半导体物理学半导体 (36).pdf

Metal-Semiconductor and Semiconductor Heterojunctions（金半接触和半导体异质结）Schottky Barrier Diode01Metal-Semiconductor Ohmic Contacts02Heterojunctions03Schottky Barrier DiodeQualitative characteristics 01Ideal junction properties02Non-ideal effect on the barrier height03Current-voltage curve04Comparison between schottky and pn diodes 05Schottky diode structures(a)Point contact (b)Face contactMetal-semiconductor diode was developed from 1920s,which is formed of point contact between metal and bare semiconductor.These metal-semiconductor diodes are hard to fabricate,and reliability is also bad,so it is replaced by pn junction in 1950s.With the development of semiconductor and vacuum technique,metal-semiconductor contact can be achieved.Schottky barrier diodeSchottky barrier diodeEnergy bands of metal and n-type semiconductor are shown.Semiconductor work function s:the difference between Ef and vacuum energyMetal work function m:The lowest energy needed by electron emitting from metal to vacuum.Electron affinity :The lowest energy needed by electron emitting from Ec to vacuum energy.Qualitative characteristicsEnergy-band diagram of a metal and semi conductor before contactElectronic affinity of several semiconductorsCu,copper 4.65Work functions of metals and electron affinity of semiconductors m sIdeal thermal equilibrium energy band diagram.The Ef of semiconductor is higher than that of metal.The electrons move from semiconductor to metal,and fixed donor atom with positive charge is left at semiconductor,forming the space charge region.Figure(a)Energy-band diagram of a metal and semiconductor before contact;(b)ideal energy-band diagram of a metaln-semiconductor junction for ms.Electronic affinity of several semiconductorsThe ideal barrier height B0Vbi is built-in voltageSchottky barrier m s=m-sIf a negative bias is applied between metal and semiconductor,barrier will increase,while B0 keep unchanged.Reverse-biased voltage m sForward-biased voltage m sIf a positive bias is applied between metal and semiconductor,barrier will decrease,while B0 keep unchanged.It is different to pn junction,current is dominated by majority carrier electrons.Under a forward bias,barrier decrease,and electrons move from semiconductor to metal more easily.Forward current is from metal to semiconductor,and current is the exponential function of Va.msSchottky diode property Electrostatic properties The electric field in the space charge region is determined from Poissons equation.Ideal junction propertiesThe electric field is zero at the space charge edge in the semiconductor,so the constant of integration is If the semiconductor doping is uniform.The electric field can be written as where VR is the magnitude of the applied reverse-biased voltage.Electric field and width of space charge region?=?=?2?(?+?1 2?=?(?)The space charge region width is similar to the p+n junction.Since the E-field is zero inside the metal,a negative surface charge must exist in the metal at the metal-semiconductor junction.Ideal junction properties A junction capacitance can also be determined in the same way as we do for the p+n junction.where C is the capacitance per unit area.If we square the reciprocal Junction capacitance of Schottky barrier diode：?=?=?2(?+?1 2?1?=2(?+?We can obtain the built-in potential barrier Vbi.The slope of the curve can calculate the semiconductor doping Nd.Combing with n,the Schottky barrier B0 can be calculated.Ideal junction propertiesThe built-in potential barrier and doping concentration of the GaAs Schottky diode are larger than that of the silicon diode.?1?=2(?+?Ideal junction propertiesn Several effects alter the actual Schottky barrier height from the theoretical value.n The Schottky effect,or image-force-induced lowering of the potential barrier.n An electron in a dielectric material at a distance x from the metal will create an electric field.The electric field can be determined by adding an image charge,e,inside the metal located at the same distance.Non-ideal effect on the barrier heightSchottky effect,the mirror image force reduction effect of the barrier.eB0eSchottky barrier reduction Xm corresponding to the maximum barrier?=?16?=?4?Non-ideal effect on the barrier heightWithout mirror image forceWith mirror image forceMirror image potentialMeasured barrier heights in GaAs and silicon Schottky diodes as a function of metal work functions.However,the barrier height and metal work function curves do not fit the monotonic relation.The barrier height is determined by both the metal work function and the semiconductor surface or interface states.?