GATE Questions on "Semiconductors (Intrinsic & Extrinsic), Drift and Diffusion, Hall Effect" (1987 to Till Date)

1.       Consider two energy levels : E1, E eV above the Fermi level and E2, E eV below the Fermi level. P1 and P2 are the probabilities of E1 and E2 being occupied by the electron respectively. Then
        a.       P1 > P2
        b.      P1 = P2
        c.       P1 < P2
        d.      P1 and P2 depend on number of free electrons
Answer:     C
               Solution :

2.       In an intrinsic semiconductor, the free electron concentration depends on
        a.       Effective  mass of electrons only
        b.      Effective mass of holes only
        c.       Temperature of the semiconductor
        d.      Width of the forbidden energy band of the semiconductor
Answer:    C
               Solution :

3.       According to the Einstein relation, for any semiconductor, the ratio of diffusion constant to mobility of carriers
        a.       Depends upon the temperature of the semiconductor
        b.      Depends upon the type of the semiconductor
        c.       Varies with life time of the semiconductor
        d.      Is a universal constant
Answer:    A
               Solution :

4.       Direct band gap semiconductors
        a.       Exhibit short carrier lifetime and they are used for fabricating BJTs
        b.      Exhibit long carrier lifetime and they are used for fabricating BJTs
        c.       Exhibit short carrier lifetime and they are used for fabricating LASERs
        d.      Exhibit long carrier lifetime and they are used for fabricating LASERs
Answer:    C
               Solution :

1.       Due to illumination by light, the electron and hole concentrations in a heavily doped N-type semiconductor increases by Δn and Δp respectively, if ni is the intrinsic carrier concentration then
        a.       Δn < Δp
        b.      Δn > Δp
        c.       Δn = Δp
        d.      Δn x Δp = ni2
Answer:    C
                 Solution :

2.       The concentration of ionized acceptors and donors in a semiconductor are NA, ND respectively. If NA > ND and ni is the intrinsic  concentration, then the position of the Fermi level with respect to the intrinsic level depends on
       a.       NA – ND
       b.      NA + ND
       c.       (NA x ND) / ni2
       d.      ni
Answer:   A 
                 Solution :


1. In a semiconductor, under high electric fields, with increasing electric fields, mobility of charge carriers ............. and velocity of charge carriers ..............

Answer:     Reduces, gets saturated so remains constant
 Solution :

2. In a semiconductor at room temperature, the intrinsic carrier concentration and resistivity are 1.5 X 1016 m-3 and 2 X 105 -m respectively. It is converted into an extrinsic semiconductor with a doping concentration of 1020 per m3. For the extrinsic semiconductor, calculate the

             a.       Minority carrier concentration

             b.      Resistivity

             c.       Shift in Fermi level due to doping

              d.      Minority carrier concentration when its temperature is increased to a value at which the intrinsic carrier concentration doubles.

Assume the mobility of majority and minority carriers to be the same and KT = 26 meV at room temperature.

a) 2.25 x 1012 /m3
b) 60 Ω-m
c) 0.228 eV
d) 9 x 1012 /m3
Solution :

1.       A silicon sample is uniformly doped with 1016 phosphorous atoms/cm3 and 2 X 1016 boron atoms/cm3. If all the dopants are fully ionized, the material is ………..
Answer:     P-type with 106 holes/cm3

   2.       An n-type silicon sample, having electron mobility µn twice the hole mobility µp, is subjected to a steady illumination such that the electron concentration doubles from its thermal equilibrium value, as a result, the conductivity of the sample increases by a factor of ………..
Answer:    2

    3.       The current in a forward biased P+N junction shown in figure (a) is entirely due to diffusion of holes from x = 0 to x = L. The injected hole concentration distribution in the n-region is linear as shown in figure (b), with P(0) = 1022 per cm3 and L = 10-3 cm. Determine

              a.       The current density in the diode, assuming that the diffusion coefficient of holes is 12 cm2/sec.
              b.      The velocity of holes in the n-region at x = 0.

