Unit-III Semiconductor Physics 2024 PDF

UNIT-III SEMICONDUCTOR PHYSICS BY: DR. VANITA THAKUR 1  INTRODUCTION  Electrical conduction is one of the main property of solids. It has been believed that the valence electrons are responsible for the electrical conduction in metals.  An evidence for this was g...

UNIT-III SEMICONDUCTOR PHYSICS BY: DR. VANITA THAKUR 1  INTRODUCTION  Electrical conduction is one of the main property of solids. It has been believed that the valence electrons are responsible for the electrical conduction in metals.  An evidence for this was given by P. Drude in the form of free electron model. According to this model, the valence electrons become free in metals and move randomly within the metal in a same way as that of the molecules of a gas confined in a container.  This model is used to explain not only the electrical properties but also the thermal, optical and magnetic properties of the solids.  The free electron theory underwent successive modifications in order to explain the electrical behavior of the solids. 2 BY: DR. VANITA THAKUR  Band Theory of Solids  Band theory of solids was given by F. Bloch in 1928.  According to this theory, potential inside the crystal is considered to be PERIODIC i.e. the potential experienced by an electron in passing through the crystal lattice is periodic.  The P.E of an electron in the field of positive ion is negative, so force between them is attractive.  The potential is minimum at the positive ion sites and maximum in between the lattice ion positions.  This periodicity extends up to infinity in all the directions within the crystal. 3 BY: DR. VANITA THAKUR  Kronig-Penney Model- Introduction to Origin of Band Gaps in Solids  Kronig-Penney model tells us about the behavior of electrons in a periodic potential.  According to this model, the potential filed of an electron in a linear arrangement of positive ions consists of periodically arranged rectangular potential wells separated by potential barriers.  These potential wells are considered to be of zero potential and width ‘a’ and  the potential barriers are of height ‘Vo’ and width ‘b’. This arrangement can be summarized as:  Region I: 0 < x < a , called Potential well region  Region II: -b < x < 0, called Potential barrier region 4 BY: DR. VANITA THAKUR  K.P Model…. The Schrodinger Equations for the two regions are given as: 𝑑2 𝜓 2𝑚 + E𝜓=0 0 Ts, the Fermi level moves upward in a linear manner somehow. ✓ At T = Ti, intrinsic behavior is established. At further higher temperatures, the p-type semiconductor loses its extrinsic behavior and acts as an intrinsic semiconductor. Thus, the Fermi level approaches the intrinsic value. 𝐸𝑔 EFp = EFi = at T ≥ Ti 2 59 BY: DR. VANITA THAKUR Variation of Fermi Energy Level With Doping Concentration (N-Type) 60 BY: DR. VANITA THAKUR  Variation of Fermi Energy Level With Doping Concentration For n-type semiconductors At low impurity concentration, there are discrete donor energy levels. With an increase in the impurity concentration, donor level undergoes splitting and it results in the formation of formation of donor band below the conduction band. With further increase in impurity concentration the width of the donor band increases. At one point, donor band overlaps with the conduction band In the process the Fermi level also shifts upwards, closer to the conduction band (with increase in impurity concentration) and finally enters the conduction band. 61 With the widening of the donor band the width of forbidden gap decreases. BY: DR. VANITA THAKUR  Variation of Fermi Energy Level With Doping Concentration (P-Type) 62 BY: DR. VANITA THAKUR  Variation of Fermi Energy Level With Doping Concentration For p-type semiconductors At low impurity concentration, there are discrete acceptor energy levels. With the increase in the impurity concentration the acceptor atoms interact. As a result the acceptor level broadens and splits into the band. acceptor band gradually broadens with increasing doping concentration. At one point the acceptor band overlaps with the valence band In this process the Fermi level also shifts downwards and at higher doping concentration it enters the valence band. 63 With the widening of the acceptor band the width of forbidden gap decreases. BY: DR. VANITA THAKUR  HALL EFFECT  Hall Effect was discovered by Edwin Hall in 1879.  