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be obtained by photoluminescence excitation (PLE), espe-

cially at very low temperatures.9116,z~,~,~ n contrast with

the AlGaAs/GaAs system, where the presence of bulk lumi-

nescence complicates the interpretation of both PL and PLE

spectra, the optical signal from an InGaAs channel can be

unambiguously distinguished from the substrate or barrier

luminescence. In this context, several methods have been

proposed for the optical determination of the 2DEG concen-

tration in PM-HEMTs. They are based either on the determi-

nation of the Fermi energy from the detection of the lumi-

nescence ntensity cutoff occurring in the high-energy side of

the PL spectra33Z25,28r, alternatively, from the Stokes shift

between the emission and the onset of the

absorption.l42~24,~

A linear dependence of the sheet carrier

density with the PL linewidth has also been observed.0*29

The very low temperatures required by these methods offer

serious doubts about their applicabi lity for routine wafer

characterization. Thus, optical techniques operating at room

temperature (RT), or even at 77 K, are desirable. The use of

RT modulation spectroscopies has been proposed to derive

the Fermi energy in HEMTs although their modeling is less

advanced.30Besides, nondestructive integrated procedures to

assess other critical device parameters, such as the QW

thickness and composition, have not yet been presented.

Therefore, the development of methods for on-line PM-

HEMT wafer assessment s still an open question.

In the present article we describe the use of PL spectros-

copy for the quantitative characterization of n-type PM

AI,Ga, -,As/In,Ga, -,As/GaAs HEMT structures at cryo-

genic and room temperatures. Quantum well parameters,

such as the InAs mole fraction X, the well thickness L, and

the transferred sheet carrier density n, are determined when

the k=O optical transitions energies are compared with the

results of self-consistent calculations of the subband struc-

ture. In the section that follows, the transistor structures un-

der consideration and the experimental techniques are de-

scribed. Section III is devoted to the theoretical method used

to calculate the energy transitions in the QW. The e ffective

band gap in the strained channel, and the contlned electron

and hole states obtained from the solution of the coupled

Schrijdinger and Poisson equations are presented. In Sec. IV,

the optical spectra at different temperatures are analyzed in

detai1. In Sec. V the specific procedure used to assess the

PM-HEMT structural parameters is developed and applied to

a significant number of samples. Results and limitations of

the method are also discussed. Conclusions are provided in

Sec. VI.

II. SAMPLES AND EXPERIMENTAL DETAILS

The samples used in this study are pseudomorphic

In,Ga, -&s modulation-doped quantum wells grown on

semi-insulating GaAs (001) substrates by molecular beam

epitaxy. The typical epitaxial layer sequence consists of a

GaAs/Al ,Ga,-,As buffer superlattice (or simply a thick

GaAs buffer layer), an undoped In,Gar-,As strained quan-

tum well, an AIYGa, -,,As undoped spacer, an A&Gal -YAs

highly Si-doped supplier layer, and a GaAs cap layer. The

range of In,Ga,-,As and A$Ga,-,As layer compositions is

0.07

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TABLE I. Variation of the InGaAs parameters as a function of the InAs

mole fraction, X.

Quantity

Variation with x

Ei (eV)

meiphd

md(m0)

mhhlih)

mhN(mO)

a eV)

b (eV)

Cl, (10 dyn/cm)

Cl2 (1O1 dyn/cm*)

e

ci (10e4 eV/K)

P (K)

1.519-1.5387x+0.475x2

0.075-0.046x

0.071

0.45-0.0385x

0.15

8.67-5.66x

1.7+0. lx

12.25-3.61x

5.7-0.85x

0.0717x

5.40-2.90x

204.0+51.0x

IV. EXPERIMENTAL RESULTS

A. 4 K photoluminescence

PL spectra

at 4 K for representative n-type

Al,,Ga, +Ys/In,Ga, -,As/GaAs PM-HEMTs with different

L, x, and 2DEG densities are shown in Fig. 2. Spectra are

made up of the recombination of electrons in the n = 1 and

12 2 conduction states with photogenerated holes thermal-

ized to the IZ= 1 heavy hole state. Depending on the tempera-

ture and on the Fermi energy position relative to the quantum

levels, both or just the low-energy transition will be observed

in the spectra. We classify our samples into two types ac-

3-c

300

1350 1400

Energy (meV)

FIG. 2. Low excitation PL spectra at 4 K for three representative n-type

PM-IIEMT structures. The arrows indicate the calculated Err and E,, tran-

sition energies. (a) Single peak spectrum corresponding to a sample having

the Fermi level below the n=2 subband edge. (b) Spectrum presenting a

second, high intensity peak in a sample having the Fermi level above the

n =2 subband edge. (c) Two-peak spectrum in the case of the Fermi level

laying below but very close to the n =2 subband edge.

cording to the number of QW transitions appearing in their

spectra and their relative intensity. Type I samples are those

whose 4 K spectrum consists of a single peak originating

from the recombination of y1= 1 electrons and 12 1 heavy

holes (e,-+hh, transition) [Fig. 2(a)]. Type II spectra present

a second, higher energy peak which arises from the recom-

bination of 12 2 electrons with n = 1 heavy holes (e.&h,

transition), and dominates over the e,-&hr transition [Fig.

