1ECE 407 – Spring 2009 – Farhan Rana – Cornell UniversityHandout 25Semiconductor HeterostructuresIn this lecture you will learn:• Energy band diagrams in real space• Semiconductor heterostructures and heterojunctions• Electron affinity and work function• Heterojunctions in equilibrium• Electrons at HeterojunctionsHerbert Kroemer (1920-)Nobel Prize 2000 for the Semiconductor Heterostructure LaserECE 407 – Spring 2009 – Farhan Rana – Cornell UniversityBand Diagrams in Real Space - IFor devices, it is useful to draw the conduction and valence band edges in real space:cEvEfExcEvEfExN-type semiconductorEnergykfEcEvEEnergykfEcEvEP-type semiconductorKTEEcfceNnKTEEvvfeNp2ECE 407 – Spring 2009 – Farhan Rana – Cornell UniversityBand Diagrams in Real Space - IIElectrostatic potential and electric field:cEvEfExN-type semiconductorAn electrostatic potential (and an electric field) can be present in a crystal:The total energy of an electron in a crystal is then given not just by the energy band dispersion but also includes the potential energy coming from the potential:Therefore, the conduction and valence band edges also become position dependent:rrErandkEnrekEkEnnreEEreEEvvccExample: Uniform x-directed electric field xeExExExExrxErExccxx00ˆxErExˆECE 407 – Spring 2009 – Farhan Rana – Cornell UniversityElectron Affinity and Work FunctionElectron affinity “” is the energy required to remove an electron from the bottom of the conduction band to outside the crystal, i.e. to the vacuum level0x0Vacuum levelPotential in a crystalConduction bandEnergyVcEvEfExWWork function “W ” is the energy required to remove an electron from the Fermi level to the vacuum level • Work function changes with doping but affinity is a constant for a given material3ECE 407 – Spring 2009 – Farhan Rana – Cornell UniversitySemiconductor N-N Heterostructure: Electron Affinity RuleHeterostructure: A semiconductor structure in which more than one semiconductor material is used and the structure contains interfaces or junctions between two different semiconductors Consider the following heterostructure interface between a wide bandgap and a narrow bandgap semiconductor (both n-type):1gE2gE121cE1vE1fE2cE2vE2fE21V1gE2gEThe electron affinity ruletells how the energy band edges of the two semiconductors line up at a hetero-interfaceECE 407 – Spring 2009 – Farhan Rana – Cornell UniversitySemiconductor N-N Heterojunction1cE1vE1fE2cE2vE2fE21V1gE2gESomething is wrong here:the Fermi level (the chemical potential) has to be the same everywhere in equilibrium (i.e. a flat line)• Once a junction is made, electrons will flow from the side with higher Fermi level (1) to the side with lower Fermi level (2)Electrons4ECE 407 – Spring 2009 – Farhan Rana – Cornell University• Electrons will flow from the side with higher Fermi level (1) to the side with lower Fermi level (2)• Electron flow away from semiconductor (1) will result in a region at the interface which is depleted of electrons (depletion region). Because of positively charged donor atoms, the depletion region has net positive charge density• Electron flow into semiconductor (2) will result in a region at the interface which has an accumulation of electrons (accumulation region). The accumulation region has net negative charge density1cE1vE1fE2cE2vE2fE21V1gE2gEDepletion regionAccumulation region1gE2gE12+++++++++++++++---------------Note: the vacuum level follows the electrostatic potential: 00xxexVxVSemiconductor N-N Heterojunction: EquilibriumECE 407 – Spring 2009 – Farhan Rana – Cornell University1cE1vE1fE2cE2vE2fE21V1gE2gE• Electron flow from semiconductor (1) to semiconductor (2) continues until the electric field due to the formation of depletion and accumulation regions becomes so large that the Fermi levels on both sides become the same• In equilibrium, because of the electric field at the interface, there is a potential difference between the two sides – called the built-in voltage • The built-in voltage is related to the difference in the Fermi levels before the equilibrium was established:Depletion regionAccumulation region1cE1vE1fE2cE2vE2fE21V1gE2gEbeV21ffbEEeVbeVSemiconductor N-N Heterojunction: Equilibrium5ECE 407 – Spring 2009 – Farhan Rana – Cornell University1cE1vE1fE2cE2vE2fE21V1gE2gEOnce a junction is made:• Electrons will flow from the side with higher Fermi level (1) to the side with lower Fermi level (2)• Holes will flow from the side with lower Fermi level (2) to the side with higher Fermi level (1)beVElectronsHolesSemiconductor P-N HeterojunctionECE 407 – Spring 2009 – Farhan Rana – Cornell University1cE1vE1fE2cE2vE2fE21V1gE2gEDepletion regionDepletion regionbeV• Electron flow away from semiconductor (1) will result in a region at the interface which is depleted of electrons (depletion region). Because of positively charged donor atoms, the depletion region has net positive charge density• Hole flow away from semiconductor (2) will result in a region at the interface which is depleted of holes (depletion region). Because of negatively charged acceptor atoms, the depletion region has net negative charge density1gE2gE12+++++++++++++++---------------Note: the vacuum level follows the electrostatic potential: 00xxexVxVSemiconductor P-N Heterojunction: Equilibrium6ECE 407 – Spring 2009 – Farhan Rana – Cornell University1cE1vE1fE2cE2vE2fE21V1gE2gEDepletion regionDepletion region1cE1vE1fE2cE2vE2fE21V1gE2gEbeVbeV• Electron flow from semiconductor (1) to semiconductor (2) and hole flow from semiconductor (2) to semiconductor (1) continues until the electric field due to the formation of depletion regions becomes so large that the Fermi levels on both sides become the same• The built-in voltage is related to the difference in the Fermi levels before the equilibrium was established:21ffbEEeVSemiconductor P-N Heterojunction: EquilibriumECE 407 – Spring 2009 – Farhan Rana – Cornell UniversityTypes of Semiconductor
View Full Document