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_I o _ (I + I ) = _ I o S R Avalanche region
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_ i , mA D
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Fig. 2-4 1. 2. The actual (measured) forward voltage drop is greater than that predicted by (2.1) (due to ohmic resistance of metal contacts and semiconductor material). The actual reverse current for VR vD < 0 is greater than predicted (due to leakage current IS along the surface of the semiconductor material).
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3. The actual reverse current increases to signi cantly larger values than predicted for vD < VR (due to a complex phenomenon called avalanche breakdown). In commercially available diodes, proper doping (impurity addition) of the base material results in distinct static terminal characteristics. A comparison of Ge- and Si-base diode characteristics is shown in Fig. 2-5. If VR < vD < 0:1 V, both diode types exhibit a near-constant reverse current IR . Typically, 1 A < IR < 500 A
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SEMICONDUCTOR DIODES
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iD, mA Ge Si
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Region of low-resistance conduction
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IR = Io + IS (Ge) IR = Io + IS (Si)
0 0.3 0.7
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_ i , mA D
Fig. 2-5
for Ge, while 10 3 A < IR < 1 A for Si, for signal-level diodes (forward current ratings of less than 1 A). For a forward bias, the onset of low-resistance conduction is between 0.2 and 0.3 V for Ge, and between 0.6 and 0.7 V for Si. For both Si and Ge diodes, the saturation current Io doubles for an increase in temperature of 108C; in other words, the ratio of saturation current at temperature T2 to that at temperature T1 is Io 2 2 T2 T1 =10 Io 1 2:2
Example 2.3. Find the percentage increase in the reverse saturation current of a diode if the temperature is increased from 258C to 508C. By (2.2), Io 2 2 50 25 =10 100% 565:7% Io 1
Static terminal characteristics are generally adequate for describing diode operation at low frequency. However, if high-frequency analysis (above 100 kHz) or switching analysis is to be performed, it may be necessary to account for the small depletion capacitance (typically several picofarads) associated with a reverse-biased p-n junction; for a forward-biased p-n junction, a somewhat larger di usion capacitance (typically several hundred picofarads) that is directly proportional to the forward current should be included in the model. (See Problem 2.25.)
THE DIODE SPICE MODEL
The element speci cation statement for a diode must explicitly name a model even if the default model parameters are intended for use. The general form of the diode speci cation statement is as follows, where the model name is arbitrarily chosen: D n1 n2 model name
Node n1 is the anode and node n2 is the cathode of the diode. Positive current and voltage directions are clari ed by Fig. 2-1(b). In addition, the .MODEL control statement must be added to the netlist code even if the default parameters are acceptable. This control statement is .MODEL model name D (parameters)
SEMICONDUCTOR DIODES
[CHAP. 2
If the parameters eld is left blank, default values are assigned. Otherwise, the parameters eld contains the number of desired speci cations in the format parameter name value. Speci c parameters that are of concern in this book are documented by Table 2-1.
Table 2-1 Parameter Is n BV IBV Rs Description saturation current emission coe cient reverse breakdown voltage reverse breakdown current ohmic resistance Reference Io of (2.1)  of (2.1) VR of Fig. 2-4 IR of Fig. 2-4 Section 2.3 Default 1 10 1 1 1 10 0
10 14
Units A
V A 
Example 2.4. The circuit of Fig. 2-6(a) can be used to determine the static characteristic of diode D provided that the ramp of source vs spans su cient time so that any dynamic e ects are negligible. Let source vs ramp from 5 V to 5 V over a span of 2 s. Use SPICE methods to plot the silicon diode static characteristic (a) if the diode is nonideal with a voltage rating of VR 4 V and (b) if the diode is ideal.
Fig. 2-6 (a) The SPICE netlist code below describes the nonideal diode for a typical saturation current Is 15 A. An emission coe cient n 4 > 2 has been used to yield a typical forward voltage drop for a silicon diode.
Ex2_4.CIR - Diode static characteristic vs 1 0 PWL (0s -5V 2s 5V) D 1 2 DMOD R 2 0 2kohms .MODEL DMOD D(n=4 Is=15uA BV=4) ; Nonideal *.MODEL DMOD D(n=0.0001) ; Ideal .TRAN .1us 2s .PROBE .END
CHAP. 2]
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