2(b)]. An intermediate si tuation appears when the ea-+hhr

recombination is observed as a low intensity transition in

type I spectra at very low temperatures [Fig. 2(c)]. Its inten-

sity increases rapidly with the excitation power, though re-

maining smaller than the e,-+hh, peak, as observed by Col-

vard et aLa This is a result of the thermal population of the

n=2 electron subband when E, is close to, but below, the

subband edge E2. The l ine-shape variation observed when

comparing the two types of spectra arises from the relative

Fermi level position respecting E,. Type I spectra corre-

spond to a Fermi energy lower than E,, whereas in type II

spectra the Fermi level is above EZ. This assertion was con-

firmed by determining the Fermi energy through two alter-

native experimental procedures, the conductivity oscillations

in SdH measurements and the absorption threshold in PLE

measurements.

Line-shape analysis is used to determine the energy shift

of the peak maxima with respect to the band edge transitions.

This is a very important point in our assessment method,

since it is based on the comparison between the experimental

energies and the results of our self-consistent model, which

provides the electron and hole band edges. Lyo and Jones3

demonstrated that the spectral line shape at low temperatures

in HEMT structures is fully accounted for by the electron

and hole scattering with the ionized impurities in the barrier

regions. They showed that the peak maximum is displaced

from the k=O transition energy due to the presence of indi-

rect recombinations provided by Coulombic interaction. The

energy shift is larger as the interaction is increased by a

reduction in the carrier-ionized impurities distance. The same

effect is produced by the increase of temperature, which

makes this fact especially important when the characteriza-

tion is carried out at 77 K or room temperature. Figure 3

shows the adjustment of the experimental line shape in a

type II sample at 4 K according to the line-shape function

Fi/=A Bij

I

Od~~(E-LLui)f(w-E-ccci)L(w,E),

03)

0

where Eij stands for the recombination rate of the ei-hhj

transition, w is the photon energy minus the effective band

gap, ,u,&~) is the electron (hole) chemical potential, f(x)

are Fermi functions, and A is a normalization parameter. 6ij

is the squared wave function overlap that is calculated self-

consistently for a given structure and carrier density. Assum-

ing that the failure of the k-selection rule is not too impor-

tant, the Lorentzian factors that account for the indirect

transitions in the original Lyo-Jones expression are substi-

tuted in E q. (8) by the Lorentzian function L which includes

a broadening parameter l? to characterize phenomenologi-

tally the carrier-ionized impurities scattering. We use the

same F value to fit the two PL peaks. The conduction band

5934

J. Appl. Phys., Vol. 76, No. 10, 15 November 1994

Gilpkez et a/.

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In

Y

5

4

2.

x

.e

t

3

C

:

ii

i

E

5

is

2

i:

- Theory

1

1250

1300 1350

Energy (meV)

1400

FIG. 3. PL line-shape fit (line) of a two-peak spectrum obtained at 4 K

(dots) as explained in the text. The arrows indicate the recombination ener-

gies of electron and holes having k =0 wave vectors.

has been demonstrated to be parabolic in the range of ener-

gies of interest.39 Although the valence band is highly non-

parabolic in the same range, the effective

mass can be-

con-

sidered constant in the section tilled by the low concentration

of photoholes. When, in addition, bound states like the Ma-

hans exciton are not taken into account, the wave function

overlap term 0, can be considered as energy independent

and thus kept out of the integration. Thermal effects in the

recombination rate are introduced by means of the Fermi

functions. Discrepancies between experiment and theory are

expected at temperatures at which the unconsidered carrier-

phonon interactions become important.

Representative PLE spectra from type I and II samples

are exhibited in Fig. 4. They were taken at 4 K with the

detection wavelength set on the maximum of the er-+hhr

transition. The intensity was normalized by the wavelength-

dependent Ti laser output power, the Ge detector response

being flat in the region of interest. The main features are

assigned to hhl+ea, hh2-+e2, and hhZ-+e, absorption pro-

cesses.A sharp and intense peak (not shown in the spectra) is

always observed at the GaAs free-exciton energy (1515

meV) associated with transitions in the undoped buffer layer.

