 𝐴 : diode area 𝐷 : diffusion coefficient, 𝐿 : diffusion length, 𝑉𝑇 : thermal voltage, ممنوع تداولها في مكاتب االستنساخ The subscripts 𝑝 and 𝑛 refer to holes and electrons. 𝐾𝐵 𝑇 𝑞 𝑉𝑇 = At room temperature, 𝑉𝑇 = 26 𝑚𝑉. The current 𝑉 𝐼 = 𝐼𝑠 [𝑒𝑥𝑝 ( ) − 1] 𝑉𝑇 I𝑠 is called the saturation 𝐼𝑠 = 𝑞𝐴𝑛𝑖2 . ( 𝐷ℎ 𝐷𝑒 + ) 𝐿ℎ 𝑁𝐷 𝐿𝑒 𝑁𝐴 The Shockley equation of a diode gives a precise variation of 𝐼 versus an applied voltage. 𝑰 − 𝑽 Characteristics Fig. 3.10. 𝑰 − 𝑽 Characteristics of an ideal 𝒑𝒏-junction diode in forward and reverse bias. 10 Electronics I Dr. Emad Aljaberi Department of Physics College of Science Fall Semester 2022/2023 • A plot of a current passing through a diode against an applied voltage is referred to as current – voltage, ( 𝐼 − 𝑉 ) characteristics of the diode. • Three different regions are seen: forward and reverse region. ➢ At point A: the forward current is zero at zero-bias condition. ➢ At point B: The current increases slightly until reaches approximately 0.7 V at the knee of the curve. After point B, the change in the forward voltage becomes not noticeable. ➢ At point C: the forward current increases rapidly. • The forward voltage at the point C is approximately equal to the built-involtage. • At zero-bias condition, the reverse current is strongly diminished. • If the reverse-bias voltage is increased, a very small reverse current is seen. • The reverse current increases rapidly, when only the applied voltage accedes a certain value called breakdown voltage (𝑉𝑅 ). ممنوع تداولها في مكاتب االستنساخ Fig. 3.11. 𝑰 − 𝑽 Characteristics of an ideal 𝒑𝒏-junction diode. 11 Electronics I Dr. Emad Aljaberi Department of Physics College of Science Fall Semester 2022/2023 Circuit Analysis of a PN Junction Diode When we need to analyze a PN-junction, it would be better to represent it as an ideal diode with parasitic elements depending on the biasing polarity. • when a diode is biased with a forward voltage, it is described as an ideal diode connected serially with a forward diode resistance 𝑟𝑑 . 𝐼𝑓 , passes through 𝑟𝑑 which is connected to a built-in-voltage source. • In reverse bias: an ideal reverse-biased diode connected to a reverse resistance 𝑟𝑅 with flowing a reverse current, 𝐼𝑅 , through the circuit. ممنوع تداولها في مكاتب االستنساخ • Fig. 3.13. Equivalent circuit of a practical PN-junction diode, (a) forward-biased diode and (b) reverse-biased diode. Quality Factor a PN Junction Diode • This may indicate to the deviation of a practical diode from the ideal behavior of a diode. • By measuring the dark I − V characteristics, the ideality factor can be extracted. • Shockley equation can be written in terms of ideality factor, n, by 12 Electronics I Dr. Emad Aljaberi Department of Physics College of Science 𝐼 = 𝐼𝑠 [𝑒𝑥𝑝 ( Fall Semester 2022/2023 