The RC circuit shown in the figure has resistance of R = 1,8 kΩ and the capacitance of C = 1,1 μF. The capacitor is initially charged at a voltage V0 = 20,4 V at t = 0, when the switch is closed. How long does it take for the current running in the circuit to go down to 45% of its initial value? Express your answer in units of ms (milliseconds) using two decimal places.
Consider the triangular prism shaped wire shown in the figure below where the triangular part is an equilateral triangle with sides c = 9,4 mm. The current runs along the length of the wire where l = 9,7 m and the wire has cylindrical hole along its length with a cross sectional area of A = 2,3 mm2. If the wire is made out of a material whose resistivity is 5,7×10−6 Ωm determine the resistance of the wire. Express your answer in unit of Ω using two decimal places.
Using V = 9 mV, and given the voltage across an inductor L = 10 mH as shown in Fig. P6.25, determine the equation of current as a function of time across the inductor during the time 0 ms < = t < = 1 ms. Assuming the solution looks like iL(t) = Xt2 + C, what is the value of X? For your answer, just put the value of X in Amperes/s2 (there should only be a number in your answer). Figure P6.25
Calculate the maximum input voltage (Vi) of the given amplifier circuit. |Vt| = 2 V, K = 0.2 A/V2 |gm| = 20 mS, rd = 10 K, R1 = 10 Ω, R2 = 20 Ω, V1 = 12 V. Please write your answer as a volt and don't use unit in the answer.
Tests with a n channel FET show that it has the iD vs vGS characteristic shown below with V1 = 2.95 V and I1 = 27.1 mA. When vGS = +V1, iD = I1. When vGS = −V1, iD = 0 mA. a. What is the value of ID0 for this FET? (Give your answer to 3 s. f. ) b. What is the value of gm for this FET? Number Units (Give your answer to 3 s. f. Hint: the units for gm are the same as for conductance.)
An a. c equivalent circuit of a BJT amplifier at midband is shown in Figure 1. Derive the expression for the current gain io/is in terms of circuit resistances and transistor parameters. Figure 1 The two graphs of the transfer characteristic of an n-channel enhancement MOSFET drawn in Figure 2 are wrong. Explain the possible errors that were made in drawing the characteristic. Figure 2
Calculate the complete response in the time domain for the first order circuit shown in Fig. 4. Notice that the switch opens (i. e. stops conducting) at t = 0 s. Assume the circuit has reached steady state before the switch has opened at t = 0 s. a) Draw the circuit diagram before t = 0 s and calculate the inductor current iL(t) just before t = 0 s. b) Draw the circuit diagram for t ≥ 0 s and calculate the time constant. Calculate the inductor current long after t = 0 s. c) What is the complete solution for iL(t) for t ≥ 0 s ? Write the numerical values in decimals. Include all units. d) Make a sketch of iL(t) with respect to time. Show all units and the values for t < 0 s, t = 0 s and t = ∞. e) On your circuit diagram for t > 0 s sketch iL(t) and show its direction on the circuit diagram you have drawn. f) Find the equation for the inductor voltage vL(t) for t ≥ 0 s. g) Determine the power dissipated by the 2 kohm resistor at t = 5 μs. Fig. 4
Use the step-by-step method to find the value of the output current just after the switch opens, i0(0+), for t > 0 in the circuit in Fig. P7.22. Given R1 = 11 kΩ, I = 14 mA, and C = 208 μF. Figure P7.22 Notes on entering solution: Enter your solution in milliAmps (mA) Enter your solution to two decimal points Do not include units in your answer ex. 5 mA is entered as 5.00
Consider the common-drain amplifier shown at the right. The MOSFET has K = 1.6 mA/V2, Vt0 = −1.2 V, rd = 16 kΩ. The supply voltages is VDD = 10 V. The resistances are RS = RL = 4 kΩ, R1 = 850 kΩ, and R2 = 350 kΩ. (a) Determine VSDQ, IDQ, and the value of gm. (b) Find the voltage gain Av = vo/vi and circuit transconductance gain Ag = io/vi. (d) Determine the output resistance Ro.
