Reinaldo Vega

junction abruptness and quantization questions

When setting up the device structure in nanoMOS, the program asks for the source/drain gaussian profile abruptness in units of dec/nm. There are two problems here. First, there’s a typo: the source/drain profile that results shows up in nm/dec, not dec/nm. Second, gaussian profiles do not have constant abruptness. Is it an actual gaussian profile, or is this another typo and the profile is really just a log-linear profile? If it is an actual gaussian profile, then in what part of the profile is the junction abruptness defined? Is it as simple as the distance from the peak where the concentration drops by one decade, or are you using some other metric?

My other question regards the quantum ballistic transport model, which also accounts for, among other things, direct source-to-drain tunneling by solving the schrodinger equation in the transport direction. Does this only model tunneling along the transport direction, or is this schrodinger equation also being applied to solve for quantization within the off-state potential barrier along the transport direction? In other words, if I have a very small gate length, say 3 nm, for NMOS there should be significant hole quantization in the valence band of the off-state barrier along the transport direction, which would change the off-state barrier height. Any input would be appreciated…

thanks, Reinaldo

1. I am only shooting the part of the question on the Gaussian doping since Kurtis has given answers to the other part.

I think the profile of Gaussian doping is a true Gaussian, which can be seen from the subroutine in doping.m regarding the Gaussian.

First is how the decay/lens is defined. Take the doping in the source as an example, the Gaussian doping means that the doping in the source is constant as specified as (N_sd-N_body); right at the source/channel junction and to the channel, the doping begins to take a Gaussian profile as N_sd*exp(-((iii_col-junction_l)*dx/decay_lens)2), and this is only for the Gaussian doping from source. If the drain doping is also Gaussian typed doping, add that to the total doping. You can see from the expression that it is a true Gaussian function typically defined as f(x)=N0*exp(-x2/(2*sigma^2)), except that in the code here decay_lens2 is equal to 2*sigma2. The parameter decay_lens is defined as (1/sqrt(log(10))*dopslope_s), meaning that the doping drops to 1/10 of N_sd when x=decay_lens to the right of source/channel junction.

### 3 Responses

1. You are correct about the typo, it should be in nm/dec, not dec/nm. I think this error has been passed down for several years. Regarding the Gaussian question, I am not entirely sure because I didn’t modify or carefully inspect the code that defines the doping, but I think it should be a true Gaussian. Another student would have a better idea about this.

I am not sure what you’re getting at with the last part regarding holes. Could it be you are talking about band-to-band tunneling? NanoMOS does not treat holes at all, so it would not include the effects of band-to-band tunneling or any hole quantization.

2. Hi Yang,

I have a question regarding the Gaussian doping. I took a look at the doping.m file. Since the decay_length2 = 2*sigma2, I calculated that the decay length should be 1/sqrt(2.3)*dopslope instead of 2/sqrt(2.3)*dopslope

because N(dopslope)/No = 1/10 = e(-dopslope2/(2*sigma^2)) solving for sigma, you get sigma = dopslope/sqrt(2*2.3) and 2*sigma2 = dopslope2/2.3 = decay_length^2
so decay_length should be dopslope*1/sqrt(2.3)

this means that whatever doping abruptness i declare in nanomos, it is actually half as abrupt of what i enter?

Thanks, Kevin Liu (Reinaldo’s undergraduate slave)  :)