Jn = 19.2 x 106 A/cm2
υn = 12 x 103 cm/sec

1.       A semiconductor is irradiated with light such that carriers are uniformly generated throughout its volume. The semiconductor is n-type with ND = 1019 cm-3. If the excess electron concentration in the steady state is Δn = 1015 cm-3 and if τp = 10 µsec (minority carrier life time), then the generation rate due to irradiation is ………….

Answer:    A
Solution :


1.       A small concentration of minority carriers is injected into a homogeneous semiconductor crystal at one point. An electric field of 10 V/cm is applied across the crystal and this moves the minority carriers a distance of 1 cm in 20 µsec. The mobility in cm2/volt-sec will be
       a.       1000
       b.      2000
       c.       5000
       d.      50000
Answer:    C
                Solution :

2.       A p-type silicon sample has a higher conductivity compared to an n-type sample having the same dopant concentration.  (TRUE / FALSE)
Answer:    FALSE
                Solution :

3.       Show that the minimum conductivity of an extrinsic silicon sample occurs when it is slightly p-type. Calculate the electron and hole concentrations when the conductivity is minimum. Given that µn = 1350 cm2/volt-sec, µp = 450 cm2/volt-sec, and the intrinsic carrier concentration, ni = 1.5 X 1010 cm-3.
Answer:     no = ni√µp∕µn and po = ni√µn∕µp
            Solution :


1.       The drift velocity of electrons, in silicon
       a.       Is proportional to the electric field for all values of electric field
       b.      Is independent of the electric field
       c.       Increases at low values of electric field and decreases at high values of electric field exhibiting negative differential resistance.
       d.      Increases linearly with electric field at low values of electric field and gradually saturates at higher values of electric field.
Answer:    D
                 Solution :

2.       In a p-type silicon sample, the hole concentration is 2.25 X 1015 cm-3. If the intrinsic carrier concentration is 1.5 X 1010 cm-3, the electron concentration is
       a.       Zero
       b.      1010 cm-3
       c.       105 cm-3
       d.      1.5 X 1010 cm-3
Answer:    C
                 Solution :

3.       The probability that an electron in a metal occupies the Fermi level at any temperature T is (T > 0oK)
Answer:    1
                Solution :

4.   In an extrinsic semiconductor, if
Answer:     a-5, b-5, c-3
                Solution :

5. The Fermi level of an n-type germanium film is 0.2 eV above the intrinsic Fermi level towards the
        conduction band. The thickness of the film is 0.5 µm. Calculate the sheet resistance of the film.
Assume :
         ni = 1013 cm-3,  
         µn = 3500 cm2/V-sec,
         µp = 1500 cm2/V-sec,
         KT/q = 26 mV.

Answer:     1.63 kΩ
Solution :



1.       The intrinsic carrier density at 300oK is 1.5 X 1010 per cm3 for silicon. For n-type silicon doped to 2.25 X 1015 atoms/cm3, the equilibrium electron and hole densities are

Answer:    C
                  Solution :

2.   An n-type silicon bar is doped uniformly by phosphorous atoms to a concentration 4.5 x 1013 cm-3. The bar has cross section of 1 mm2 and length of 10 cm. It is illuminated uniformly for region x < 0 as shown.
Assume optical generation rate as 1021 electron-hole pairs per cm3 per second, the hole lifetime and electron lifetime are equal to 1 µsec.
Evaluate the hole and electron diffusion currents at x = 36.4 µm.

