UNIVERSITY OF CALIFORNIA College of Engineering Department of Electrical Engineering and Computer Sciences EE 130 Prof. King Spring 2003 Term Project Due by 5 PM on Thursday, 4/24/03 NOTE: YOU MUST WORK ONLY WITH YOUR PARTNER ON THIS PROJECT Part I: Manual Design of Ideal BJT Structure [75 points] A. Design an NPN bipolar junction transistor with uniformly doped emitter, base and collector regions to meet the stated performance specifications over the temperature range 300K to 360K, with the stated constraints on design. (Specify the thicknesses WE, WB and WC of the emitter, base and collector regions, respectively, in addition to the doping concentrations NE, NB and NC.) Performance Specifications: • βdc, edge of saturation > 50 @ IC = 1 mA • VA, edge of saturation > 10 V @ IC = 1 mA • Vpunchthrough > 10 V • fT, edge of saturation > 20 GHz @ IC = 1 mA Notes: i. Edge of saturation => VBC = 0 V ii. Vpunchthrough = |VBC| at which base width W = 0, for VBE = 0 V Design Constraints: • The BJT has a uniform cross-sectional area of 10µm×1µm • Maximum emitter doping NE = 1E20 cm-3 • Maximum emitter thickness WE = 0.2 µm • Minimum base width WB = 0.1 µm • Minimum collector doping NC = 1E15 cm-3 • Epitaxial layer thickness (WE + WB + WC) ≤ 4 µm • Minimum collector thickness WC = 2.0 µm • Sub-collector doping = 1E19 cm-3 • Sub-collector thickness = 1 µm • minority-carrier lifetimes τE = τB = τC = 1µs. B. Determine the impact of +/-10% changes in base width WB and base doping NB on your design. (You should vary WB and NB individually, i.e. you do not need to vary them simultaneously.) Your device design should be able to meet the performance specifications despite these variations, which can arise from typical variations in a transistor fabrication process.Detailed Instructions/Guidance for Manual Design: Assume that the collector, base, and emitter are formed using a combination of epitaxy (to grow a lightly doped n-type layer of Si on top of the heavily doped sub-collector) and ion-implantation and diffusion (to form the Base and Emitter doping profiles), resulting in the following ideal doping profiles: Note that the emitter and base regions are compensated. Setting Up: First, determine the constants that apply within the various regions of the BJT. • Use the empirical equations given on pages 83-84 of the textbook to determine the minority-carrier mobilities (dependent on the total doping concentration as well as the temperature), for each region (including the sub-collector) of the BJT. You will also need to determine the majority-carrier mobility in the collector, in order to calculate the resistivity of the collector rC. • Use the Einstein relationship to determine the minority-carrier diffusion coefficients for each region (including the sub-collector) of the BJT. • Calculate the minority-carrier diffusion lengths for each region of the BJT. • Use the following empirical equation (given on page 56 of the textbook) to determine the intrinsic carrier concentration for a moderately doped semiconductor: kTieTn/5928.02193001015.9−×= • Determine the equilibrium carrier concentrations within each region of the BJT. Include the effect of bandgap narrowing (due to high dopant concentration) on ni2 when determining the minority-carrier concentration in the emitter: ()TNEennEgEkTEiiEEg300105.3 e wher3/18/22−∆×=∆= • Determine the built-in potentials (VbiE, VbiC). (Assume that the Boltzmann approximation is valid for the base and collector regions, but that the emitter is degenerately doped.) Doping Conc. 1E19 cm-3Depth epitaxial layer thickness Emitter Base CollectorSub-Collector≤ 0.2 µm ≥ 0.1 µmNext, define various parameters as functions of the applied biases (VBE, VBC): • emitter-junction and collector-junction depletion widths • emitter-junction and collector-junction depletion capacitances • quasi-neutral-region widths (WE’, W, WC’) • Current components JEp, JEn, JCp, JCn Then, you can calculate various performance parameters as follows: • Terminal currents JE = JEp + JEn and JC = JCp + JCn and JB = JE - JC o Find the value of VBE which gives IC = 1 mA; use this value for calculating βdc, VA and fT. • Common-emitter dc gain βdc = JC / JB • Early voltage 0==BCVdBCBACQV where QB = q(NB-NC)W is the integrated dopant dose in the quasi-neutral base and CdBC is the collector-junction depletion capacitance. • Punchthrough voltage Vpunchthrough Notes: i) You may assume that the emitter, base and collector regions are “short”, i.e. WE’ << LE, W << LB, and WC’ << LC. ii) For the sole purpose of calculating the minority-carrier diffusion current in the collector, you should account for the boundary between the collector and sub-collector in your analysis, similarly as for a poly-Si emitter described in the text on page 428. (The bottom of the sub-collector can be considered as an ohmic contact.) As a result, WC’ should be replaced by +′SCCorsubcollectCDDtW in the equation for IC, where tsubcollector is the width of the sub-collector (1 µm) and DC and DSC are the minority-carrier diffusion constants in the collector and sub-collector, respectively. • fT: Calculation of this parameter is a little more involved: o Calculate the base transit time τt. o Determine the base-emitter voltage VBE at which IC = mA at the edge of saturation, i.e. VBC = 0 V. o Calculate the total excess minority charge in the quasi-neutral base )(21)(0pBEBWBBnxnqWdxxnqQ ∆≅∆=∫ where xpBE is the location of edge of the emitter-junction depletion region in the base. o Calculate the total excess minority charge in the quasi-neutral emitter )('21)(0nBEEEWEEpxpqWdxxpqQE∆≅∆=∫′ where xnBE is the location of edge of the emitter-junction depletion region in the emitter. o Calculate τF ≈ [(QnB + QpE)/ QnB]* τt. o Calculate the collector resistance rc:′=AWNqrCCnCCµ1 where µnC is the majority-carrier mobility in the collector, and Wc’ is the width of the quasi-neutral collector region. (Note that the series resistance of the sub-collector is considered to be negligible.) o Use the following equation to calculate fT: ()()[]()dBCCCdBCdBEFTCrqIkTCCf+++=/21τπ where CdBE and CdBC are the equilibrium (zero applied bias) emitter-junction and
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