TITLE PAGE ---------- THz Hot Hole Lasers P Kinsler, Tom Wenckebach Why HHLasers? --> applications for THz and lack of compact sources HHL's have large gain bandwidth Presented results are based on Monte Carlo simulations, using modified Delft code III-V's easy for growth A BULK HOT HOLE LASER? ---------------------- e.g. 1x1x10mm^3 p-Ge crystal in cryostat with crossed E & B fields at temperatures: ~10,20K p-Ge: typical gains ~ 0.25 cm^{-1}, microsecond pulses with 10W peak power, 1kHz rep rate doping/impurity concentrations ~ 10^{14} cm^{-3} Crystal orientation dependent operation, polarization dependent emission Fields: E limit -- impact ionisation; B limit -- landau levels Diagram (1) HH Streaming up to E_{LO} (2) OP emission to bottom of LH (or HH) band (3) LH cyclotron orbits (4) photon emission from LH->HH transition This type of scheme has a long history, going back to the '70s (various) and even earlier (Kromer 1958, Lax 1960). The first observations were in Ge in the early 80's. COMPLICATIONS: charge distribution... ALSO: schemes involving strain, acceptor levels, Landau levels; Quantum Well designs OTHER MATERIALS? III-V's like GaAs (lots of existing GaAs apps esp QW's) (A) HH streaming must be not-too disrupted by scattering -- hence low temperatures to reduce LO phonon absorption & thermally assisted emission (B) Scattering to LH band from HH sufficiently likely (C) "good" LH cyclotron orbits to give localised inversion (D) the emitted photons are not too strongly absorbed These are correlated ABC by the ratio of effective masses, and BD by scattering (B:LO emission, D:intraband HH acoustic+impurity) Most of the scattering does not help the inversion -- the lasing cycle is "parasitic" on a sea of other scatterings SCATTERING PROCESSES -------------------- ACD: acoustic phonons -- weak scattering, and low Energy exchange. Generally not significant, but will depopulate LH band IIM: impurity scattering (coulomb-like) -- rate proportional to 1/(delta_k), but small delta_k scatterings have only weak effects (ie small deflections) OPD: optical phonon (emission) -- fixed delta_E = E_{LO}, strong threshold effect when hole kinetic E >= E_LO Hole-Hole: doing this properly is not difficult but adds significant complications to the simulation. However, since it would be a screened coulomb interaction, it is thus not dissimilar to IIM. Thus we model it as IIM, doubling the impurity density for IIM scattering calcs. POLAR MATERIALS: ACP: pizeo-electric acoustic phonons (weak) cf ACD OPP: polar optical phonon (emission) -- fixed delta_E = E_{LO}, threshold effect for low lattice temperatures, *and* rate is proportional to 1/dk, so LH-HH transitions relatively strong. HHL: p-GaAs ----------- E=8kV/cm [+2-1-1], B=7T [+0-1+1], n_i=0.025 Monte Carlo simulation: large gain from inversion (right graph), and then allow for the optical absorption -> (left graph) net gain 0.08 cm^{-1} LH band scattering time is t_{LH} = 3.8ps HH band scattering time is t_{HH} = 0.7ps mHH/mLH ~ 8 B/E ratio is ~ 0.8 Also done: InSb simulations BULK RESULTS ------------ What can we learn from comparing Ge and III-V simulations in bulk HH lasers? Tables of scattering counts mHH/mLH -- signature in B/E ratios mHH/mLH -- signature in HH->LH efficiencies (cf Ge & GaAs to InSb) new! GaAs IIM rates (791) double those of Ge (354) -- due to ratio of dielectrics (ratio 1.2^4) new! OPP in GaAs neutral cf OP processes (more HH-LH balanced by more LH-HH), but adds +25% to LH-HH (mostly ACD & IIM) new! OPP in InSB bad, adds +50% to LH-HH (mostly ACD & IIM) InSb low fields are bad, as the Streaming is slow and consequently more disrupted by ACD and IIM scattering. (Need Landau code) QUANTUM WELL HHLs ----------------- Modulation doping... reduce IIM scattering in active region while still maintaining doping concentrations Bulk GaAs E8-B7n025 but no iim, net gain x-section 4.7->5.1e-20 but then I can use any doping level to get any multiple of 5.1 for the gaim/cm HH and LH bands --> multiple HH and LH subbands To increase controllability of band dispersion and separation Fix optimum orientations of "active" well material by growth, not just ExB First: infinite wells; then Real wells (WMB code) [101] QUANTUM WELL HOT-HOLE LASER --------------------------------- A QW bandstructure is, in the ideal infinite QW case, just like a slice through the bulk bandstructure at k_z's fixed by the well width. Which slice is chosen is determined by the orientation in which the well material grows along the growth direction. Since the (bulk) bandstructure is warped, the slices can have very different shapes. Eg. a [101] well looks like (graph). Flat bottomed HH's in X, with a more "normal" psuedo-parabolic shape along Y. Not