Again, spectra of both type of samples show very different

characteristics. Absorption processes can only involve unoc-

cupied electron states with energy higher than E,. Thus, in

the parabolic bands approximation, the onset of the absorp-

tion to IZ= i states is displaced with respect to the k=O emis-

sion by the Burstein-Moss shift (l+~~,lm~~)E,. Here we

use m,=0.071 and mb=0.15 for the electron and heavy-

hole in-plane effective masses respectively.41 In all the

structures analyzed, the energy ET, = El1 + (1

+ m,/mhh)E, results to be higher than E,,. Therefore, the

absorption threshold will be at Ezl in type I samples, and at

E& = EFI - m,lmM(E2, -

E r r) in type II samples. The PLE

spectra of all type I sampl es reveal excitonic absorption to

the IZ=2 and n =3 bands [Fig. 4(a)], while the excitonic be-

E

1350

1375 1400

1425

3

1450

2

0

E

E

(cl

it

f; ii1 lZ2

E

132

i-:-

j :

i :

.: \

r--T

_...** *. 1350 1400 1450 1500

.

1375

1400 1425 1450 1475

Enei-gy (meV)

FIG. 4. PLE spectra in several selected samples recorded at 4 K. The arrows

indicate calculated energies Eij for the band edge transitions hh,-+q and

ci+hhi in the absorption (full line) and emission (dashed linesj processes,

respectively. The symbol (*) represents the absorption energies shifted by

the Burstein-Moss effect. The Fermi level is below the n =2 band in (a) and

above in (b) and (c).

havior related to 12 2 tends to vanish in type II spectra [Figs.

4(b) and 4(c)] which then show step-like absorption. The

change in the nature of the absorption is attributed to the

presence of carriers in the subband. Transitions to empty

subbands give rise to excitonic peaks, even though lower

energy subbands have a high 2DEG density. The excitonic

character is removed once the subband is populated, even for

low subband populations, due to a reduced exciton binding

energy.

The FES (Mahans exciton)r2 is an effect resulting from

the final-state multiple Coulomb scattering occurring be-

tween the optically generated holes and the electron Fermi

sea giving rise to an enhanced oscillator strength for optical

transitions involving electron states near the Fermi edge.

Such scattering phenomena are not allowed for electrons be-

low the Fermi level, due to the Paulis exclusion principle,

Therefore, the many-body exciton will be very sensitive to

changes in the temperature as the Fermi surface is broadened

in the order of the exciton binding energy.r3-l7 The depen-

dence of the excitonic enhancement on the carrier

densityr214 and on the effective masses has been also

studied. Furthermore, Chen et al.17 have reported the reso-

nant coupling of the Fermi level and an n=2 excitonic state

when E, is below and very near E, (0.6 meV) at 2 K. Such

hybridization has been theoretically studied by Mueller,

who predicted the observation of the Fermi enhancement in

this special case. Experimentally, most of the reported results

concern samples with only one electron subband

J. Appt. Phys., Vol. 76, No. IO, 1.5 November 1994 Gilp6rez et al. 5935

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(0)

-..__

I

\

8

yyy

I

------ ,......___

:

I

. ,-a

,,I :,

..- . ..___./. .**

: s,

\

.

2

. .___..

,:

-44K i.

0))

.

1400 1420

1440

Energy (meV)

FIG. 5. PLE spectra measured at several temperatures n samples showing

many-body excitonic effects. Transitions to empty states in the n=l and

n=2 bands, abeled by (*), result in singularity peaks. A single many-body

exciton is observed when the Fermi level is below the n=2 band (a),

whereas wo excitonic peaks are observedwhen the Fermi level is above he

n =2 band (b).

populated,314717xcept for the work of Skolnick et aLL6who

investigated the temperature dependenceof the FE3 associ-

ated with n =2 electron states in samples with E,>E, .

Many-b ody excitonic effects associated with n = 1 elec-

trons are not observed in the emission spectra of our

samples, principally due to the lack of available holes for

direct recombination at the Fermi k vector, kF. This limit

does not exist for electrons near the band edge (k=O) as in

the case of n=2 electrons, so the Fermi singularity should

appear more easily i n type II samples associated with the

ez-+hh, recombination. Nevertheless, we ha ve not found ex -

perimental eviden ce of any intensity enhan cement related to

this transition either in the emission spectra. Concerni ng our

PLE measurements , weak many -body singularities at E,

were observed in some samples of both types. Figure 5

shows a seque nce of PLE spectra at different temperatures.

