A sample of N-type silicon is at the room temperature. When an electric field with a strength of 1000V /cm is applied to the sample, the hole velocity is measured and found to be 2 × 105 cm/sec.

a. Estimate the thermal equilibrium electron and hole densities, indicating which is the minority carrier. [5 pts]

b. Find the position of EF with respect to Ec and Ev. [10 pts]

c. The sample is used to make an integrated circuit resistor. The width and height of the sample are 10µm and 1.5µm, respectively, and the length of the sample is 20µm. Calculate the resistance of the sa]

a) 222/cm^3

b) The Ec with respect to Ef and Ev = -0.107ev

c) Resistance, R = 467 ohms

Explanation:

(a) From the velocity and the applied electric field, we can calculate the mobility of holes:

υdp = µpε, µp = υdp/ε = 2×10^5/1000

= 200cm2/V.s

From a), we find Nd is equal to 4.5×1017/cm3

. Hence,

n = Nd = 4.5×10^17/cm3

, and p = ni^2/n

= ni^2/Nd

= 10^20 / 4.5×10^17 = 222/cm3

.

Clearly, the minority carrier is hole.

(b) The Fermi level with respect to Ec is

Ef = Ec - kTln(Nd/Nc) = Ec - 0.107 eV.

(c) R = ρL/A. Using Equation, we first calculate the resistivity of the sample:

σ = q(µn n + µp p) ≈ qµn n = 1.6×10^-19 × 400 × 4.5×10^17 = 28.8/Ω-cm, and

ρ= σ

-1 = 0.035 Ω-cm.

Therefore, R = (0.035) × 20µm / (10µm× 1.5µm) = 467 Ω.

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