In the circuit diagram, given the BJT parameters: β = 100, VA = −50 V, VCC = 5.7 V, Rsig = 2 kΩ, R1 = 30 kΩ, R2 = 15 kΩ, RC = 1 kΩ, RE = 1.1 kΩ, RL = 4 kΩ, calculate the following. (18 points) (a) The operating point of the BJT IBQ, ICQ, VCEQ (6 points) (b) Draw the small-signal equivalent circuit of the circuit. (4 points) (c) Calculate the input resistance (Rin), output resistance (Rout ), voltage gain (Av), and overall voltage gain (Gv). (8 points)
In the amplifier circuit diagram, given that the BJT has β≫1 and ro ≠ ∞, answer the following questions. (12 points) (a) Derive the expressions for ICQ and VCEQ at the operating point of the BJT. (4 points) (b) Draw the small-signal equivalent circuit of the amplifier. (2 points) (c) Derive the expressions for the input resistance (Rin) and voltage gain (Av) of the amplifier. (6 points)
QUESTION 6: A simplified class-AB output stage with BJTs is shown below. The circuit parameters are VCC = 23 V and RL = 1800 Ω. For each transistor, IS = 8×10−15 A. Currents iCn = iCp = 1 mA when vl = 0. For vO = −4.8 V, determine iL, iCn, iCp, and vl. What is the power dissipated in Qn, Qp, and RL? iL (mA) iCn (mA), iCp (mA), and vl (V) PQn (mW) PQp (mW) PRL (mW) format :
4.35 For the circuit in Fig. P4.35 let VCC = 10 V, RC = 1 kΩ, and RB = 10 kΩ. The BJT has β = 50. Find the value of VBB that results in the transistor operating (a) in the active mode with VC = 2 V; (b) at the edge of saturation; (c) deep in saturation with βforced = 10. Assume VBE≃0.7 V. Figure P4.35
a) Derive an expression for the potential distribution in an ideal MOS capacitor in the depletion condition in terms of the surface potential ϕs and the depletion width at the surface xd taking the zero for potential in the silicon bulk. The silicon is doped p type and x = 0 at the oxide silicon interface. b) For Parts(i) through (ii) below, consider the following low-frequency gate capacitance (per unit area) vs. gate voltage characteristic for a metal gate n-channel MOSFET. (5) (i) On the above figure label, the approximate regions or points of Weak inversion Flatband Strong inversion Accumulation Threshold and depletion (ii) What is the oxide capacitance per unit area?
Consider the following MOS capacitor situation described below. Assuming that semiconductor is silicon with doping of NA = 3.5×1017 acceptors /cm3, and no charges exist on the surface of the oxide nor inside the oxide. Semiconductor with electron affinity = 4.0 V and energy bandgap = 1.12 eV. Assuming no interface states exist at the junction and operation temperature at 300 K. Effective density of states in conduction band (Nc) = 3.22×1019 cm−3. Effective density of states in valence band (Nv) = 1.83×1019 cm−3, KT/q = 0.02586 V (at T = 300 K ). ni = 1010 /cm3. ε0 = 8.854×10−14 F/cm. (a) What will be the value of the metal work function if the flat band potential is zero. (5 points) (b) Calculate the surface potential required to make the semiconductor surface intrinsic. (4 points) For the questions (c-d) assuming when VG < 0 and with above obtained metal work function. (c)Sketch the energy band diagram (clearly labeling energy levels) (4 points)
Problem 1: MOS Fundamentals Consider an ideal MOS capacitor maintained at T = 300 K with the following characteristics:Gate material is p+ polycrystalline-silicon (work function ΦM = 5.15 eV )Substrate is n-type Si, with doping concentration 1018 cm−3 Oxide thickness xo = 2 nm a) What is the flat-band voltage, VFB, of this capacitor? b) Sketch the energy-band diagrams, labeling qVG, qϕs, qVox (no numerical values required), for the following bias conditions: i) flat-band ii) accumulation iii) equilibrium iv) strong inversion c) What is the threshold voltage, VT, of this device? d) Suppose we want to change the gate material to be n+ polycrystalline-silicon (work function ΦM = 4.03 eV). How would we need to change the substrate doping in order to keep VT the same? (A numerical answer is required.)
A MOS capacitor has 300 Angstroms oxide thickness and silicon substrate with 10E16 cm^−3 acceptor density. When the semiconductor surface is at the onset of strong inversion, determine the surface potential. Answer: A MOS capacitor has 300 Angstroms oxide thickness and silicon substrate with 10E16 cm^−3 acceptor density. The oxide permittivity is 3.9×8.85E−14 F/cm. When the semiconductor surface is at the strong inversion, determine the oxide capacitance per unit area in F/cm^2
Consider the MOS capacitor with the energy band diagram shown below. The oxide thickness is 4 nm. The voltage applied to the oxide is 1 V. The N+poly-Si gate doping is Npoly = 7×1019 cm−3. The P−Si substrate Na = 2×1017 cm−3. (a) Calculate the poly gate depletion layer thickness Wdpoly (b) Calculate the depletion induced potential in the poly depletion region ϕpoly (c) Calculate the flat band voltage Vfb (d Calculate the surface potential at threshold ϕst (e) Calculate the gate voltage Vg at the threshold
Q2. The energy band diagram for an MOS capacitor is sketched below. Assume T = 300 K and an oxide thickness = 1.1 nm. Answer the following questions: (5×10) = 50 points (a) Is the semiconductor (Si) N-type or P-type? Find the doping density. (1+4) (b) What is the mode of operation (accumulation, flat band, depletion or inversion) of the MOS capacitor shown above? Explain your answer. (c) What are electron and hole density at the x = 0?
The below curve shows a C-V characteristics for a silicon MOS capacitor. What is the oxide capacitance value per unit area? On the curve above, sketch the high frequency curve for this MOS capacitor. Please explain why this happens. (4 points)
Consider a MOS capacitor with p+ polysilicon gate and p-type silicon substrate with NA = 1016 cm−3, EF = EV in the polysilicon gate. Assume the following parameters: tox = 200 o, QSS′ = 0, ni = 1.5×1010 cm−2, εo = 3.9×8.854×10−14 F/cmεs = 11.7×εo, εox = 3.9×εo a) (5 points) Calculate the metal-semiconductor work function difference. b) (5 points) Calculate the surface potential at the threshold inversion. c) (5 points) Calculate the depletion width (in μm ) at the threshold inversion. d) ( 5 points) Calculate the flat band voltage. e) (5 points) Determine the threshold voltage.
Consider an ideal MOS capacitor fabricated on P-type silicon with a doping of Na = 5×1016 cm−3 with an oxide thickness of 2 nm and an N+poly-gate (heavily doped, such that Ef is at the valence band edge). (a) What is the flat-band voltage, Vfb, of this capacitor? (b) Calculate the maximum depletion region width, Wdmax (c) Find the threshold voltage, Vt of this device.
The energy band diagram for an ideal MOS-capacitor operated at T = 300 K is sketched as follows. The semiconductor band is such bended that EFS = Ei at the Si/SiO2 interface, and the Fermi level of the metal is aligned with the valence band of the semiconductor in the Si bulk. (a) Calculate ϕF, ϕs, VG, Δϕox, depletion width and oxide thickness; (b) Draw the block charge diagram for the MOS-C corresponding to the state pictured in the energy band diagram; (c) Sketch the electric field inside the oxide and the semiconductor as a function of position; (d) Sketch the general shape of the low-frequency C-V characteristic for this MOS-capacitor.
The C-V characteristic of an ideal MOS capacitor is shown below. (a) Is the semiconductor component of the MOS-C doped N-type or P-type? Indicate how you arrived at your answer. (b) Draw the MOS-C energy band diagram corresponding to (2) on the plot above. Clearly label all important parameters. (c) Draw the block charge diagram corresponding to (1) on the plot above. (d) If the area of the MOS-C is 5⋅10−3 cm2, what is the oxide thickness (x0)?
The capacitance vs. gate voltage characteristic of a simple MOS capacitor of area 100 μm×100 μm is as shown: Assume that there are no oxide charges. a) What is the thickness of the gate oxide (SiO2) ? b) Estimate the values of VFB and VT. c) Is the gate material metal or n+ poly-Si? How do you know this? d) Is the substrate lightly doped ( < 1018 cm−3) ? How do you know this?
The C-V characteristic curve of an MOS capacitor is shown in the figure below. The area of the device is 1×10−3 cm2. The metal-semiconductor work function difference is ϕms = −0.50 Volts, the oxide is SiO2, the semiconductor is silicon and the semiconductor doping concentration is 3×1016 cm−3. Calculate the oxide thickness
Consider the C-V characteristic below for a silicon MOS capacitor. (a) Is the semiconductor p-type or n-type? (2 pts) (b) Is this a low frequency or high frequency measurement? (2 pts) (c) What is the threshold voltage of this device? (2 pts) (d) What would happen to the capacitance in region 1 if the oxide thickness x0 is increased? Increase, decrease, or stay the same? (2 pts)
Problem 1: Consider a silicon MOS capacitor with a C-V characteristic as shown below. The gate insulator is SiO2. The measured maximum and minimum capacitance values are Cmax = 1.2×10−2 F/m2 and Cmin = 9.5×10−4 F/m2. Assume T = 300 K. (a) Is this C-V characteristic measured at low frequency or high frequency? (10 points) (b) What is the thickness of the SiO2 gate insulator? (10 points) (c) What is the depletion layer capacitance at the onset of inversion? (10 points) (d) What is the doping density of silicon in this MOS capacitor? (10 points)
The C-V curve for a MOS capacitor is shown, and has the following measured data points: At point A:C = 8.3 pF, Vg = −0.23 V At point B: C = 1.1∗3.3 pF, Vg = 0 V At point C:C = 3.3 pF, Vg = 0.49 V At point D:C = 3.3 pF, Vg = 1.71 V At point E:C = 8.3 pF, Vg = 1.71 V Based on this measured data, what is the maximum depletion region width in nanometers? Assume that the area of this MOS capacitor is 3503 μm^2. Use: ες = 11.7, ε0x = 3.9, and ε0 = 8.854×10^−14 F/cm. Answer: The correct answer is: 66
Consider the C−V characteristic below for a silicon MOS capacitor. I. (5 pts) Consider the bias points 1, 2, 3, 4, 5 shown on the C-V curve. Complete the following table. II. (1 pts) Is this an n-channel or p-channel device? n-channel or p-channel III. (2 pts) Is this high or low frequency measurement? High frequency or Low frequency IV. (2 pts) What is the threshold voltage for this device? V. (2 pts) When an MOS capacitor is biased into inversion, the source of the inversion layer charge is, a. The contact to substrate b. Leakage current from the gate c. Generation in or within a diffusion length of the depletion region a. Depletion of the majority carriers leaves behind minority carriers in the inversion region
5.1 MOS technology is used to fabricate a capacitor, utilizing the gate metallization and the substrate as the capacitor electrodes. Find the area required per 1−pF capacitance for oxide thickness ranging from 2 nm to 10 nm. For a square plate capacitor of 10 pF, what dimensions are needed? 5.2 Calculate the total charge stored in the channel of an NMOS transistor having Cox = 9 fF/μm2, L = 0.36 μm, and W = 3.6 μm, and operated at Vov = 0.2 V and VDS = 0 V. 5.3 Use dimensional analysis to show that the units of the process transconductance parameter kn′ are A/V2. What are the dimensions of the MOSFET transconductance parameter kn?
A company is interested in making a MOS capacitor devices and conducting some experiments. The MOS-caps are made with heavily doped N-type Crystalline Polysilicon gate material, SiO2 insulator and P-type Si substrate. Two MOS capacitors are fabricated and tested by measuring their capacitances versus the gate-voltage profile as shown in the figure. As observed in the profiles above the capacitors do not seem to behave ideally for the higher gate voltages. Answer the following questions. Draw the band diagram for Vg > Vth (where Vth is the threshold voltage) for an ideal MOS device, MOS-1 device and MOS-2 device. Draw the effective capacitance model for the ideal MOS, MOS-1 and MOS-2 cases.
5). In this problem, you are asked to consider the ac hybrid- π model for an NMOS transistor and to relate the capacitors to the physical device structure. Recall the oxide capacitance per unit area (Cox) appears in the DC ID−VGS relationship for triode and saturation regions. The NMOS transistor has kn′ = 0.2 mA/V2, W = 10 μm, L = 1 μm and μn = 1000 cm2 /Vsec. a) Find the total gate-to-channel capacitance for small VDS, CG-ch0. Hint: this is the parallel-plate capacitance between the gate and the full channel area. b) Next, consider a bias point in the saturation regime. Since the channel charge density at the drain end of the channel decreases with increasing VDS ("pinch-off"), CG−ch0 does not divide equally between G-S and G-D components. Assuming that Cgs is 80% of CG-ch0 and Cgd is 10% of CG-ch0, find Cgs and Cgd. c) Suppose that this transistor is used in a CS amplifier with the topology of the 2 nd stage in Prob. 1 (i. e. this transistor is used as M6). The DC hybrid- π parameters at the DC bias point are gm = 2 mS and ro = 100 kΩ. Find the Miller capacitance (См) for this CS stage. Note that for an inverting amplifier, CM = Cgd(1−Av). d) Find the total effective capacitance between G and S(Cgs + CM).
The energy band diagram for an ideal MOS-capacitor under bias is shown in figure (a) below. a. Is the voltage VG applied to the gate a positive or negative value with respect to Si? b. Is the semiconductor in accumulation, depletion, inversion, deep inversion or flat band condition? c. Suppose we apply the gate voltage such that the semiconductor is just in start of inversion. Draw the band diagram for this case.
A MOS capacitor is fabricated by using Metal layer deposited on top of 20 nm thick SiO2 oxide layer on top of p-type silicon with doping concentration of NA = 1×1014 cm−3. Dielectric coefficients of silicon and oxide layer is given as KS = 11.8, KO = 3.9, ε0 = 8.86×10−14 F/cm. Calculate the threshold voltage required to create inversion layer. (Assume flat band approximation is valid).
The electric field distribution in an MOS capacitor is shown. The flatband voltage VFB = 0. (a) Is the substrate p-type or n-type? Give your reason. (b) Determine the oxide dielectric constant, Ko. (c) Determine the oxide voltage, the surface potential, and the gate voltage. Assume the substrate is grounded. (d) Determine the oxide capacitance (in F/cm2) (e) Determine the substrate doping density (in cm−3) (f) Draw the potential to scale, i.e. , quantitatively. Use Ks = 12.
Q. 4 The capacitance-voltage (C−V) characteristic of a silicon MOS capacitor is shown in Figure Q4. The capacitor comprises a metal gate with a work function of 5.62 eV. The gate dielectric is made of silicon-dioxide (SiO2) with a relative permittivity of 3.9. (a) Sketch the block charge diagram corresponding to point (1) on the C - V curve. [4 marks] (b) If the capacitor area is 2×10−3 cm2, determine the oxide thickness. [3 marks] (c) Determine the depletion layer width at point (2). [4 marks] (d) Briefly describe two ways to reduce the threshold voltage of the capacitor. [4 marks] (e) If the flatband voltage is 0.7 V, determine the work function of the substrate. [3 marks] (f) Sketch the energy band diagram corresponding to point (2) on the C - V curve. Is the capacitor under accumulation, depletion, or inversion? Briefly explain. [7 marks] Figure Q4: Capacitance-voltage (C−V) characteristic of a silicon MOS capacitor.
Consider an MOS capacitor made of crystalline silicon described by the band diagram below. Note that unmarked values may not be to scale. Assume that εox = 3⋅105 V/cm, tox = 1.0 nm, Kox = 4, KSi = 12, and Eg = 1.12 eV. a. Is this MOS-C in accumulation, flat-band, depletion, or inversion? b. What is the numerical value of the electric field in the semiconductor near the oxide (x = 0+)? c. What is the level of p-type doping NA in the semiconductor? d. What is the numerical value of the surface potential? e. What is the depletion width (in the semiconductor)? f. What is the electrostatic potential voltage of the gate electrode with respect to the semiconductor?
The C-V curve of MOS capacitor is shown below. What is thickness of oxide layer? What is the type of substrate doping ? What is the maximum depletion layer width? What is the doping concentration in the substrate? What is the flat band voltage for the capacitor? If the oxide has a fixed charge Qf/q = 2×1010 /cm2, is the contact of the capacitor made of n+ or p+ polysilicon?
The capacitance vs. gate voltage characteristic of a simple MOS capacitor of area 100 um×100 um is as shown: Assume that there are no oxide charges. a) What is the thickness of the gate oxide (SiO2)? b) Indicate the device is NMOS or PMOS and the values of VFB and VT. c) Is the gate material metal or poly-Si? How do you know this? d) Is the substrate lightly doped ( < 1018 cm−3) ? How do you know this?
A. Determine the value of the oxide capacitance (Cox). B. Determine the value of total junction capacitance (Cj). C. Total overlap capacitance (Cov). D. Determine the zero-bias value of the: Gate-Source capacitance (CGS), Gate-Drain capacitance (CGD) and the Gate-Body capacitance (CGB). E. Repeat D when the MOSFET is in saturation region. F. Repeat D when the MOSFET is in Linear region. 0.25 μm technology Cjo = 3 mF/m2 Cjswo = 0.275 n F/m.
MOS C-V Characteristic. The capacitance vs. gate voltage characteristic of a simple MOS capacitor of area 100 μm×100 μm is as shown: Assuming that there are no oxide charges, answer the following questions: a) What is the thickness of the gate oxide (SiO2)? b) Estimate the values of VFB and VT. c) Is the substrate lightly doped ( < 1018 cm−3) ? Explain how you have arrived to the answer?
Consider the following diagram for non-ideal MOS C-V characteristics, where there seems to be a deviation from the expected ideal performance as shown in the following chart. Red-dotted: ideal performance. Black: actual. Answer the following questions. A. Which region of the MOS operation is impacted by the non-ideality (i. e. accumulation, depletion or inversion)? B. What is the name of the phenomenon in the MOS capacitor device which is causing this deviation? C. Explain using physical terms such as location of charges etc. why the capacitance is reduced for the non-ideal case? D. Draw a capacitor model for the non-ideal MOS in the accumulation, depletion and inversion regions that consider the non-ideality. (it should be combination of series / parallel or both capacitors) E. How does this non-ideality effects the device performance? Explain in terms of how this effects the ability to obtain certain amount of charge at the insulator-substrate interface (i.e. Qinv or QACC) for a given applied Vg F. Is this a desirable effect? Explain your answer.
(Flatband capacitance) Considering MOS capacitor in the flatband condition flat band If you have measured the C−V curves as the blue dashed line in the following figure, then explain the detailed procedures to determine VFB (Assumption: substrate doping concentration NA and oxide thickness Tox are already known)
An ideal MOS capacitor is constructed on a p-type Si substrate with NA = 1 e16 cm−3 doping. When following material parameters are given, answer the questions: ϕm; metal work function = 4.65 eV χ; electron affinity of silicon = 4.03 eV tox ; oxide thickness = 15 nm εox; oxide permittivity = 4 ε0 εs; silicon permittivity = 12 ε0 ε0; free space permittivity = 8.85×10−14 F/cm (a) Find the threshold voltage VT, the depletion width, and draw its band diagram. (b) Sketch the charge distribution as a function of position when VT is applied. (c) Sketch the surface potential ϕs, the depletion width Wd, and charge density as a function of bias including VFB and VT. (d) Calculate the unit area capacitances when VFB and VT is applied. (e) What is the electric field of the oxide in an ideal MOS given in this problem? What is the assumption you made to obtain the oxide electric field in an ideal MOS? (f) In general, charges in the oxide cause a shift in the gate voltage required to reach the threshold condition: ΔVT = −1 εox∫0 tox xρox(x)dx If ρox(x) = Aδ(x−b) is given, find the threshold voltage shift for the following cases where δ(x−b) is a delta function and A is a arbitrary constant. (1) b = 0 (2) b = tox/2 (3) b = tox
A MOS capacitor is made from Si. When VG is applied to the gate of the capacitor, the band diagram looks as shown below. Answer the questions that follow. (a) Is the applied gate voltage VG positive or negative? Explain. (b) Is the semiconductor p-type or n-type? What is the doping concentration? (c) Calculate the number of electrons and holes in the bulk of the semiconductor. (d) Calculate the number of electrons and holes near the surface of the semiconductor. (e) Is the semiconductor under depletion, inversion or in flat-band condition? (f) If we define the electrostatic potential, φ(x) = (1 /q) [Ei(bulk) − Ei(x)], plot φ(x) versus x. (g) Plot the charge density as a function of x. Identify in your plot which are mobile charges and which are ionized donors or acceptors.