In type I samples Fig. 5(a)], a many-body exciton associated

with n=l electrons states at k, is observed at the energy

E,*, above the absorption threshold. Its intensity decreas es

rapidly with the temperature as expecte d for such a Fermi

energy enhancement.The singularity is no longer resolved at

40 K. Thi s behavior contrasts with the atomic exciton peaks,

the intensity, and width of which remain unc hange d in t he

same range of temperatures. n type II samples [Fig. 5(b)] we

note two singularity p eaks at E& and E:, in their PLE spec-

tra. Their intensities are reduce d with respect to the continu-

ous as the temperature increases, showing the many-body

nature of both transitions.

We must remark that no sign of enhancement s found in

the emission spectra at the energy E& in samples where the

absorption shows the FES behavior at the same energy. The

ratio of the es-&h1 and er--+hht transition intensities, I,,

and I,, respectively, agrees with the calculated relative

electron-hole wave function overlap in all the samples ana-

lyzed, except for sample 6 (see Table II), in whi ch the PLE

specfrum does not show singularity peaks. We have per-

formed the same calculations for the structures reported in

Ref. 16, finding a good agreement with their experi mental

intensities ratio. Thus, the determination of singularity ef-

fects in the emission spectra by means of the comparison

between the calculated overlaps and the experimental inten-

sities is not clear. In fact, both factors are very sensitive to

variations in t he QW width or in the sheet charge density,

TABLE II. Low-temperature assessment f PM-HEMTs . The parameters I,,

L, and x are calculated self-consistently (SC) using the 4 K PL energ y transitions

and compared with independent measurement sby Shubnikov-de Haas (SdH), transmission electron microscopy (TEM), and Auger spectroscopy (AS),

respectively, and the nominal structure (NS). The Fermi level energy with respect o the n =2 subband edge (E,-E,), the peak energy distance (AS), and

the peak relative intensity (12,/111) obtained from the PLF and PL spectra are also compared with the SC results.

Sample

No.

n, (lo* cm-*)

SdH SC

E,- E, (meV)

PLE SC

AE (meV)

L 61

-r (45)

Id11

PL SC NS SC TEM NS SC AS PL SC

1 2.10 2.08 10 10

67 65 150 150 ... 20 18.5 ...

7.76 7.78

3

2.08 2.07

5 5

69 70 150 120 ._. 15 14.2 . . .

2.03 2.52

3 2.01

2.09

8 7 70 67 130 140

... 15

15.5

...

6.31

8.09

4 1.86 1.92 1 1

40 41 150 175 175 15 122 124

4.62 4.34

5 1.76 1.79 4 4

76 74 130 120 ... 20 20.0 ...

218

1.91

6 1.57 1.62 3 3

68 66 130 130 I.. 18 19.2 ...

5.68 2.22

7 1.20 1.22 -9 -9

53 51 150 150 ... 15 13.5 *..

1.. 2.89

8 1.08 1.11 . . . . . .

56 56 150 130 ... 15 12.0 ...

1.57 1.74

9 1.06 1.03 -16 -15

54 52 150 145 *.. 15 15.0 . . .

. . . 2.09

10 1.05

1.03 -13 -13

50 48 150 145 140 11 12.0 11.6

... 2.52

11 1.01

1.04

. . . . . .

51 50

150

140 140

15 11.5 11.0

...

2.08

12 0.99 1.03 2 2

47 47 160 165

. . .

7 7.5

r.1

7.10 6.80

13 ... 0.96 . . . . . .

47 46 150. 145 145

10

9.0 8.7

...

2.43

14 0.87 0.91 . . . . . .

51

49 150

150 ... 15 15.0 . . .

6.1

5.19

15 0.65 0.70 . . . . . .

58 57 150 140

..

15 16.0

I..

2.6 2.13

16 . . . 0.92 -4 -5

34 36 1 80 200 ... 15 12.0 . . .

. . . 7.30

5936

J. Appl. Phys., Vol. 76, No. 10, 15 November 19 94

Gilp6rez et

al.

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-2

4

.z?

5

%

ii

1 1250 1300 1350

1400

Energy (maV)

FIG. 6. Evolution of the PL spectra at 10 K from a HEMT structure grown

on an nS substrate under reverse applied voltages.

and to the measurement conditions,

making

it difficult to

reach any conclusion

from

their correlation.

B. 10 K photoluminescence in gated samples

The change in the PL line shape from a single peak to a

two-peak spectrum was studied at 10 K by modulating the

Fermi level with respect to the QW energy levels in semi-

transparent gated samples under different reverse biases.

