Set 6 Web Solutions LC

8/22/2019 Set 6 Web Solutions LC

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P3000, LON-CAPA Set 6 Sample Solutions:

1. Two-terminal

MOS capacitor:

From Neamen Sect. 6.2. The figure above shows the choices of energy band diagrams forthis question and the following 3 questions.The dc charge distribution of an ideal MOS capacitor is shown below.

In the first box, type "n" or "p" to indicate if the semiconductor in the device shown is n-type or p-type respectively.In the second box, type "a" if the device is biased in the accumulation mode, "d" if it isbiased in the depletion mode, or "i" if it is biased in the inversion mode.In the third box, type the letter "A", "B", "C", "D", "E", or "F" to indicate which of theeenrgy band diagrams shown above most closely corresponds to this device and bias.

Cor r ect , comput er get s: p, i , C


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The dc charge distribution of another ideal MOS capacitor is shown below.

In the first box, type "n" or "p" to indicate if the semiconductor in the device shown is n-type or p-type respectively.

In the second box, type "a" if the device is biased in the accumulation mode, "d" if it isbiased in the depletion mode, or "i" if it is biased in the inversion mode.In the third box, type the letter "A", "B", "C", "D", "E", or "F" to indicate which of theeenrgy band diagrams shown above most closely corresponds to this device and bias.

Cor r ect , comput er get s: p, d, B


In the first box, type "n" or "p" to indicate if the semiconductor in the device shown is n-type or p-type respectively.In the second box, type "a" if the device is biased in the accumulation mode, "d" if it isbiased in the depletion mode, or "i" if it is biased in the inversion mode.

In the third box, type the letter "A", "B", "C", "D", "E", or "F" to indicate which of theeenrgy band diagrams shown above most closely corresponds to this device and bias.

Cor r ect , comput er get s: n, i , D



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In the first box, type "n" or "p" to indicate if the semiconductor in the device shown is n-type or p-type respectively.In the second box, type "a" if the device is biased in the accumulation mode, "d" if it isbiased in the depletion mode, or "i" if it is biased in the inversion mode.In the third box, type the letter "A", "B", "C", "D", "E", or "F" to indicate which of the

eenrgy band diagrams shown above most closely corresponds to this device and bias.

Cor r ect , comput er get s: p, a, F


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2. Two-terminal MOS Capacitor:From Neamen Sect. 6.2. Consider p-type Ge in a MOS capacitor structure at T=300 K.Assume that the doping concentration is N_a = 3.001016 cm^-3. What is the potentialdifference, phi_F_p, between the Fermi energy, E_F, and the intrinsic Fermi level, E_Fi?Enter your answer in volts.

Corr ect , comput er get s: - 1. 84e- 01

Hint: Think about the sign. If E_F is below E_Fi, should phi_Fp be positive or negative?

What is the maximum space charge width, x_dT? Enter your answer in cm.

Corr ect , comput er get s: 1. 48e- 05

What is the MAGNITUDE of the maximum space charge density per unit area,|Q'_SD(max)|? Enter your answer in C/cm^2.



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3. Voltage in a MOS capacitor: From Neamen Sect. 6.3. A MOS device is fabricatedon a p-type silicon substrate with a doping concentration of N_a = 1.001015 cm^-3. Theoxide thickness is t_ox = 430 angstroms and the equivalent fixed oxide charge is Q'_ss =8.8010-9 C/cm^2. The dielectric constant (or relative permittivity) of silicon is 11.70 andthe dielectric constant (or relative permittivity) of the oxide is 3.90. The temperature is T

= 300 K. What is the potential difference, phi_F_p, between the Fermi energy, E_F, andthe intrinsic Fermi level, E_Fi? Enter your answer in volts.


Hint: Think about the sign. If E_F is below E_Fi, should phi_Fp be positive or negative?

What is the maximum space charge width, x_dT? Enter your answer in cm.


What is the maximum space charge density per unit are, |Q'_SD(max)|? Enter youranswer in C/cm^2.



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Calculate (V_TN - phi_ms), the difference between the threshold voltage and themetal/semiconductor work function difference. Enter your answer in V.


The figure above is a copy of Fig. 21 from the text byNeamen. Assume that the gate on the device described in theprevious questions is aluminmum. Using this figure, or theone in the text if it is clearer, to estimate the metal-semiconductor work function difference, phi_ms, calculatethe threshold voltage V_TN from your previous answer.Enter your answer in V.



