03_RevSemicon - Review of Semiconductors ELEG620: Solar...

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ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner Review of Semiconductors
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ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner Review of Semiconductors Origin of Band Gaps and Band Diagrams Direct and Indirect Band Gaps Carrier Concentration – The Fermi-Dirac Distribution – Density of States – Carrier Population in a Band Intrinsic Material Doping of Semiconductors Generation and Recombination Carrier Transport – In Electric Field – Due to Diffusion
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ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner Energy of Electrons In ‘free space’ electrons can take on any energy and form a continuum The electrons each have a momentum associated with its energy which means the mass of the electron is related to the energy also …. more generally Call this the effective mass Becomes important later As does this
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ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner Energy of Electrons In real world electrons are almost never free In atoms there is a Coulombic attraction between the protons (+ve) in the nucleus and the electrons (-ve) When we apply quantum mechanics and solve the Schrödinger equation we get a series of possible values for the energy (orbitals) V = q is electronic charge (constant) and r is distance to nucleus, ε is free space permittivity 0 Energy spectrum “Classical” view of orbitals Actual s p d
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ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner Band Gaps When atoms are put together (e.g. a crystal) the splitting of the single energy levels form bands of allowed and forbidden energies Outermost forbidden gap between non-conducting and conducting bands is referred to as the band gap of the material Size of band gap determines whether material is a conductor (0 band gap), semiconductor ( <4 eV) or insulator (> 4eV)
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ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner Metal, Semiconductor, Insulator? Classification depends on band gap and the number of electrons in outer most band (conduction) In a metal the bands can overlap or be partially filled so electrons available for conduction is high
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ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner Energy Dispersion Curve When Schrödinger equation is solved for a crystal get a complex series of allowed energy states according to k the crystal momentum Electrons can only occupy energy states on the E-k curves all other energy states are forbidden Band gap is minimum difference in energy between two outermost bands Using symmetry energy states can be folded into reduced zone Near maxima and minima, curves are parabolic – approximate as ‘free’ Each ‘band’ has it’s own curvature and hence effective mass Effective mass varies as a function of k Actual Simplification
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03_RevSemicon - Review of Semiconductors ELEG620: Solar...

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