Some considerations on VTH and TVTC equations and real examples

AN2386

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and real examples

Looking at (Equation 30) it is possible see that the threshold voltage is the sum of three

components: the metal-oxide work function (it is negative when the polysilicon is of n-type

and the silicon substrate is of p-type, while, it is positive when the polysilicon is of p-type),

two times the Fermi potential (it is positive for p-type silicon substrate) and the voltage drop

on the oxide (it is positive for a p-type silicon substrate). TVTC (see Equation 42) also

depends on three contributes: the metal-oxide work function divided by the temperature (it is

a negative value for n-type gate doped in p-type silicon), two times the Fermi potential

divided by the temperature (for a p-type silicon it is a positive value) and a third contribute

function of the Fermi potential thermal coefficient and other parameters as the oxide

thickness and the body concentration of impurity (it is a negative contribute because of its

negative the Fermi potential thermal coefficient).

Considering low voltage power MOSFETs working in linear zone in applications like air fans,

it is important have devices with standard threshold voltage (around 3V in ambient

temperature) and very low TVTC in absolute value, in order to avoid the thermal instability

behavior that could bring the component to fail.

The modern MOSFETs have TVTC in the negative value range (it becomes more negative

when the temperature increases). Therefore, when the device works in linear zone, a power

pulse is dissipated on the component, the temperature increases, the threshold voltage

decreases and the drain current rises.

To avoid the thermal run-away of the device, it is important to minimize the TVTC in absolute

value. The parameters that make TVTC negative, considering an n-type gate and p-type

silicon, are the metal-oxide work functions divided by the temperature and the term of the

Fermi potential thermal coefficient. Instead, the parameter that makes TVTC positive is the

Fermi potential divided by the temperature (T). As shown in (Equation 32), the metal-oxide

work function divided by T depends on the doping concentration of the gate, silicon and the

intrinsic carrier concentration. This parameter increases in absolute value, increasing the

doping concentration of the gate or substrate, while it decreases in absolute value when the

temperature increases because of the intrinsic carrier concentration increases too. In order

to minimize this parameter, the gate and substrate doping concentration must be lowered.

The Fermi potential divided by T depends on the doping concentration of the substrate and

the intrinsic concentration of the carriers. When the doping concentration of the substrate

increases, the parameter also increases its value. By increasing the temperature, the

parameter decreases because the intrinsic carrier concentration increases. In order to

maximize the parameter, the substrate doping concentration should be increased.

The threshold voltage thermal coefficient (see Equation 41) depends on the Fermi potential

divided by T, minus a constant and minus a term function of the inverse of T. Its value is

negative because the parameter with the minus sign is generally higher than the term, due

to the Fermi potential divided by T. When the temperature increases, the parameter also

increases in absolute value because the Fermi potential decreases too. Thus, in order to

minimize the Fermi potential thermal coefficient, the substrate doping concentration must be

increased. However, the third term of (Equation 42), as previously explained, also depends

on the substrate doping concentration root-square. Therefore, considering the modern

MOSFET technology, this term increases in absolute value when the substrate doping

concentration also increases.