Enhancement of Ionization Efficiency of Acceptors by Their Excited States in Heavily Doped p-type GaN and Wide Bandgap Semiconductors

Transcription

1 Enhancement of Ionization Efficiency of cceptors by Their Excited States in Heavily Doped p-type GaN and Wide Bandgap Semiconductors Hideharu Matsuura Osaka Electro-Communication University 2004 Joint International Meeting, Honolulu Hawaii, Oct

2 Our focus Problem in heavily doped p-type wide bandgap semiconductors The acceptor density, which is determined by the curve-fitting procedure using the temperature dependence of the hole concentration, is always much higher than the doping density. Why?

3 Hole Concentration [cm -3 ] cceptor density in heavily Mg-doped GaN Heavily Mg-doped GaN : Experimental p(t) /T [K -1 ] 2. SIMS 1. Hall-effect measurement Fermi-Dirac (FD) distribution function 1 f ( E ) = FD N = E 1+ 4exp E kt Results determined by curve-fitting E = 154 mev 19 cm Concentration of Mg in GaN: 2 10 cm Is the FD distribution function available for Mg acceptors in GaN? F 3 3

4 Contents 1. How to determine the densities and energy levels of impurities from p(t) or n(t) without any assumptions regarding the impurities. 2. How to investigate a distribution function suitable for acceptors in heavily doped p-type wide bandgap semiconductors 3. How do the excited states of deep acceptors influence p(t) in heavily doped case?

5 1. In order to determine the densities and energy levels of impurities from the temperature dependence of the majority-carrier concentration without any assumptions regarding the impurities. graphical peak analysis method Free carrier concentration spectroscopy (FCCS)

6 Free Carrier Concentration Spectroscopy (FCCS) Using an experimental n(t), the FCCS signal is defined as H n( T ) E ( ) T, E exp ref ref ( kt) 5 / 2 kt This FCCS has peaks corresponding to donor levels 2 From each peak temperature and value, E kt D peak,i N +,i D, i kt peak, i E ref H ( T, E peak, i ref )exp(1)

7 Undoped 3C-SiC The temperature dependence of the electron concentration Electron concentration (cm -3 ) /T (K -1 )

8 H ( T, E ) ref n( T ) ( kt ) 2 5 / 2 exp E ref kt Donor1 Donor3 Peak2 Donor2 51 mev 7.1x10 16 cm -3 Free Windows pplication software: See at Web site p/labs/matsuura/

9 The FCCS signal is theoretically written as H ( T, E ref ) = i N N kt C0 kt Di N exp E exp E ref Di kt E kt E ref F I D ( E ) FCCS signal, in which the influence of the previously determined donor species is removed, is expressed as 2 n( T ) E N E E H 2 ref E 5 / 2 D ( kt) kt kt kt ref D2 D2 ref ( T, E ) = exp exp I ( ) Di D2

10 Osaka Electro-Communication University Web site Peak1 Donor1 18 mev 3.8x10 16 cm -3 Peak3 Donor3 114 mev 1.1x10 17 cm -3

11 The n(t) simulation is in agreement with the experimental n(t). The values determined by FCCS are reliable.

12 2. In order to investigate a distribution function suitable for deep acceptors in heavily doped semiconductors distribution function including the influence of excited states of acceptors

13 cceptor level and excited state levels E r = 13.6 ev p-type wide bandgap semiconductors (GaN, SiC, diamond) 1.Their dielectric constants are lower than that of Si 2.Their hole effective masses are heavier than their electron effective masses Semiconductor ε cceptor level (r=1) 1 2 s m m * h 0 r st excited state level (r=2) SiC 146 mev 37 mev GaN 101 mev 25 mev The acceptor levels become deep, and also the excited state levels are still close to acceptor levels in Si.

14 The excited states should affect p(t)! Position of Fermi level in heavily doped p-type case E F (T) [mev] : Heavily l-doped 6H-SiC : Lightly l-doped 6H-SiC E cceptor levels E F (T) E E F (T) E V Temperature [K] Heavily doped case cceptor level Fermi level 1 st excited state 2 nd excited state Valence band Since the Fermi level is close to the excited state levels, a lot of holes exist at the excited states.

15 distribution function suitable for deep acceptors 1. Fermi-Dirac distribution function not including the influence of excited states of acceptors f FD E ( ) = 1+ g 1 E exp E kt 2. The distribution function including the influence of excites states of acceptors 1 f ( E ) = E E 1+ g T F ( )exp kt The difference between two functions is only the acceptor degeneracy factor, g and g (T). F

16 In f FD ( E ) g = 4 In f ( E ) g cceptor degeneracy factor E E E T T = g + g r ( ) ( ) 1 r exp exp ex r= kt kt E ex ( T ) = 2 r= 2 Degeneracy factors of excited states E E E Er gr exp kt E exp E g r r kt ( ) 1+ r= 2 Excited state levels verage energy of acceptor level and excited state levels r

17 Hole Concentration [cm -3 ] Heavily l-doped 6H-SiC Heavily l-doped 6H-SiC : Experimental p(t) /T [K -1 ] H(T,0.248) [x10 42 cm -6 ev -2.5 ] Heavily l-doped 6H-SiC Peak Temperature [K] From this peak, N = cm -3 and E =180 mev for f FD ( E ) N = cm -3 and E =180 mev for f ( E ) Since the l-doping density is cm -3, the influence of excited states on p(t) should be considered.

18 Comparison between Heavily and lightly l-doped 6H-SiC Heavily doped Lightly doped f( E ) f FD ( E ) f( E ) f FD ( E ) N [cm -3 ] 3.2x x x x10 15 E [mev] Doping density [cm -3 ] 4.2x10 18 ~6x10 15 In lightly doped case, holes at the excited states are few because the Fermi level is far from E V. Using each distribution function, the reasonable acceptor density is obtained. Only in heavily doped samples, f FD ( E ) cannot be used to analyze p(t).

19 Hole Concentration [cm -3 ] Heavily Mg-doped GaN : Experimental p(t) Heavily Mg-doped GaN /T [K -1 ] H(T, 0.237) [x10 43 cm -6 ev -2.5 ] Heavily Mg-doped GaN Experimental H(T,E ref ) Simulated H(T,E ref ) : f FD ( E ) : f( E ) Peak Temperature [K] From this peak, N = cm -3 and E =154 mev for f FD ( E ) N = cm -3 and E =149 mev for f ( E ) Since the Mg-doping density is cm -3, f( E ) is suitable for heavily doped GaN.

20 3. How do the excited states of acceptors influence p(t)? Do the excited states enhance the ionization efficiency of acceptors, or not?

21 Temperature dependence of acceptor degeneracy factor 4 p-type GaN 3 g (T) 2 1 Simulations : g (T) : g Temperature [K] g (T) is less than g of 4 at high temperatures, which enhances the ionization efficiency at high temperatures.

22 Ionized acceptor density in Mg-doped GaN Ionized cceptor Density [cm -3 ] Simulations N = 8.9x10 18 cm -3 E = 149 mev N D = 1.5x10 17 cm -3 : f FD ( E ) : f( E ) Mg-doped GaN Temperature [K] Since g (T) is less than g at high temperatures, the ionized acceptor density for f( E ) is higher than that for f FD ( E ).

23 Summary The distribution function suitable for deep acceptors has been proposed and tested. This distribution function is necessary for determining N in heavily doped p-type wide bandgap semiconductors. The excited states of acceptors enhance the ionization efficiency of acceptors at high temperatures.