BASIC ELECTRONICS Module 1 Introduction to Semiconductors Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Syllabus for module 1 Semiconductor Theory Energy bands Classification of materials based on energy bands Intrinsic semiconductor Covalent bonding Conduction in semiconductors Doping, Extrinsic semiconductor Conduction in extrinsic semiconductor Drift and Diffusion current Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Classification of materials Insulators, Semiconductors and Metals Insulator poor conductor of electricity Metal good conductor of electricity Semiconductor conductivity lies between above two Energy band diagram Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Classification of materials Diamond crystal (insulator) EG ≈ 6 eV (1 eV = 1.6 × 10 –19 J) Valence band is full, Conduction band is empty Even with applied electric field, energy will not be sufficient to put the electrons in the conduction band, crossing the forbidden gap Hence diamond is insulator Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Classification of materials Semiconductor Silicon : EG ≈ 1.21 eV at 0 K (1.1 eV at 300 K) Germanium : EG ≈ 0.79 eV at 0 K (0.67 eV at 300 K) At 0 K, valence band is full, conduction band is empty Si and Ge are insulators at 0 K Conductivity increases (or resistivity decreases) with increase in temperature Semiconductors possess negative temp coeff of resistance At room temp and above, Si and Ge are semiconductors i.e., some electrons are present in conduction band Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Classification of materials At room temperature, some valence electrons acquire thermal energy sufficient to cross the forbidden gap These electrons are now free to move under the influence of small electric field Now the material begins to conduct. Hence the name semiconductor When an electron leaves the valence band and enters conduction band, a vacancy called “hole” is created in valence band Parent atom now has less number of negatively charged electrons than positively charged protons – ionization Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Classification of materials Metal The valence band and conduction band overlap Even at 0 K, conduction band has electrons So metals are good conductors of electricity Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Intrinsic Semiconductors Semiconductors such as Si and Ge have 4 electrons (tetravalent) in the outermost shell In crystal structure of these materials, atoms are arranged in tetrahedron structure with one atom at each vertex Each atom contributes 4 valence electrons to the crystal; Each atom shares one electron each from its 4 neighbours, thus forming covalent bond Because of covalent bonding, electrons are tightly bound to crystal – not available for conduction Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Intrinsic Semiconductors Bond structure of Si and Ge at 0 K Si Si Si Covalent bond Si Si Si Valence electrons Si Si Si Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Intrinsic Semiconductors Bond structure of Si and Ge at 300 K Si Si Si Covalent bond Si Si Si Hole Valence electrons Free electron Si Si Si Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Intrinsic Semiconductors Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Intrinsic Semiconductors Free electrons are “free” to wander throughout the crystal Hole is the absence of an electron in the covalent bond In intrinsic semiconductor, each free electron gives rise to one hole. Concentration of holes and free electrons are same. Denoted as ni (called intrinsic charge concentration) Free electrons and holes are now available for conduction A hole may get filled up by another electron liberated from another covalent bond – effective movement of hole Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Intrinsic Semiconductors Hole effectively moves in opposite direction as that of free electron Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Conduction in semiconductors Both free electrons and holes contribute to current flow Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Conduction in semiconductors Let concentration of free electrons = n Let concentration of holes = p In intrinsic semiconductor, n = p = ni Current density = conductivity × electric field intensity J = σ E (Ohm’s law) Conductivity is given by: σ = n q μn + p q μp = ni q (μn + μp) μn is mobility of free electrons μp is mobility of holes (μn > μp) q is electronic charge = 1.6 × 10 –19 C Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Conduction in semiconductors Some properties at 300 K Ge Si Electron mobility μn (m2/V-s) 0.38 0.13 Hole mobility μp (m2/V-s) 0.18 0.05 Intrinsic Concentration ni (m–3) 2.5 × 1019 1.5 × 1016 Intrinsic resistivity (Ω-m) 0.45 2300 Concentration of atoms in crystal (cm–3) 4.4 × 1022 5.0 × 1022 Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Conduction in semiconductors Determine the conductivity and resistivity of pure germanium at 300 K. If the length of the Ge is 4 cm and cross section area is 1 cm2, then what is its resistance? If a potential difference of 5 V is applied between the two ends of semiconductor, what is the amount of current that flows? Resistivity ρ = 1/σ Resistance R = ρ L / A Repeat the above calculations with silicon. L I V Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Conduction in semiconductors Velocity of charge particle = mobility × electric field v = μE Free electron velocity is vn = μnE Hole velocity is vp = μpE What is the electron velocity and hole velocity in a bar of silicon at room temperature (300 K), when an electric field of 1800 V/m is applied across it? (Ans: 234, 90 m/s) A bar of intrinsic Ge, 6 cm long, has a potential difference of 12 V applied across its ends. If the electron velocity in the bar is 76 m/s, what is the electron mobility? (Ans: 0.38 m2/V-s) Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Conduction in semiconductors A bar of pure silicon at 300 K is applied with electric field of 500 V/m. Determine: Component of current density in bar due to free electrons Component of current density in bar due to holes Total current density in the bar (Ans: 156, 60, 216 mA/m2) A bar of silicon has cross sectional area of 3×10–4 m2. How long the bar should be in order that current in it be 1.2 mA, when 9 V is applied across its ends. (Ans: 0.972 mm) Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Conduction in semiconductors As noted from previous examples, conductivity is very low What is the reason for low conductivity? For silicon, ni = 1.5 × 1016 m–3 atom concentration in crystal is 5.0 × 1022 cm–3 = 5.0 × 1028 m–3 i.e., approximately 3 free electrons for every 1012 Si atoms !! For germanium, situation is only slightly better – approximately 2 free electrons for every 109 Ge atoms !! Concentration of free electrons, and thereby conductivity can be increased by a process called “Doping” Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Doping Addition of small percentage of foreign atoms into the crystal lattice of silicon or germanium in order to change its electrical properties is called Doping Atoms used for doping are called “dopants” Two types of dopants – Donors and Acceptors Donor – Pentavalent (5 electrons in outermost shell) Examples: Phosphorus (P), Arsenic (As), Antimony (Sb), and Bismuth (Bi) Donates one electron to the crystal lattice One free electron per donor atom Concentration of free electrons increases Concentration of holes decreases Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Doping N-type semiconductor Si Si Si Free electron Si P Si Si Si Si Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