                  Solution :


1.       The electron and hole concentrations in a intrinsic semiconductor are ni and pi respectively. When doped with a P-type material, these changes to n and p respectively. Then
       a.       n + P = ni + Pi
       b.      n + ni = p + pi
       c.       npi = nip
       d.      np = nipi
Answer:    D
                Solution :

2.       A long specimen of p-type semiconductor material
       a.       Is positively charged
       b.      Is electrically neutral
       c.       Has an electric field directed along its length
       d.      Acts as a dipole
Answer:    B
                Solution :

3.       The units of (q/KT) are
       a.       V
       b.      V-1
       c.       J
       d.      J/K
Answer:    B
                Solution :



1.       N – Type silicon is obtained by doping silicon with
       a.       Germanium
       b.      Aluminum
       c.       Boron
       d.      Phosphorous
Answer:    D

2.       The band gap of silicon at 3000K is
       a.       1.36 eV
       b.      1.10 eV
       c.       0.80 eV
       d.      0.67 eV
Answer:    B
               Solutoin :

3.       The intrinsic carrier concentration of silicon sample at 300oK is 1.5 x 1016 m-3. If after doping, the number of majority carriers is 5 x 1020 m-3, the minority carrier density is 

a.       4.50 x 1011 /m3
b.      3.33 x 104 /m3
c.       5.00 x 1020 /m3
d.      3.00 x 10-5 /m3  
Answer:    A
                Solutoin :

4.       An N type silicon bar 0.1 cm long and µm2 in cross sectional area has a majority carrier concentration of 5 x 1020 m-3 and the carrier mobility is 0.13 m2/V-sec at 300oK. If the charge of an electron is 1.6 x 10-19 coulomb, then the resistance of the bar is

a.       106
b.      104
c.       10-1
d.      10-4

Answer:    A
                Solutoin :

5.       The electron concentration in a sample of uniformly doped N type silicon at 300oK varies linearly from 1017 cm-3 at x = 0 µm to  6 x 1016 cm-3 at x = 2 µm. Assume a situation that electrons are supplied to keep this concentration gradient constant with time. If electronic charge is 1.6 x 10-19 coulomb and the diffusion constant Dn = 35 cm2/sec, the current density in the silicon, if no electric field is present is
       a.       Zero
       b.      -112 A/cm2
       c.       +1120 A/cm2
       d.      -1120 A/cm2
Answer:    D
                Solutoin :


1.       The impurity commonly used for realizing the base region of a silicon NPN transistor is
       a.       Gallium
       b.      Indium
       c.       Boron
       d.      Phosphorous
Answer:    C
               Solution :

2.       The resistivity of a uniformly doped N type silicon sample is 0.5 -cm. If the electron mobility (µn) is 1250 cm2/V-sec and the charge of an electron is 1.6 x 10-19 coulomb, then the donor impurity concentration (ND) in the sample is

a.       2 x 1016 / cm3 
b.      1 x 1016 / cm3 
c.       2.5 x 1015 / cm3 
d.      2 x 1015 / cm3 
Answer:           B           
Solution :


1.       The band gap of silicon at room temperature is
       a.       1.3 eV
       b.      0.7 eV
       c.       1.1 eV
       d.      1.4 eV
Answer:    C
                Solution :

2.       The primary reason for the widespread use of silicon in semiconductor device technology is
       a.       Abundance of silicon on the surface of the earth
       b.      Larger band gap of silicon in comparison to germanium
       c.       Favorable properties of silicon – dioxide (SiO2)
       d.      Lower melting point
Answer:    A
                 Solution :

3.       A silicon sample A is doped with 1018 atoms/cm3 of boron. Another sample B of identical dimensions is doped with 1018 atoms/cm3 of phosphorous. The ratio of electron to hole mobility is 3. The ratio of conductivity of the sample A to B is
       a.       3
       b.      1/3
       c.       2/3
       d.      3/2
Answer:    B
                 Solution :


1.       The concentration of minority carriers in an extrinsic semiconductor under equilibrium is
       a.       Directly proportional to the doping concentration
       b.      Inversely proportional to the doping concentration
       c.       Directly proportional to the intrinsic concentration
       d.      Inversely proportional to the intrinsic concentration
Answer:    B
                Solution :

2.       Under low level injection assumption, the injected minority carrier current for an extrinsic semiconductor is essentially the
       a.       Diffusion current
       b.      Drift current
       c.       Recombination current
       d.      Induced current
Answer:    A
                Solution :

