MOSFETs - An Introduction Chapter 17. MOSFETs - An Introduction Sung June Kim kimsj@snu.ac.kr http://nanobio.snu.ac.kr

CONTENTS Qualitative Theory of Operation Quantitative ID - VD Relationships Subthreshold Swing ac Response

Qualitative Theory of Operation Assumption Ideal Structure Long Channel Enhancement-Mode MOSFET=MOS-Capacitor + 2 pn junctions n - channel (p-type substrate)

Visualization of various phases of VG > VT MOSFET operation

VD = 0 Case When VG  VT, very few electrons in the channel, an open circuit between the n+ region When VG > VT, Inversion layer is formed The conducting channel (induced “n-type” region, inversion layer) connects the D & S VG → the pile up of electrons & conductance   VG determines the maximum conductance Thermal equilibrium prevails, and ID=0

The VD is increased in small steps starting from VD = 0 The channel acts like a simple resistor ID  VD The reverse bias junction current is negligible voltage drop from the drain to the source starts to negate the inverting effect of the gate VD → Depletion of the channel & # of carriers & conductance & slope-over in the IV

Pinch - off (VD = VDsat) Disappearance of the channel adjacent to the drain The slope of the ID-VD becomes approximately zero(Point B)

Post-pinch-off (VD > VDsat) The pinched-off portion widens from just a point into a depleted channel section L The pinched-off section absorbs most of the voltage drop in excess of VDsat For L << L, the shape of the conducting region and the potential across the region do not change & Constant ID For L ~ L, ID will increase with VD > VDsat

ID - VD Characteristics General form of the ID - VD (L << L ) For VG  VT , ID  0 For VG >VT , transistor action: ID is modulated by VG VD > VDsat : saturation region VD < VDsat : linear(triode) region The slope increases with VG VDsat increases with VG

Quantitative ID - VD Relationships Effective Mobility : Impurity Scattering + Lattice Scattering + Surface Scattering

Effective Mobility

Square - Law Theory VD < VDsat Drift current is dominant At an arbitrary point y Inversion layer charge density(q/cm^2)

Integrating

VD  VDsat ID is approximately constant

Bulk-Charge Theory As VD increases, the depletion width widens from S to D. With changes in the depletion width, W(y), taken into account, where, making use of the delta-depletion results, Combinig (1) to (2), and introducing One obtains the bulk-charge theory analogue of QN(y) …(1) …(2)

Bulk-Charge Theory ID -VD relationship An expression for VDsat can be obtained by noting when , Inversion layer charge density(q/cm^2)

Inversion layer charge density(q/cm^2)

Subthreshold transfer characteristics At weak inversion, diffusion current dominates In long channel MOSFETS the subthreshold current varies exponentially with VG and is independent of VD provided VD > a few kT/q

Subthreshold swing

17.3 a.c. Response Cgs(Cgd): The interaction between G and the channel charge near S(D) Cgsp,Cgdp: parasitic or overlap capacitances

Small-signal equivalent circuit D in MOSFET out S S G S D vd + - vg gmvgs gd

A capacitor behaves like an open circuit at low frequencies. G S D vd + - vg gmvgs gd Cgd Cgs A capacitor behaves like an open circuit at low frequencies.

ID(VD,VG) + id = ID(VD + vd , VG +vg) id = ID(VD + vd , VG +vg) - ID(VD,VG)

id G S D vd + - vg gmvgs gd

Table 17.1 Below pinch-off (VD≤VDsat) Above pinch-off (VD>VDsat)

At the higher operational frequencies encountered in practical applications, the circuit must be modified to take into account capacitive coupling between the device terminals. The overlap capacitance is minimized by forming a thicker oxide in the overlap region or preferably through the use of self aligned gate procedures.  Cgd is typically negligible. G S D vd + - vg gmvgs gd Cgd Cgs

17.3.2. Cutoff Frequency The fT be defined as the frequency where the MOSFET is no longer amplifying the input signal under optimum conditions.  Value of the output current to input current ratio is unity

Small Signal Characteristics gd vs. VG(VD=0) Extrapolating the linear portion of the gd-VG characteristics into the VG axis and equating the voltage intercept to VT Deduce the effective mobility from the slope

Gate Capacitance vs. VG (VD=0) Diagnostic purposes in much the same manner as the MOS-C C-VG characteristics Unlike the MOS-C , a low-frequency characteristics is observed even for frequencies exceeding 1MHz Because the source and drain islands supply the minority carries