# GATE Questions & Answers of Electronic Devices Electronics and Communication Engg

#### Electronic Devices 102 Question(s) | Weightage 08 (Marks)

Two identical nMOS transistors M1 and M2 are connected as shown below. The circuit is used as an amplifier with the input connected between G and S terminals and the output taken between D and S terminals. Vbias and VD are so adjusted that both transistors are in saturation. The transconductance of this combination is defined as $\style{font-family:'Times New Roman'}{g_m=\frac{\partial i_D}{\partial\nu_{GS}}}$ while the output resistance is $r_o=\frac{\partial v_{{}_{DS}}}{\partial i_D}$ , where $\style{font-family:'Times New Roman'}{i_D}$ is the current flowing into the drain of M2 . Let $\style{font-family:'Times New Roman'}{g_{m1},\;g_{m2}}$ be the transconductances and $\style{font-family:'Times New Roman'}{r_{o1},\;r_{o2}}$ be the output resistances of transistors M1 and M2, respectively

Which of the following statements about estimates for $\style{font-family:'Times New Roman'}{g_m}$ and $\style{font-family:'Times New Roman'}{r_o}$ is correct?

In a p-n junction diode at equilibrium, which one of the following statements is NOT TRUE?

A p-n step junction diode with a contact potential of 0.65 V has a depletion width of 1μm at equilibrium. The forward voltage (in volts, correct to two decimal places) at which this width reduces to 0.6 μm is _______.

There are two photolithography systems: one with light source of wavelength $\lambda_1=156$ nm (System 1) and another with light source of wavelength $\lambda_2=325$ nm (System 2). Both photolithography systems are otherwise identical. If the minimum feature sizes that can be realized using System1 and System2 are $L_{min1}$ and $L_{min2}$ respectively, the ratio $L_{min1}/L_{min2}$ (correct to two decimal places) is__________.

Red (R), Green (G) and Blue (B) Light Emitting Diodes (LEDs) were fabricated using p-n junctions of three different inorganic semiconductors having different band-gaps. The builtin voltages of red, green and blue diodes are $V_R$, $V_G$ and $V_B$, respectively. Assume donor and acceptor doping to be the same ($N_A$ and $N_D$, respectively) in the p and n sides of all the three diodes.

Which one of the following relationships about the built-in voltages is TRUE?

In the circuit shown below, the $\left(W/L\right)$ value for M2 is twice that for M1. The two nMOS transistors are otherwise identical. The threshold voltage $V_T$ for both transistors is 1.0V. Note that $V_{GS}$ for M2 must be $>$1.0 V.

The voltage (in volts, accurate to two decimal places) at $V_x$ is _______.

A solar cell of area 1.0 cm2 , operating at 1.0 sun intensity, has a short circuit current of 20 mA, and an open circuit voltage of 0.65 V. Assuming room temperature operation and thermal equivalent voltage of 26 mV, the open circuit voltage (in volts, correct to two decimal places) at 0.2 sun intensity is _______.

A junction is made between $p^-$ Si with doping density $N_{A1}=10^{15}$ cm-3 and $p$ Si with doping density $N_{A2}=10^{17}$ cm-3 .

Given: Boltzmann constant $k=1.38\times10^{-23}J\cdot K^{-1}$ , electronic charge $q=1.6\times10^{-19}$ C. Assume 100% acceptor ionization.

At room temperature ($T$ = 300K), the magnitude of the built-in potential (in volts, correct to two decimal places) across this junction will be _________________.

A bar of Gallium Arsenide (GaAs) is doped with Silicon such that the Silicon atoms occupy Gallium and Arsenic sites in the GaAs crystal. Which one of the following statements is true?

An n+ -n Silicon device is fabricated with uniform and nono-degenerate donor doping concentration of ND1 =1 × 1018 cm-3 and ND2 =1 × 1015 cm-3 corresponding to the n+ and n regions respectively. At the operational temperature T, assume complete impurity ionization, kT/q=25mV, and intrinsic carrier concentration to be ni = 1 × 1010 cm-3. What is the magnitude of the built-in potential of this device?

