Subthreshold Current An n-channel MOSFET process is to be built in a p-type region doped with 8 × 10^16 cm^-3 , acceptors using an n^+ polysilicon gate. The oxide thickness is 15 nm, and the gate length is 0.8 μm. What is the ratio of the leakage currcnt that flows at VG = VT to that at VG = 0?

Question

Subthreshold Current

An n-channel MOSFET process is to be built in a p-type region doped with [latex] 8 × 10^{16} cm^{-3} [/latex] , acceptors using an [latex]n^+ [/latex] polysilicon gate. The oxide thickness is 15 nm, and the gate length is 0.8 μm. What is the ratio of the leakage currcnt that flows at [latex] V_G = V_T [/latex] to that at [latex] V_G = 0 [/latex]?

Accepted Answer

For an [latex] n^+ [/latex] polysilicon gate, n-channel MOSFET doped with [latex] N_a = 8 imes 10^{16} [/latex] acceptors [latex] cm^{-3} [/latex] the flat-band voltage and [latex] \phi_p [/latex] are estimated from Table 8.1 and the discussion in Sec. 8.3 to be -0.9 V and 0.36 V, respectively.

TABLE 8.1 Work Functions ( [latex] \pmb{\Phi _M} [/latex] and [latex] \pmb{\Phi _S} [/latex] )and Flat-Band Voltages for Commonly Used Gate Materials and p-Type Silicon with [latex] \pmb{N_a=1.1 imes 10^{15} \ cm^{-3}} [/latex] .

Gate material parameter	Aluminum	[latex] \pmb{n^+} [/latex] polysilicon	[latex] \pmb{p^+} [/latex] polysilicon	Tungsten
[latex] Φ_M (V) [/latex]	4.1	4.05	5.17	4.61
[latex] Φ_S (V) [/latex]	4.9	4.9	4.9	4.9
[latex] V_{FB} (V) [/latex]	-0.8	-0.85	0.27	-0.29

The gate-oxide capacitance [latex] C_{ox} [/latex] is [latex] 2.3 imes 10^{-7} F cm^{-2} [/latex], and the threshold voltage is calculated to be 0.41 V from Equation 8.3.18.

[latex] V_T=V_{FB}+V_C+2\left|\phi _p ight| +\frac{1}{C_{ox}} \sqrt{2\epsilon _sqN_a(2\left|\phi _p ight|+V_C-V_B )} [/latex] (8.3.18)

We calculate [latex] x_{dmax} = 1.28 imes 10^{-5} cm = 0.128 [/latex] μm from Equation 8.3.6, and therefore [latex] C_d = 8.2 imes 10^{-8} F \ cm^{-2} [/latex].

[latex] x_{dmax}=\sqrt{\frac{4\epsilon _s\left|\phi _p ight| }{qN_a} } [/latex] (8.3.6)

From Equation 9.1.29, n = 1.36, and S = 82 mV/decade.

[latex] n=1+\frac{C_d}{C_{ox}} [/latex] (9.1.29)

For a threshold voltage of 0.41 V, the current is (0.41/0.082) decades lower at [latex] V_G = 0 [/latex] than at [latex] V_T [/latex]. That is, the current at [latex] V_G = V_T [/latex] is [latex] 10^5 [/latex] times that at [latex] V_G = 0 [/latex].

Question 9.2: Subthreshold Current An n-channel MOSFET process is to be b...

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