1. The Shockley diode equation

\[i_D = I_S \left[\exp\left(\frac{v_D}{n\cdot V_T}\right) - 1\right]\]

Very often (see day09_diode-equation), we ignore the “-1” and use

\[i_D = I_S \exp\left(\frac{v_D}{n\cdot V_T}\right)\]
iD

current through the diode
IS

scale current or (reverse-bias) saturation current
vD

voltage across the diode
n

ideality factor or emission coefficent. =1 for an “ideal” diode and is 1 to 2 for a real device.

2. Temperature dependence

Temperature has a large effect on the value of IS, go back in the notes to see how it is affected by geometry, doping, material, and temperature.

hw09 deals with this mathematically.

There are two rules of thumb for a pn junction’s temperature dependence:

  • For a constant current: vD changes by about −2 mV / °C.

  • For a constant voltage: iD doubles every 10 °C increase.

2.1. 1N4148 datasheet

See this temperature dependence in the datasheet for the 1N4148

diode_1N4148_Vishay.pdf

  • Fig. 1 shows vD vs. temperature

  • Fig. 2 shows iD vs. vD

Vishay’s datasheet also has good information about maximum temperatures and power dissipation (remember: vD × iD is power absorbed).

But it curiously lists two maximum power dissipation numbers (440{mW} vs. 500{mW}).

day10_thermal-tutorial.pdf gives a brief tutorial on how to use thermal resistance to predict temperatures from power dissipation numbers and explains why the datasheet quotes two numbers..

3. First application circuit

The first (interesting!) circuit we can make with a diode once we know the Shockley equation is a proportional to absolute temperature (PTAT) circuit.

Have two pn junctions that are held to the same temperature but the second has a junction area M times larger. Glue the packages together, or, better yet, fabricate them on the same piece of silicon somehow.

  • Force the same current through both diodes.

  • Measure the voltage across each diode.

The difference between these voltages is:

\[v_1 - v_2 = \frac{k_B T}{q} \ln\left(M\right)\]

Notice that this has nothing to do with:

  • doping

  • absolute size of the junction (just the size ratio)

  • diffusion or mobility constants

Just the temperature scaled by three well-known constants!

4. Ultra doping

Consider a pn junction and dope the p side heavier.

Further increase NA on the p side.

Keep doping more and more.

We know that increasing the doping makes the region more conductive. If the doping is obscenely large, this region will be conductive perhaps like a metal.

  • Can you just replace the p side with a metal?

Yes! This is called a Schottky diode.

5. Reverse-bias until something breaks

If you reverse bias a pn junction and keep increasing the amount of reverse voltage, current will suddenly begin to flow.

Normally, the built-in and applied E-fields add and oppose current flow, but there are two phenomena that come into play.

  • Zener breakdown









  • Avalanche breakdown