The dependence of draft velocity of electrons field in a semiconductor is shown below. The semiconductor has a uniform electron concentration of =1 × 1016 cm-3 and electronic charge =1.6 × 10-19 C. If a bias of 5 V is applied across a 1 µm region of this semiconductor, the resulting current density in this region, in kA/cm2, is____________.

As shown, a uniformly doped Silicon (Si) bar of length L=0.1 µm with a donor concentration ND=1016 cm-3 is illuminated at x=0 such that electron and hole pairs are generated at the rate of ${G}_{L}={G}_{LO}\left(1-\frac{x}{L}\right),0\le x\le L$, where GLO=1017 cm-3 S-1.Hole lifetime is 10-4s, electronic charge q=1.6×10-19 C, hole diffusion coefficient DP=1000 cm2/s and low level injection condition prevails. Assuming a linearly decaying steady state excess hole concentration that goes to 0 at x=L, the magnitude of the diffusion current density at x=L/2, in A/cm2, is__________.

As shown, two Silicon (Si) abrupt p-n junction diodes are fabricated with uniform donor doping concentration of ND1=1014 cm-3 and ND2=1016 cm-3 in the n-regions of the diodes, and uniform acceptor doping concentrations of NA1=1014 cm-3 and NA2=1016 cm-3 in the p-regions of the diodes, respectively. Assuming that the reverse bias voltage is » built-in potentials of the diodes, the ratio C 2/C1 of their reverse bias capacitances for the same applied reverse bias, is_________.

In the figure, D1 is a real silicon pn junction diode with a drop of 0.7 V under forward bias condition and D2 is a Zener diode with breakdown voltage of -6.8 V. The input Vin(t) is a periodic square wave of period T, whose one period is shown in the figure.

Assuming  10 $\tau$ << T, where $\tau$ is the time constant of the circuit, the maximum and minimum values of the waveform are respectively.

For a particular intensity of incident light on a silicon pn junction solar cell, the photocurrent density (JL) is 2.5 mA/cm2 and the open-circuit voltage (Voc) is 0.451 V. Consider thermal voltage (VT) to be 25 mV. If the intensity of the incident lights is increased by 20 times, assuming that the temperature remain unchanged, Voc (in volts) will be_________

An abrupt pn junction (location at = 0) is uniformly doped on both p and n sides. The width of the depletion region is W and the electric field variation in the x-direction is (). Which of the following figures represents the electric field profile near the pn junction?

A small percentage of impurity is added to an intrinsic semiconductor at 300 K. Which one of the following statements is true for the energy band diagram shown in the following figure?

Consider the following statements for a metal oxide semiconductor field effect transistor (MOSFET):

P: As channel length reduces, OFF-state current increases.
Q: As channel length reduces, output resistance increases.
R: As channel length reduces, threshold voltage remains constant.
S: As channel length reduces, ON current increases.

Which of the above statements are INCORRECT?

What is the voltage Vout in the following circuit?

Consider a silicon p-n junction with a uniform acceptor doping concentration of 1017 cm−3 on the pside and a uniform donor doping concentration of 1016 cm−3 on the n-side. No external voltage is applied to the diode. Given: $kT/q=26\;\mathrm{mV},\;{\mathrm n}_\mathrm i=1.5\times10^{10}\;\mathrm{cm}^{-3},{\mathrm\varepsilon}_\mathrm{Si}=12{\mathrm\varepsilon}_0,\;{\mathrm\varepsilon}_0=8.85\times10^{-14}\mathrm F/\mathrm m$, and q = 1.6 ×10−19 C.

The charge per unit junction area (nC cm−2) in the depletion region on the p-side is ___________

Consider an n-channel metal oxide semiconductor field effect transistor (MOSFET) with a gate-tosource voltage of 1.8 V. Assume that $\frac{W}{L}=4,{\mu }_{N}{C}_{ox}=70×{10}^{-6}{\mathrm{AV}}^{-2}$ the threshold voltage is 0.3V, and the channel length modulation parameter is 0.09 V−1. In the saturation region, the drain conductance (in micro seimens) is ________

The figure below shows the doping distribution in a p-type semiconductor in log scale

The magnitude of the electric field (in kV/cm) in the semiconductor due to non uniform doping is _________

Consider a silicon sample at T = 300 K, with a uniform donor density Nd = 5×1016 cm−3, illuminated uniformly such that the optical generation rate is Gopt= 1.5×1020 cm−3 s-1 throughout the sample. The incident radiation is turned off at t = 0. Assume low-level injection to be valid and ignore surface effects. The carrier lifetimes are ${\tau }_{po}=0.1$= 0.1 μs and${\tau }_{n0}=0.5$ = 0.5 μs.

