Optimized terminal current calculation for Monte Carlo device simulation

Abstract

We present a generalized Ramo-Shockley theorem (GRST) for the calculation of time-dependent terminal currents in multidimensional charge transport calculations and simulations. While analytically equivalent to existing boundary integration methods, this new domain integration technique is less sensitive to numerical error introduced by calculations of finite precision. Most significantly, we derive entirely new optimized formulas for the ensemble Monte Carlo estimation of steady-state terminal currents from the time-independent form of our GRST, which are in general not equivalent to the time-average of the true time-dependent terminal currents. We then demonstrate, both analytically and by means of example, how our new varianceminimizing terminal current estimators may be exploited to improve estimator accuracy in comparison to existing methods.

DEPFET sensor design using an experimental 3d device simulator

“…Contact currents are computed by using the properties of the discrete weak formulation and test functions defined by approximate solutions of the adjoint discrete problem (compare [16], too). Together with Newton's method (in a positivity preserving form) this allows to compute contact currents fulfilling the balance relation much better than 10 À10 P j jI j j4j P j I j j (I j current at contact j) for typical distances from the thermal equilibrium.…”

“…Gä rtner, R.H. Richter / Nuclear Instruments and Methods in Physics Research A 568 (2006)[12][13][14][15][16][17] …”

Shockley-Ramo theorem measures conformation changes of ion channels and proteins

“…We follow Yoder et al (1997): v j and r j are the instantaneous velocity and position vectors, respectively, of the particle j with charge q j when the clamped voltage E m is applied. W is the electric field that would be generated by removing all particle charges (mobile and fixed) from the domain and setting the clamped voltage to 1 volt.…”

Relating Microscopic Charge Movement to Macroscopic Currents: The Ramo-Shockley Theorem Applied to Ion Channels

“…We use the nomenclature of Yoder et al (1997) where v j and r j are the instantaneous velocity and position vectors, respectively, of the particle j with charge q j when the clamped voltage E m is applied. W is the electric field that would be generated by removing all particle charges (mobile and fixed) from the domain and setting the clamped voltage to 1 volt.…”