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## CHAPTER 4

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**CHAPTER 4**SERIES RESISTANCE, CHANNEL LENGTH AND WIDTH, AND THRESHOLD VOLTAGE**Semiconductor devices is degraded by series resistance.**• Series resistance depends on semiconductor resistivity, contact resistance, and the geometrical factors.**Log(Ι) versus V for a diode with series resistance.**The upper dashed line is for rs=0**Open-Circuit Voltage Decay**Open-circuit voltage decay of a pn junction showing the voltage discontinuity at t=0**Capacitance-Voltage**1. f low, such that 2πfrsC<<1, to obtain C 2. f high, such that 2πfrsC>>1,calculate rs from the data of Cm vs. f. 3. This method is used when DC method is unavailable, such as in MOS capacitor.**4.3 SCHOTTKY**BARRIER DIODES**Series Resistance**The method of extracting rs for pn diode can also be used for Schottky diode.**Norde function F is defined as:**It can also be written as: For low voltage Irs<<V, dF/dV≒1/2-1=-1/2 For high voltage Irs ≒V, dF/dV≒-1/2+1=1/2 Therefore, there exists a Fmin. From Fmin. to determine Vmin. and then find out Imin..**Another method is define H as:**Plot H vs. I, the slope is rs and the intercept is nψB.**A modified Norde function is defined as:**Plot F1 vs. V for different Temp., each curve has a F1min , which has a corresponding Vmin and Imin. Plot the left side of the above equation vs. q/kT, then n and A* can be extracted from the slope and the intercept, respectively.**SOLAR CELLS**Equivalent circuit of a solar cell.**Multiple Light Intensities**Current-voltage characteristic of a solar cell.**Series resistance**determination of a solar cell.**Constant Light Intensity**This method (area method) is suitable for concentrator cells with high Iph, it overestimates rs at 1-sun. This method (area method) is suitable for concentrator cells with high Iph, it overestimates rs at 1-sun.**Constant Light Intensity**For high intensity flash illumination method, neglecting rsh, I≒Voc/(RL+rs). By varying the load resistance RL at constant light intensity, we have RL should be on the order of rs.**Shunt Resistance**Rewrite the above equation as**For rs<<rsh and Iscrs<<nkT/q,**rs≒0.1Ω, Isc≦3mA it becomes At very low light intensities, the second term is neglected, then**BIPOLAR JUNCTION TRANSISTORS**An npn bipolar junction transistor and its parasitic resistances. The base resistance is composed of intrinsic and extrinsic resistance.**Gummel plots showing the effects of emitter-base space**-charge region recombination (n≈2), quasineutral region recombination (n≈1), and series resistance.**Emitter Resistance**RE≒1Ω for discrete BJT and around 5~100Ω for IC transistors. Emitter resistance measurement setup and IB -VCE plot.**Emitter Resistance**Another method is to supply current from B1 only, and no current flow through B2. Then VBE2=VBEeff+IERE. RE=(VBE2-VBEeff)/IE Where**Collector Resistance**Common emitter output characteristics. The two lines show the limiting values of RC .**Base Resistance**Plot ΔVBE/IB vs β has a slope of RE and an intercept on the ΔVBE/IB axis of RB+RE. But it is difficult to change β of a transistor without changing other parameters.**Base Resistance**Rewrite the equation of IB in the following form Measured device characteristics for a self-aligned, high-speed digital BJT. The βmust be varied in this measurements, and RBi/β must be a constant.**Base Resistance**The intrinsic base resistance for rectangular emitter with 1 contact is: RBi=RshiW/3L. The intrinsic base resistance for rectangular emitter with 2 contact is: RBi=RshiW/12L. Square emitter with contact on all sides: RBi=Rshi/32. (W=L) Circular emitter with contactall around: RBi=Rshi/8π.**Equivalent emitter-base portion**of the “two-base contact” BJT.**Measured base resistance versus emitter window width as a**function of base-emitter voltage. d is the deviation between emitter window and the effective base width. Rshi is a function of VBE due to base conductivity modulation.**Frequency Measurements on RB**The input impedance circle method measures the Zin as a function of frequency. The real axis intersections give:**Series Resistance and Channel Length— I-V**ξ=0.37, 0.58, 0.75, 0.9; xch: channel thickness • A MOSFET with source and drain resistances, (b) device cross • section showing the actual gate length L and Leff =L-∆L with • ∆L=2δL. The substrate resistance is not shown.**Short channel devices have a channel length dependent**threshold voltage. • VG↗, Leff ↗, RSD↘. • Keep VG at a fixed value, change VT by changing VSB.