Lecture 18 Field-Effect Transistors 3

Transcription

1 Lecture 18 Field-Effect Transistors 3 Schroder: Chapters, 4, 6 1/38 Announcements Homework 4/6: Is online now. Due Today. I will return it next Wednesday (30 th May). Homework 5/6: It will be online later today. This one will be a little different, and will basically be a data analysis exercise. It will still carry the same weight (7.5% of overall grade). Due Wednesday May 30th at 10:00am. I will return it the following Wednesday (6 th June). /38 1

2 Other Sources of Information It turns out that the information on FETs in Schroder is not well organized. It is spread across multiple chapters. There are some other good sources of information on this subject if you are interested: Review Articles: Books: Course ECE599 Thin Film Electronics, John Labram, Fall /38 Lecture 18 FET Conductance. Series Resistance. Threshold Voltage. Other Parameters. 4/38

3 FET Conductance 5/38 Mobility Last lecture we talked about how to evaluate fieldeffect mobility (either μ lin or μ sat ). Mobility is actually quite a specific parameter, and should be a property of a material, not just a device. Fundamentally: μ = v E Carrier velocity Electric field strength And this shouldn t matter how you measure it. However we know that this is not always the case. 6/38 3

4 Linear Mobility Last lecture we showed we can describe the mobility in the linear regime (μ lin ) as: W: Channel width. L: Channel length. μ lin = L WC ox V D di D d C ox : Capacitance per unit area. E.g. in F/cm. V D : Applied source-drain voltage. I D : Measured source-drain current. V D : Applied source-gate voltage. 7/38 Linear Mobility However we saw that in reality measured mobility does depend on applied gate voltage. I D (A) (V) V D = 10V di D /d (A/V) (V) V D = 10V Mobility should just be a property of a material (at a certain temperature, in a certain direction). 8/38 4

5 Saturation Mobility The same is also true when analyzing the saturation mobility I D (A) (V) V D = 100V d d I D d I D d (di D 1//d ) (A/V ) (A /V ) d I D /d (V) V D = 100V V D = 100V (V) 9/38 Validity of Mobility Recall from Lecture that our description of mobility relies on the fact that v E. v v = μe ~10 7 cm s -1 linear transport E When the drain voltage is large enough, nonlinear transport effects may be relevant such that the validity of the mobility assumption is suspect. 10/38 5

6 Interface Scattering Carriers are normally very close to the oxidesemiconductor interface. This means that they experience additional scattering involving interfacial roughness and insulator charge, in addition to normal bulk scattering. + + Oxide e - + e Semiconductor This additional scattering reduces the channel mobility. The larger the gate-induced electric field, the closer channel electrons are to the interface. 11/38 New FET Concepts Source gated transistors: Sporea et. al. Sci. Rep. 4, 495 (014) 1/38 6

7 New FET Concepts Metal-Insulator Transition. Some materials exhibit discreet change in electronic properties at certain temperatures. Can we induce phase-transition using electrical signals? /38 Conductance The point here is that while certain situations and transistor designs may have good switching characteristics, their strict mobility may be underestimated or over-estimated using the gradual channel approximation (GCA). It is sometimes more appropriate to talk about channel conductance (g) rather than mobility. g = di dv Where we are here only making a statement on electrical characteristics. 14/38 7

8 Output Conductance Since we have -voltages we can very, we must specify the type of conductance we mean. We define the Output Conductance (g d ) as: g d = I D V D Which must be defined at some. Hence g d is the slope of an output curve: I D V D,SAT g d 0 g d = big linear (wrt V D ) = constant V D 15/38 Output Conductance The undepleted channel conductance, (G c ) is typically assessed as the output conductance evaluated in the linear regime. Our main result from the GCA is: I D = W L μc ox V T V D V D In the undepeled (linear) regime V D V T. We showed last time that: I D = W L μ linc ox V T V D 16/38 8

9 Output Conductance We can hence say: G c = g d linear = I D V D G c = W L μ linc ox V T In the post-pinch-off (saturation) regime: As you would expect. g d saturation = 0 In a real device, the saturation output conductance is often greater than zero. I D ( A) Saturation V D (V) 17/38 Linear Transconductance The other type of conductance is the transfer conductance, often called transconductance. This is the conductance of the transfer curve: g m = I D This is what we used when evaluating mobility in the last Lecture. μ lin = L di D L μ WC ox V D dv lin = g G WC ox V m D 18/38 9

10 Series Resistance 19/38 Effective Channel Length The actual, physical channel length of a FET, L, is not always equal to its effective channel length, L eff, which is an electrical parameter. These two lengths are related via: L eff = L L. An example of how this could occur is given below: n + δl L SiO n + L eff δl L = δl This is just a question of terminology and identifying the area of the device in which carriers travel. 0/38 10