=(?Non-ideal effect on the barrier heightInterface States：donor type,acceptor type:Donor-type surface state:the energy level is neutral after being occupied by electrons;without electrons,it is positively charged.Acceptor-type surface state:the energy level is neutral without electrons;if there are electrons,it is negatively charged.Non-ideal effect on the barrier heightn Surface potential 0:There is an energy level at the surface that is e0 from the top of the valence band,e0 is about 1/3 of the forbidden band width.n Donor surface state:When electrons fill surface state level below 0,the surface is neutral and it is positively charged when empty.n Acceptor surface state:When electrons fill surface state level above 0,the surface is negatively charged and it is neutral when empty.Non-ideal effect on the barrier heightn The surface state density is constant and equal to Dit states/cm2 eV.The relation between the surface potential and surface state density is Two limiting cases：n Case 1 Let Dit.In this case,the right side goes to zero.l The barrier height is only fixed by the bandgap and the potential 0.l The barrier height is totally independent of the metal work function and the semiconductor electron affinity.l The Fermi level becomes“pinned”at the surface.01()BngEee01()2()()igBnsdBnnmBnititEeeeNeDeDSurface state density expressionnCase 2 Let Dit 0.It is the ideal expression.l The Schottky barrier height is a function of the electric field in the semiconductor through the barrier lowering effect.l The barrier height is also a function of the surface states.l The barrier height is modified from the ideal theoretical value.l Since the surface state density is not predictable with any degree of certainty,the barrier height must be an experimentally determined parameter.()BnmSurface state density expressionn The current transport in a metal-semiconductor junction is due mainly to majority carriers as opposed to minority carriers in a pn junction.n The basic process in the rectifying contact with an n-type semiconductor can be described by the thermionic emission theory.Current-voltage relationshipn Thermal electron emission theory:The electrons in the semiconductor have enough energy to exceed the apex of the barrier,and can freely enter the metal through the barrier layer.Current-voltage relationshipThe net current density in the metal-to-semiconductor junction can be written as?=?which is defined to be positive in the direction from the metal to the semiconductor.where The parameter A*is called the effective Richardson constant for thermionic emission.It can be written in the usual diode form as Current-voltage relationship?4?Current-Voltage Relationshipwhere JsT is the reverse-saturation current density Two important differences between a Schottky diode and a pn junction diode:The first is in the magnitudes of the reverse-saturation current densities and the second is in the switching characteristics.The reverse-saturation current density of the Schottky barrier diode is Compare of the Schottky Barrier Diode and the pn Junction Diode The ideal reverse-saturation current density of the pn junction diode can be written as?=?+?The current mechanism in the two devices is different：The current in a pn junction is determined by the diffusion of minority carriers.The current in a Schottky barrier diode is determined by thermionic emission of majority carriers over a potential barrier.Compare of the Schottky Barrier Diode and the pn Junction Dioden pn junction diode:The reverse-biased current is dominated by the generation current.It is two to three orders less than the reverse saturation current density of the Schottky barrier diode.n Schottky barrier diode:The generated current also exists.But the generated current is negligible relative to the JsT value.Reverse bias Compare of the Schottky Barrier Diode and the pn Junction DiodeSince JsTJs,their forward-bias characteristics are also different.The effective turn-on voltage of the Schottky diode(0.3V)is less than that of the pn junction diode(0.6V).Compare of the Schottky Barrier Diode and the pn Junction DiodePositive biasThe Schottky barrier diode is a majority carrier device.It means that no diffusion capacitance associated with a forward-biased.Compare of the Schottky Barrier Diode and the pn Junction DiodeFrequency response,switching characteristicWhen switching from forward to reverse bias,there is no minority carrier charge or discharge.A typical switching time for a Schottky diode is in the picosecond range,while for a pn junction it is normally in the nanosecond range.