Lecture 2 Semiconductor Physics Sunday 4/10/2015 Semiconductor Physics 1-1
Outline Intrinsic bond model: electrons and holes Charge carrier generation and recombination Intrinsic semiconductor Doping: Extrinsic semiconductor Charge Neutrality Introduction to Charge Carrier Transport Semiconductor Physics 1-2
Test Yourself 1. Can you differentiate between: Semiconductors Conductors Insulators 2. What is the difference between charge carriers and free charge carriers? Semiconductor Physics 1-3
Semiconductor Materials Three most used semiconductors: carbon (C), silicon (Si) and germanium (Ge) Carbon Silicon Germanium Semiconductor Physics 1-4
Silicon (most common semiconductor material) Bond Model Si in Column IV of the periodic table Electronic structure of silicon atom: 10 core electrons (tightly bound) 4 valence electrons (loosely bound, responsible for most of the chemical properties Other semiconductors: Single crystal: Ge, C (diamond form) Compound: GaAs, InP, InGaAs, InGaAsP, ZnSe, CdTe (on the average, 4 valence electrons per atom) Semiconductor Physics 1-5
Silicon crystal structure Diamond lattice: atoms tetrahedrally bonded by sharing valence electrons covalent bonding Each atom shares 4 electrons low energy situation Si atomic density: 5 x 10 22 atoms/cm 3 Semiconductor Physics 1-6
Simple flattened model of Si crystal At 0 o K: All bonds are satisfied (all valence electrons engaged in bonding) No free electrons (or holes) This bonding of atoms, strengthened by the sharing of electrons, is called covalent bonding Molecules or ions tend to be most stable when the outermost electron shells of their constituent atoms contain eight electrons Semiconductor Physics 1-7
Creation of electron-hole pair At room temperature (default 27 o C or 300 o K), approximately 1.5X 10 10 free carriers in 1 cm 3 of intrinsic silicon material Intrinsic semiconductor material means material has been refined to a very low level of impurities. Semiconductor Physics 1-8
Creation of electron-hole pair Electron-hole pairs in a silicon crystal. Free electrons are being generated continuously while some recombine with holes Electrons and holes in semiconductors are fuzzier : they span many atomic sites At finite temperature, some bonds are broken free electrons Mobile negative charge -1.6 x 10-19 C free holes Mobile positive charge, +1.6 x 10-19 C Semiconductor Physics 1-9
Definitions electron means free electron Not concerned with bonding electrons or core electrons Define: n (free) electron concentration [cm -3 ] p hole concentration [cm -3 ] Law of Mass Action (at thermal equilibrium) n 2 n. i Where n i intrinsic carrier concentration [cm 3 ] p Semiconductor Physics 1-10
Generation and Recombination Generation: break-up of covalent bond to form electron and hole pairs In an intrinsic semiconductor the number of holes is equal to the number of free electrons Generate new hole-electron pairs per unit volume per second requires energy from thermal or optical sources Generation rate: G = G(th) + G opt +. [cm 3. s 1 ] Recombination: formation of covalent bond by bringing together electron and hole Releases energy in thermal or optical form Recombination rate R [cm 3. s 1 ] 1 recombination event requires 1 electron + 1 hole On an average, a hole (an electron) will exist for ζ p (ζ n ) seconds before recombination. This time is called the mean lifetime of the hole (electron) Semiconductor Physics 1-11
Intrinsic Semiconductors Thermal Equilibrium where Steady state plus absence of external energy sources With increasing temperature, the density of holeelectron pairs (free charge carriers) increases in an intrinsic semiconductor. n 2 i AT 3 e E kt n i intrinsic carrier concentration [cm 3 ] E G0 is the energy gap (the energy required to break a covalent bond) at 0 o K k is the Boltzmann constant in electron volts per degree kelvin (J/K) [k = 1.38x10-23 J/K] A is a material-dependent constant independent of T Semiconductor Physics 1-12 G 0
Intrinsic Semiconductors In Si at 300 o K ( room temperature ): ni 1x10 10 cm -3 In a sufficiently pure Si wafer at 300 o K ( intrinsic semiconductor): n = p = n i 1 10 10 cm 3 n i is a very strong function of temperature T n i Semiconductor Physics 1-13
Effect of Temperature on Conductivity Conductor increase resistance with increase in heat ( number of carrier do not increase) have a positive temperature coefficient w.r.t. resistance Semiconductor increase conductivity with increase in heat ( number of carrier increase) have a negative temperature coefficient w.r.t. resistance Semiconductor Physics 1-14
Controlling the properties of a Semiconductor Doping = engineered introduction of foreign atoms to modify semiconductor electrical properties Doping is the process of deliberately adding impurities to the crystal during manufacturing and increases the number of current carries (electrons or holes) Impurities (extraneous elements) Doping process create n-type and p-type of semiconductors A semiconductor material that has been subjected to the doping process is called an extrinsic material Semiconductor Physics 1-15
