Explicit continuous charge-based compact model for long channel heavily doped surrounding-gate MOSFETs incorporating interface traps and quantum effects

Abstract

An explicit solution for long-channel surrounding-gate (SRG) MOSFETs is presented from intrinsic to heavily doped body including the effects of interface traps and fixed oxide charges. The solution is based on the core SRGMOSFETs model of the Unified Charge Control Model (UCCM) for heavily doped conditions. The UCCM model of highly doped SRGMOSFETs is derived to obtain the exact equivalent expression as in the undoped case. Taking advantage of the undoped explicit charge-based expression, the asymptotic limits for below threshold and above threshold have been redefined to include the effect of trap states for heavily doped cases. After solving the asymptotic limits, an explicit mobile charge expression is obtained which includes the trap state effects. The explicit mobile charge model shows very good agreement with respect to numerical simulation over practical terminal voltages, doping concentration, geometry effects, and trap state effects due to the fixed oxide charges and interface traps. Then, the drain current is obtained using the Pao-Sahʼs dual integral, which is expressed as a function of inversion charge densities at the source/drain ends. The drain current agreed well with the implicit solution and numerical simulation for all regions of operation without employing any empirical parameters. A comparison with previous explicit models has been conducted to verify the competency of the proposed model with the doping concentration of ´-1 10 cm 19 3 , as the proposed model has better advantages in terms of its simplicity and accuracy at a higher doping concentration.

Modeling of inversion and centroid charges of long channel strained-silicon surrounding gate MOSFETs incorporating quantum effects

“…These parameters are calculated based on energy splitting, which includes on the conduction band (DE c ) and valence band (DE v ). The threshold voltage in equations (10), ( 11) is formulated based on strain effect and simplified differently compared to the previous model in [15,17]. The implicit form in equation ( 9) can be converted into a direct solution which can be solved explicitly using the extra functions in [28].…”

“…The inversion charge in equation ( 9) is a more accurate model for exceeding the threshold. In order to maintain a unified form for Q , in the explicit form of the threshold voltage is required for a final inversion charge as introduced by [17,18]. Thus, a final unified threshold based on strain effect can be simplified as…”

“…For modeling work, a compact model can be derived using the charge or surface potential approach. Both of them can be solved either by using the implicit (numerical method) or explicit method (direct solution) [15][16][17][18]. The compact model is preferable compared to the numerical model which needs to consider significant physical geometry effects using a simple mathematical solution.…”

“…Another consequence contributed by the numerical method is the convergence issue which requires a longer time to solve thus making the calculation very slow. The compact model in previous works has been derived for unstrained SG MOSFETs [15][16][17][18]23]. Moreover, several attempts have been initiated to model the device with the incorporation of quantum effect which applies for both intrinsic and unstrained devices [5,24,25].…”

Investigation of Electrical Behaviors Observed in Vertical GaN Nanowire Transistors Using Extended Landauer-Büttiker Formula

“…Moreover, a common model used to study GaN-based metal-oxide-semiconductor field effect transistors (MOSFETs) performance is gradual channel approximation (GCA) [15]- [17], although it still cannot explain the nonlinear behavior of thecurve. Meanwhile, the Mott-Gurney law is less appropriate for solving the device issues [9].…”