3.       The majority carriers in an N-type semiconductor have an average drift velocity V in a direction perpendicular to a uniform magnetic field B. The electric field E induced due to hall effect acts in the direction

Answer:    B
                Solution :

4.       A heavily doped N-type semiconductor has the following data:
Hole – electron mobility ratio         :  0.4
Doping concentration                :  4.2 x 108 /m3
Intrinsic concentration             :  1.5  x 104 /m3
The ratio of conductance of the N-type semiconductor to that of the intrinsic semiconductor of same material and at the same temperature is given by
       a.       0.00005
       b.      2000
       c.       10000
       d.      20000
Answer:    D
                Solution :


1.       The electron and hole concentrations in an intrinsic semiconductor are ni per cm3 at 300oK. Now if acceptor impurities are introduced with a concentration of NA per cm3 (where NA > ni), then electron concentration per cm3 at 300oK will be
       a.       ni
       b.      ni + NA
       c.       NA – ni
       d.      ni2 / NA
Answer:    D
               Solution :


1.       Which of the following is TRUE?
       a.       A silicon wafer heavily doped with boron is a P+ substrate
       b.      A silicon wafer lightly doped with boron is a P+ substrate
       c.       A silicon wafer heavily doped with Arsenic is a P+ substrate
       d.      A silicon wafer lightly doped with Arsenic is a P+ substrate
Answer:    A
                Solution :

2.       Silicon is doped with boron to a concentration of 4x1017atoms/cm3. Assuming the intrinsic carrier concentration of silicon to be 1.5x1010 cm-3 and the value of KT/q to be 25 mV at 300oK. Compared to undoped silicon, the Fermi level of doped silicon
       a.       Goes down by 0.13 eV
       b.      Goes up by 0.13 eV
       c.       Goes down by 0.427 eV
       d.      Goes up by 0.427 eV
Answer:    C
                Solution :


1.       In an N type silicon crystal at room temperature, which of the following can have a concentration of 4x1019 cm-3?
       a.       Silicon atoms
       b.      Holes
       c.       Dopant atoms
       d.      Valence electrons
Answer:    C
                Solution :

2.       The ratio of the mobility to the diffusion coefficient in a semiconductor has the units
       a.       V-1
       b.      cm. V-1
       c.       V. cm-1
       d.      V.sec
Answer:    A
                Solution :


1.       Linked Answer Question:
The silicon sample with unit cross sectional area shown below is in thermal equilibrium. The following information is given:
T = 300oK
Electron charge = 1.6x10-19 C
Thermal voltage = 26 mV
Electron mobility = 1350 cm2/volt-sec 

              i.                     The magnitude of the electric field at x = 0.5 µm is
              a.       1 KV/cm
              b.      5 KV/cm
              c.       10 KV/cm
              d.      26 KV/cm
Answer:    C
              ii.                   The magnitude of the electron drift current density at x = 0.5 µm is
              a.       2.16x104 A/cm2
              b.      1.08x104 A/cm2
              c.       4.32x103 A/cm2
              d.      6.48x102 A/cm2
Answer:    A
                Solution :


1.       Drift current in semiconductors depends upon
       a.       Only the electric field
       b.      Only the carrier concentration gradient
       c.       Both the electric field and the carrier concentration
       d.      Both the electric field and the carrier concentration gradient
Answer:    C
               Solution :


Set – 1 (15th February 2014 (Forenoon))

SET – 2 (15th February 2014 (Afternoon))

1.       A silicon bar is doped with donor impurities ND = 2.25 x 1015 atoms/cm3. Given the intrinsic carrier concentration of silicon at T = 300oK is ni = 1.5 x 1010 cm-3. Assuming complete impurity ionization, the equilibrium electron and hole concentrations are
       a.       no = 1.5 x 1016 cm-3, p0 = 1.5 x 105 cm-3 
       b.      no = 1.5 x 1010 cm-3, p0 = 1.5 x 1015 cm-3 
       c.       no = 1.5 x 1015 cm-3, p0 = 1.5 x 1010 cm-3 
       d.      no = 1.5 x 1015 cm-3, p0 = 1.5 x 105 cm-3 
Answer:    D
                  Solution :

