Semiconductor Theory Notes PDF

# Semiconductor Theory ## Semiconductor Theory * Semiconductor theory is based on energy band diagrams. * In an atom, inner energy levels are less energized and outer energy levels are more energized. ### Insulators * Conduction band (CB): 6-7 eV * Forbidden gap * Valence Band (VB) ### Semicon...

# Semiconductor Theory ## Semiconductor Theory * Semiconductor theory is based on energy band diagrams. * In an atom, inner energy levels are less energized and outer energy levels are more energized. ### Insulators * Conduction band (CB): 6-7 eV * Forbidden gap * Valence Band (VB) ### Semiconductors * Conduction band (CB): 0.1-2 eV * Valence band (VB) * Examples: Si, Ge ### Conductors * There is overlapping of CB and VB. * Examples: Al, Cu, Si ## Properties of Semiconductors * We can control the conductivity of semiconductors. * In case of intrinsic (pure) semiconductors, whenever electrons form, there will be the formation of holes. These all are temperature dependent. * Free electrons: n_i - Intrinsic carrier concentration * p holes: p_i - Intrinsic carrier concentration * Electron concentration is the same as hole concentration: n_i = p_i ## Extrinsic Semiconductors * **n-type semiconductors (extrinsic)**: * n-type semiconductor has a donor impurity concentration (N_D). * Donor impurity concentration is greater than hole concentration (n > p). * The majority carrier is the electron, and the minority carrier is the hole. * The concentration of majority carriers depends on doping. * **p-type semiconductors (extrinsic)**: * p-type semiconductors have an acceptor impurity concentration (N_A). * Acceptor impurity concentration is greater than electron concentration (p > n). * The majority carrier is the hole, and the minority carrier is the electron * **Mass action law:** n_i²= np. This law holds true for both intrinsic semiconductors and extrinsic semiconductors. ## Conduction of Current in Semiconductors * **Drift velocity:** * Whenever an external electric field is applied to a semiconductor, the charge carriers constitute a current called as drift current. * Under a steady state condition, each charge carrier attains a velocity called as drift velocity, which is proportional to the applied electric field. * Velocity equation: V = μE, where μ- mobility * μ_h = mobility of hole * μ_e= mobility of electron * μ_e> μ_h * Mobility unit: m²/Vs. * **Let's consider:** N number of electrons move across length l in time t. * **Drift current:** I = dq/dt = Nq/τ. * **Drift velocity:** vd = l/τ = I/Nq = V/L = I/nqA (Ampere (A)). * **Current density** J = I/A = nqv * **J = nqv = nμE = σE** (σ- conductivity) ## Resistivity * Resistivity: ρ = 1/ σ = (ohm.m) ## Case of Intrinsic Semiconductors * Conductivity of intrinsic semiconductors: σ_i = σ_n + σ_p * Since n=p in intrinsic semiconductors: σ_i = nqμ_n + pqμ_p. * Therefore, σ_i = (nqμ_n + pqμ_p). E. ## Case of Extrinsic Semiconductors * **n-type:** * J = J_n + J_p= ngμ_nE + pqμ_pE. * As n >> p. * J ≈ J_n. * J = nqμ_nE. * The majority concentration is equal to the donor concentration: n = N_D. * Applying mass action law: p = n_i²/N_D. * Current density: J = N_Dqμ_nE. * **p-type:** * J = J_n + J_p = ngμ_nE + pqμ_pE. * As p >> n. * J ≈ J_p. * J = pqμ_pE. * The majority concentration is equal to the acceptor concentration: p = N_A. * Applying mass action law: n = n_i²/N_A. * Current density: J = N_Aqμ_pE. ## Majority and Minority Carrier Concentration * **At room temperature:** * **Germanium:** μ_n = 3800, μ_p = 1800, n_i = 2.5 x 10¹³. * **Silicon:** μ_n = 1300, μ_p = 500, n_i = 1.5 x 10¹⁰. ## Example: * Calculate the conductivity of intrinsic Silicon at room temperature and find current density with applied electric field of 10 V/cm. To this intrinsic Silicon, if a donor impurity of 10¹⁸/cm³ is added, what will be the conductivity and current density when the electric field is 10 V/cm? 1. **Intrinsic Silicon:** * n_i = p_i = 1.5 x 10¹⁰/cm³ * σ_i = n_i qμ_n + p_iqμ_p * σ_i = 1.5 x 10¹⁰ x 1.6 x 10^-19 x 1300 + 1.5 x 10¹⁰ x 1.6 x 10^-19 x 500 * σ_i = 208 + 80 = 288 * ρ_i = 1/σ_i = 1/288 * ρ_i = 3.12 x 10^-6 * J_i = σ_i E = 4.32 x 10^-5 A / m². 2. **Extrinsic Silicon:** * n = N_D = 10¹⁸/cm³ * σ = ngμ_n + pqμ_p. * σ = 10¹⁸ x 1.6 x 10^-19 x 1300 + 10¹⁰ x 1.6 x 10^-19 x 500 * σ = 2080 * J = σE = 2.08 x 10³ A/ m². ## P-N Junctions * A p-n junction is a semiconductor device consisting of an n-type semiconductor joined to a p-type semiconductor. The p-side is positively charged, while the n-side is negatively charged. The junction has a depletion region with an electric field pointing from n-side to p-side. * **Carrier concentration:** * **Abrupt junction:** The depletion region is narrow and the carrier concentration on either side is high. * **Graded junction:** The depletion region is wide and the concentration changes gradually on both sides. * **Depletion region width:** * The depletion region