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**Semiconductor Device Physics**

Lecture 2 Dr. Gaurav Trivedi, EEE Department, IIT Guwahati

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**Electronic Properties of Si**

Silicon is a semiconductor material. Pure Si has a relatively high electrical resistivity at room temperature. There are 2 types of mobile charge-carriers in Si: Conduction electrons are negatively charged, e = –1.602 10–19 C Holes are positively charged, p = 10–19 C The concentration (number of atom/cm3) of conduction electrons & holes in a semiconductor can be influenced in several ways: Adding special impurity atoms (dopants) Applying an electric field Changing the temperature Irradiation

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**Bond Model of Electrons and Holes**

2-D Representation Hole When an electron breaks loose and becomes a conduction electron, then a hole is created. Si Conduction electron

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What is a Hole? A hole is a positive charge associated with a half-filled covalent bond. A hole is treated as a positively charged mobile particle in the semiconductor.

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**Conduction Electron and Hole of Pure Si**

Covalent (shared e–) bonds exists between Si atoms in a crystal. Since the e– are loosely bound, some will be free at any T, creating hole-electron pairs. ni = intrinsic carrier concentration ni ≈ 1010 cm–3 at room temperature

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**Si: From Atom to Crystal**

Energy states (in Si atom) Energy bands (in Si crystal) The highest mostly-filled band is the valence band. The lowest mostly-empty band is the conduction band.

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**Energy Band Diagram Ec EG, band gap energy Ev**

Electron energy Ec EG, band gap energy Ev For Silicon at 300 K, EG = 1.12 eV 1 eV = 1.6 x 10–19 J Simplified version of energy band model, indicating: Lowest possible conduction band energy (Ec) Highest possible valence band energy (Ev) Ec and Ev are separated by the band gap energy EG.

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**Measuring Band Gap Energy**

EG can be determined from the minimum energy (hn) of photons that can be absorbed by the semiconductor. This amount of energy equals the energy required to move a single electron from valence band to conduction band. Photon photon energy: hn = EG Ec Ev Electron Hole Band gap energies

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Carriers Completely filled or empty bands do not allow current flow, because no carriers available. Broken covalent bonds produce carriers (electrons and holes) and make current flow possible. The excited electron moves from valence band to conduction band. Conduction band is not completely empty anymore. Valence band is not completely filled anymore.

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**Band Gap and Material Classification**

= ~8 eV SiO2 v E c v E c v G = 1.12 eV Si Metal E v c Insulators have large band gap EG. Semiconductors have relatively small band gap EG. Metals have very narrow band gap EG . Even, in some cases conduction band is partially filled, Ev > Ec.

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**Carrier Numbers in Intrinsic Material**

More new notations are presented now: n : number of electrons/cm3 p : number of holes/cm3 ni : intrinsic carrier concentration In a pure semiconductor, n = p = ni. At room temperature, ni = 2 106 /cm3 in GaAs ni = 1 1010 /cm3 in Si ni = 2 1013 /cm3 in Ge

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**Manipulation of Carrier Numbers – Doping**

By substituting a Si atom with a special impurity atom (elements from Group III or Group V), a hole or conduction electron can be created. Acceptors: B, Ga, In, Al Donors: P, As, Sb

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**Doping Silicon with Acceptors**

Example: Aluminium atom is doped into the Si crystal. Al– is immobile The Al atom accepts an electron from a neighboring Si atom, resulting in a missing bonding electron, or “hole”. The hole is free to roam around the Si lattice, and as a moving positive charge, the hole carries current.

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**Doping Silicon with Donors**

Example: Phosphor atom is doped into the Si crystal. P+ is immobile The loosely bounded fifth valence electron of the P atom can “break free” easily and becomes a mobile conducting electron. This electron contributes in current conduction.

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**Donor / Acceptor Levels (Band Model)**

▬ E c Donor Level ED Donor ionization energy + E v Acceptor Level A Acceptor ionization energy ▬ + Ionization energy of selected donors and acceptors in Silicon Acceptors Ionization energy of dopant Sb P As B Al In EC – ED or EA – EV (meV) 39 45 54 67 160 Donors

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**Dopant Ionization (Band Model)**

Donor atoms Acceptor atoms

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**Carrier-Related Terminology**

Donor: impurity atom that increases n (conducting electron). Acceptor: impurity atom that increases p (hole). n-type material: contains more electrons than holes. p-type material: contains more holes than electrons. Majority carrier: the most abundant carrier. Minority carrier: the least abundant carrier. Intrinsic semiconductor: undoped semiconductor n = p = ni. Extrinsic semiconductor: doped semiconductor.

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**Density of States g(E) is the number of states per cm3 per eV.**

Ec Ev DE E Ec Ev gc(E) gv(E) density of states g(E) g(E) is the number of states per cm3 per eV. g(E)dE is the number of states per cm3 in the energy range between E and E+dE).

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**Density of States Near the band edges: E DE gc(E) Ec Ec**

Ev DE E Ec Ev gc(E) gv(E) density of states g(E) Near the band edges: E Ec E Ev mo: electron rest mass

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**Fermi Function EF is called the Fermi energy or the Fermi level.**

The probability that an available state at an energy E will be occupied by an electron is specified by the following probability distribution function: k : Boltzmann constant T : temperature in Kelvin EF is called the Fermi energy or the Fermi level.

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**Effect of Temperature on f(E)**

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**Effect of Temperature on f(E)**

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**Equilibrium Distribution of Carriers**

n(E) is obtained by multiplying gc(E) and f(E), p(E) is obtained by multiplying gv(E) and 1–f(E). Intrinsic semiconductor material Energy band diagram Density of states Probability of occupancy Carrier distribution

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**Equilibrium Distribution of Carriers**

n-type semiconductor material Energy band diagram Density of States Probability of occupancy Carrier distribution

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**Equilibrium Distribution of Carriers**

p-type semiconductor material Energy band diagram Density of States Probability of occupancy Carrier distribution

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**Important Constants Electronic charge, q = 1.610–19 C**

Permittivity of free space, εo = 8.85410–12 F/m Boltzmann constant, k = 8.6210–5 eV/K Planck constant, h = 4.1410–15 eVs Free electron mass, mo = 9.110–31 kg Thermal energy, kT = eV (at 300 K) Thermal voltage, kT/q = V (at 300 K)

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