V A ( ) 2 = A. For Vbe = 0.4V: Ic = 7.34 * 10-8 A. For Vbe = 0.5V: Ic = 3.49 * 10-6 A. For Vbe = 0.6V: Ic = 1.

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1 1. A BJT has the structure and parameters below. a. Base Width = 0.5mu b. Electron lifetime in base is 1x10-7 sec c. Base doping is NA=10 17 /cm 3 d. Emitter Doping is ND=2 x10 19 /cm 3. Collector Doping is ND=10 18 /cm 3. Hole diffusion length is 10um. Electron diffusivity Dn=20cm 2 /sec. Hole diffusivity Dp=5cm 2 /sec. Early voltage VA=20V. BJT cross-sectional area = 100mu x 100mu. For the BJT with parameters above, graph the collector current versus the collector-emitter voltage for the voltage range 0 < Vce < 5 and Vbe = (0.4, 0.5 and 0.6)V while accounting for the Early effect. Response: I C = I s e V BE I S = qad nn i 2 W B N A V T (1 + V CE V A ) = C 10 4 cm 2 20 cm2 s ( ) cm 1017 cm 3 = A Without Early Effect V BE I C = I s e V T For Vbe = 0.4V: Ic = 7.34 * 10-8 A For Vbe = 0.5V: Ic = 3.49 * 10-6 A For Vbe = 0.6V: Ic = 1.65 * 10-5 A With Early Effect I C = I s e V BE V T (1 + V CE V A )

2 1. For the above BJT at the following bias voltages: (Vbe,Vce)=(0.5, 4)V, perform the following: a. Calculate the base-emitter capacitor Cπ.

3 b. Calculate the base-collector capacitor Cμ. c. Calculate the small signal base-emitter resistance rπ. d. Calculate the small signal transconductance gm e. Calculate the output resistance ro

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6 2. Using the methods we developed in class, where we found the various components of current by solving the relevant semiconductor equations (typically current and continuity equations), derive the current gain β, and the current components for the base, emitter and collector for a PNP BJT in forward active mode. Remember, PNP forward active is Ve > Vb > Vc.

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10 4. a) Draw two cross-sections of an N-MOSFET. Label the source, drain, gate, body, oxide, substrate, and indicate the type of doping in each region. Draw one crosssection with zero gate voltage, and another when gate voltage is large enough to establish a channel. (a) Zero gate voltage --- no channel formation (b) Positive gate voltage, inversion channel b) What is meant by the inversion layer, how is it formed? What are the mobile carriers in the channel for a N-Channel MOSET and a P-Channel MOSFET. The flow of electrons from the source to the drain is controlled by the voltage applied to the gate. A positive voltage applied to the gate, attracts electrons to the interface between the gate dielectric and the semiconductor. These electrons form a conducting channel between the source and the drain, called the inversion layer. No gate current is required to maintain the inversion layer at the interface since the gate oxide blocks any carrier flow. The net result is that the current between drain and source is controlled by the voltage which is applied to the gate. Mobile carriers for N-channel MOSFET: Electrons Mobile carriers for P-channel MOSFETs: Holes 5) Describe qualitatively how a MOSFET works. Include words like gate voltage, pn junction, channel, drain voltage, etc. Response: the MOSFET is a voltage controlled current source. In an N-Channel MOSFET, the current that flows into the the drain and out of the source is largely controlled by the voltage applied to the gate. Since the current flow between two terminals (the source and

11 drain), is controlled by a voltage applied to a third terminal (the gate), we refer to the MOSFET as a voltage controlled current source. the NMOS transistor has the source grounded and the body grounded. A positive voltage is then applied to the gate, and another positive voltage is applied to the drain. The positive potential applied between the gate and source (VGS) acts to forward bias the source-substrate (N-P) region near oxide at the top of the device. The electric field arising from the gate-tosource voltage points in the direction that is opposite the built-in field due to the sourcesubstrate PN junction. This reduces the total electric field and allows electrons from the source to diffuse into the substrate region at the top of the source near the gate oxide. Now, these electrons that diffuse out of the source are also pulled up against the insulating oxide by the gate field. However, since the oxide is an insulator, the electrons from the source cannot enter the gate electrode but will gather under the oxide, resulting in a large concentration of mobile electrons in the P-substrate right under the gate oxide. This large concentration of electrons under the oxide is called the channel of mobile electrons, or just the channel. The value of the gate-source voltage (VGS) necessary to create a channel is called the Threshold Voltage or VTH. Once a channel is formed, current can flow between the source and the drain. If a voltage is now applied to the drain, with the source still grounded, then the field that results from this drain-source voltage (VDS), acts to pull the electrons that are in the channel into the drain and eventually into the drain contact wire. This electron flow out of the drain contact then manifests itselb and drain current (ID), which flows into the drain. In the steady state, these gate and drain voltages are kept fixed, and electrons will continue to flow out of the source, into the channel, and into the drain. 6) Why is the DC input resistance of a MOSFET equal to infinity. Why is a MOSFET a field effect device, while a BJT is not. Response: In a MOSFET the gate is insulated from the current carrying channel by an insulating layer of Silicon dioxide (SiO2), and NO direct current can flow into gate. Hence, the DC input resistance of a MOSFET gate equals infinity. The concentration of channel electrons and thus the magnitude of channel current is mainly controlled by the gate voltage and the electric field that results from this gate voltage. On the other hand, in a BJT there is current flowing into the base, and the current between the emitter and the collector is directly proportional to the base current (IC= B). And of course for their respective operations, the base of a BJT is analogous to the gate of MOSFET. The signal applied to the MOSFET gate mainly controls the current between the source and the drain. The signal applied to the BJT base, mainly controls the current between the emitter and collector.

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