Branch : Computer Science and Engineering
Subject : Fundamental of Electronic Devices
Unit : Transistors
MOSFET: Threshold Voltage
Influence of materials parameters on threshold voltage:
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The voltage required to achieve flat band should be added to the threshold voltage equation obtained for the ideal MOS structure (for which we assumed a zero flat band voltage):
VT = Φms- Qi/Ci - Qd/Ci 2ΦF
- Thus the voltage required to create strong inversion must be large enough to first achieve the flat band condition (Φms and Qi/Ci, terms), then accommodate the charge in the depletion region (Qd/Ci), and finally to induce the inverted region (2ΦF).
- This equation accounts for the dominant threshold voltage effects in typical MOS devices. It can be used for both n-type and p-type substrates if appropriate signs are included for each term.
- Typically Φms is negative, although its value varies. The interface charge is positive, so the contribution of the -Qi/Ci term is negative for either substrate type.
- On the other hand, the charge in the depletion region is negative for ionized acceptors (p-type substrate, n-channel device) and is positive for ionized donors (n-type substrate, p channel). Also, the term ΦF which is defined as (Ei - EF)/q in the neutral substrate, can be positive or negative, depending on the conductivity type of the substrate.
- Considering the signs in Fig, we see that all four terms give negative contributions in the p-channel case.
- we expect negative threshold voltages for typical p-channel devices. On the other hand, n-channel devices may have either positive or negative threshold voltages, depending on the relative values of terms in Eq. shown in above.
- All terms in Eq.except Qi/Ci depend on the doping in the substrate. The terms Φms and ΦF have relatively small variations as EF is moved up or down by the doping.
- Large changes can occur in Qd, which varies with the square root of the doping impurity concentration as in Eq.
- We illustrate the variation of threshold voltage with substrate doping in Fig. above.
- As expected from Eq. , VT is always negative for the p-channel case. In the n-channel case, the negative flat band voltage terms can dominate for lightly doped p-type substrates, resulting in a negative threshold voltage.
- However, for more heavily doped substrates, the increasing contribution of Na to the Qd term dominates, and VT becomes positive.