Tags: breakdown voltage, CMOS, depletion capacitance, diode, energy levels, equations, junction capacitance, models, silicon, SPICE, storage capacitance

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Diode equation – Shockley diode equation

diode - Shockley equation

ID – diode current

ISscale (saturation) current

Vd – voltage across the diode. The anode A (p-type material) is assumed positive with respect to the cathode K (n-type material)

VT – thermal voltage equal to kT/q where k is Boltzmann’s constant

T – temperature in Kelvin

n – emission coefficient (a term that is related to the doping profile and affects both the exponential behavior of the diode and the diode’s turn-on voltage)

q – electron charge

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Diode current is exponential with applied diode voltage. For room temperature, when diode voltage is 0.3 V, very little current flows; at 0.6 V the current is substantial; and at 0.9 V very large.

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[Camenzind] “The diffusion current IS depends on the doping level of n-type and p-type impurities, the area of the diode and (to a very high degree) on temperature. A reasonable starting point for a small geometry IC diode is IS=1E-16.”

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Energy levels

http://www.electronicshub.org/wp-content/uploads/2015/01/3.-PN-junction-at-Thermal-Equilibrium.jpg

Vbi is the diode bult-in potential. It is the forward voltage value that must be applied to the diode to move the conduction energy levels of p-type and n-type material to the same level. When Vbi is applied, the current flows. Vbi is given by equation:

diode - built-in potential equation

where:

  • NA – doping in p-type material (acceptors)

  • ND – doping in n-type material (donors)

  • ni – number of holes and electrons in intrinsic silicon (~14.5 x 109 carriers/cm3)

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The more doped n+ and p+ region the bigger Vbi voltage.

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Breakdown voltage

Breakdown voltage depends on the concentration of dopants. The higher the concentration, the lower the breakdown voltage.

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Junction (depletion) capacitance Cj

for plot see: http://m.eet.com/media/1155793/293252-an_led_s_intrinsic_capacitance_works_in_a_650_mv_lrc_circuit_figure_2.jpg

diode - junction capacitance equation

Cj0 – zero-bias capacitance of the pn junction. The capacitance when the voltage across the diode is zero.

VD – voltage across the diode

m – grading coefficient (showing how the silicon changes from n-type to p-type material)

Vbi – built-in potential

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Storage capacitance Cs

When the current flows, electrons from the n-type material move to the p-type material and then to the metal contact. Two types of diodes are distinguished:

  • a long base diode – when the electron recombines in the p-type material before hitting the metal contact

  • a short base diode – when the electron reaches the metal contact before recombining. In this case, the distance between the junction and the metal contact is short.

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For the electron, the time between crossing the junction and recombining is called the carrier lifetime τT (transit time). In silicon the carrier lifetime τT is equal to ~10us.

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Electrons in p-type material and holes in n-type material that crossed the junction can be characterized by storage capacitance CS which is equal to:

diode - storage capacitance equation

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When the diode is turned on, the current flows through it. If then the diode is turned off, by for example changing its voltage from positive to 0 V (or to negative voltage), the stored carriers must be firstly removed (storage capacitance CS must be discharged). After removing the stored carriers, the diode behaves as voltage dependent capacitor that follows junction capacitance Cj equation.

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SPICE

Extended version of Baker’s table filled with data from

http://www.seas.upenn.edu/~jan/spice/spice.overview.html#Diode

diode - spice parameters v2

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How to define diode in SPICE:

.model model_name D (vj= is= rs= cj0= tt= bv= ibv= n= m= )

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Resources:

  • Baker R. Jacob, CMOS Circuit Design, Layout, and Simulation, 3rd Edition, 2010, John Wiley & Sons

  • Camenzind H., Designing Analog Chips, February 2005