N-type Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Doping Semiconductor doped with donor impurity is called N-type semiconductor, because free electrons are in majority than holes (thermally generated) Donor energy level is just below the conduction band Conduction band 0.05 eV (0.01 for Ge) Donor energy level 1.1 eV Valence band Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Doping Acceptor – Trivalent (3 electrons in outermost shell) Examples: Boron (B), Aluminum (Al), Gallium (Ga) and Indium (In) Accepts one electron from the crystal structure One hole per acceptor atom Concentration of holes increases Concentration of free electrons decreases Resulting semiconductor is called P-type semiconductor, because holes are in majority than free electrons (thermally generated) Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Doping P-type semiconductor Si Si Si Si B Si Hole Si Si Si Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Doping-p type Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Doping Acceptor energy level is just above the valence band Most valence electrons can easily jump (hop) into the hole even at lower temperatures Conduction band Acceptor energy level 1.1 eV 0.05 eV (0.01 for Ge) Valence band Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Charge densities In intrinsic (pure) semiconductor, concentration of free electrons is equal to concentration of holes (n = p = ni) In extrinsic N-type semiconductor, n >> p In extrinsic P-type semiconductor, p >> n Under thermal equilibrium, product of negative and positive charge concentrations is a constant, equal to square of intrinsic concentration – called law of Mass Action n p = ni2 Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Charge densities Suppose that a semiconductor is doped with both donor and acceptor impurities Let donor atom concentration = ND Let acceptor atom concentration = NA After donating one free electron to the crystal structure, donor atom now has deficit of one negative charge (i.e., net positive) Similarly, after accepting one electron from crystal structure, acceptor atom now has one extra electron (i.e., net negative) Total negative charge concentration = n + NA Total positive charge concentration = p + ND Under equilibrium condition, n + NA = p + ND Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Charge densities In N-type semiconductor, NA = 0. Hence n = p + ND But n >> p. Hence n ≈ ND Now, p = ni2/n = ni2 / ND Similarly in P-type semiconductor, ND = 0. Hence p = n + NA But p >> n. Hence p ≈ NA Now, n = ni2/p = ni2 / NA Note: If ND = NA then, semiconductor behaves like intrinsic If ND > NA then semiconductor is N-type If NA > ND then semiconductor is P-type Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Conduction in Extrinsic Semiconductors A bar of silicon with intrinsic concentration of 1.5 × 1016 m–3 is doped until the hole density becomes 8.5 × 1021 m–3. The mobilities of free electrons and holes are 0.13 and 0.05 m2/Vs respectively. Determine free electron concentration and electrical conductivity. (Ans: 2.65 × 1010 m–3, 68 S/m) How many free electrons are present in a bar of extrinsic germanium measuring 5mm×50mm×2mm, if the extrinsic hole density is 7.85×1014 m–3, given that intrinsic concentration is 2.5×1019 m-3 ? (Ans: 3.98×1017 electrons) Determine the concentrations of free electrons and holes in p-type Ge at 300 K, if conductivity is 100 S/cm. (Ans: ?) Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Conduction in Extrinsic Semiconductors What is the current density in an extrinsic silicon whose hole density is 4.5×1018 m–3 when an electric field of 8 kV/m is applied. Given that for silicon, ni = 1.5×1016 m–3, μn and μp are 0.13 and 0.05 m2/Vs respectively. (Ans: 288 A/m2 ?) For a pure silicon sample, indium is added at the rate of 1 atom per 2×108 silicon atoms. Find the nature of the material and charge carrier concentration given that ni= 1.5×1016 m–3 , concentration of Si atoms in the crystal is 5.0×1028 m–3. (a) Find the conductivity of pure germanium at 300K. (b) If donor impurity is added at the rate of 1 per 107 Ge atoms, then find the conductivity. (c) If acceptor impurity is added at the rate of 1 per 107 Ge atoms, then find the conductivity. (Ans: 2.24, 267.52, 126.72 S/m) Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Drift and Diffusion currents Drift current Motion of charge carriers due to applied electric field Free electrons move towards positive potential Holes move towards negative potential Conduction so far discussed is due to drift mechanism Drift current densities given by: Electron drift current density Hole drift current density Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Drift and Diffusion currents Results due to flow of charge carriers from the region of higher concentration to the region of lower concentration Suppose that hole-concentration varies with distance x, then concentration gradient is dp/dx If dp/dx is negative, then it results in a current in positive x direction Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Drift and Diffusion currents Hole diffusion current density is: Electron diffusion current density is: Dp and Dn are diffusion constants Diffusion constants are related to mobilities VT is volt-equivalent of temperature T is temperature in kelvin Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

Drift and Diffusion currents So, total current density is the sum of drift current density and diffusion current density Overall total current density due to both holes and free electrons is: Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA

End of module 1 Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA