GATE Electronics and Communications (EC) 2020 Solved Papers

Question : 39 of 65

Marks: +1, -0

The band diagram of a p-type semiconductor with a band-gap of

1 {eV}

is shown. Using this semiconductor, a MOS capacitor having VTH of

-0.16 {V}, {C}^{'}

ox of

100 {nF} \/ {cm}^{2}

and a metal work function of

3.87 {eV}

is fabricated. There is no charge within the oxide. If the voltage across the capacitor is

{V}_{ {TH}}

, the magnitude of depletion charge per unit area (in

{C} \/ {cm}^{2})

Solution:

From the figure,

{Ec}- {Ev}=1 {eV}=0.5 {Ev}+ {q} φ {B}+0.2 {eV}

⇒ {q} φ {B}=0.3 {eV}

⇒ φ{B}=0.3 {V}

, where

{q} φ {B}= {E}_{ {i}}- {EFS}

The magnitude of depletion charge density

ρ_{S}=√{2 E_{S} N_{A} ψ_{S}} \;\; . . .(1)

where,

Ψ_{s}=2 ϕ_{B}=2 × 0.3 {V}=0.6 {V}

..........(2)
Voltage across capacitor,

{V}_{ {TH}}= {V}_{ {FB}}+\;{√{2 ∈_{ {S}} {N}_{ {A}} ψ_{ {S}}}}/{ {C}_{ {ox}}^{'}}+ψ_{ {S}}

...(3)
where,

V_{F B}=φ_{m s}=φ_{m}-φ s

=3.87-4.8

{V}_{ {FB}}=φ_{ {mS}}=-0.93 {V}

....(4)
From (1), (2), (3) & (4)

ρ_{s}=1.7 × 10^{-8} {C} {/} {cm}^{2}

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