Muddiest Points

Muddiest Points: • “What are the differences between intrinsic and

extrinsic semiconductors?”

• “What are the differences between n type and p type extrinsic semiconductors?”

• “How does temperature affect each type of semiconductor?”

• “What are the differences in the conductivity equation for intrinsic and extrinsic semiconductors?”

• “What is the relation of electron and electron-hole mobility to conductivity?”

Electronic Properties II: Intrinsic & Extrinsic Semiconductors

Intrinsic Semiconductors

No Dopants

ENER

GY

Less than 1021/m3 impurity atoms (10-6 wt% impurities)

electron-hole pairs (n=p=ni) Conductivity increases with

an increase in temperature (creates more e-h pairs)

Energy Gap (Eg) is constant and between 0.1eV-2eV

Group IV elemental semiconductors

Group III + Group V are compound semiconductors

Extrinsic Semiconductors: p-type

p-type Dopants

ENER

GY

Impurity atoms have one less valence electron than the host

Majority Charge Carriers: electron holes (p>>n)

Minority Charge Carriers: electrons (n<<p)

Acceptor States (contribute electron holes)

Saturation = all acceptor states filled

Example: Boron (B3+), Group III, impurity atoms within a Silicon host (Si4+), Group IV

Extrinsic Semiconductors: n-type

n-type Dopants

ENER

GY

Impurity atoms have one more valence electron than the host

Majority Charge Carriers: electrons (n>>p)

Minority Charge Carriers: electron holes (p<<n)

Donor States (contribute electrons)

Exhaustion = every donated electron in Cond. Band

Example: Phosphorus (P5+), Group V, impurity atoms within a Silicon host (Si4+), Group IV

Intrinsic - Electron and Hole Migration EN

ERG

Y

- - + +

Si4+

Si4+ Si4+

Extrinsic p-type: Majority Carriers - Holes EN

ERG

Y

Si4+

B3+

*No electric field applied

Extrinsic n-type: Majority Carriers - Electrons EN

ERG

Y

Si4+

P5+

*No electric field applied

Effect of Temperature: Intrinsic

𝛔 = 𝒏𝒊𝒒(𝛍𝒆 + 𝛍𝒉)

𝒏𝒊 ∝ 𝒆−𝑬𝒈

𝟐𝒌𝑻

ni = intrinsic carrier density (# of carriers/m3) Eg = energy gap (eV) k = Boltzmann Constant (8.6173 x 10-16 eV-K-1) T = Temperature (K)

Effect of Temperature: Intrinsic

𝛔 = 𝒏𝒊𝒒(𝛍𝒆 + 𝛍𝒉)

𝒏𝒊 ∝ 𝒆−𝑬𝒈

𝟐𝒌𝑻

ni = intrinsic carrier density (# of carriers/m3) Eg = energy gap (eV) k = Boltzmann Constant (8.6173 x 10-16 eV-K-1) T = Temperature (K)

Effect of Temperature: Extrinsic

Freeze-out region: not enough thermal energy for dopant activation

Extrinsic region: limited temperature effect on extrinsic conductivity

Intrinsic region: an increase in temperature, increases thermal energy creating a large number of electron-hole pairs

Conductivity Equation

𝛔 = 𝐧𝐪𝛍𝒆 + 𝐩𝐪𝛍𝒉

Intrinsic Semiconductors (n=p=ni)

σ = conductivity (ohm-m)-1

ni = intrinsic carrier density (# of carriers/m3)

q = electric charge 1.6x10-19 (C)

μe = electron mobility (m2/(V-s))

μh = electron hole mobility (m2/(V-s))

𝛔 = 𝒏𝒊𝒒(𝛍𝒆 + 𝛍𝒉)

Conductivity Equation: p-type

𝛔 = 𝐧𝐪𝛍𝒆 + 𝐩𝐪𝛍𝒉

Extrinsic Semiconductors: p-type (p>>n)

σ = conductivity (ohm-m)-1

p = positive carrier density (# of carriers/m3)

q = electric charge 1.6x10-19 (C)

μh = electron hole mobility (m2/(V-s))

𝛔 ≈ 𝒑𝒒𝛍𝒉

Example 1: p-type Conductivity

What is the conductivity of silicon containing 3.13 x 1021 boron dopant atoms per m3? Silicon has an electron mobility of 0.14 (m2/(V-s)) and a hole mobility of 0.05 (m2/(V-s)).

𝛔 = 𝐧𝐪𝛍𝒆 + 𝐩𝐪𝛍𝒉 𝛔 ≈ 𝒑𝒒𝛍𝒉

𝛍 𝒉= 0.05 (m2/(V-s)) 𝒑= 3.13 x 1021 m-3

𝛔 = (3.13 x 1021 m-3)(1.6x10-19 C)(0.05 m2/(V-s))

𝛔 = 𝟐𝟓. 𝟎𝟒 (Ω-m)-1

Conductivity Equation: n-type

𝛔 = 𝐧𝐪𝛍𝒆 + 𝐩𝐪𝛍𝒉

Extrinsic Semiconductors: n-type (n>>p)

σ = conductivity (ohm-m)-1

n = negative carrier density (# of carriers/m3)

q = electric charge 1.6x10-19 (C)

μe = electron mobility (m2/(V-s))

𝛔 ≈ 𝒏𝒒𝛍𝒆

Example 2: n-type Conductivity

What is the conductivity of silicon containing 3.13 x 1021 phosphorus dopant atoms per m3? Silicon has an electron mobility of 0.14 (m2/(V-s)) and a hole mobility of 0.05 (m2/(V-s)).

𝛔 = 𝐧𝐪𝛍𝒆 + 𝐩𝐪𝛍𝒉 𝛔 ≈ 𝒏𝒒𝛍𝒆

𝛍 𝒆= 0.14 (m2/(V-s)) 𝐧= 3.13 x 1021 m-3

𝛔 = (3.13 x 1021 m-3)(1.6x10-19 C)(0.14 m2/(V-s))

𝛔 = 𝟕𝟎. 𝟏𝟏 (Ω-m)-1

Wrap-Up

• “What are the differences between intrinsic and extrinsic semiconductors?”

• “What are the differences between n type and p type extrinsic semiconductors?”

• “How does temperature affect each type of semiconductor?”

• “What are the differences in the conductivity equation for intrinsic and extrinsic semiconductors?”

• “What is the relation of electron and electron-hole mobility to conductivity?”

Electronic Properties II: Intrinsic & Extrinsic Semiconductors