Samples were designed to locate the Fermi energy above the

n=2 band edge in order to observe two transition peaks at

zero bias. Figure 6 shows the evolution of the PL spectra in

a HEMT structure grown on an n substrate under different

applied voltages. The same types of measurements were

made on samples grown on semi-insulating substrates with

analogous results. As the gate voltage is increased, transition

energies are blue shifted, whereas their absolute intensities

evolve mversely: Ia1 is reduced while I,, increases. Both

effects are produced by the modification of the potential pro-

file due to electron depletion. The characteristic band bend-

ing at zero bias (Fig. 1) is progressively reduced as the chan-

nel is emptied out, and then the QW tends to the square

potential shape of the undoped case. Conduction and valence

band confined states shift to lower energies (although the

whole effect is an increase of the transition energies) and the

electron and hole wave functions move from the QW-barrier

interfaces to the center of the QW.

In Fig. 7 experimental and calculated transition energies

are compared as a function of the applied gate voltage. The

two sets of da ta agree very accurately for reverse voltages up

to 1.8 V, while the measured El, energies diverge from the

numerical values for biases above this point. G iven this situ-

ation, and considering that the doped substrate and channel

ohmic con tacts were short circuited during the measurement,

two different ranges of voltages can be distinguished. For

low bias, the electron channel is a highly conductive layer

and the effective voltage is applied between the QW and the

gate at the surface. The PL transitions undergo large varia-

v, (Volts)

FIG. 7. Exp erimental (dots) and calculated (line) transition ene rgies as a

function of the applied reverse gate voltage.

tions in this range, due to the high sensitivity of the QW

energy levels with the variations in the 2DEG population.

The depletion of the conductive channel converts the QW

into a poor conductive layer above a certain voltage. The

effective voltage is now applied between the substrate and

the surface. Due to the potential drop taking place in the

GaAs buffer layer, a large increase in the applied voltage is

necessary in order to achieve a small variation in the QW

effective electric field. PL energies are thus only slightly

modified by the gate voltage in this second range. The mea-

surements performed in structures grown on semi-insulating

substrates show no changes in the PL peak energies or inten-

sities for reverse bias above the pinch-off voltage, poin ting

out that there are no variations in the QW electric field. Up to

this voltage value, we find the same good agreement as that

observed in the doped substrate case. These results show that

the model presented in Sec. III is also quite suitable to pre-

dict the gate charge control processes in HEMT devices.

Further details concerning the comparison between the

calculated and experimental transition energies are obtained

by studying the relative evolution of the Err and E,, energies

with the applied bias. Figure 8 shows the E2, energy respect-

ing Err for different voltages together with the theoretical

prediction. The experimental result follows very accurately

the linear tendency extracted from the numerical calcula-

tions, with a very small discrepancy be tween their respective

values. The obtained slope indicates a red shift of E,, in

respect to Err with an increasing reverse bias. Consequently,

the energy distance between both transitions is progressively

reduced. This fact is explained considering that the energy

1340

3

QJ1335

E

,-1330

t

w

1325

1265265

1275275

1265265

E,, (mev)

FIG. 8. Experimental (dots) and calculated (line) relative energy shifts of

the transition energies E,,

and E2, as a function of n, .

J. Appt. Phys., Vol. 76, No. 10, 16 November 1994 Gilpkez et al. 5937

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1

>\

Y

E

J

+

iif

TJ

z

.-

-d

E

iz

0

8

Experimental I,,

8

- o,,

from model

0.5 1.0 1.5 2.0

-2

rbs (~10~ cm )

FIG. 9. Normalized intensity of the PL spectra (dots) and calculated overlap

factor IT+,, line) as a function of n, for the E, transition.

FIG. 10. Experimental (dots) and calculated (full line) intensity ratios

Z,,/Z,, as a function of E,- E2. he evolution of the wave function overlap

ratio 4&Y11 is also displayed.

shift of conduction states due to the channel depletion is

more i mportant for n = 1 than for n=2 states, since the

former lies on the lower part of the QW.

Considering that the previous results provide a good

validation of our calculations, we are able to extract the val-

ues of n, and EF from the corresponding experimental PL

energies. The semiempirical values of II, and E, are used to

study the changes of the PL peak intensities with the applied

voltage. In the case of the er-+hhr transition, an increase in

the peak intensity is observed as the QW is depleted (see Fig.

6). According to the model predictions, the Fermi energy

remains well above the n = 1 subband edge even for the high-

est reverse bias, so the subband population can be considered

constant in the calculation of the recombination rate [Eq.

