Bera, M

De, S S

Ghosh, A K

Haidar, JC

SiI, D

Sinha, P K

IACS Institutional Repository

Indian J. Phyx. 6 9 A  (2), 285 -  29 0  (1995)N O TE1I J P Aan international journalStudies on some parameters in heavily doped AlxGai_xAs/GaAs double heterostructureS S He, A K Ghosh, M Bera, P K Sinha, I) Si I and .1 C HaidarC'cntic ol Advanced Sludy in Radio Rhysicsand hlccrionks,IJnivcisily ol C'alcuira, I, Ginsh Vidyaiatna Lane, CiiIlui la-700 ()()<), IndiaAVi u v v i l  2 2  l n l \  1 9 9 4 .  m  c q * i * l  7  ( h  l o b e r  1 9 9 4A hslracl : The vanation ol several paiameieis wiihin heavily doped A lx(ia, ^As/GiiAs doulile heleioslmuiue lias been mvesli^aied Iheorelieally lakiny inlo aecounl hand »^ap nuiiowmg and eamei degeneracy as heavy dopin'- ellrcis I he lesulls ol the computational analyses aie shown piaphie.ilIyKeywords : HelerosmietuiePA(\S No. : 71 40 KpThe minority cairiet lilcltmc in III-V semiconductors like GaAs and AlxGaj xAs is an important parameter lot a number ol applications To produce electrical and optical devicesLike high electron mobility transistors (llKMTs) 11], double hcteroslructure lasers [2] and high-efficiency devices [3], AlxGa, xAs/GaAs heterostructuie is commonly used. Time resolved photo-luminescence |4| technique is used to measure minority carrier lifetime in some 111 V semiconducting materials. Minority carnei lifetime is useful for minority-carrier devices like light emitting diodes (LEDs), photovoltaic cells, bipolar transistors Various methods are used widely to determine the minority carnei lifetime in photovoltaic devices [5—7|. In III-V compounds, tune-resolved photoluminescence decay method is uselul for the measurement of the minority carrier lifetime. Carrier lifetime in silicon is measured by using pulse optical excitation and photo-conductivity decay technique. Heavy doping effects play important role in producing high emitter efficiency in bipolar transistors and high open-circuit voltage m solar cells, and have influence on lifclinic in band-to-band processes. Experimentally measured lifetimes [4,8] of heavily doped GaAs and quaternary alloy anc reported earlier to study Auger effects.In this presentation, assuming uniform distribution of SRH (Shocklcy-Read-HalJ) defects within specified region, the variation of bulk minority carrier lifetime with carnei<& 1995 I ACS286 S S De, A K Ghosh, M Bern, P K Sinha, D Sil and J  C Haidardensity and photolum incscence lifetim e with interface recom bination ve loc ity  in h eavily  doped  A lxG a ! xA s/G a A s double heterostructure have been in vestiga ted . B and gap narrow ing and  carrier d eg e n e ra c y  are co n sid ered  a s h e a v y  d o p in g  e f fe c ts .  A s  b a n d -to -b a n d  A u g er  recom bination  e ffec t is a m ust, the variation o f  quantum  e ffic ien cy  and p h o to lu m in escen ce  life tim e w ith  nom ina l current d en sity  arc studied  for the sam e hetero-structure. Sp atia l variation  o f  m inority  earner density  has been ignored o w in g  to lo w er  va lue o f  d iffusion  tran sit-tim e  com p ared  to the m inority  carrier l ife t im e . T h e  resu lts  s o  o b ta in ed  by  com putational analyses are show n graphically. For A1XG  a] _xA s/G aA s double heterostructure, ph oto lu m in cscen ce  [9] lifetim e, under low  interface recom bination  v e lo c ity , approaches the bulk m inority carrier lifetim e. The photolum inescence lifetim e rPL is given  by [10]where1 1 1 11 _ _V ~ + TSR1I ~r Ts1 2 .VT.v ~ T(1)tr is the radiative lifetim e; rSRH, the Sh ock ley-R ead-H all lifetim e; r s , the surface lifetim e; S , the interface recom bination velocity, and cl is the active layer thickness.T he relationship am ong m inority carrier diffusiv ity  ( / ) ) ,  decay time ( t) and m obility (//)  can be written asd 2 K Jl )  =  —  and D  = ----- u y (2 )2 / qw here K  is the B o ltzm an n  constant; q , the e le c tr o n ic  ch arge, and T  is  the a b so lu te  temperature. For n-type sem icon ductor w ith donor concentration N D, the e lectron  m o b ility  fj  is g iven  by [ 1 1  ]i + K / " c n ) “(3)f i0 is the d ifferen ce  betw een  the exp ected  m axim um  and m in im u m  m o b ilitie s; p nijn, the exp ected  m inim um  m obility  value; N cf]-, a reference concentration , and a  is an exp on en tia l factor that controls the slope around N n =  ff .■ A gain the radiative and SR H  life tim e  [12] are given  bytr =AnB n p'An  r 1tsr. i = —  l V "  + + T„ (P  + » ,)]. (4)where A n is the ex cess  photogenerated carrier; /?, the radiative recom bination  co effic ien t; n„ the in tr in sic  carrier co n cen tra tion  and r p and t„ are the h o le  and e lectro n  life tim e s ,  resp ectively . U nder heavy dop ing condition , e lectron  ( n ) and h o le  (p )  concentrations can be  exp ressed  as [13]Studies on some parameters in heavily doped etc 287AAE^ E - E ,  K T  1 K T(5a)( 1 - A )A £  £ , - £  --------------- -- e x p --------- —/r r  k t(5b)P =  " F u i ^ p )  exp  (~T]p ) e x p ------—where Fin ( t} „ )  is the Fermi-Dirac integral o f  order 1/2; 77, the reduced Fermi energy; A, the asym m etry factor; A E g, the handgap narrowing; the intrinsic Ferm i energy, and Ep, and Ejp are the quasi-Ferm i energies o f  electron and hole, respectively. At equilibrium, E p -  E p .M oreover, the interface recombination velocity (S )  is related to recom bination current density (./<) asS  =  - 4 " ’ (6)qAn+ ^Aug]’ > (7)where /?SRIT is the interface recom bination due to SRI I process [14 ,15] and is the net Auger recom bination. These arc expressed asnp -  nt_______________[________SRH Tn(p+n,) + TP(~n+n,'>’= r' V r 1 ' '2 \np-n(n + p ),(8)(9)r is ihe Auger recombination coefficient Thus, from eqs. (1 ) -  (9), one obtains1 nT pj AnAE. f 1Fm ^ n ) F m {T}„) exp  exp  { - ( %  +  Vp )}r r r ( 1  -  A )A Ex [n,B  +  K  {F i/2 < V  ex P V  exp ------LX eXPf fc|A T~) + ’ 1 + Tr{Fi«(,J«) CXPx  e x p ---------  ex p  — ---------I +1 K T  y  [ K T2q_ (K T  J1/21 + ( N D/ N t( f ) a +* 1/2[[* . {F„2 < V288 S S De, A K Ghosh, M Bera, P K Sinha, D Sil a n d J C  Haidar(1 -A)AE *  exp ( - 77^) e x p ------— — exp( E  - E .  \_J____fP_, K T+ i4 i ^ 1/2 ^ 1.) exp (- v  cxp“ ^ r + exp£■ -  F K T+ 1+ r {/ri/ 2  (»!-) CXP ( - n , )  exp —x  exp ft i K T+ ^1/2 ( Sp > CXP (*~ ^  ) eXP(l- i4 )d £K T* exP I ^ 4 ^ 1 } ]  [ Fl/2< V  eXPK Tx  exp { - ( r 7n + ^ } - l ] ] .  