Doping Silicon: 4 valence electrons Each Si atom bonds to four others Replace some Si atoms with atoms that do not have four valence electrons These atoms will have: - an extra electron (group V) Donors - an extra hole (group III) Acceptors Doping increases the number of carriers Semiconductor Physics 1-16
Donors Introduce electrons to semiconductors (but not holes) For Si, group V elements (dopants) with 5 valence electrons (Arsenic As, phosphorus P, antimony Sb ) Semiconductor Physics 1-17
Donors Four of five electrons participate in bonding The 5 th electron easy to release at room temperature, each donor releases 1 electron that is available for conduction Donor site become positively charged (fixed charge) Define: N d donor concentration [cm -3 ] If N d << n i doping is irrelevant Intrinsic semiconductor n = p = n i If N d >> n i, doping controls carrier concentration Extrinsic semiconductor n = N d and p = n i2 / N d Note: n >> p : n-type semiconductor In general: N d 10 15 10 20 cm -3 Semiconductor Physics 1-18
Acceptors Introduce holes to semiconductors (but not electrons) For Si, group III elements with 3 valence electrons (usually Boron(B), Gallium (Ga) and Indium (In)) Semiconductor Physics 1-19
Acceptors Three electrons participate in bonding One bonding site unsatisfied making it easy to accept neighboring bonding electron to complete all bonds at room temperature, each acceptor releases hole that is available for conduction Acceptor site becomes negatively charged (fixed charge) Semiconductor Physics 1-20
Acceptors Define: Na acceptor concentration [cm -3 ] If N a << n i doping is irrelevant Intrinsic semiconductor n = p = n i If N a >> n i, doping controls carrier concentration Extrinsic semiconductor p = N a and n = n i2 / N a Note: p >> n : p-type semiconductor In general: N a 10 15 10 20 cm -3 Semiconductor Physics 1-21
Summary of Charge Carriers Semiconductor Physics 1-22
Majority and Minority Carriers n-type material, the electron is called majority carrier and hole the minority carrier p-type material, the hole is called majority carrier and electron the minority carrier Semiconductor Physics 1-23
Charge Neutrality The semiconductor remains charge neutral even when it has been doped Overall charge neutrality must be satisfied In general: the net charge density ρ (C/cm 3 ) in a + semiconductor = ρ = q (p n + N d N a ) Where q: electric (elementary) charge = 1.6 Х 10-19 C Semiconductor Physics 1-24
Charge Neutrality Example Let us examine this for: N d = 10 17 cm -3, Na = 0 Then, n = N d = 10 17 cm 3, p = n i2 /N d = 10 3 cm 3 Using the equation ρ = q (p n + N d N a ), we find that ρ 0!! What is wrong?? Semiconductor Physics 1-25
Charge Neutrality Nothing wrong! We just made the approximation when we assumed that n = N d We should really solve the following system of equations (for N a =0): p n + N d = 0 n.p = n i 2 n 2 - n. N d - n i 2 = 0 n N d Semiconductor Physics 1-26
Charge Carrier Transport Any motion of free carriers in a semiconductor leads to a current Different causes for having motion Associated random motion due to the thermal energy (Thermal Motion) Motion can be caused by an electric field due to an externally applied voltage (Carrier Drift) Motion from regions where the carrier density is high to regions where the carrier density is low (Carrier Diffusion) Semiconductor Physics 1-27
Thermal Motion In thermal equilibrium, carriers are not sitting still: Undergo collisions with vibrating Si atoms (Brownian motion) Electrostatically interact with each other and with ionized (charged) dopants Semiconductor Physics 1-28
Thermal Motion (cont d) Characteristic time constant of thermal motion mean free time between collisions T c Collison time (seconds) In between collisions, carriers acquire high velocity: v th thermal velocity (cm/second) Characteristic length of thermal motion: λ mean free path [cm] = v th T c Example: For Si at room temperature (27 o C or 300 o K), we have the following numbers T c 10 13 seconds, v th 10 7 cm/second λ 0.01 μm Carriers undergo many collisions as they travel through devices Semiconductor Physics 1-29
Lecture Summary Covered material Continue Semiconductor Materials Types of semiconductors Two types of carriers (mobile charge particles): electrons and holes Creation of electron-hole pairs Doping Donors n-type semiconductor material Acceptors p-type semiconductor material Important equations under thermal equilibrium conditions: (p n + N d N a = 0) and (n.p = n i2 ) Material to be covered next lecture Continue Semiconductor Physics Carrier Transport (Carrier Drift and Carrier Diffusion) pn junctions (or diodes) Basics Semiconductor Physics 1-30