Low and High field transport Handout

Low and High field transport Handout - University of...

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- 123 - University of California, Berkeley EE230 - Solid State Electronics Prof. J. Bokor Low field mobility in Si and GaAs In doped samples, at low T, ionized impurity scattering dominates: where , and . is approximately constant. Plug in (maximum of integrand in ). Define: The we get for the mobility: Notice that this increases with temperature ~ . Faster electrons get deflected less. Acoustic phonons : (Moderate T, mainly important in Si ) τ E () 1 N D ------ 2 m π e 4 -------------- 1 γ 2 + γ 2 1 γ 2 + ------------- ln 1 E 32 = τ o Ek T = τ o kT N D ---------- 2 m π e 4 1 γ 2 + γ 2 1 γ 2 + ln 1 = γ 2 8 m EL D 2 h _ 2 = τ o E ˆ 3 = E τ E ⟨⟩ μ B e m Γ 4 Γ 52 ------------------ 2 m N D π e 4 ---------------- 1 γ B 2 + γ B 2 1 γ B 2 + ln 1 = h ω LO Si 63 meV = τ o 2 π h _ 4 ρ v s 2 D A 2 2 m ------------------------------ = μ AP π h _ 4 ρ v s 2 e D A 2 2 m ----------------------------------------------------- Γ 2 Γ =
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- 124 - University of California, Berkeley EE230 - Solid State Electronics Prof. J. Bokor AP mobility decreases with increasing temperature as (kT) -3/2 - increased phonon popula- tion Multiple scattering mechanisms (read Lundstrom 4.32, 4.7, 3.7) relaxation - time approximation: recall As we have seen, for most scattering mechanisms: , and if s 1 = s 2 = s both mechanisms have same E - dependence, then so Mathiessen’s rule This is only true if both mechanisms have the same E - dependence. This is rarely the case, but Mathiessen’s rule is often used anyway, since it’s hard to do otherwise. Only matters when several rate’s are comparable. Often one process dominates. f t ---- coll f E () τ 1 E ------------- fE τ 2 E τ eff E ---------------- = μ e m ------ τ E ⟨⟩ e m E τ E E ------------------------- = τ i E () τ oi Ek T s i = 1 μ -- m e 1 τ o 1 ------- Γ 52 Γ s + --------------------------- 1 τ o 2 Γ Γ s + + = Expect for Si log ( μ ) log T N 3 N 2 N 1 T 32 T ADP: Imp:
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- 125 - University of California, Berkeley EE230 - Solid State Electronics Prof. J. Bokor High field transport High field effects: qualitative discussion velocity saturation : typical in Si . For low fields, , independent of E . At high fields, the drift energy becomes large enough that equivalent intervalley optical phonon-scatt turns on. This creates a strong energy loss for electrons with velocity . This leads to a roll- off of the drift velocity, and eventually, full saturation. velocity overshoot (in Si) For time scales shorter than the equivalent intervally scattering time, τ opt , a transient drift velocity, can occur. Equivalently, in devices that are small enough that electrons can traverse the device structure in such a short time, the average propagation velocity can μ log 1 10 100 1000 log T GaAs POP kT () 1 imp N 3 N 2 N 1 v d μ E = μμ 0 = v d μ 0 E = v d E v dsat v d v dsat >
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- 126 - University of California, Berkeley EE230 - Solid State Electronics Prof. J. Bokor also exceed . Velocity Overshoot (GaAs) . In GaAs, there is no intervalley process for For low energies, POP scattering dominates. Recall that the rate for POP scattering, 1/ τ , is nearly independent of electron energy. It is also fairly weak. So the low field mobility in GaAs is rather high, about 8000 cm 2 /V-s. Once the electron energy reaches 0.29 eV, the
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Low and High field transport Handout - University of...

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