Hall Effect is a Galvano magnetic effect. When a metal or semiconductor carrying current is placed in a transverse magnetic field, a voltage is developed across the specimen in a direction perpendicular to both the current and the magnetic field. This phenomenon is called the Hall effect and voltage so developed is called the Hall voltage.  Consider a p-type semiconductor, carrying a current Ix in the x-direction. When a uniform magnetic field Bz is applied along the z-axis. Current through the wafer is given by I = peAvd 𝐼 Current density, Jx = = p e vd ___________(1) 𝐴 On the application of magnetic field, holes experience a deflection because of Lorentz force (FL), given by FL_____ = e (𝑣𝑑 x 𝐵) = e vd B sin 90o = e vd B ____ (2) The holes are deflected towards the lower surface and get accumulated there producing a net positive charge. Simultaneously, a net negative charge appears on the upper surface. This creates an upward electric field called Hall field (EH). Due to action of electric field EH, holes experience an electric force FE in addition to Lorentz force. FE = e EH ________(3)  When an equilibrium is reached, the magnetic deflecting force on the charge carriers are balanced by the electric forces due to electric Field. F =F E H e EH = e vd B 𝑉𝐻 If w = width of semiconductor wafer, EH = 𝑤 So, above relation becomes, 𝑉𝐻 e = e vd B 𝑤 𝑉𝐻 = vd B ______ (4) 𝑤 𝑱𝒙 From equation (1), vd= 𝒑𝒆 𝑉𝐻 𝐽𝑥 Equation (4) becomes = B 𝑤 𝑝𝑒 𝑤𝐵𝐽𝑥 𝑤𝐵𝐼 VH = = 𝑝𝑒 𝑝𝑒 𝐴 If t = thickness of Semiconductor wafer, A = wt 𝒘𝑩𝑱𝒙 𝑩𝑰 66 VH = = __ _____(5) 𝒑𝒆 𝒑𝒆 𝒕 BY: DR. VANITA THAKUR  Hall Coefficient (RH) is defined as Hall field per unit current density per unit magnetic induction. 𝑬𝑯 𝑽𝑯 /𝒘 Thus, RH = = 𝑱𝒙 𝑩 𝑱𝒙 𝑩 𝑉𝐻 Using relation (4) i.e. = vd B , we get 𝑤 vd B vd RH = = 𝐽𝑥 𝐵 𝐽𝑥 𝐽𝑥 From eqn. (1), vd = 𝑝𝑒 𝐽𝑥 1 1 RH = = 𝑝𝑒 𝐽𝑥 𝑝𝑒 1 RH = 𝑝𝑒 Using this value, eqn. (5) can be rewritten as BI RH t VH VH = or RH = 𝑩𝑰 𝒕 67 BY: DR. VANITA THAKUR  Drift Velocity Acc. to equilibrium condition, F E = FH e EH = e vd B V e H= e vd B 𝑤 𝑽𝑯 vd = 𝑩𝒘 Carrier Concentration 1 RH = 𝑝𝑒 𝟏 p= 𝑹𝑯 e −1 In case of conductors and n-type semiconductor, RH = 𝑛𝑒 −𝟏 n= 𝑹𝑯 e 68 where n is concentration of electrons BY: DR. VANITA THAKUR  Hall Mobility Mobility is defined as the drift velocty acquired in unit electric field. Since, J = p e vd Also 𝐽=𝜎𝐸 So, p e vd = 𝜎 𝐸 𝑣𝑑 𝜎 = 𝐸 𝑝𝑒 μ h= R H 𝝈 69 BY: DR. VANITA THAKUR  APPLICATIONS OF HALL EFFECT  Hall Effect is used to find whether a semiconductor is N-type or P-type.  Hall Effect is used to find carrier concentration.  Hall Effect is used to calculate the mobility of charge carriers (free electrons and holes).  Hall Effect is used to measure conductivity.  Hall Effect is used to measure a.c. power and the strength of magnetic field (RH α B) 70 BY: DR. VANITA THAKUR P-N JUNCTION FORMATION p-n junction = semiconductor in which impurity changes abruptly from p-type to n-type ; “diffusion” = movement due to difference in concentration, from higher to lower concentration; in absence of electric field across the junction, holes “diffuse” towards and across boundary into n-type and capture electrons; electrons diffuse across boundary, fall into holes (“recombination of majority carriers”);  formation of a “depletion region” Depletion region is the region without free-charge carriers. charged ions are left behind (cannot move): negative ions left on p-side  net negative charge on p-side of the junction; positive ions left on n-side  net positive charge on n-side of the junction  electric field builds up across the junction which prevents further diffusion. Formation of depletion region in pn-junction: The diode current Equation: I =I0 [eqV/nkT – 1] pn Junction – built-in potential barrier No applied voltage across pn-junction The junction is in thermal equilibrium —the