(S)]. Then, the peak intensity is expected to be governed only

by the wave function overlap. This fact is shown in Fig. 9,

where the, normalized 1,r intensity is compared with the cal-

culated values of Sr, as a function of n,, finding a good

agreement between the two sets of data. In the case of the

ea-+hhl transition, the n=2 subband population is relevant

to the calculation of the recombination rate. In this way, a

fast increase of I,, is expected as E, approach E2 from lower

energies. Experimental and calculated values of lal/lrl are

compared in Fig. 10 as a function of E,-E,. The slope

change of the calculated ratio e,,l9r, for E,> = E2 is due to

a stronger reduction of 13,~ y a well potential sharpening,

which is more acute when E,>E,, since the density of

states doubles. A good correspondence between the experi-

mental data and the calculated relative intensity is found for

E,>E,, pointing to the absence of FES effects in this

sample. Although transitions from an empty subband are not

expected, electron overheating by laser excitation produces

anomalously high I,, values when E,- E,ki, direct recombination is restricted by the range of

valence states available and, then, the peak width is limited.

Once kg

To determine the evolution of peak width with respect to

the applied bias, the dependence of the full width at the half

maxi mum (FWHM) on the 2DEG density has been studied.

Figure 11 shows the eI-+hhI ?ZWHM as a function of the

FIG. 11. FWH M of the c,-+hh, transition as a function of the applied bias

in two different PM-J3EMT structures: (a) sample grown on a semi-

insulatin g substrate; (b) sample grown on an n substrate.

5938

J. Appl. Phys., Vol. 78, No. 10, 15 November 1994

Gilpkrez et al.

6

0

-30

-20

-10 0

10

EF-E2 (mev)

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1350

1400

Energy (meV)

FIG. 12 PL spectra at 77 K for samples having the Fermi level below (a)

and abo ve (b) the n =2 subba nd edge. The arrows indicate the calculate d E,,

and E,, transition energies.

C. 77 K photoluminescence

When considering routine PM-HEMT wafer assessment,

PL characterization at moderate low temperatures of 77 K

may

be a practical solution to be considered, as compared to

He-based cryogenics determinations. Although some sign&

cant physical features are lost-at 77 K, the relevant param-

eters for the PM-HEMT structure assessment can be ex-

tracted from the PL measurement at this temperature. Spectra

corresponding to type I and type II samples at 77 K are

exhibited in Fig. 12. The thermal population of the n=2

conduction sub band in type I samples permits the observa-

tion of the ea-hh, transition, not visible at 4 K, for standard

PM-HEMT design. This fact favors the determination of the

QW parameters at 77 K, since both types of spectra provide

two energies to be compared with the numerical calculations

at this temperature. Theoretical line shapesare estimated ac-

cording to Eq. (8), finding a good agreement with the experi-

mental spectra for the sa me broadening parameter and

chemical potentials used at 4 K. As mentioned earlier, the

effect of the temperature increase on the shift of the peak

maxima with respect to the k=O transition energies must be

added to the Coulombic interaction contribution. If this ef-

fect is not considered, deviation of the derived x, L, and n,

parameters rom the actual structure can be important and the

adequate correction of the PL energies must be taken into

account.

The domi nant feature in the variation in the spectral line

shape rom 4 to 77 K is the change of the relative intensity of

the two transitions involved. Figure 1 3 shows the evolution

with temperatur e of the experimental relative intensities for

different samples, together with the calculated F,,IF,, ratios

for different EF--E, values. The relative intensity evolution

is different i n the two types of samples: in type I sampl es,

lzl/lrl increases with temperatur e, while in type II samples

it decreases. The same result was found in a single gated

sample where the Fermi level was modulated by applying an

external field. The temperature was varied for different ga te

voltages from 4 to 7 7 K, finding that, abov e a certain volt-

(a>

v 8 meV

F:,Y&,

n

5 meV

v 4 meV

/ t \ \

i. - w \

0 3 meV

t A .

_ 0 2 meV

4

N

k

0 25 50 75

Temperature (K)

FIG. 13. Evolution with temperature of the experimental relative PL inten-

sities for samp les with different she et densities, having the F ermi level

above (a) and below (b) the n =2 subband edge. Dashed ines represent the

calculated transition intensity ratios for different E,- E, values.

age, the behavior of the intensity ratio with temperatur e

changes rom a decreasing to a n increasing tendency.

In the case of type I sampl es (E,E,), both transitions appe ar in the 4 K spectra. Their

relative intensity depen ds on the electron and hole wave

functions overlap, which is highly depende nt on the QW

width and the 2DEG density. Contrary to type I samples, the

f2r/11r ratio is reduced as the temperatur e increases. This

behavior is conne cted with the change in the distribution of

the photogenerated holes with temperature. For a finite hole

effective m ass or a low degr ee of hole Iocalization, the rela-

tive filling of the

n=l

conduction subband and the heavy-

hole subband mplies that k$>k$. In this situation, not only

the peak width but also the peak intensity are limited by the

range of hol e wave vectors available. As the temperature is

increased, the hole distribution spreads n k values, alIowing

recombina tion with more energeti c electrons. The result is

the broadening of the transition peak together with an in-

crease n maxi mum intensity. On the other hand, recombina-

tion of n =2 electrons is not limited by the hole distribution,

since k$

7/23/2019 1.358416

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E2ll

cc>

L

El 11 :':;.