0 0 )The computational analyses o f  cq. (10) have been earned out ior a fixed  com position  under different circumstances. Figure 1 represents the variation ol bulk ifiinorily earner lifetime otFigure i. Bulk minority-earner lifetime versus Figure 2. Photoluminescence lifetim e vm u searner density of an Al0 3Ga07As/GaAs/Al03Ga07As interface recombination velocity of an Al03Ga07DH device (d= 4 gm). As/GaAs/AloiGa^As DH device {d = 4\im).heavily doped A l0 iG a 0 .7 Aa/GaAs/Alo.3Gao.7 A 8  D H  (d = 4  /jm) w ith carrier density under 2 0  m w  focu ssed  pow er. The nature o f  variation reveals that bulk m inority carrier lifetim e  decreases in a  nonuniform  m anner w ith the increase o f  concentrations under the focussedStudies on some parameters in heavily doped etc 289power for a given cross-sectional area and thickness of a double heterostructure. Numerical computations of equation ( 10) are worked out considering A E g -  10.23 (N /lO  1 + 13.12 (A71018)1* + 2.93 (tf/1018)1'2 meV [16], T  = 300 K, R  ~ 10’ *° c n $ s ~l . The values WP> tin* F m  (Vp)  and Fj /2 ( t]„) are chosen suitably [17] for the given carrier densities. In numerical analysis, change of carrier lifetime with carrier densities is considered.NOMINAL CURRENT DENSITY (KA/cm* |im) NOMINAL CURRENT DENSITY (KA/cmz- j^m)Figure 3. Variation of quantum efficiency with Figure 4. Variation of photoluminescence lifetnnominal current density of an A1 q 3Ga0 7 As/GaAs/Al0v with nominal current density of an A l03Cia(Cia07A.s Dll device (</= 2 fim). As/GaAs/Al03Ga07As DH device ( d=2  |lm).The values of minority carrier lifetimes are chosen within 5 x 10"7 -  1(W s when majori carrier concentration varies in the range 1018 -  lO ^cm -3. Again, the values of majority cam lifetimes are chosen within 10"* -  10~12 s when minority carrier concentration varies in U range (1-8) x 1016 cm 3. These data are used to study the change of photoluminescen lifetime with interface recombination velocity of an Alo 3Ga0 vAs/GaAs/AlojGao 7As D (d = 4 |im ), which is depicted in Figure 2. Figure 3 represents the change of quantc efficiency with nominal current density for the same semiconducting compound with the sar composition and d  -  2 fim . The variation of photoluminescence lifetime with nominal cum density of the same DH (Alo ^Ga q -jA s /G slA s/A Iq^ q jA s) with d  * 2 pm  is shown Figure 4.References11] R Dingle, H LStormer, A C Cos.sard and W Wiegmonn Appl. Phys. Lett. 33*665 (1978)12] 1 Hayashi, M B Pamsh and F K Reinhart 7. AppL Phys. 411929 (1971)[3] R J Nelson and R G Sobers Appl. Phys. Lett. 32 761 (1978)[4] B Sermage, H J Eichler. J P Heritage, R J Nelson and N K Duita Appl. Phys. Lett. 42 259 (1983)6QA<2Y-13290 S S Dp, A K Ghosh, M Bern. P K Sinha, D Sil and J C Haidar151 J Furlan und S Amon Solid Stale Llei mm 28 1241 (1985)161 S R Dhanwal IEE Proc. 127 Pt I 20 (1980)[7] J E Mahan. T W Fkstedl, l< I Frank and R Kaplow I ELL 7riwv. Electron Devu e\ E D -2 6  733 (1979)[8 | G Duggan, G B ScoU. C T Foxon and J J Hums Appl. Pli\s Lett 38 246 (1980)(9 1 R K A hicnkid. B M Keyes, T C Shen, JI Chyi and H Morkoe J Appl Phys 69 3094 (1991)1 1 0 ) G W HooIt and C Van Opdnip J Appl Plu s 60 1065 (1986)[II] f  R Selvakumar Solid State hle< trim 30 773 (1987)| !2 | F Slein J Appt Phys 47 5382 (1976)[13] A 11 Marshak, M A Shihih. J G Possum and 1 A Lindholm ILIA: lions Lledr^n Denies E D -2 8  291(1981)114) W Sliuekley and W T Read lr Plus Her 87 815 (1952)[I5 | R N Hall Phys Rev 87 387 (1952)|16] S ( ’ lam and I) 1 Rnulsion SolidStaie Elettron, 34 453 (1991)117 1 S N Mohammad and A V Heims ILLt Turns Idee turn Devu e\ E D -39  2826 ( 1992)

Studies on Some Parameters in Heavily Doped AlxGa1-xAs/GaAs Double Heterostructure

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Studies on Some Parameters in Heavily Doped AlxGa1-xAs/GaAs Double Heterostructure

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