ECEN 3320 Spring 2022 Semiconductor Devices Problem Set # 10
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit
Problem Set # 10
ECEN 3320 Spring 2022
Semiconductor Devices
Figure 1: A schematic depiction of the n-channel metal semiconductor field effect transistor (MESFET) with a channel of depth a. length L and a width of W that is perpendicular to the plane of the paper.
A MEtal Semiconductor Field Effect Transistor (MESFET, as first fabricated by Mead in 1965) consists of a Schottky contact on top of a conductive channel (extending from the surface to a depth of a, of length L along the channel and of a width W transverse to the channel, see Fig. 1) that is attached at either channel end to an Ohmic contact. The Schottky contact is characterized by its built-in potential
Nc
φi = φB - kT log
where φB is the barrier potential, that is, the difference between the metal work function and the electron affinity of the semiconductor. The built-in potential is also related to the depletion layer width xd that would exist in absence of the Ohmic contacts by
φi = qNdxd(2)
Inline with this relation (as derived in the full depletion approximation), the channel would be
pinched off by application of a potential Vp defined by
qNda2
2es .
Given that there is a built-in potential, the voltage that would be needed to close the channel then can be defined by a threshold potential, VT defined by
VT = φi - Vp = -
The most interesting quantity in determining control of MESFET operation is then the difference between the gate source voltage Vgs and the threshold voltage VT. In general, the quantity Vgs - VT will be small, that is, the gate source voltage is the control parameter of interest.
Figure 2: A depiction of the I-V curves for an n-channel depletion mode metal semiconductor field effect transistor (MESFET). As can be seen, the MESFET channel turns off at voltage VJζ leV兰 and saturates at a voltage where VJζ - V兰 exceeds the drain source voltage V占ζ .
An analysis of channel current flow coupled to that of a depletion layer that varies along the flow direction results in the conclusion that there is little or no current flow when VGS s VT independent of VDS > 0 and that the current level saturates when VGS - VT > VDS. The rather complicated expression
IDS = G0 ┌ VDS - ╱ \┐
where
Wa
interpolates between the IDS values of 0 and the saturation value.
The IV curve situation can be summarized as
,
ì ì ì
IDS = (
ì ì ì
0
G0 ┌ VDS - ╱ (φ扌 +V台甘 −Vè甘V(|)〉(幺)− (φ扌 −Vè甘)岁|幺 、┐ G0 (Vè甘V扛)幺
VGS - VT s 0 s VDS
0 s VDS s VGS - VT
0 s VGS - VT s VDS
It should be noted that there is a regime in which IDS is approximately linear in VDS when VGS > VT but when VDS is strictly greater than VGS - VT. The above relation can be rewritten to Taylor approximated to be (overly) linear in the transition region as
,
ì ì
IDS = (
ì ì
0
G0 (Vè甘扛 )V台甘 G0 (Vè甘V扛)幺
VGS - VT s 0 s VDS
0 s VDS s VGS - VT
0 s VGS - VT s VDS
1. A MESFET Resistor
Consider an n-channel MESFET that we choose to use as a depletion mode resistor. Assume that G0 = 0.001 Mho and Vp = 2.5V and φi = 0.5V.
(a) Calculate the range of VGS over which the MESFET can be operated as a resistor. (b) Calculate the range of resistance values over that the MESFET can achieve.
(c) Calculate the value of a necessary to achieve this values of Vp when the metal is Au and the channel is GaAs doped to Nd = 2 × 1015/cm3 (see Figure 3).
(d) Calculate the W necessary to achieve the G0 value in the above described silicon channel assuming an L = 10µm and any values needed from Figure 4.
Figure 3: A table of work functions for various metals and resulting barrier heights on various doped semiconductors.
Figure 4: A table of material parameters for GaAs. Values taken from Van Zeghbroeck.
2. MESFET IV Characterists
Consider an n-channel depletion mode metal semiconductor field effect transistor (MESFET) in GaAs doped at 2 × 1015 /cm3 . Assume the contact is Al, channel length is L = 10µm, the channel thickness is a = 1µm and the channel width is W = 4µm.
(a) Calculate the threshold voltage.
(b) Calculate the conductance G0 .
(c) Calculate the gate to source voltage and drain to source voltage at which the current saturates to 2 mA.
(d) Make a sketch of the variation of the drain to source current with the gate to source voltage.
A two port representation of a MESFET is given in Figure 5. A two-port representation of a three terminal device clearly requires that one terminal to be grounded and that biases be applied to the others. Here, the assumption is n-channel depletion mode operation with a common source.
Figure 5: A two port model for a common source MESFET.
In our assumed bias and operation scheme, evidently, the gate current is zero in low frequency and quite small even at high frequency. A high frequency small signal representation of the MSE- FET could appear as in Figure 6. The primary limitation that the high frequency model represents is the capacitance. When combined with the line resistance, the capacitance will result in an RC time constant to charge the junction in order to achieve present the applied voltage to the channel.
Figure 6: A small signal model two port representation for a common source n-channel MESFET.
The gate source capacitance is close to that of the junction itself
e0 esA
where the area A is the channel length L multiplied by the transverse width of the channel W . The capacitance can also more generally be defined as the derivative of the stored charge with respect to the gate source voltage.
The conductances can be defined as
gm =
g0 =
∂Ids
∂Vgs
∂Ids
∂Vds
3. MESFET Small Signal Parameters
Consider a MESFET to be used as a linear signal amplifier. The MESFET is connected between two transmission lines of characteristic impedance 50 Ω. Model the input line as a sinusoidal voltage source of amplitude vi with a series source resistance rs. Take the output line to be a series load resistance rl with voltage vo across it. Assume rl 冬 (1/go).
(a) Calculate the amplitude and phase of vgs in terms of rs and Cgs .
(b) Calculate the amplitude and phase of vo .
(c) Calculate the 1/e bandwidth of the amplifier.
(d) Evaluate the bandwidth of the amplifier assuming rs = 50Ω, that the area in the capac- itance is 50µm2 and the values for an n-channel MESFET with doping of 1016 /m3 .
(e) Sketch a plot of the bandwidth as a function of the junction area.
2022-03-18