: '0

+

---- k--1--:

1200 1300 1400

1500

Energy (r%eV)

FIG. 14. PL spectra at room temperature for representative sampl es. Full

line i s the experimental spectra and dashed ines are the contributions due to

quantum well subbands, the GaAs buffer layer, and the phonon-assisted

transitions (black arrow). (a) and (b) correspond to type I and type II spectra

at low temperature, respectively. (c) corresponds to a type I spectrum at low

temperature in a wide QW sample (200 A).

in the case of the Fermi level lying very near to the subband

edge. The intensity ratio becomes saturated at a certain tem-

perature in both types of spectra, as the electron and hole

Fermi functions become smoother, which tends to level off

the recombination probabilities for the different k values.

D. Room-temperature photoluminescence

As pointed out before, wafer assessment by room tem-

perature, on-line, nondestructive techniques is an important

objective. Thus, the prospective use of RT PL for PM-HEMT

screening has a great interest to avoid wafer damage or re-

sidual stresses because of the cooling down to 77 K. From

our experience, good quality samples from a transport point

of view usually provide high intensity transitions at RT.

Typical PL spectra are shown in Fig. 14, where we discern

up to four peaks corresponding to the expected transitions.

The two main peaks always detected are associated with the

el-+hh, and e,--&h, transitions, which are those relevant in

our study. A shoulder at the high-energy side of the el+hh,

peak is seen in Figs. 14(b) and 14(c). It is related with optical

phonon assisted transitions, due to the interaction of the lat-

tice with the electron gas. Its intensity increases with tem-

perature, confirming this hypothesis. The highest energy

peak at 1425 meV in spectra [b) corresponds to recombina-

tions in the GaAs buffer layer, not appearing at low tempera-

tures. Its intensity is also more significant with the increase

in temperature. We believe that this is due to the presence of

a mechanism favoring the recombination of the photogener-

ated electrons before reaching the InGaAs quantum well,

such as the reduction in mobility when the temperature is

increased.

In order to separate the different peak contributions to

the spectra, line shape analysis is performed. Equation (8)

does not provide a good agreement with the experimental

lines at temperatures at which the carrier-phonon interactions

are relevant. A commercial software package performing a

least-squares adjustment is used instead. Band-to-band re-

combinations are adjusted by exponentially modified Gauss-

ian functions, while phonon-assisted transitions correspond

to simple Gaussi an functions. The exponential decay at the

high-energy size of the main peaks is found to be faster in

the e,-+hh, transition than in the el--+hh, recombination in

all the samples analyzed. Furthermore, the ez+hhl decay is

very similar to that of the GaAs undoped buffer layer which

corresponds to the simple thermal distribution of carriers.

For the n = 1 subband, where the electron concentration is

usually at least one order of magnitude larger than the n=2

density, the scattering process with the ionized donors is

much more important. Consequently, the effect of the blue

shift of the near k=O recombinations in the el-+hhl line

shape is quite significant. Thus, the carrier-ionized donor

scattering i s also important at RT and needs to be taken into

account in the determination of the k=O transition energies

relevant in this study. In this sense, and based on the line

shape adjustment, we estimate an energy shift of about 20

meV when the Fermi level is 50-60 meV above the band

edge (e,+hh, transition), while it is approximately 10 meV

when the Fermi level is 5 meV (e2-+hh, transition). This is

quite a significant effect in the structure characterization at

RT, as we will see in the following section.

v. PM-HEMT WAFER ASSESSMENT: DETERMINATION

OF x, L, AND II,

As demonstrated in Sec. III, the PL energies arising from

intersubband transitions in the channel layer depend on the

effective band gap in the strained In,Ga,-,As and on the

eigenenergies of the confined electron and hole states [Eq.

(4)]. These latter values are determined by the QW conduc-

tion and valence bands, which are given by the band bend-

ing, the band gap discontinuities, and the QW width. All the

indicated factors are a function of three main HEMT stmc-

ture parameters: the InAs mole fraction, the well thickness,

and the transferred 2DEG density. The effect of small varia-

tions in these three variables in the recombination energies is

much more significant than the error bars due to the uncer-

tainties in the interpolated alloy constants, band offsets, or

AlGaAs barrier composition . Thus, it seems possible to es-

tablish a direct relationship between the PL spectra and the

PM-HEMT structural parameters X, L, and n, , which should

be controlled during the growth process. The use of PL to

assess he deviation of the parameters in the grown structure

from the intended values is, therefore, feasible by comparing

the intersubband transitions extracted from the PL spectra

and the energies calculated according to the model presented

in Sec. III.