Fermi energy level is constant throughout the entire system. ▪ Electrons in the conduction band of the n region see a potential barrier in trying to move into the conduction band of the p region. This potential barrier is referred to as the built-in potential barrier and is denoted by Vbi (or V0). ▪ The potential Vbi maintains equilibrium, so no current is produced by this voltage. “biased p-n junction”, i.e. p-n junction with voltage applied across it “forward biased”: p-side more positive than n-side; “reverse biased”: n-side more positive than p-side; Forward Biased Diode: the direction of the electric field is from p-side towards n-side  holes in p-side are pushed towards and across the p-n boundary, Electrons in n-side are pushed towards and across n-p boundary  current flows across p-n boundary Forward biased pn-junction Depletion region and potential barrier are reduced Energy band Diagram under Forward Biasing Reverse Biased Diode: applied voltage makes n-side more positive than p-side  electric field direction is from n-side towards p-side  pushes charge carriers away from the p-n boundary  depletion region widens, and no current flows Reverse biased pn-junction Depletion region becomes wider, barrier potential becomes higher  The electrostatic potential barrier at the junction is lowered by a forward bias Vf from the equilibrium contact potential V0 to the smaller value V0-Vf. This lowering of the potential barrier occurs because a forward bias (p positive with respect to n) raises the electrostatic potential on the p side relative to the n side. For a reverse bias (V=-Vr ) the opposite occurs; the electrostatic potential of the p side is depressed relative to the n side, and the potential barrier at the junction becomes larger (V0 + Vr ).  Applications of semiconductor devices to computer architecture Semiconductors are the Brains of Modern Electronics. n- and p-type semiconductors are used to create transistors, small devices that are essential components in modern computers. When a small electrical current is input through a transistor’s ‘gate’, the device outputs a large current. The effect acts as both an amplifier and an electrical switch. Semiconductors are very special materials that allow you to create binary switches called transistors and are the basis of all digital computing, memory and storage from the simplest electronic to massive supercomputers. These semiconductor-based devices are crucial to microchip manufacturing, from processors to memory cards.  Memory Chips: From the perspective of functionality, semiconductor memory chips store data and programs on computers and data storage devices. Random-access memory (RAM) chips provide temporary workspaces, whereas flash memory chips hold information permanently unless erased. Read-only memory (ROM) and programmable read-only memory (PROM) chips cannot be modified.  Microprocessors: Microprocessors contain one or more central processing units (CPUs). Computer servers, personal computers (PCs), tablets, and smartphones may each have multiple CPUs.  Graphic Processing Units (GPUs): Technically a type of microprocessor, Graphics Processing Unit (GPU) is capable of rendering graphics for display on an electronic device. The GPU was introduced to the wider market in 1999 and is best known for its use in providing the smooth graphics that consumers expect in modern videos and games.  Before the arrival of GPUs in the late 1990s, graphic rendering was handled by the Central Processing Unit (CPU).  Monitor: Alternatively referred to as a VDT (video display terminal) and VDU (video display unit), a monitor is an output device that displays video images and text. A monitor is made up of circuitry, a screen, a power supply, buttons to adjust screen settings, and casing 82 that holds all of these components. Like most early TVs, the first computer monitors were comprised of a CRT (cathode ray tube) and a fluorescent screen. Today, all monitors are created using flat-panel display technology, usually backlit with LEDs (light-emitting diode). That’s all!!!! Thank You… 83