EE 105 Spring 2005 Discussion Notes written by Amin Monday May 2 2005 EE 105 Discussion Section 101 Announcements The Importance of BJTs There are two major types of transistors i MOSFETs and ii BJTs While MOSFETs are currently the prevalent technology due to their superior digital performance BJTs play important roles in certain analog applications To name a few examples BJTs are preferred choice for power amplifiers i e amplifiers that are designed to deliver a large amount of power to a load Also BJTs provide more gm as compared to their MOSFET counterparts for the same bias current Hence one can obtain larger gain for less power using BJT transistors Lastly the transit frequency i e T of BJTs has historically been larger than MOSFETs for any given technology node This translates into better frequency response for the BJT transistor It should be noted however that recent lithographic and manufacturing advancements have narrowed the gap between the T of the BJT and MOSFET transistor The focus in EE105 is to have enough understanding of BJT operation such that one can analyze and design BJT amplifier circuits To this end we will follow the same outline as that for the MOSFET More specifically 1 Develop a model based upon device physics that relates the DC currents set up in response to DC voltages applied at the terminals of the device This essentially encapsulates the development of the BJT large signal equations thereby allowing one to analyze biasing issues in BJT circuits 2 Construct the equivalent small signal model for the BJT based upon the derived large signal equations 3 Use the small signal model to analyze and design circuits that process small changes in current and or voltage i e small signals BJT Structure and Regions of Operation The bipolar junction transistor is nothing more than two pn junctions in series to one another back to back This is pictorially depicted in Figure 1 As was the case for MOSFETs BJTs come in two different flavors While the transistor structure appears to be symmetrical based upon Figure 1 it is not in practice More specifically the doping in the emitter and collector regions are quite different from one another 1 EE 105 Spring 2005 Discussion Notes written by Amin E B C C B E WE eff Figure 1a NPN BJT WB eff E B C E B C Figure 1b PNP BJT Legend n type Si p type Si The effective base width see Figure 1 WB eff is an important device parameter for the BJT Analogous to the length of a MOSFET one strives to have as small of a WB eff as possible for performance Also the dashed regions in Figure 1 are indicating the depletion regions present in the BJT structure Considering that the BJT consists of two diodes it takes on 3 regions of operation 1 Cutoff Both pn junctions are reverse biased with very little current ideally zero flowing through the resultant device 2 Saturation Both pn junctions are forward biased and 3 Active One pn junction is forward biased while the other is reverse biased Note The saturation region of operation should be avoided for amplifier design as was the case for the triode region for MOSFETs The region resembling the MOSFET saturation region in BJTs is the active region of operation Note Here the forward active region of operation shall be the focus This region of operation is marked by the BE junction being forward biased and the CB junction reverse biased The reverse active region of operation is when the BE junction is 2 EE 105 Spring 2005 Discussion Notes written by Amin reverse biased and the CB junction forward biased These two regions are different from one another because the emitter and collector dopings of the device are different from one another in practice Large Signal Model for the PNP Transistor in Forward Active In order to derive equations for the DC currents set up in a BJT in response to DC voltages applied at the terminals one needs to focus on the minority carrier concentrations within the device The reason for this is discussed in EE130 As such let s first focus on the minority carrier concentrations present within the PNP structure at thermal equilibrium Using relationships discussed in the early part of the semester the minority carrier concentrations are as follows nemitter pbase ni2 1 N A emitter ni2 2 N D base ncollector ni2 3 N A collector Note In practice N A emitter N D base N A collector Figure 2 depicts a PNP transistor biased in the forward active region of operation through the application of a couple of DC bias voltage sources As will be discussed in EE130 E B C 2 I diffusion p IE IC 1 5 6 I diffusion n 3 4 IB VEB VBC Figure 2 PNP in Forward Active Region 3 EE 105 Spring 2005 Discussion Notes written by Amin V the minority carrier concentrations at the depletion edges of a pn junction are exp Vth times their corresponding thermal equilibrium values where kT 26mV at room temp and Vth q V the change in forward bias voltage undergone by the particular diode at hand Using this relationship then yields the following expressions VEB exp N A emitter Vth V EB ni2 exp p2 N D base Vth n1 ni2 V BC 0 exp N D base Vth V BC ni2 0 exp n4 N A collector Vth p3 ni2 4 5 6 7 Note The expressions in 6 and 7 are approximately zero because the exponential term ends up being a very small number in practice e g typical values for VBC are 1 2V In areas far away from the depletion regions the minority carrier concentrations are approximately those at thermal equilibrium Hence n5 n6 ni2 N A emitter ni2 N A collector 8 9 In order to then approximate the minority carrier concentrations in the regions in between a linear concentration gradient is assumed between the aforementioned end points Note This simplification is only valid if one neglects recombination of minority carriers It will suffice however for our purposes here in EE105 Note Concentration gradients are developed in the base and emitter regions As a result diffusion currents are set up across the BE junction considering that it is forward biased Although a concentration gradient is also set up in the collector it 4 EE 105 Spring 2005 Discussion Notes written by Amin does not give rise to diffusion current across the CB junction because it is reversebiased The positive direction of current will be taken in the positive x axis direction as indicated in Figure 2 The diffusion current density is proportional to the concentration gradient specifically d p x dx d n x dx J diffusion p 10 J diffusion n 11 More Note The negative signs in 10 and 11 make intuitive
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