width depends on the doping concentration on both sides and the intrinsic carrier concentration. The higher the donor impurity concentration, the narrower the depletion region width on the n-side and vice versa. * **Barrier potential:** * It is the potential difference across the depletion region. * For a p-n junction, there is a built-in potential barrier that prevents the majority carriers from freely crossing the junction. * The barrier potential is given by: V₀ = VTln(N_AN_D/n_i²) * V_T = k_BT/q = Thermal voltage or volt equivalent of temperature. * T is the temperature in Kelvin: k_B = 1.38 x 10^-23 J/K, the Boltzmann constant. * q = 1.6 x 10^-19 C, the charge of an electron. * V_T = 26 mV at room temperature. * **Factors affecting the barrier potential:** * **Temperature:** As the temperature increases, the barrier potential decreases. * **Doping concentration:** The higher the doping concentration on either side of the junction, the higher the barrier potential. * **Material:** The barrier potential depends on the material of the semiconductor. ## Diode * **Diode:** A diode is a two-terminal semiconductor device that allows current to flow in only one direction. It is known as a rectifier because it can convert alternating current (AC) to direct current (DC). * **Diode characteristics:** The diode characteristics are shown in the figure. The voltage in the figure is measured across the diode. The current is measured through the circuit containing the diode. * **Forward bias:** The diode is forward biased when the positive terminal of the battery is connected to the p-type semiconductor and the negative terminal is connected to the n-type semiconductor. * The diode conducts and current flows in the forward direction. * The current is represented by I_F. * **Reverse bias:** A diode is reverse biased when the positive terminal of the battery is connected to the n-type terminal, and the negative terminal is connected to the p-type terminal. * The diode stops conducting, and there is very little current flow in the reverse direction. * The current is represented by I_R. * **Cutin voltage:** The minimum forward voltage at which the diode begins to conduct current. * **Reverse saturation current:** The small reverse current that flows in the reverse biased condition. * **Breakdown voltage:** The reverse voltage at which the diode stops conducting. When the reverse bias voltage reaches a certain value, the diode breaks down. * **Shockley diode equation:** * This equation relates the current through a diode to the voltage across it: I = I₀(e^V/V_T - 1) * I₀ is the reverse saturation current * V is the voltage across the diode. * V_T = kT/q = thermal voltage * The Shockley diode equation is valid only for forward biased diodes. ## Diode Resistance * **Static resistance:** This is the ratio of the voltage across the diode to the current flowing through it. * R = V/I * **Dynamic resistance:** This is the ratio of a small change in voltage across the diode to the corresponding small change in current through it. * r = ΔV/ΔI = nV_T/I₀e^V/V_T. * The dynamic resistance is a function of the applied voltage. * The dynamic resistance is typically much lower than the static resistance, especially in the forward bias region. ## Diode Applications * **Rectifier:** A diode can convert an alternating current (AC) signal into a direct current (DC) signal by allowing current to flow in one direction only. This is called rectification. * **Voltage clamp:** A diode can be used to limit the voltage across a circuit to a certain level. * **Switching:** A diode can be used as a switch by changing its bias. When the diode is forward biased, it is 'on' and allows current to flow. When the diode is reverse biased, it is 'off' and blocks the current flow. ## Bipolar Junction Transistor (BJT) * A bipolar junction transistor (BJT) is a three-terminal semiconductor device that amplifies or switches electronic signals. It has three regions: emitter, base, and collector. The emitter region is heavily doped, followed by the base, and finally the collector. The base is lightly doped. * The three regions of the transistor are connected by two p-n junctions. * **Operation of BJT:** * **Emitter junction:** The emitter junction is forward biased to allow majority charge carriers to be injected into the base region. * **Collector junction:** The collector junction is reverse biased, which creates a strong electric field between the base and collector. When a forward-biased emitter injects holes (or electrons) into the base, those holes (or electrons) are pulled across the collector junction by this electric field. This constitutes the collector current I_C. * **Types of BJT:** * **NPN transistor:** The emitter, base, and collector regions of an NPN transistor are n-type, p-type, and n-type, respectively. * **PNP transistor:** The emitter, base, and collector regions of a PNP transistor