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The Practical Diode

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The Practical Diode Section B3: The Practical Diode OK, the ideal diode is an extraordinarily well-behaved creature that allows us to deal with its nonlinearities in unbelievably reasonable terms. But...and there’s always a but... we have to look at the deviations from ideal that materials, fabrication and miscellaneous stuff introduces. We’re going to approach this by removing some of the ideal approximations to define a semi-ideal case. Then, as promised by the title of this section, practical considerations will be introduced and we’ll end up with a pretty realistic device. To begin, recall from our discussion of diffusion that the free electrons in the n-type material and the free holes in the p-type material will move across the junction until equilibrium is reached. The width of the resulting depletion region is related to the barrier potential and is a function of applied bias. I realize that all these terms are somewhat overwhelming, but if they are not comfortable, please review The pn Junction discussion. These concepts are fundamental to the design, operation and manipulation of all semiconductor devices and the sooner they are internalized, the less “painful” future material will be! Now, with that said, let’s look at how a diode actually works... The diode current equation presented in Equation 3.26 defines an exponential relationship between the diode current (the dependent variable) and the diode voltage (the independent variable) and is derived from the physics of Section A. This equation holds over at least seven orders of magnitude of current and is truly valuable in defining the behaviors of semiconductor diodes (and later bipolar junction transistors). NOTE: Please refer to notation conventions for a description as to significance of upper and lower case characters. vD nVT iD = IO(e − 1) (Equation 3.26) where: iD is the current through the diode vD is the voltage (potential difference) measured across the diode terminals IO is the reverse saturation current n is a device constant between 0.5 and 2 that is dependent on material, diode construction, and operational considerations. Unless otherwise explicitly stated, the standard simplification of n=1 will be used for all examples and may be made for all analyses. VT is defined as the thermal voltage and is approximately 26mV at room temperature (25oC). o Note: VT=kT/q where k is Boltzmann’s constant (1.38x10-23 J/ K), T is the absolute temperature in degrees Kelvin (oK=273 + the temperature in oC), and q indicates the fundamental charge of an electron (1.60x10-19 Coulombs (C=J/V)). The general shape of the IV curve based on Equation 3.26 is illustrated in the figure below: Let’s look more closely at this figure and Equation 3.26. From observation (and quick-and-dirty-math), we can define three distinct regions for the diode: 1. For zero bias, or the portion of the curve about vD ≈ zero, iD is approximately equal to zero. The curve is approximated by a straight line with a slope close to zero. This results in a near zero conductance (g=i/v) or an infinite resistance (r=v/i). 2. For the reverse bias situation, vD < 0 and the exponential term is less than one. If the reverse bias magnitude is greater than a few VT, the exponential term becomes negligible and iD≅-I0. The slope is still essentially zero, so the conductance remains close to zero and the diode resistance is considered infinite. 3. For any forward bias greater that a few VT (i.e., 50mV or so at room temperature), the exponential term in Equation 3.26 becomes much larger than one and may be considered dominant. In this case, the diode current expression may be simplified to iD≅I0exp(vD/nVT). The curve quickly becomes a straight line with a very large slope. At any point on this section of the curve, the dynamic resistance (which is approximately equal to the diode forward resistance, Rf) of the diode is defined by nVT rd ≈ Rf = . (Equation 3.31) iD So…now we’ve got a semi-ideal diode that’s based on physics and is still pretty well behaved. Since we can never let well enough alone, let’s goof with it, shall we? The first change that must be made when discussing practical devices is the removal of the assumption of the ideal, instantaneous change of material type at the pn junction. Instead of an ideal junction, the doping near the junction may be graded – that is, doping concentrations are a function of distance from the junction definition. This arises from the use of diffusion and implantation techniques – we don’t actually have two distinct material types and “stick” them together. We’re not actually going to do anything with this here (ah, for a solid state class), but I just wanted to bring it to your attention. The most important modification we must make in the forward bias region is the applied voltage required to get a measurable diode current (known as turn-on voltage). Rather than the few VT we used in the semi-ideal diode discussion above, this value (called VON) is approximately 0.7 V for silicon, 0.2 V for germanium, and 1.2 V for gallium arsenide diodes. Yep, this is the potential barrier voltage, Vo, of the pn junction we talked about in Section A6. There is also a difference in the reverse bias region due to both material characteristics and fabrication of the diode junction. The semi-ideal diode had a leakage current across the junction (the reverse saturation current, shown by –Io in the figure above), but had no restrictions on the magnitude of the applied reverse voltage. Practical devices have a breakdown voltage VBR (also called the peak inverse voltage (PIV) on manufacturer’s spec sheets). For magnitudes less than this breakdown voltage, the IV characteristics of the diode have a slope of 1/Rr. If the magnitude of the reverse bias approaches VBR, avalanche breakdown occurs. In this case, the junction breaks down, a large current flows, the device overheats, and a normal diode may be destroyed. These practical considerations are illustrated in Figure 3.18 of your text (reproduced below). For illustration, compare this figure to that for the semi- ideal (and ideal) diode. The last effect on diode operational characteristics we’re going to look at has to do with temperature. Going back to the thermal effects at the material level (Remember? More free carriers through EHP generation with increasing temperature?), there is more current, both for the forward and reverse operating regions, as the temperature increases. Therefore, the turn on voltage of the diode is directly related to the device temperature – as T increases, VON decreases and vice versa. Although there are numerous components to this dependence, it is standard practice to express the temperature dependence as a constant kT (see below). Equation 3.32 defines this temperature dependence numerically in terms of the relationship between room temperature parameters and a “new” temperature, which may be greater than or less than room temperature. VON(TNew ) − VON(Troom) = kT (TNew − Troom) (Equation 3.32) where: o Troom is generally considered approximately 25 C VON(Troom) is 0.7V for Si, 0.2V for Ge, and 1.2V for GaAs o TNew is the new diode temperature in degrees Centigrade ( C) VON(TNew) is the diode turn-on voltage at new temperature o kT is a temperature coefficient (kT = -2.0 mV/ C for Si and − 2.5 mV/oC for Ge) Finally, we can quantify the effect of temperature on the reverse saturation current. Equation 3.33 allows us to calculate the change in I0 at two temperatures T1 and T2 (Note: temperatures must be expressed in degrees Celcius!). The constant ki in equation 3.33 is material dependent and is defined at 0.15/oC for silicon. ki (T2 −T1 ) I0(atT2) = I0(atT1)e (Equation 3.33) Figure 3.19 in your text illustrates the temperature dependence of a standard silicon diode in the forward bias region as a sequence of curves generated for temperature increments of 25oC. This figure should be no surprise – again, it comes back to the physics of the junction. Remember that EHP generation is directly related to thermal excitation – as the temperature increases, the more free carriers are generated. So…with an increase in temperature the curves in forward bias shift left since less applied potential is required for the same current. Likewise, as temperature decreases, the curves will shift right. Regardless of the temperature change, the overall shape of the curve remains the same since it is controlled by the exponential relationship defined in equation 3.26. .
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