that X&Y, the in-plane directions can chosen arbitrarily. Imagine independent termalised distributions in easch of the HH1 and HH2 subbands -- the flatter bottomed HH2 will have wider wings along +-ky; as compared to the more centrally peaked HH1. We might therefore hope that we can get the wings of HH2 to be higher than the tails of HH1 at +-ky, leaving us with inversion at +-ky. For bulk, we had the streaming/cyclotron cycle that produced inversion and gain. How might it work for this 100A [101] well? LH1 is higher than HH1 & HH2, so can ignore. This means we can avoid the necessity of using a magnetic field to confine LH's (cf bulk). E_y field: (A-D) as per diagram. Note that this is the "ideal" lasing cycle, and in fact many other processes take place: intra-subband scattering; acceleration to high KE on HH1 and HH2, followed by LO phonon emission; some scattering to LH1; etc (C) Here the HH2 band is flat in k_x (if not in k_y), HH2's are more likely to accumulate at this k_x than HH1's. Also, HH2's are more strongly confined in k_x; so they get "squeezed out" to larger k_y's. This would leads to inversion for k_x~0, +-k_y, but the HH1 distribution is pushed under the +k_y by the E_y field. E_x field: distributions at bottom of page -- they are spread out a signficant amount by the many scattering processes. This leads to a similar lasing cycle; with the spreading-out represented by A'. Otherwise the cycle is rather similar. Inversion is better since the HH1 peak is no longer displaced to sit underneath one of the inversion-creating HH2 wings. If you look closely at the HH distributions at the bottom of the page, you could see that at Ex=1kV/cm, displaces HH1 distrib by ~ 2.5e8/m; HH2 distrib by ~ 2.0e8/m. Also note the strongly peaked HH1, but the "squeezed-out" HH2 with its wings at +-k_y. [001] QUANTUM WELL HOT-HOLE LASER --------------------------------- A different growth orientation takes a different slice of the bulk bandstructure, and hence provides a diifferent quantum well bandstructure. Here we have chosen [001], which gives a bandstructure symmetric in x and y; but the HH subbands now have local maxima at the origin, the HH2 moreso than the HH1. This is harder to simulate, as E(k) is no longer single valued. Since we haven't yet adjusted our code to cope, I dont have any simulation results. However, by looking at the bandstructure we can see how a hot-hole laser might operate. Steps ABCD as per slide. (Note: no magnetic field) Note the point(s) of inflection in HH1 and HH2 are offset. The LH1 band is close to the HH2 band at the origin, so it will have some effect (unlike in the [101] well). The HH2-HH1 separation is 32meV, just less than the LO phonon energy and hence we wont have LO phonon emission competing with the THz emission and reducing the efficency (or destroying the inversion) [101] INVERSION AND GAIN ------------------------ Note the low E fields -- this is because we only need to accelerate the HH's to the anti/crossing point XX; not right up to E_LO as in the bulk hot-hole laser. Ex: The top two lines show results for two strengths of an X-direction electric field. Note that due to constraints on CPU time, there is a noticeable amount of statistical noise on these graphs. On the Left we see the region of inversion, which is symetric in k_y, and displaced slightly to positive k_x by the E field. The inversion is localised around the two flat parts of the HH2 band just beyond the edges of the flat part(s) of the HH1 subband. Statistical noise: remember, these are the ratio of two noisy distribution functions, and so suffer more from noise than just one function itself. The inversion stretches along k_y from the anti/crossing to the flat parts of HH1, thus emission is possible from roughly 0 to ~15meV ... and we see this on the Right hand graphs Ey: With an Ey electric field, the bulk of the HH1 distribution shifts along y to sit underneath what would be the +ky inversion peak. We can see at low fields (250V/cm) there is still a small area of inversion there, but at 100V/cm we just see some scattered noise and no significant inversion at all. However, the -ky inversion peak now has less of the HH1 distribution underneath it, and so the -ky inversion is stronger. Although the inversion sits over the same energy range as for the Ex field, the optical gain is rather different, being peaked towards the 15meV end of the range. This is because the optical gain takes into account photon-absorption processess, which are now likely to occur in the region of swamped inversion at +ky. This is worse towards the lower frequency parts, and reduces the gain for 250V/cm; but leaves an isolated peak at 100V/cm. CONCLUSIONS ----------- Read the slide