The hole concentration at $t$=0 and the hole concentration at $t$=0.3 μs, respectively, are

The Ebers-Moll model of a BJT is valid

A long-channel NMOS transistor is biased in the linear region with VDS = 50 mV and is used as a resistance. Which one of the following statements is NOT correct?

Assume that the diode in the figure has Von = 0.7 V, but is otherwise ideal.

The magnitude of the current i2 (in mA) is equal to ________

A voltage VG is applied across a MOS capacitor with metal gate and p-type silicon substrate at T=300 K. The inversion carrier density (in number of carriers per unit area) for VG = 0.8 V is 2×1011 cm−2. For VG = 1.3 V, the inversion carrier density is 4×1011 cm−2. What is the value of the inversion carrier density for VG = 1.8 V?

Consider avalanche breakdown in a silicon p+n junction. The n-region is uniformly doped with a donor density ND. Assume that breakdown occurs when the magnitude of the electric field at any point in the device becomes equal to the critical field Ecrit. Assume Ecrit to be independent of ND. If the built-in voltage of the p+n junction is much smaller than the breakdown voltage, VBR, the relationship between VBR and ND is given by

Consider a region of silicon devoid of electrons and holes, with an ionized donor density of ${N}_{d}^{+}={10}^{17}$ cm−3. The electric field at x=0 is 0 V/cm and the electric field at x=L is 50 kV/cm in the positive x direction. Assume that the electric field is zero in the y and z directions at all points.
Given q=1.6×10−19 coulomb, , ${\in }_{r}=11.7$ for silicon, the value of L in nm is ________

The I-V characteristics of three types of diodes at the room temperature, made of semiconductors X, Y and Z, are shown in the figure. Assume that the diodes are uniformly doped and identical in all respects except their materials. If EgX, EgY and EgZ are the band gaps of X, Y and Z, respectively, then

The figure shows the I-V characteristics of a solar cell illuminated uniformly with solar light of power 100 mW/cm2. The solar cell has an area of 3 cm2 and a fill factor of 0.7. The maximum efficiency (in %) of the device is __________

The injected excess electron concentration profile in the base region of an npn BJT, biased in the active region, is linear, as shown in the figure. If the area of the emitter-base junction is 0.001 cm2, μn = 800 cm2/(V-s) in the base region and depletion layer widths are negligible, then the collector current IC (in mA) at room temperature is __________

(Given: thermal voltage VT = 26 mV at room temperature, electronic charge q = 1.6 × 10−19 C)

Figures I and II show two MOS capacitors of unit area. The capacitor in Figure I has insulator materials X (of thickness t1 = 1 nm and dielectric constant ${\epsilon }_{1}=4$) and Y (of thickness t2 = 3 nm and dielectric constant ${\epsilon }_{2}=20$). The capacitor in Figure II has only insulator material X of thickness tEq. If the capacitors are of equal capacitance, then the value of tEq (in nm) is __________

The I-V characteristics of the zener diodes D1 and D2 are shown in Figure I. These diodes are used in the circuit given in Figure II. If the supply voltage is varied from 0 to 100 V, then breakdown occurs in

A region of negative differential resistance is observed in the current voltage characteristics of a silicon PN junction if

A silicon sample is uniformly doped with donor type impurities with a concentration of 1016/cm3. The electron and hole mobilities in the sample are 1200 cm2/V-s and 400 cm2/V-s respectively. Assume complete ionization of impurities. The charge of an electron is 1.6 X 10-19 C. The resistivity of the sample (in $\mathrm{\Omega }$-cm) is _______.

In the circuit shown below, the Zener diode is ideal and the Zener voltage is 6 V. The output voltage Vo (in volts) is _______.

The built-in potential of an abrupt p-n junction is 0.75 V. If its junction capacitance (CJ) at a reverse bias (VR) of 1.25 V is 5 pF, the value of CJ (in pF) when VR = 7.25 V is_________.

A MOSFET in saturation has a drain current of 1 mA for VDS =0.5 V. If the channel length modulation coefficient is 0.05 V-1, the output resistance (in kΩ) of the MOSFET is_________

For a silicon diode with long P and N regions, the accepter and donor impurity concentrations are 1 x 1017 cm-3 and 1 x 1015 cm-3, respectively. The lifetimes of electrons in P region and holes in N region are both 100 $\mathrm{\mu }$s. The electron and hole diffusion coefficients are 49 cm2/s and 36 cm2/s, respectively. Assume kT/q = 26 mV , the intrinsic carrier concentration is 1 X 1010 cm-3, and q = 1.6 X 10-19 C. When a forward voltage of 208 mV is applied across the diode, the hole current density (in nA/cm2) injected from P region to N region is _________.

For the NMOSFET in the circuit shown, the threshold voltage is Vth , where Vth > 0. The source voltage VSS is varied from 0 to VDD. Neglecting the channel length modulation, the drain current ID as a function of VSS is represented by

An n-type silicon sample is uniformly illuminated with light which generates 1020 electron hole pairs per cm3 per second. The minority carrier lifetime in the sample is 1 μs. In the steady state, the hole concentration in the sample is approximately 10x, where x is integer. The value of x is __________

A piece of silicon is doped uniformly with phosphorous with a doping concentration of 1016/cm3. The expected value of mobility versus doping concentration for silicon assuming full dopant ionization is shown below. The charge of an electron is 1.6X10-19 C. The conductivity (in S cm-1) of the silicon sample at 300 K is ______.

A dc voltage of 10 V is applied across an n-type silicon bar having a rectangular cross-section and a length of 1 cm as shown in figure. The donor doping concentration ND and the mobility of electrons ${\mu }_{n}$ are 1016 cm-3 and 1000 cm2 V-1s-1 , respectively . The average time (in μs) taken by the electrons to move from one end of the bar to other end is________.

In a MOS capacitor with an oxide layer thickness of 10 nm, the maximum depletion layer thickness is 100 nm. The permittivities of the semiconductor and the oxide layer are εs and εos respectively. Assuming εsox= 3, the ratio of the maximum capacitance to the minimum capacitance of this MOS capacitor is _____________.

The energy band diagram and the electron density profile n(x) in a semiconductor are shown in figures. Assume that $\mathrm{n}\left(\mathrm{x}\right)={10}^{15}{e}^{\left(\frac{qax}{kT}\right)}{\mathrm{cm}}^{-3}$ , with $\alpha$ = 0.1 V/cm and x expressed in cm. Given $\frac{kT}{q}$=0.026 V, $D_n$ = 36cm2s–1 , and $\frac{D}{\mu }=\frac{kT}{q}$ . The electron current density (in A/cm2) at x = 0 is

Which one of the following process is preferred to form the gate dielectric (SiO2) of MOSFETs ?

If the base width in a bipolar junction transistor is doubled, which one of the following statements will be TRUE?

The electric field profile in the depletion region of a p-n junction in equilibrium is shown in the figure. Which one of the following statements is NOT TRUE?

The current in an enhancement mode NMOS transistor biased in saturation mode was measured to be 1 mA at a drain-source voltage of 5 V. When the drain-source voltage was increased to 6 V while keeping gate-source voltage same, the drain current increased to 1.02 mA. Assume that drain to source saturation voltage is much smaller than the applied drain-source voltage. The channel length modulation parameter $\lambda$ (in V-1) is ______.

An npn BJT having reverse saturation current Is = 10-15 A is biased in the forward active region with VBE = 700 mV. The thermal voltage (VT) is 25 mV and the current gain ($\beta$) may vary from 50 to 150 due to manufacturing variations. The maximum emitter current (in μA) is _____.

When the optical power incident on a photodiode is 10µW and the responsivity is 0.8 A/W, the photocurrent generated (in µA) is ________.

In the figure, assume that the forward voltage drops of the PN diode D1 and Schottky diode D2 are 0.7 V and 0.3 V, respectively. If ON denotes conducting state of the diode and OFF denotes nonconducting state of the diode, then in the circuit,

If fixed positive charges are present in the gate oxide of an n-channel enhancement type MOSFET, it will lead to

A BJT is biased in forward active mode. Assume VBE = 0.7 V, kT/q = 25 mV and reverse saturation IS=10-13 A. The transconductance of the BJT (in mA/V) is________.

The doping concentrations on the p-side and n-side of a silicon diode are 1×1016CM-3 m and 1×1017CM-3 m , respectively. A forward bias of 0.3 V is applied to the diode. At T = 300 K, the intrinsic carrier concentration of silicon ni=1.5×1010CM-3 m and $\frac{kT}{q}=26$ mV. The electron concentration at the edge of the depletion region on the p-side is ___________.

A depletion type N-channel MOSFET is biased in its linear region for use as a voltage  controlled resistor. Assume threshold voltage VTH= -0.5 V, VGS= 2.0 V, VDS= 5 V, W/L = 100, COX= 10-8 F/ Cm2 and μn= 800 Cm2 /V-s. The value of the resistance of the voltage Controlle resistor (in Ω) is_____.

A silicon bar is doped with donor impurities ND = 2.25 x 1015 atoms / cm3. Given the intrinsic carrier concentration of silicon at T = 300 K is ni = 1.5 x 1010 cm-3. Assuming complete impurity ionization, the equilibrium electron and hole concentrations are

An increase in the base recombination of a BJT will increase

In CMOS technology, shallow P-well or N-well regions can be formed using

Assume electronic charge q = 1.6×10-19 C, kT/q = 25 mV and electron mobility μn = 1000 cm2/V-s. If the concentration gradient of electrons injected into a P-type silicon sample is 1×1021/cm4, the magnitude of electron diffusion current density (in A/cm2) is _________.

Consider an abrupt PN junction (at T = 300 K) shown in the figure. The depletion region width Xn on the N-side of the junction is 0.2 μm and the permittivity of silicon (εsi) is 1.044×10-12 F/cm. At the junction, the approximate value of the peak electric field (in kV/cm) is _________.

When a silicon diode having a doping concentration of NA = 9 × 1016 cm-3 on p-side and ND = 1 × 1016 cm-3 on n-side is reverse biased, the total depletion width is found to be 3 μm. Given that the permittivity of silicon is 1.04 × 10–12 F/cm, the depletion width on the p-side and the maximum electric field in the depletion region, respectively, are

The diode in the circuit shown has Von = 0.7 Volts but is ideal otherwise. If Vi = 5sin(ωt )Volts, the minimum and maximum values of Vo (in Volts) are, respectively,

For the n-channel MOS transistor shown in the figure, the threshold voltage VTh is 0.8 V. Neglect channel length modulation effects. When the drain voltage VD=1.6 V, the drain current ID was found to be 0.5 mA. If VD is adjusted to be 2 V by changing the values of R and VDD, the new value of ID (in mA) is

For the MOSFETs shown in the figure, the threshold voltage |Vt| = 2 V and

The value of ID (in mA) is _______ .

In MOSFET fabrication, the channel length is defined during the process of

A thin P-type silicon sample is uniformly illuminated with light which generates excess carriers. The recombination rate is directly proportional to

At T = 300 K, the hole mobility of a semiconductor and $\frac{kT}{q}=26\mathrm{mV}$ The hole diffusion constant Dp in cm2/s is ________

The donor and accepter impurities in an abrupt junction silicon diode are 1 x 1016 cm-3 and 5 x 1018 cm-3, respectively. Assume that the intrinsic carrier concentration in silicon ni = 1.5 x 1010 cm-3 at 300 K, $\frac{kT}{q}$ = 26 mV and the permittivity of silicon ${\mathit{\in }}_{si}$ =1.04×10−12F/cm. The built-in potential and the depletion width of the diode under thermal equilibrium conditions, respectively, are

The slope of the ID vs.VGS curve of an n-channel MOSFET in linear regime is 10−3Ω−1 at VDS=0.1 V. For the same device, neglecting channel length modulation, the slope of the $\sqrt{{I}_{D}}$ vs. VGS curve (in $\sqrt{A}}{V}$) under saturation regime is approximately _________.