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4. MOSFET Operation: From Neamen Sect. 6.5. The oxide thickness of an ideal n-channel MOSFET is found to be t_ox = 450.00 angstroms. The dielectric constant (orrelative permittivity) of silicon dioxide is 3.90. What is the gate oxide capacitance perunit area, C_ox? Enter your answer in F/cm^2.


The figure shows the experimental characteristics of this ideal n-channel MOSFET when it is biased in the saturation region. Theequation of the line on the graph issqrt(I_D) = 0.0119 A^0.5/V * V_GS - 2.367e-3 A^0.5The width-to-length ratio of the channel is 11. What is themobility, mu_n, of the majority carriers in the channel. Enteryour answer in cm^2/V-s.

Corr ect , computer get s: 3. 36e+02

What is the threshold voltage, V_TN, for this device. Enter your answer in volts.

Corr ect , comput er get s: 0. 20


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5. MOSFET Scaling: From Neamen Sect. 7.1. An NMOS transistor with parametersK_n = 1.0010-4 A/cm^2 and threshold voltage V_TN = 0.80 V is operating with gateand drain voltages of 5.0 V. In the first box, enter the magnitude of the drain current in A.In the second box, enter the power dissipation in the device in W.

Corr ect , comput er get s: 1. 76e- 03, 8. 82e- 03

assume that a constant-field scaling factor of 0.62 is now applied to the transistor and itsoperating parameters but that assume, also, that the threshold voltage, V_TN, remains

constant.In the first box, enter the magnitude of the drain current in A under this constant-fieldscaling condition. In the second box, enter the power dissipation in the device in W underthis constant-field scaling condition.

Corr ect , comput er get s: 8. 53e- 04, 2. 65e- 03


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In the first box, enter the ratio of the drain current under the constant-field scalingcondtions to the drain current in the original transistor. In the second box, enter the ratioof the power dissipated under constant-field scaling conditions to the power dissipated in

the original transistor.

Corr ect , comput er get s: 0. 484, 0. 300


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6. Non-ideal Effects: From Neamen Sect. 7.2. A silicon n-channel MOSFET has anacceptor doping concentration of N_a = 4.201016 cm^-3 and a threshold voltage of V_T= +0.75 V. It is biased with a drain-source voltage of V_DS = 5.00 V and a gate-sourcevoltage of V_GS = 4.80 V. This bias results in V_DS > V_DS(sat) so that the channellength is reduced by an amount DeltaL. As a first step in calculating the channel length

modulation, calculate the potential difference, phi_FP, between the intrinsic Fermi leveland the Fermi Energy in the p-type semiconductor. Enter your answer, including the sign,in volts. Assume that the temperature is 300 K and that the intrinsic carrier concentrationin silicon at 300K is 1.501010 cm^-3.


Calculate V_DS(sat) for this device. Enter your answer in volts.

Corr ect , computer get s: 4. 05e+00

Calculate the change (reduction) in length, delta L, of the channel under these biasingconditions. Enter your answer in cm. You may assume that the dielectric constant (orrelative permittivity) of silicon is 11.70.



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Now assume that the device in the previous three questions has the following properties:electron mobility mu_n = 650 cm^2/V-s, oxide thickness t_ox = 215.00 angstroms, achannel length of L = 2.0010-4 cm, and width to length ratio of W/L = 10. What is the

capacitance per unit area, C_ox, of the gate/oxide layer of the device? Enter your answerin F/cm^2. The dielectric constant (or releative permittivity) of the oxide is 3.90.


Calculate the ideal drain current, I_D, for this device assuming that there is no channellength modulation effect. Enter your answer in A. Remember that the gate-sourcepotential difference for this situation is V_GS = 4.80 volts, the threshold voltage is V_TN= 0.75 volts, and the drain-source potential difference is 5 volts. Because V_DS >V_DS(sat), the ideal current under these conditions is I_D = I_D(sat).


Hint: You may find it helpful to review section 6.5.2 of your textbook (Neamen).


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Finally, calculate the actual drain current (under saturation conditions) taking intoaccount the channel length modulation effect calculated three questions ago. Enter youranswer in A.


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Set 6 Web Solutions LC