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
I_{D} – diode current
I_{S} – scale (saturation) current
V_{d} – voltage across the diode. The anode A (ptype material) is assumed positive with respect to the cathode K (ntype material)
V_{T} – 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 turnon 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 I_{S} depends on the doping level of ntype and ptype 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 I_{S}=1E16.”
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Energy levels
http://www.electronicshub.org/wpcontent/uploads/2015/01/3.PNjunctionatThermalEquilibrium.jpg
V_{bi} is the diode bultin potential. It is the forward voltage value that must be applied to the diode to move the conduction energy levels of ptype and ntype material to the same level. When V_{bi} is applied, the current flows. V_{bi} is given by equation:
where:

N_{A} – doping in ptype material (acceptors)

N_{D} – doping in ntype material (donors)

n_{i} – number of holes and electrons in intrinsic silicon (~14.5 x 10^{9} carriers/cm^{3})
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The more doped n+ and p+ region the bigger V_{bi} 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 C_{j}
for plot see: http://m.eet.com/media/1155793/293252an_led_s_intrinsic_capacitance_works_in_a_650_mv_lrc_circuit_figure_2.jpg
C_{j0} – zerobias capacitance of the pn junction. The capacitance when the voltage across the diode is zero.
V_{D} – voltage across the diode
m – grading coefficient (showing how the silicon changes from ntype to ptype material)
V_{bi} – builtin potential
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Storage capacitance C_{s}
When the current flows, electrons from the ntype material move to the ptype material and then to the metal contact. Two types of diodes are distinguished:

a long base diode – when the electron recombines in the ptype 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 τ_{T} (transit time). In silicon the carrier lifetime τ_{T} is equal to ~10us.
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Electrons in ptype material and holes in ntype material that crossed the junction can be characterized by storage capacitance C_{S} which is equal to:
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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 C_{S} must be discharged). After removing the stored carriers, the diode behaves as voltage dependent capacitor that follows junction capacitance C_{j} 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
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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