MOS capacitor transient response

[hasib_eee]

Hello.

Suppose we have a MOS capacitor (n-substrate). When we give negative voltage the majority carrier (electrons) are repelled from the oxide-substrate interface and move towards the bulk.

Say the bias is -0.3 volts. The substrate is depleted and in steady-state. Suddenly if the bias is changed from -0.3 to -0.6, I know that the width of depletion region will increase definitely.

My question is how long will it take to reach the new steady state? Does it depends on some form of life time or response time? I found typical example in textbooks for optical step excitation where they showed (1-exp(t/tao)) like shape to reach steady-state.

How can I model the movement of majority carriers (electrons) under step bias?

Please give me some information.

Thanks.

M. Satter.

 

[ranger]

Hi hasib_eee,

I think I may have found an article that answers (to a certain degree) your question. Among the test conditions were step like bias voltages. I assume that your school gives you free access to various scientific journals. Here is the abstract:

We present an experimental study of charge transfer in polymer thin-film field-effect devices. The rearrangement of the charge-carrier density in the transistor channel upon a gate-voltage swing has been monitored in real time and space by means of noncontact scanning potentiometry. The experimental results are in excellent agreement with a simple theory, in which the charging currents are assumed to be driven by drift in the self-induced electric field. The charge density exponentially approaches its final value with a time constant given by L²/µ|Vg|pi², where L is the characteristic device dimension, µ the field-effect mobility, and Vg the final gate voltage.

See:
L. Bürgi, R. H. Friend, and H. Sirringhaus. Applied Physics Letters; 3/3/2003, Vol. 82 Issue 9, p1482, 3p

 

[ravenprp]

Hello M. Satter,

Thank you for your question. The transient response of a MOS capacitor to a change in bias voltage is an important aspect of its behavior. The time it takes for the capacitor to reach a new steady state depends on a few factors, including the device parameters and the applied voltage.

The time it takes for the majority carriers (electrons) to move and reach the new steady state can be modeled using the concept of carrier lifetime. Carrier lifetime is a measure of how long a majority carrier remains in a specific region before recombining or moving to a different region. In the case of a MOS capacitor, the majority carriers (electrons) move towards the bulk when the bias voltage is changed. This movement is affected by the carrier lifetime, as well as the electric field and the mobility of the carriers.

The transient response of a MOS capacitor can be modeled using the Shockley-Read-Hall (SRH) recombination model, which takes into account the carrier lifetime and the recombination rate. This model can be used to calculate the time it takes for the capacitor to reach a new steady state.

In terms of the movement of majority carriers, it can be described using the continuity equation, which relates the rate of change of carrier density to the carrier generation, recombination, and drift. Under a step bias, the majority carriers will experience a sudden change in the electric field, which will result in a change in their drift velocity and movement towards the bulk.

I hope this information helps answer your question. Thank you for your interest in MOS capacitors and their transient response. Best of luck with your studies.