1. Two –Temperature Model (Chap 7.1.3)
6 Dec 2011
Injoo Hwang

2. Contents
1. Two – Temperature Model 1
2. Conclustion 2

3. Two-Temperature Model
A pair of coupled nonlinear equations governing the effective
temperatures of electrons and phonons (by S.I. Anisimov et al. 1974)
Assumed in the Two – Temperature Model
Electron System
Phonon System
Mutually
Equilibrium
Equilibrium
Non-Equilibrium

4. Two-Temperature Model
: Electron System
: Phonon System
: the volumetric heat capacity
: the electron – phonon coupling constant
: the source term ( during the laser pulse )
: the thermal conductivity
( ∵ heat conduction by phonons is neglected )

5. Two-Temperature Model
Examining parameters
- The volumetric heat capacity
- The coupling constant or
- The thermal conductivity
G is independent of temperature and proportional to the square of the speed of sound in the metal

6. Two-Temperature Model
The associated electron and phonon temperatures near the surface
Ultrafast thermoreflectance experiments
Pump beam
Thermoreflec-tance signal
Probe beam
Specimen
The electron temperature rises quickly during the pulse and begins to decrease afterward
The lattice temperature gradually increases until the electron and lattice systems reach a thermal equilibrium
Measuring the effective electron temperature by no contact thermometer which performs the femtosecond or picosecond thermoreflectrance technique

7. Two-Temperature Model
Differential equations for the electron temperature

8. Two-Temperature Model
Differential equations for the phonon temperature
Identical to the lagging heat equations
Following the general trends
τq : Thermalization time
(thermal time constant for the electron system to reach
an equilibrium with the phonon system)

9. Two-Temperature Model
- For noble metals at room temperature -
Relaxation time : τ ~ 30 to 40 fs
Thermalization time : τq ~ to 0.8 ps
Retatdation time : τT ~ to 90 ps
The two-temperature model cannot be applied to t < τ
( the limitation of Fourier’s law )
- Difficult issues -
The processes below 20 fs (relaxation time of Cr is about 3 fs)
Electron – electron inelastic scattering
Thermionic emission, ionization, phase transformation, chemical reaction
The reduced pulse width include widened frequency spectrum
Increased pulse intensity, decreased pulse energy

10. Conclusion Two – Temperature Model Examine parameters
(their own local equilibrium not in mutual equilibrium)
Examine parameters
(the volumertic heat capacity, the thermal conductivity, the coupling constant)
The behavior of the electron and phonon temperatures
Non contact thermometer
( thermoreflctance technique known as pump-and-probe method)
Derive PDE for the electron or phonon temperature

11. Thank You !