11 Effective Channel Length L eff is an extracted electrical parameter which is chosen as a linear best-fit to a plot of channel resistance versus channel length. One way to measure L eff, as well as the total sourcedrain series resistance, R SD = R S + R D, is now considered using the figure below. G S R S R D D 1/38 Effective Quantities In the previous lecture we showed the source-drain current in an FET can be given by: I D = W L μc ox V T V D V D If we denote the effective gate length, gate width and mobility by W eff, L eff, and μ eff respectively, then we can say: I D = W eff L eff μ eff C ox V T V D V D /38 11

12 External and Internal Voltages The gate and drain voltages are primed ( and V D ) to indicate that they are internal not external voltages. This is because some of the applied voltage drops across series resistances: We can relate external and internal voltages by: = + I D R S V D = V D + I D R S + R D 3/38 Contact Resistance By applying an external bias of V D V T we assume the device is in the linear regime. By assuming the contact resistance is symmetric we can say: R S = R D = R SD In this case, we can show that: I D = W eff μ eff C ox V T V D L L + W eff μ eff C ox V T R SD 4/38 1

13 Contact Resistance One way of proceeding is to take the reciprocal of this equation and to then solve for the measured resistance R m : R m = V D I D = R ch + R SD = L L W eff μ eff C ox V T + R SD Where R ch is the intrinsic channel resistance. We identify this as an equation for a straight line. 5/38 Contact Resistance L may be found by plotting R m versus L for devices with differing gate length, for differing gate voltages. The intersection of these lines gives R SD and L, from which L eff is obtained. R m (Ω) R SD L (μm) L 6/38 13

14 Threshold Voltage 7/38 Threshold Voltage Recall we talked about trapped charge last time. These effects lead to the FET turning on a that is not necessarily =0. We encapsulated this behavior into a parameter we call the threshold voltage: V T. ± ± ± S D ± Semiconductor ± ± ± ± Dielectric Metal (Gate) + ± ± ± 8/38 14

15 Threshold Voltage Below is some example data: Bias-stressing a device can shift V T. Fu-Yen Jian et al. Electrochem. Solid-State Lett. 010;13:H95-H97 9/38 Threshold Voltage For a threshold voltage V T, if we apply a gate voltage and the dielectric capacitance per unit area is C ox, we say we induce a mobile charge density of C mob : Q mob = C ox V T Unfortunately, it doesn t have a much clearer definition than this. This makes estimating the threshold voltage, V T, a bit tricky since it is a sloppy, imprecise quantity. It is important to be aware that the above definition does not lead to an abrupt transition between on and off states. 30/38 15

16 Linear Extrapolation Method There are two main ways to extract V T. Typically they both involve extrapolating data to I D = 0. The linear extrapolation method is used to extract V T when the device is operating in the linear regime. Consider the main result from the GCA: I D = W L μc ox V T V D V D Transfer characteristics involve plotting I D vs. We can just do this on a linear-linear scale. 31/38 Linear Extrapolation Method At I D = 0: I D = V T + V D V T + V D Near V T the I D - curve deviates from a straight line due to subthreshold current (we will come to this). At >V T, the I D - curve deviates from a straight line due to series resistance and/or mobility degradation. 3/38 16

17 Saturation Extrapolation Method The other technique, the saturation extrapolation method is used to extract V T when the device is operating in the saturation regime. We saw in Lecture 17 that when V D V T, we can say: I D = W L μ satc ox V T In this case, we could take the square root of the drain current: I D = W L μ satc ox V T 33/38 Saturation Extrapolation Method If we extrapolate this to I D =0, we get: = V T Experimental Fit I D (A 1/ ) I D 1/ V T (V) This must be carried out in the saturation region only to be accurate: V D V T. 34/38 17

18 Other Parameters 35/38 On/Off Ratio The on/off ratio simply quantifies the difference in source-drain current when the transistor is off and on. I on ΤI off 10 This parameter is just -9 approximated from transfer characteristics. (V) It turns out this is a very important parameter in logic circuit design. Quoted to nearest power of 10. E.g or I D (A) I on I off 36/38 18

19 Subthreshold Swing Subthreshold swing characterizes the slope of the transfer curves near the region where the device begins to switch on. d S = d log 10 I D Used to characterize the sharpness of the transition from off to on. A low value is desirable in logic and switching applications. I D (A) d d log 10 I D (V) 37/38 Next Time Optical Characterization 1. Time-resolved microwave conductivity (TRMC). Microwave Source and Detectors Microwaves Sample Optical Laser EM Wave Cavity Antenna 38/38 19