are p-type, n-type, and p-type, respectively. * **Current gain:** * **α = I_C/ I_E:** The common base current gain, which is the ratio of the collector current to the emitter current. * **β = I_C/ I_B:** The common emitter current gain, which is the ratio of the collector current to the base current. ## BJT Configuration * The BJT can be configured in three different ways: * **Common base configuration (CB):** The input signal is applied to the emitter, the output is taken from the collector, and the base is common to both. * **Common emitter configuration (CE):** The input signal is applied to the base, the output is taken from the collector, and the emitter is common to both. * **Common collector configuration (CC):** The input signal is applied to the base, the output is taken from the emitter, and the collector is common to both. * **Characteristics of different configurations:** * **CB Configuration:** * Input resistance: Very low. * Output resistance: High. * Current gain: Less than 1 (α < 1). * Voltage gain: High. * Application: Amplifiers with good frequency response. * **CE configuration:** * Input resistance: Medium. * Output Resistance: High. * Current gain: High (β > 1). * Voltage gain: High. * Application: General-purpose amplifiers used in audio and RF applications. * **CC configuration:** * Input resistance: High. * Output resistance: Low. * Current gain: Approximately 1. * Voltage gain: Less than 1. * Application: Buffer amplifiers, impedance matching, and voltage followers. * **h-parameter model:** * The h-parameter model is a small-signal model most commonly used for electronic transistors. It uses four parameters to represent the behavior of the transistor in the linear region of operation. The parameters are hie, hfe, hre, and hoe. * A detailed description of the h-parameters is explained in detail later. ## BJT as an Amplifier * **Why BJT is an amplifier?** * The BJT is characterized by a large current gain (β >> 1). This means that a small change in the base current induces a large change in the collector current, resulting in amplification. * **Operating point of transistor:** * The operating point or quiescent point (Q-point) is the DC bias point of a transistor amplifier which is the value of collector current and collector to emitter voltage when no signal is applied. * **Factors affecting operating point:** * **Temperature:** The operating point of a BJT *changes with temperature change*. This because of change in Ic with temperature. * **Doping concentration:** The operating point *changes with doping concentration* change in semiconductors. * **Early effect:** The early effect is the tendency of the collector current, IC, to increase with increasing collector-emitter voltage, VCE. * The early affect is a result of the widening of the depletion region, reducing the effective base width as VCE increases. * **Bias circuits:** * **Fixed bias:** The fixed bias circuit uses a single resistor to bias the base of a transistor. It is simple to implement but has poor stability. * **Voltage divider bias:** The voltage divider bias circuit uses a voltage divider network to bias the base. It has better stability than the fixed bias circuit. * **Collector feedback bias:** The collector feedback bias circuit provides feedback from the collector to the base. It has good stability but can be more complex to implement. * **Stability factor:** * The stability factor (S) is a measure of how sensitive the operating point of a transistor amplifier is to changes in temperature or other parameters. * The stability factor is defined as: S = (ΔI_C / ΔI_B) * A lower stability factor indicates a more stable operating point. * **Common base configuration output characteristic:** * In the common base configuration of a BJT, the output characteristic is a plot of the collector current (I_C) against the collector-emitter voltage (V_CE) for a constant base current (I_B). * **Common emitter configuration output characteristic:** * The common emitter output characteristic is a plot of the collector current (I_C) against the collector-emitter voltage (V_CE) for a constant base current (I_B). * **Common collector configuration output characteristic:** * In the common collector configuration of a BJT, the output characteristic is a plot of the collector current (I_C) against the collector-emitter voltage (V_CE) for a constant base current (I_B). * **Advantages of BJT:** * High current gain. * High power handling capability. * Wide availability and low cost. * **Disadvantages of BJT:** * Can be temperature sensitive. * Can be complex to design. ## Field Effect Transistor (FET) * **What is a FET?