Simulation of Time-Resolved Carrier Dynamics Project Goals Femtosecond Pump and Probe Technique Computer Simulation and Results

Femtosecond Pump and Probe Technique Concept of Pump and Probe Experimental Setup Pump and Probe Measurement Photo-excited Carrier Relaxation Media file Flash file Flash file Next page

Time Scale for Different Carrier Relaxation Processes Photoexitation : ~immediately Hole interband relaxation : ~few femtoseconds ( 10-15sec ) Hole intraband relaxation : ~few sub~picoseconds (10-13sec) Electron intraband relaxation : ~few picoseconds (10-12 sec) Go!! Flash file

Femtosecond Pump and Probe Technique BS Femtosecond Laser pulse Mirror

Computer Simulation and Results

Equations N5 τ56 N6 N4 τ34 N3 These equations represent the state population of N1~N6 states (N1~N4: holes, N5, N6: electrons). Tau’s are the relaxation times of each states, and our goal is to find their values. ‘Gexp” term means the pump effect, that participates in N1, N3, N5, N6 states. N4 and N6 are stable states while others are just transition states. τ23 N2 τ12 N1

Based on these equations, our simulation calculates the electron and hole state populations, which represent the number of electrons and holes on valence and conducting bands, to fit the data points. Time evolution of these state population of GaAs will directly affect its optical reflectivity. Our project goal is to find the best fit of the experimental data with proper fitting parameters. {τ12,τ23,τ56 } Our experiment measures the reflectivity difference with ‘probe light’ (we just let go the pump light). Proper: Our knowledge of physics shows that τ12=10fs, τ23, τ34=!0~100fs, τ56=1000~10000fs. @ The probe light surely affects the state populations just as the pump light, but we have known its effect and our simulation can cope with this issue, so it doesn’t matter. (Actually the red curve shows how it affects the curve.)

It looks perfect, but when we get closer near zero there is some problem. This is an experimental data (sample: GaAs(1,0,0) 150mW) red curve is our simulation. We divide the fitting into two parts: 1st τ5 because long term behavior is purely N5 effect; 2nd τ12, τ23 (with data excluding N5 effect because) they are coupled and much harder to fit. Because the effect before 0 is not concerned in our model the simulation doesn’t fit well near t=0, and τ12~1fs which is too small.

There is a valley before time origin, which is not involved in our fitting model. Hence, near t=0 the curve does not fit well.

Fitting Results τ τ56 τ23 τ12 τ τ12~1fs, τ23~200fs, τ56~8000fs,except τ12 basically the result are plausible. Below 50mW the results vary dramatically because the feature of the curve changes (the concave at t=100~400 disappears.) therefore our fit doesn’t work well.

Conclusion Our simulation can fit the experimental curves very well in the range of 100fs to 10ps. We find that hole relaxation time is ~10-200fs and electron relaxation time is ~10ps. As pump power increases, the carrier relaxation times decrease due to stronger carrier-carrier scattering. The signal near delay time zero is not taken into account in our simulation model.