半导体物理学半导体 (64).pdf

Base Width Modulation It is tempting to neglect the effects of base current in a transistor since the base current is usually much smaller than either the collector or the emitter current.Current CrowdingCross section of an npn bipolartransistor showing the basecurrent distribution and thelateral potential drop in the baseregionThe base region is typically less than a micrometer thick,so there can be a sizable base resistance.The nonzero base resistance results in a lateral potential difference under the emitter region.For the npn transistor,the potential decreases from the edge of the emitter toward the center.The emitter is highly doped,so as a first approximation the emitter can be considered an equipotential region The number of electrons from the emitter injected into the base is exponentially dependent on the BE voltage Current crowding effect:with the lateral voltage drop in the base between the edge and center of the emitter,more electrons will be injected near the emitter edges than in the center,causing the emitter current to be crowded toward the edgesCross section of an npn bipolar transistor showing the emitter current crowding effect.Current CrowdingThe larger current density near the emitter edge may cause localized heating effects as well as localized high-injection effectsThe nonuniform emitter current also results in a nonuniform lateral base current under the emitter A two-dimensional analysis would be required to calculate the actual potential drop versus distance because of the nonuniform base currentAnother approach is to slice the transistor into a number of smaller parallel transistors and to lump the resistance of each base section into an equivalent external resistancelarger current density near the edgen+Cross section of an npn bipolar transistor showing the emitter current crowding effect.Current CrowdingPower transistors：handle large currents,require large emitter areas to maintain reasonable current densitiesTo avoid the current crowding effect,these transistors are usually designed with narrow emitter widths and fabricated with an interdigitated designIn effect,many narrow emitters are connected in parallel to achieve the required emitter area(a)Top view and(b)cross section of an interdigitated npn bipolar transistor structureCurrent CrowdingThere are two breakdown mechanisms in a bipolar transistor.The first is called punch-through.As the reverse-biased BC voltage increases,the BC space charge region widens and extends farther into the neutral base.BC depletion region to penetrate completely through the base and reach the BE space charge region,the effect called punch-through.Breakdown Voltage1.Punch-throughWhen a small CB voltage,VR1,is applied,the BE potential barrier is not affected;thus,the transistor current is still essentially zero.When a large reverse-biased voltage,VR2,is applied,the depletion region extends through the base region and the BE potential barrier is lowered because of the CB voltage.The lowering of the potential barrier at the BE junction produces a large increase in current with a very small increase in CB voltage.Energy-band diagram of an npn bipolar transistor(a)in thermal equilibrium,and(b)with a reverse-biased BC voltage before punch-through,VR1,and after punch-through,VR2.Breakdown VoltageAssume that NB NC are the uniform impurity doping concentrations in the base and collector,respectively.Punch-through occurs when xdB=xBO.We can write that where Vpt is the reverse-biased BC voltage at punch-through.Neglecting Vbi compared to Vpt,we can solve for Vpt as Calculating the punch-through voltageGeometry of a bipolar transistor to calculate the punch-through voltageBreakdown VoltageAn npn transistor with a reverse-biased voltage applied to the BC junction and with the emitter left open.The current ICB0 is the reverse-biased junction current.2.Avalanche breakdownThe second breakdown mechanism to consider is avalanche breakdown,but taking into account the gain of the transistor.The transistor with an applied CE voltage and with the base terminal left open.The current in the transistor for this bias configuration is denoted as ICE0Breakdown VoltageThe current ICB0 shown in the figure is the normal reverse-biased BC junction current.Part of this current is due to the flow of minority carrier holes from the collector across the BC space charge region into the base.The flow of holes into the base makes the base positive with respect to the emitter,and the BE junction becomes forward biased.is the common-base current gain.We therefore havewhere is the common-emitter current gain.The reverse-biased junction current ICB0 is multiplied by the current gain when the transistor is biased in the open-base configuration.Breakdown Voltage1.BC breakdown voltage with the emitter left open BVCB0：where n is an empirical constant,usually between 3 and 6,and BVCB0is the BC breakdown voltage with the emitter left open.The emitter left openWhen the transistor is biased in the open-emitter configuration as in the Figure,the current ICB0 at breakdown becomes ICB0MICB0，where M is the multiplication factor.An empirical approximation for the multiplication factor is usually written asBreakdown Voltage2.The base open：The condition for breakdown corresponds to：Base openWhen the transistor is biased with the base open circuited as shown in Figure 12.34b,the currents in the BC junction at breakdown are multiplied,so thatBreakdown Voltage Breakdown voltage in the open-base configuration：assuming that VCBVCE,where BVCE0is the CE voltage at breakdown in the open-base configuration.Solving for it:where,again,is the common-base current gain.The common-emitter and common-base current gains are related byNormally 1，so thatThenBreakdown VoltageThe breakdown voltage in the open-base configuration is smaller,by the factor than the actual avalanche junction breakdown voltage.This characteristic is shown in Figure.Relative breakdown voltages and saturation currents of the open-base and open-emitter configurations.Breakdown Voltage