An ideal MOS capacitor has boron doping-concentration of 1015 cm-3 in the substrate. When a gate voltage is applied, a depletion region of width 0.5 μm is formed with a surface (channel) potential of 0.2 V. Given that ε0 = 8.854 × 10-14 F/cm and the relative permittivities of silicon and silicon dioxide are 12 and 4, respectively, the peak electric field (in V/μm) in the oxide region is _____________.

For the MOSFET M1 shown in the figure, assume W/L = 2, VDD = 2.0 V, and VTH = 0.5 V. The transistor M1 switches from saturation region to linear region when Vin (in Volts) is__________.

At T = 300 K, the band gap and the intrinsic carrier concentration of GaAs are 1.42 eV and 106 cm-3, respectively. In order to generate electron hole pairs in GaAs, which one of the wavelength (λC) ranges of incident radiation, is most suitable? (Given that: Plank’s constant is 6.62 × 10-34 J-s, velocity of light is 3 × 1010 cm/s and charge of electron is 1.6 × 10-19 C)

In the figure, ln (ρi) is plotted as a function of 1/T, where ρi is the intrinsic resistivity of silicon, T is the temperature, and the plot is almost linear.

The slope of the line can be used to estimate

The cut-off wavelength (in μm) of light that can be used for intrinsic excitation of a semiconductor material of bandgap Eg= 1.1 eV is ________

Consider a silicon sample doped with ND = 1×1015/cm3 donor atoms. Assume that the intrinsic carrier concentration ni = 1.5×1010/cm3. If the sample is additionally doped with NA = 1×1018/cm3 acceptor atoms, the approximate number of electrons/cm3 in the sample, at T=300 K, will be ______.

Consider two BJTs biased at the same collector current with area A1 = 0.2 μm × 0.2 μm and A2 = 300 μm × 300 μm. Assuming that all other device parameters are identical, kT/q = 26 mV, the intrinsic carrier concentration is 1 × 1010 cm-3, and q = 1.6 × 10-19 C, the difference between the base-emitter voltages (in mV) of the two BJTs (i.e., VBE1 – VBE2) is _____.

An N-type semiconductor having uniform doping is biased as shown in the figure.

If EC is the lowest energy level of the conduction band, EV is the highest energy level of the valance band and EF is the Fermi level, which one of the following represents the energy band diagram for the biased N-type semiconductor?

A BJT in a common-base configuration is used to amplify a signal received by a 50 Ω antenna. Assume kT/q = 25 mV. The value of the collector bias current (in mA) required to match the input impedance of the amplifier to the impedance of the antenna is________.

In a forward biased pn junction diode, the sequence of events that best describes the mechanism of current flow is

In IC technology, dry oxidation (using dry oxygen) as compared to wet oxidation (using steam or water vapor) produces

The return loss of a device is found to be 20 dB. The voltage standing wave ratio (VSWR) and magnitude of reflection coefficient are respectively

The i-v characteristics of the diode in the circuit given below are

The current in the circuit is

The source of a silicon (ni = 1010 per cm3) n-channel MOS transistor has an area of 1 sq μm and a depth of 1 μm. If the dopant density in the source is 1019/cm3, the number of holes in the source region with the above volume is approximately

In the three dimensional view of a silicon n-channel MOS transistor shown below, $\delta$= 20 nm. The transistor is of width 1 $\mu$m. The depletion width formed at every p-n junction is 10 nm. The relative permittivities of Si and SiO2, respectively, are 11.7 and 3.9, and ${\epsilon }_{0}$ = 8.9 $×$ 10-12 F/m.

The gate-source overlap capacitance is approximately

In the three dimensional view of a silicon n-channel MOS transistor shown below, $\delta$= 20 nm. The transistor is of width 1 $\mu$m. The depletion width formed at every p-n junction is 10 nm. The relative permittivities of Si and SiO2, respectively, are 11.7 and 3.9, and ${\epsilon }_{0}$ = 8.9 $×$ 10-12 F/m.

The source-body junction capacitance is approximately