Q2. The energy band diagram for an MOS capacitor is sketched below. Assume T = 300 K and an oxide thickness = 1.1 nm. Answer the following questions: (5×10) = 50 points (a) Is the semiconductor (Si) N-type or P-type? Find the doping density. (1+4) (b) What is the mode of operation (accumulation, flat band, depletion or inversion) of the MOS capacitor shown above? Explain your answer. (c) What are electron and hole density at the x = 0 ? (d) What is the voltage drop in Si ? (e) Find the value of depletion width ( Wdep ). (f) Calculate the voltage drop in oxide. (g) Calculate the electric field in oxide. (h) Calculate the electric field in Si at x = 0. (i) Find the flat band voltage.
A MOS capacitor is at 300 K on a Si substrate. The substrate is doped with 3×1015 cm−3 phosphorus atoms. What is the value of the semiconductor (depletion) charge at strong inversion? 1.6×10−11 C/cm2 −1.6×10−11 C/cm2 −2.56×10−8 C/cm2 2.56×10−8 C/cm2
The capacitance per unit area of a MOS capacitor is measured as a function of the applied DC voltage by a low-frequency probe and a high-frequency probe. Assume the area of the capacitor is 0.02 cm2. From the results show below, determine the capacitance of the depletion region (Cs) and the capacitance of the oxide (Cox).
A Si MOS capacitor (εox = 4, ε0 = 8.85×10−12 F/m, Eg(Si) = 1.12 eV, me∗ = mh∗) with a gold metal contact and a cross section area of A = 8×10−5 cm2 has following C-V characteristics: a) Is the silicon material n-type or p-type doped, and why? Explain the shape of the graph in the areas 1, 2, and 3. b) Sketch the cross section of a MOSFET using this MOS gate diode (include the doping levels and the type of inversion channel). c) Calculate the thickness of the oxide layer. d) Sketch the complete band diagram for the case that ΦM = ΦSi and no applied voltage. e) Sketch the complete band diagram with the threshold voltage (case of strong inversion) applied.
For a n+ polysilicon gate MOS capacitor with P substrate, it is given that CaxWL = 180 pF, NA = 5×1017 cm−3 and area = 1.0×10−3 cm2, find: a) the flatband voltage (assuming the workfunction of the n+ polysilicon is at the conduction band edge of silicon) b) the MOS capacitance at flat-band c) the minimum MOS capacitance in the C-V curve d) the threshold voltage of the MOS capacitor.
Consider MOS capacitor with an n+poly silicon gate doped to 3×1019 cm−3. P-type silicon is doped with NA = 1016 cm−3, and an oxide (SiO2) thickness is 4 nm. Interface charge density (Qi) is 1010 cm−2.4. Calculate the flat band voltage (VFB) 5. Calculate the threshold voltage (VT) 6. Draw equilibrium band diagram of the MOS capacitor. 7. Draw band diagram at flat-band 8. Draw band diagram at accumulation 9. Draw band diagram at strong inversion
A n-channel MOS capacitor has Na = 4×1016 /cm3 and tox = 15 nm. a. The capacitor is biased so that at the surface EF − Ei = ϕFp 2. Find the voltage across the semiconductor (Vs) and across the oxide (Vox). b. Find the electric field in the oxide for the bias condition of part a.