𝑞𝑉 ) − 1] 𝑛𝐾𝐵 𝑇 If V ≥ 3qK B T , the equation reduces to 𝐼 ≊ 𝐼𝑠 𝑒𝑥𝑝 ( 𝑞𝑉 𝑛𝐾𝐵 𝑇 ), in terms of natural log 𝐿𝑛(𝐼 ) = 𝐿𝑛 (𝐼𝑠 ) + ( 𝑞 )𝑉 𝑛𝐾𝐵 𝑇 𝐿𝑛(𝐼) against 𝑉 gives the slope of the curve that is equal to 𝑞 ⁄𝑛𝐾𝐵 𝑇, and the intercept gives 𝐿𝑛 (𝐼𝑠 ). • The ideal value of 𝑛 =1. • The ideality factor is a powerful tool for the characterization of a diode. • The ideality factor ≠ 1 indicates that either recombination mechanisms occur. • In a practical diode such behavior departs slightly from the ideality because of participation of other parasitic such as the resistance of the PN junction. • In semi-log 𝐼 − 𝑉 characteristics of a practical diode: three distinct regions in the forward bias: ممنوع تداولها في مكاتب االستنساخ Fig. 3.12. Semi log 𝑰 − 𝑽 Characteristics of a practical PN-junction diode. Two regions in the forward bias can be seen: (a) low linear region and (b) exponential 13 Electronics I Dr. Emad Aljaberi Department of Physics College of Science Fall Semester 2022/2023 region. (b) Semi log 𝑰 − 𝑽 Characteristics of a practical PN-junction diode demonstrating the reverse-saturation current. Series and Dynamic Resistances • Series resistance, 𝑅𝑆 , is one of the significant parasitic causes a difference between real and ideal diodes. • The series resistance reduces the voltage across the junction with amount of 𝐼𝑅𝑆 . • The resistance is given by 𝑅𝑆 = 𝑉2 − 𝑉1 𝐼𝐹 The dynamic diode resistance is given in terms of the reciprocal of the dynamic diode conductance by 1 ) 𝑑𝐼/𝑑𝑉 𝑉=𝑐𝑜𝑛𝑠 ممنوع تداولها في مكاتب االستنساخ 𝑟𝑑 = ( 𝑑𝐼 𝑑 𝑉 = 𝐼𝑠 𝑒𝑥𝑝 ( ) 𝑑𝑉 𝑑𝑉 𝑉𝑇 𝑑𝐼 𝐼𝑠 𝑉 = 𝑒𝑥𝑝 ( ) 𝑑𝑉 𝑉𝑇 𝑉𝑇 𝑑𝐼 𝐼 = 𝑑𝑉 𝑉𝑇 𝑟𝑑 = 1 𝐼 ⁄𝑉𝑇 𝑟𝑑 = 𝑉𝑇 𝐼 14 Electronics I Dr. Emad Aljaberi Department of Physics College of Science Fall Semester 2022/2023 Examples (1) A rod of intrinsic silicon of a length of 2 cm, a diameter of 0.5mm, motilities 𝜇𝑒 = 0.12 𝑚2 ⁄𝑉. 𝑠 and 𝜇ℎ = 0.06 𝑚2 ⁄𝑉. 𝑠 . Calculate the conductivity 𝜎 of the silicon. (𝑛𝑖 = 1.5 × 1010 𝑐𝑚−3 ). Ans. 𝜎 = 𝑛𝑖 (𝜇𝑒 + 𝜇ℎ) 𝑞 = 1.5 × 1010 𝑐𝑚−3 (1200 𝑐𝑚2 ⁄𝑉. 𝑠 + 600 𝑚2 ⁄𝑉. 𝑠 ) × 1.6 × 10−19 𝑐𝑜𝑙 = 4.32 × 10−4 𝑆/𝑚 (2) A 𝑃+ 𝑁 junction has 𝑁𝐴 = 1020 𝑐𝑚−3 and 𝑁𝐷 = 1017 𝑐𝑚−3 . What is (a) builtin-potential, (b) depletion region width, (c) 𝑥𝑛 , and (d) 𝑥𝑝 ? (𝑛𝑖 = 1.5 × 1010 𝑐𝑚−3 ). Ans. 𝑉𝑏 = 𝐾𝐵 𝑇 𝑁𝐷 𝑁𝐴 𝑙𝑛 ( 2 ) 𝑞 𝑛𝑖 1.38 × 10−23 𝐽⁄𝐾 × 300 𝐾 1017 × 1020 𝑐𝑚−3 𝑉𝑏 = 𝑙𝑛 ( ) 1.6 × 10−19 𝑐𝑜𝑙 2.25 × 1020 𝑐𝑚−3 𝑉𝑏 = 0.99 𝑉 𝑁𝐴 ≫ 𝑁𝐷 Thus 𝑁𝐴 + 𝑁𝐷 1 ≅ 𝑁𝐴 𝑁𝐷 𝑁𝐷 15 Electronics I Dr. Emad Aljaberi Department of Physics College of Science 𝑤 ≅√ = Fall Semester 2022/2023 2𝜀𝑠 𝑉𝑏 𝑞𝑁𝐷 𝐹 × 0.99𝑉 𝑐𝑚 1.6 × 10−19 𝑐𝑜𝑙 × 1017 𝑐𝑚−3 −14 √2 × 12 × 8.85 × 10 = 114 𝑛𝑚 Since 𝑁𝐴 ≫ 𝑁𝐷 , the entire depletion layer exists on the N-side 𝑥𝑛 , which is approximately equal to 𝑤. 𝑥𝑝 = 𝑥𝑛 𝑁𝐷 𝑁𝐴 𝑥𝑝 = 𝑥𝑛 𝑁𝐷 𝑁𝐴 114 × 10−7 𝑐𝑚 × 1017 𝑐𝑚−3 𝑥𝑝 = 1020 𝑐𝑚−3 𝑥𝑝 = 11.46 × 10−10 𝑐𝑚 𝑥𝑝 = 0.1146 𝑛𝑚 16