** * A field-effect transistor (FET) is a three-terminal semiconductor device that controls the flow of current between a source and drain terminal by varying the electric field in a region called the channel. * **Types of FETs:** * **Junction Field-Effect Transistor (JFET):** * It utilizes a PN junction to control the resistance of a channel. * The channel is a region of a given conductivity type. * **Metal Oxide Semiconductor Field-Effect Transistor (MOSFET):** * It uses an insulating layer of silicon dioxide (SiO₂) between the gate and the channel to control the channel resistance. * The gate does not directly touch the channel. * **Operation of JFET:** * The gate is reverse biased, which creates a depletion region in the channel. * **Depletion mode JFET:** In a depletion mode JFET, the channel is initially conductive, and the gate voltage is used to reduce the channel conductance by widening the depletion region. * **Enhancement mode JFET:** In an enhancement mode JFET, the channel is initially non-conductive, and the gate voltage is used to create the channel by attracting charge carriers to the channel. * **Operation of MOSFET:** * The gate is control voltage which is used for creating or eliminating the channel depending on the mode of operation. * **Depletion mode MOSFET:** It uses a negative gate voltage to pinch-off the channel. * **Enhancement mode MOSFET:** It uses a positive gate voltage to create the channel. * **Characteristics of MOSFET:** * The threshold voltage (V_th) is the minimum gate voltage required to turn on the MOSFET. The V_th is positive for an enhancement-mode MOSFET and negative for a depletion-mode MOSFET. * The trans-conductance (g_m) is the change in drain current (I_D) divided by the change in gate voltage (V_GS). * The output resistance (r_o) is the resistance between the drain and the source terminals. * **MOSFET applications:** * **Amplifiers:** MOSFETs are widely used in amplifiers because of their high input impedance, low noise, and high gain. * **Switches:** MOSFETs can act as switches in digital circuits. * **Memory cells:** MOSFETs are the basic building blocks of dynamic random access memory (DRAM) chips. * **Logic gates:** MOSFETs form the core of digital logic circuits used in computers, microprocessors, and other electronic devices. * **Advantages of MOSFET:** * High input impedance. * Low noise. * High gain. * Wide range of applications. * **Disadvantages of MOSFET:** * Can sometimes be more complex to design and implement. * Can be more sensitive to electrostatic discharge or ESD. ## h-Parameters * The h-parameters are used to represent the small-signal behavior of linear two-port networks, like transistors. They are used to determine the input and output impedance, voltage gain, and current gain of a transistor. * **Four h-parameters are used:** * **h_ie:** Input impedance: Ratio of input voltage to input current, with output shorted. * **h_fe:** Forward current gain: Ratio of output current to input current, with output shorted. * **h_re:** Reverse voltage gain: Ratio of output voltage to input voltage, with output opened. * **h_oe:** Output admittance: Ratio of output current to output voltage, with input opened. ## Amplifier Design using h-Parameters * **Amplifier design using h-parameters:** * **Voltage gain:** A_V = - h_feR_L/(1+h_oeR_L). * **Input impedance:** R_i = h_ie+ h_reR_L. * **Output impedance:** R_o = 1/h_oe. ## Common Base Amplifier * **Common base amplifier:** It is a type of amplifier that has the base terminal common to both the input and output circuits. The signal is applied to the emitter, and the output is taken from the collector. * **Common base amplifier characteristics:** * High input impedance. * High output impedance. * High voltage gain. * Lower current gain. * Excellent frequency response for high-frequency applications. * Primarily used for matching input and output impedances. ## Common Emitter Amplifier * **Common emitter amplifier:** It is a type of amplifier that has the emitter terminal common to both the input and output circuits. The signal is applied to the base, and the output is taken from the collector. * **Common emitter amplifier characteristics:** * Medium input impedance. * High output impedance. * High current gain. * High voltage gain. * Widely used in a vast range of applications, including audio and RF amplifiers. ## Common Collector Amplifier * **Common collector amplifier:** The emitter follower uses the collector terminal common to both the input and output circuits. The signal is applied to the base, and the output is taken from the emitter. * **Common collector amplifier characteristics:** * High input impedance. * Low output impedance. * Current gain is approximately 1. * Voltage gain less than 1. * Primarily used as a buffer or impedance matching device. It is important to remember that these are just some of the basic concepts and types of transistors. There are many other aspects of transistor theory and applications that are not covered here. However, understanding these basic principles is essential for understanding how transistors work and for designing and building circuits that use them.