Due: Thursday, 9/21/00

Remember to turn in clearly written and easy to follow homework!

1.     An nMOS transistor is formed in a Si substrate doped with N_A=2x10¹⁵ cm^-3.  If the device is biased for operation in the inversion region, and has V_SB = 0:
a)  What is the Fermi potential, f_f, in the semiconductor, and what is the electrostatic potential at the oxide-semiconductor interface (f_sur)?
b)  What is the depletion layer thickness, x_d?
c)  If we assume x_d =0.6mm, f_f=0.3 V, how much charge is in the depletion layer?

2.     An nMOS transistor has the following data: the oxide capacitance is 80nF/cm², the work function difference between the gate and the semiconductor is -0.1 V, f_F = 0.3 V, Q_b = -2.5x10^-8 coulombs/cm², and Qss = 10^-8 coulombs/cm².
a)  Calculate the equilibrium threshold voltage, Vto,
b)  If g = 0.25 V^½, what is the threshold voltage if V_SB is 1V?

3.     An n-channel transistor has a substrate concentration of N_A = 1.4 x 10¹⁷ cm^-3, m_nC_ox = 188 mA/V², W=6mm, L=0.6 mm, and V_th=0.8V.
a)  If the device is biased at V_GS= 1.2V and V_DS = V_eff (V_eff = V_GS – V_th), which region of operation (cutoff, triode, saturation) is the device operating in?
b)  If we ignore channel length modulation, what is the drain current?
c)  If V_DS increases by 0.5V, what is the new drain current if l = 0.01 V^-1?

4.     An nMOS transistor in the saturation region is measured to have the drain current of 20 mA when V_DS = V_eff.  When V_DS is increased by 0.5V, I_D increases to 23 mA.
a)  Calculate the channel length modulation factor, l, for this device.
b)  What is the output resistance, r₀, of this transistor?

5.     An n-channel enhancement mode MOSFET has parameters: V_th=2V, K=0.4mA/V² (K=½mC_OXW/L)
a)  If V_GS=4.3V, how large must V_DS be for constant current operation?
b)  What value of I_D flows for V_GS=4.3V?
c)  What region of operation is the device in if V_DS is reduced to 2V?
d)  What value of I_D flows at V_DS=2V?

6.     An nMOS transistor has parameters W=100 m, L=10 mC_OX = 20 mA/V²,l=0.01V^-1, t_ox=0.12mm, f_f=0.3V, V_t0=1.1V, N_A=10¹⁵ cm^-3.  For the following cases, you should prepare a table of values (at least 3-4 values for each case, appropriately spread over the range of interest) and then plot those values.
a) Sketch the I_D – V_DS characteristics for V_DS from 0 to 10V at V_GS=0.5,1.5 and 3V.  Assume V_SB= 0V
b) Sketch the I_D – V_GS characteristics for V_GS from 0 to 3V at V_SB = 0, and 2 V.  Assume V_DS=5V.

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