Exploring the Short-Channel Characteristics of Asymmetric Junctionless Double-Gate Silicon-on-Nothing MOSFET

Abstract

This paper presents an analytical model of an asymmetric junctionless double-gate (asymmetric DGJL) silicon-on-nothing metal-oxide-semiconductor field-effect transistor (MOSFET). Solving the 2-D Poisson’s equation, the expressions for center potential and threshold voltage are calculated. In addition, the response of the device toward the various short-channel effects like hot carrier effect, drain-induced barrier lowering and threshold voltage roll-off has also been examined along with subthreshold swing and drain current characteristics. Performance analysis of the present model is also demonstrated by comparing its short-channel behavior with conventional DGJL MOSFET. The effect of variation of the device features due to the variation of device parameters is also studied. The simulated results obtained using 2D device simulator, namely ATLAS, are in good agreement with the analytical results, hence validating our derived model.

Appendix

$\phi (x,0) = K_{1} (x) = \phi_{C} (x)$ with $\phi_{c} (x)$ representing the central potential is a function of x only.

Electric field at y=t_si/2 determined by gate and front oxide layer thickness is given by:

$$ \left. {\frac{\partial \phi (x,y)}{\partial y}} \right|_{{y = \frac{{t_{\text{si}} }}{2}}} = - \frac{{C_{\text{ox}} }}{{\varepsilon_{\text{si}} }}(\phi_{f} (x) - V_{{{\text{gs}}1}} + V_{fb} ) $$

(A.1)

Electric field at y=-t_si/2 determined by gate and air thickness is given by:

$$ \left. {\frac{\partial \phi (x,y)}{\partial y}} \right|_{{y = \frac{{ - t_{\text{si}} }}{2}}} = \frac{{C_{\text{air}} }}{{\varepsilon_{\text{si}} }}(\phi_{b} (x) - V_{\text{gs2}} + V_{fb} ) $$

(A.2)

$\phi_{f} (x)$ and $\phi_{b} (x)$ denote front and back surface potentials, respectively.

Using (2), (A.1) and (A.2), arbitrary constants are derived as:

$$ K_{2} (x) = \frac{1}{{2\varepsilon {}_{\text{si}}}}(C_{\text{air}} \phi_{b} (x) - C_{\text{ox}} \phi_{f} (x) + (V_{\text{gs1}} - V_{fb} )C_{\text{ox}} - (V_{\text{gs2}} - V_{fb} )C_{\text{air}} ) $$

(A.3)

$$ K_{3} (x) = - \frac{1}{{2t_{\text{si}} \varepsilon {}_{\text{si}}}}(C_{\text{ox}} \phi_{f} (x) + C_{\text{air}} \phi_{b} (x) - (V_{\text{gs1}} - V_{fb} )C_{\text{ox}} - (V_{\text{gs2}} - V_{fb} )C_{\text{air}} ) $$

(A.4)

Using (2), front and back potentials can be expressed as:

$$ \phi_{f} (x) = \phi_{c} (x) + K_{2} (x)\frac{{t_{\text{si}} }}{2} + K_{3} (x)\frac{{t_{\text{si}}^{2} }}{4} $$

(A.5)

$$ \phi_{b} (x) = \phi_{c} (x) - K_{2} (x)\frac{{t_{\text{si}} }}{2} + K_{3} (x)\frac{{t_{\text{si}}^{2} }}{4} $$

(A.6)

Putting the values of K₂(x) and K₃(x) in (A.5) and (A.6), front and back potentials in terms of central channel potential are calculated as:

$$ \phi_{f} (x) = \frac{{\phi_{c} (x) + (V_{\text{gs}} - V_{fb} )\frac{{3C_{\text{ox}} C_{\text{si}} + C_{\text{ox}} C_{air} }}{{8C_{\text{si}}^{2} + 4C_{\text{air}} C_{\text{si}} }} - (V_{\text{gs2}} - V_{\text{fb}} )\frac{{C_{\text{air}} }}{{8C_{\text{si}} + 4C_{\text{air}} }}}}{{\frac{{8C_{\text{si}}^{2} + 3C_{\text{si}} C_{\text{air}} + 3C_{\text{si}} C_{\text{ox}} + C_{\text{ox}} C_{\text{air}} }}{{8C_{\text{si}}^{2} + 4C_{\text{air}} C_{\text{si}} }}}} $$

(A.7)

$$ \phi_{b} (x) = \frac{{\phi_{c} (x)\frac{{2C_{\text{si}} + C_{\text{ox}} }}{{2C_{\text{si}} }} - (V_{\text{gs1}} - V_{fb} )\frac{{C_{\text{ox}} }}{{8C_{\text{si}} }} + (V_{\text{gs2}} - V_{\text{fb}} )\frac{{3C_{\text{air}} }}{{8C_{\text{si}} }} + \frac{{8C_{\text{ox}} C_{\text{air}} }}{{64C_{\text{si}}^{2} }}}}{{\frac{{8C_{\text{si}}^{2} + 3C_{\text{si}} C_{\text{air}} + 3C_{\text{si}} C_{\text{ox}} + C_{\text{ox}} C_{\text{air}} }}{{8C_{\text{si}}^{2} }}}} $$

(A.8)

Again, using (A.5) and (A.6) in (2), and differentiating twice with respect to x and y, and eliminating front and back potentials, we can write:

$$ \frac{{\partial^{2} \phi_{C} (x)}}{{\partial x^{2} }} - \frac{{8C_{\text{si}}^{2} (C_{\text{air}} + C_{\text{ox}} ) + 8C_{\text{air}} C_{\text{ox}} C_{\text{si}} }}{{t_{\text{si}} \varepsilon_{\text{si}} (8C_{\text{si}}^{2} + C_{\text{air}} C_{\text{ox}} + 3C_{\text{ox}} C_{\text{si}} + 3C_{\text{air}} C_{\text{si}} )}}\left[ {\phi_{c} (x) - \left\{ {V_{{{\text{gs}}1}} \frac{{4C_{\text{air}} C_{\text{ox}} C_{\text{si}} + 8C_{\text{ox}} C_{\text{si}}^{2} }}{{8C_{si}^{2} (C_{\text{air}} + C_{\text{ox}} ) + 8C_{\text{ox}} C_{\text{si}} C_{\text{air}} }} + V_{\text{gs2}} \frac{{4C_{\text{air}} C_{\text{ox}} C_{\text{si}} + 8C_{\text{air}} C_{\text{si}}^{2} }}{{8C_{\text{si}}^{2} (C_{\text{air}} + C_{\text{ox}} ) + 8C_{\text{ox}} C_{\text{si}} C_{\text{air}} }}} \right\} + V_{fb} - \frac{{qN_{d} t_{\text{si}} (8C_{\text{si}}^{2} + C_{\text{air}} C_{\text{ox}} + 3C_{\text{ox}} C_{\text{si}} + 3C_{\text{air}} C_{\text{si}} )}}{{8C_{\text{si}}^{2} (C_{\text{air}} + C_{\text{ox}} ) + 8C_{\text{air}} C_{\text{ox}} C_{\text{si}} }}} \right] $$

(A.9)

Hence, the generalized scaling equation can be expressed as:

$$ \frac{{\partial^{2} \phi_{C} (x)}}{{\partial x^{2} }} - \frac{1}{{\lambda_{c}^{2} }}(\phi_{c} (x) - \varPhi_{C} ) = 0 $$

(A.10)