2.       Assume electron charge q = 1.6 x 10-19C, KT/q = 25 mV and electron mobility µn = 1000 cm2/volt-sec. If the concentration gradient of electrons injected into a P type silicon sample is 1 x 1021 per cm-3, the magnitude of electron diffusion current density (in A/cm2) is ………….
Answer:    4000
                  Solution :

SET – 3  (16th February 2014 (Forenoon))

1.       A thin P type silicon sample is uniformly illuminated with light which generates excess carriers. The recombination rate is directly proportional to
       a.       The minority carrier mobility
       b.      The minority carrier recombination lifetime
       c.       The majority carrier concentration
       d.      The excess minority carrier concentration
Answer:    D
                  Solution :

2.       At T = 300oK, the hole mobility of a semiconductor µp = 500 cm2/volt-sec and KT/q = 26 mV. The hole diffusion constant Dp in cm2/sec is ………
Answer:    13
                  Solution :

SET  - 4  (16th February 2014 (Afternoon))

1.       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

              a.       Band gap energy of silicon
              b.      Sum of electron and hole mobility in silicon
              c.       Reciprocal of the sum of electron and hole mobility in silicon
              d.      Intrinsic carrier concentration of silicon
Answer:    A
                  Solution :

2.       Consider a silicon sample doped with ND = 1 x 1015 /cm3 donor atoms. Assume that the intrinsic carrier concentration ni = 1.5  x 1010 cm-3. If the sample is additionally doped with NA = 1 x 1018 cm-3 acceptor atoms, the approximate number of electrons /cm3 in the sample, at T = 300oK, will be…………
Answer:    225
                  Solution :

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

Answer:    D
                  Solution :



1.       A silicon sample is uniformly doped with donor type impurities with a concentration of 1016 cm-3. The electron and hole mobilities in the sample  are 1200 cm2/V-sec and 400 cm2/V-sec respectively. Assume complete ionization of impurities. The charge of an electron is 1.6x10-19 C. The resistivity of the sample (in Ω-cm) is _______________
Answer:    0.52
 Solution :   

2.   A piece of silicon is doped uniformly with phosphorous with a doping concentration of 1016 per cm3. The expected value of mobility verses doping concentration for silicon assuming full dopant ionization is shown below. The charge of an electron is 1.6x10-19 C. The conductivity (in Simons/cm) of  the silicon sample at 300oK is _______________

Answer:     1.92
   Solution :

3.   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 an integer. The value of x is _________________

Answer:      14
Solution :   

4.   The energy band diagram and the electron density profile n(x) in a semiconductor are shown in the figures.
Answer:     D
Solution :

5.   A DC voltage of 10 volts is applied across an N-type silicon bar having a rectangular cross section and length of 1 cm as shown. The donor doping concentration ND and the mobility of electron µn are 1016 cm-3 and 1000 cm2/V-sec respectively. The average time (in µs) taken by the electrons to move from one end of the bar to the other end is _______________

Answer:      100
  Solution :  


  1. can anyone help me solving 1997 the figure one 2nd question or provide the link for that

  2. At 300 K, if acceptor density in a semiconductor is 1018 cm-3 while the intrinsic carrier concentration is 1010 cm-3, then the difference between the Fermi level of doped semiconductor and the intrinsic Fermi level is:

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  16. in question no 4 .....
    according to your solution the ans of this question is 2.2*(10)^-2...but i think ans is wrong because,the concentration of doping is not uniform throughout the SC, thus to maintain the equilibrium internal electric field is generated due to which the band of the SC is varying with slope -0.1eV/cm.
    the generated electric field opposes the diffusion of carriers due to concentration gradient and thus there will be no current flow inside the SC.

  17. sir, 2010 paper you have taken electron concn as 10^6 but in the problem it is given as 10^16

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