(4) Consider a metal-oxide-silicon (MOS) capacitor at T = 300 K that has the low-frequency capacitance-voltage characteristic show on the left below. At some particular gate voltage, the capacitor has the band diagram shown on the right below. Assume the δ-depletion approximation applies. (25 pts) (a) Determine which region of operation is associated with the band diagram (accumulation, flatband, depletion, onset of inversion, or strong inversion). (2 pts) (b) Determine the flatband voltage, VFB. (3 pts) (c) Determine the oxide thickness, x. ( 5 pts) (d) Determine the ratio of the maximum depletion width to the oxide thickness. In other words, determine WT/xo. (5 pts) (e) Determine the gate voltage, VG, associated with the band diagram. (5 pts) (f) At VG = VT, determine the absolute value of the potential drop across the oxide. (5 pts)
Problem 3. Consider MOS system with p type substrate. Given: Explain qualitatively that the total capacitance for the depletion condition is the series combination of oxide capacitance and depletion capacitance for low frequency ac and slowly varying input ramp (DC). (10 points) Explain qualitatively that the total capacitance for the strong inversion condition is the oxide capacitance for low frequency ac and slowly varying input ramp (DC). (10 points)Do we have an inversion layer at the surface for high frequency ac and slowly varying input ramp? Explain. (10 points) How does the total capacitance change for high frequency ac and slowly varying ramp in strong inversion condition? Explain it with the plot of Cg/Cox vs. Gate voltage. (10 points) Why the depletion width does not change in strong inversion condition for high frequency ac and slowly varying input ramp? Explain. (10 points)
The dc block charge diagram of an ideal MOS capacitor is shown. (a) Is the semiconductor substrate n-type or p-type? Explain. (b) Is the device in accumulation, depletion, or inversion? (c) Draw the energy band diagram corresponding to the charge state pictured in the block charge diagram.
The block charge diagram for four ideal MOS-capacitors are shown in the following figure. For each case, (i) determine if the semiconductor is n- or p-type; (ii) determine the biasing condition for each case (accumulation, depletion or inversion); (iii) draw the energy band diagram for each MOS-capacitor.
A MOS capacitor has an n+ polysilicon gate with EF = EC+0.15 eV in the polysilicon, a 50 nm thick SiO2 gate dielectric with Qss = 0, and a p-type silicon substrate with Na = x.5×1016 /cm3, where x is the last digit of your student number. For silicon at room temperature ni = 1010 /cm3, Nv = 1.8×1019 /cm3, Nc = 3.2×1019 /cm3, and ϵSi = 11.7ϵ0. For SiO2 ϵSiO2 = 3.9ϵ0. a. Find the threshold voltage for this MOS capacitor. b. If the capacitor is made into a MOSFET with L = 2 μm, W = 200 μm, and a channel field effect mobility of 450 cm2/V⋅s, find ID for VGS − VT = 2 V and VDS = 1 V. c. Suppose it is desired to have a depletion mode MOSFET and that any gate oxide thickness is possible, but no other parameters can be changed. What is the most negative threshold voltage that is possible for the MOS capacitor with your substrate doping? d. Suppose it is desired to have a MOSFET with a threshold voltage of +0.5 V and again any gate oxide thickness is possible, but no other parameters can be changed. What oxide thickness will give VT = 0.5 V ? e. Suppose the source, drain, and body of the MOSFET are all grounded and the capacitance-voltage characteristics are measured. Sketch the high and low frequency capacitance-voltage characteristics and label significant features.
MOS capacitor. The energy band diagram for an MOS capacitor (no charges in the oxide or at the oxide/semiconductor interface) maintained at 300 K is shown below. Note that the slopes of the bands in the oxide are constant. a) (3 pts) For the pictured condition determine the gate bias VG and the operation mode of the MOS capacitor. Explain. b) (3 pts) Sketch on the semi-logarithmic plot the hole concentration [log(p)] inside the semiconductor as a function of x. c) (4 pts) Determine the metal-semiconductor workfunction difference, ΦMS. Explain your steps and sketch the vacuum level. d) (4 pts) Sketch the block charge diagram and the electric field E(x) vs. x.