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Lecture 2 OUTLINE Semiconductor Basics Reading: Chapter 2

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**Announcement Office Hours for tomorrow is cancelled**

(ONLY for this week) There will be office hours on Friday (2P-3P) Thursday’s class will start at 4P

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**What is a Semiconductor?**

Low resistivity => “conductor” High resistivity => “insulator” Intermediate resistivity => “semiconductor” conductivity lies between that of conductors and insulators generally crystalline in structure for IC devices In recent years, however, non-crystalline semiconductors have become commercially very important polycrystalline amorphous crystalline

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**Semiconductor Materials**

Phosphorus (P) Gallium (Ga)

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**Energy Band Description**

For current flow, one needs to have electrons in the conduction band or holes in the valence band Completely full or completely empty bands cannot carry current

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**Energy Band Description**

Current due to electron flow and hole flow will add up

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**Silicon Atomic density: 5 x 1022 atoms/cm3**

Si has four valence electrons. Therefore, it can form covalent bonds with four of its nearest neighbors. When temperature goes up, electrons can become free to move about the Si lattice.

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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; Holes are positively charged. The concentration (#/cm3) of conduction electrons & holes in a semiconductor can be modulated in several ways: by adding special impurity atoms ( dopants ) by applying an electric field by changing the temperature by irradiation

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**Electron-Hole Pair Generation**

When a conduction electron is thermally generated, a “hole” is also generated. A hole is associated with a positive charge, and is free to move about the Si lattice as well.

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**Carrier Concentrations in Intrinsic Si**

The “band-gap energy” Eg is the amount of energy needed to remove an electron from a covalent bond. The concentration of conduction electrons in intrinsic silicon, ni, depends exponentially on Eg and the absolute temperature (T):

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Doping (N type) Si can be “doped” with other elements to change its electrical properties. For example, if Si is doped with phosphorus (P), each P atom can donate a conduction electron, so that the Si lattice has more electrons than holes, i.e. it becomes “N type”: Notation: n = conduction electron concentration

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Doping (P type) If Si is doped with Boron (B), each B atom can accept an electron (creating a hole), so that the Si lattice has more holes than conduction electrons, i.e. it becomes “P type”: Notation: p = hole concentration

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**Terminology donor: impurity atom that increases n**

acceptor: impurity atom that increases p 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: n = p = ni extrinsic semiconductor: doped semiconductor

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**Intrinsic vs. Extrinsic Semiconductor**

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**Electron and Hole Concentrations**

Under thermal equilibrium conditions, the product of the conduction-electron density and the hole density is ALWAYS equal to the square of ni: N-type material P-type material

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Dopant Compensation An N-type semiconductor can be converted into P-type material by counter-doping it with acceptors such that NA > ND. A compensated semiconductor material has both acceptors and donors. N-type material (ND > NA) P-type material (NA > ND)

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Doping What is the electron and hole density if you dope Si with Boron to 1018 /cm3 ?

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**Charges in a Semiconductor**

Negative charges: Conduction electrons (density = n) Ionized acceptor atoms (density = NA) Positive charges: Holes (density = p) Ionized donor atoms (density = ND) The net charge density (C/cm3) in a semiconductor is

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Carrier Drift The process in which charged particles move because of an electric field is called drift. Charged particles within a semiconductor move with an average velocity proportional to the electric field. The proportionality constant is the carrier mobility. Hole velocity Electron velocity Notation: mp hole mobility (cm2/V·s) mn electron mobility (cm2/V·s)

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Velocity Saturation In reality, carrier velocities saturate at an upper limit, called the saturation velocity (vsat).

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Drift Current Drift current is proportional to the carrier velocity and carrier concentration: Total current Jp,drift= Q/t Q= total charge contained in the volume shown to the right t= time taken by Q to cross the volume Q=qp(in cm3)X Volume=qpAL=qpAvht Hole current per unit area (i.e. current density) Jp,drift = q p vh

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**Conductivity and Resistivity**

In a semiconductor, both electrons and holes conduct current: The conductivity of a semiconductor is Unit: mho/cm The resistivity of a semiconductor is Unit: ohm-cm

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Resistivity Example Estimate the resistivity of a Si sample doped with phosphorus to a concentration of 1015 cm-3 and boron to a concentration of 6x1017 cm-3.

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