半导体物理学半导体 (38).pdf

Heterojunctions(异质结)Heterojunction materials01Energy band diagrams02Equilibrium electrostatics03Current-voltage characteristics04n The semiconductor material is homogeneous throughout the structure.This type of junction is called a homojunctionn Heterojunction:a junction formed by two different semiconductor materials Heterojunction bipolar transistor:improving the injection efficiency of emitterHeterojunction FET:forming carrier transport channel of high mobility2Heterojunctionsn Heterojunction:the energy band on the surface of the heterojunction is discontinuous because the two materials of the heterojunction have different band gap width.n Abrupt junction：the semiconductor changes abruptly from a narrow-bandgap material to a wide-bandgap material.n Graded heterojunction:for GaAs-AlxGa1-xAs system,x continuously varies.By changing the value of x,We can design the bandgap energy.Heterojunction materialsn Lattice match:the lattice constants of the two materials must be well matched.The lattice match is important because any lattice mismatch can introduce dislocations resulting in interface states.Lattice mismatchLattice mismatch=a1-a2/a1When lattice mismatch 5%,it is total match.When 5%lattice mismatch25%,it is total mismatch.The alignment of the bandgap energies is important in determining the characteristics of the junction.When the forbidden bandgap of the wide-gap material completely overlaps the bandgap of the narrow-gap material is called straddling.The other possibilities are called staggered and broken gap.StraddlingEnergy band diagramsFigure 9.16 Relation between narrow-bandgap and wide-bandgap energies:(a)straddling,(b)staggered,and(c)broken gap.StaggeredBroken up6There are four basic types of heterojunction,where the capital letter indicates the larger-bandgap material：Anisotype heterojunction:the dopant type changes nP or Np anisotype junctionsIsotype heterojunction:the dopant type remains nN and pP isotype heterojunctions Four basic types of heterojunctionThe electron affinity of the wide-bandgap material is less than that of the narrow-bandgap material.The difference between the two conduction band and valence band energies are denoted by Ec,Ev,respectively.n-GeP-GaAs nP anisotype heterojunction Figure 9.17 Energy-band diagrams of a narrow-bandgap and a wide-bandgap material before contact.Figure 9.18 shows a typical ideal n-P heterojunction in a thermal equilibrium state.Forming space charge area near metallurgical junction The space charge width into the n-type region is xn and the space charge width into the P-type region is xpVacuum energyn-GeP-GaAs nP Anisotype n In the space charge region,there are potential differences on one side of the n-type and p-type regions,which are equivalent to the built-in potential differences on both sides of the junction.n The built-in potential barrier is defined as the potential difference between the two ends of the vacuum level.The built-in potential barrier is the sum of the potential differences of all space charge areas.Equilibrium ElectrostaticsFigure 9.18 Ideal energy-band diagram of an n-P heterojunction in thermal equilibrium.Assuming that n and p are of the same order of magnitude,the larger potential difference is across the lower-doped region.The ratio of the built-in potential barriers can then be determined asThe electric potential of n region and p region can be found by integrating the electric field through the space charge region,respectively.Built-in potential of anisotype heterojunction The total built-in potential barrier：We can solve for depletion width:The total depletion width is：?=?2?+?12 Built-in potential of anisotype heterojunctionA change in depletion width with a change in junction voltage yields a junction capacitance.For the n-P junction:A plot of(1/Cj)-2 versus VR yields a straight line.The extrapolation of this plot of(1/Cj)2=0 is used to find the built-in potential barrier Vbi.Built-in potential of anisotype heterojunctionThe experimentally determined values of Ec and Ev may differ from the ideal values determined using the electron affinity rule.One possible explanation for this difference is that heterojunctions have interface states.Assuming that the electrostatic potential is continuous through the junction,then the electric flux density will be discontinuous due to the surface charge trapped in the interface states.The interface states will then change the energy-band diagram of the semiconductor heterojunction.Interface states of heterojunctionConsidering the general characteristics of the energy-band diagrams of the other types of heterojunction.Figure shows the energy band diagram of an N-p heterojunction.The same Ec and Ev discontinuities exist,influencing the I-V characteristics.N-p heterojunctionFigure 9.23 Ideal energy-band diagram of an N-p heterojunction in thermal equilibrium.n The isotype heterojunctions are n-N and p-P junctions.n Electrons will flow from wide-bandgap into narrow-bandgap.A positive space charge region exists in wide-bandgap and an accumulation layer of electrons now exists at the interface in narrow-bandgap.Isotype n-N heterojunctionsFigure 9.19 Ideal energy-band diagram of an n-N heterojunction in thermal equilibrium.Positive space charge regionAccumulation layer of electronsHoles from the wide-bandgap material will flow into the narrow-bandgap material,creating an accumulation layer of holes in the narrow-bandgap material at the interface.These types of isotype heterojunctions are not possible in a homojunction.Isotype p-P heterojunctionsFigure 9.24 Ideal energy-band diagram of a pP heterojunction in thermal equilibrium.Accumulation layer of holesNegative space charge regionDiscuss a unique characteristic of an isotype n-N GaAs-AlGaAs heterojunction:2D electron gas.Electrons have quantized energy levels in one spatial direction(perpendicular to the interface),but are free to move in the other two spatial directions.2-D electron gasElectrons from wide-bandgap AlGaAs flow into GaAs forming an accumulation layer of electrons.The potential function near the interface can be approximated by a triangular potential well.Figure shows the conduction band edges near the abrupt junction interface and the approximation of the triangular potential well and quantized energy levels.Figure 9.20 (a)Conduction-band edge at N-AlGaAs,n-GaAs heterojunction;(b)triangular well approximation with discrete electron energies.2-D electron gasn The movement of the electrons parallel to the interface will still be influenced by the coulomb attraction of the ionized impurities,and a graded AlGaAs-GaAs heterojunction can reduce this effect.Ionized impurity regionElectron mobility regionn The conduction-band edges across a graded AlGaAs-GaAs heterojunction.The electrons in the potential well are further separated from the ionized impurities so that electron mobility is increased above that in an abrupt heterojunction.2-D electron gasn One immediate difference between a homojunction and a heterojunction is in the barrier heights seen by the electrons and holes.n The relative magnitude of the electron and hole currents are determined by the relative doping levels.Current-voltage characteristicsThe energy-band diagrams demonstrate that the barrier heights for electrons and holes in a heterojunction can be significantly different.The barrier height for electrons is larger than that for holes,so we would expect the current due to electrons to be insignificant compared to the hole current.Figure 9.18 Ideal energy-band diagram of an n-P heterojunction in thermal equilibrium.Current-Voltage Characteristicsn Derive the current-voltage characteristics of a heterojunction on the basis of thermionic emission of carriers over the barrier.Ew is an effective barrier height.The barrier height can be increased or reduced by an applied potential.The heterojunction I-V characteristics need to be modified to include diffusion effects and tunneling effects.The general form of the IV equation is still similar to that of a Schottky barrier diode and is generally dominated by one type of carrier.Current-voltage characteristics of heterojunction