In the following we present the method used for the

assessment of the PM-HEMT wafer parameters X, L, and n,

5940

J. Appl. Phys., Vol. 76, No. 10, 15 November 1994

Gilpkez et al.

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at 4 K, 77 K and room temperature in a number of selected

samples. An analytical approximation is first derived based

on the dependence of the QW energy levels on x, L, and n, .

Next, the same method is presented graphically allowing a

less precise but faster determination of the parameters of

interest. For a set of samples the results of such an analysis

are compared with independent measurements of those pa-

rameters, providing information about the uncertainty of the

present characterization method at different temperatures.

In the assessment of the PM-HEMT, we assume a linear

dependence of the recombination energies on the parameters

x, L, and n, when they are close to the reference values x0,

Lo, and YZ~.Usually, x0 and Lo are taken from the nominal

structure, while n, is the corresponding carrier density. The

k=O transition energies Ei, can be approximated by a tmn-

cated series expansion,

Eil=E~~ -t

7/23/2019 1.358416

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1350

2

E

-

?

1325

aI

Lz 1300

1275

18.5 19.0 19.5 20.0 20.5

In 09

FIG. 1.5. Calculated transition energies as a function of the In content for a

range of well thicknesses and 2DEG densities at 4 K. Full and dashed lines

correspond to calculations for a 120 and 130 b channel thickness, respec-

tively. In each set of lines, the central li ne corresponds to the nominal sheet

density (1.7XlOt cm-) and the lines above and below it correspond to

error bars of 1X10 cm.-. Horizontal lines are the experimental energy

transitions.

To check and validate the assessment procedure de-

scribed above, it was applied to a series of samples with

different X, L, and 2DEG densities. A summary of the results

obtained by using the 4 K PL energies is shown in Table II.

We first used the lowest temperature spectra since they pro-

vide the smallest uncertainty in the determination of the k =0

transition energies. These energies are deduced through the

line-shape analysis following Eq. (8), where ru,i are the val-

ues calculated self-consistently and luvj and l? are adjustable

parameters. In the case of type I samples, the sample tem-

perature or the laser excitation power needs to be slightly

increased until the Ezl peak is observed in the logarithmic

PL intensity scale. The calculated 2DE G densities are com-

pared with the values obtained from magnetoresistance os-

cillations in SdH measurements at 1.2 K. In this context, i n

most of the type II samples, only one single frequency can be

extracted from the Fourier transfo rm spectra of the SdH data.

We found that EF have to be about 10 meV above Ez to

observe a second, lower frequency signal, corresponding to

the n =2 subband population. Thus, in most of these samples,

we compared the calculated and experimental n = 1 subband

population instead of the total carrier density. Equally, the

Fermi energy distance with respect to E2 was compared with,

that obtained from the analysis of PL and PLE measure-

ments. An excellent agreement was obtained between the

experimental and the calculated values in both cases, provid-

ing additional support of the validity of our technique. Fi-

nally, the derived x and L parameters were contrasted with

the nominal values, and, in

some

selected samples, they were

also compared with additional experimental determinations

by Auger spectroscopy and TEM, respectively. The discrep-

ancies initially found by our method between the nominal

Once the sample parameters were determined from the 4

K assessment, the same procedure was carried out using 77

K and RT PL spectra. Equations (9) and (14) are also appli-

cable at these temperatures with slight modi fications in the

coefficients & , &, and &,, . The main difficulty in charac-

terization at high temperatures arises in the determination of

the k=O transition energies from the PL spectra. This was

initially performed by a line-shape analysis of the PL peaks,

as it was shown in Sec. IV After this method was applied to

a large number samples, a practical rule was extracted. It

consists of selecting the energy corresponding to the peak

half amplitude at the low-energy side, rather than the peak

maximum energy. We have verified that, for present analysis,

the energies obtained in this way at different temperatures

are a good approximation of the k=O energies. The error

produced by this approximation is within the uncertainty as-

sumed in the determination of t he parameters X, L, and IZ, . In

fact, we observed that using these peak half amplitude ener-

gies, the X, L, and n, values obtained at 4 K are very similar

to those derived from the 77 K and RT spectra. Both 4 K and

RT determinations are compared in Table III, which shows a

very good agreement between the low- and room-

temperature results in all our samples when the correct k=O

transition energies are determined. Thus, the assessment

method used at 4 K, 77 K, and RT is basically the same,

except for the obvious changes in the temperature-dependent

parameters.

Other features of the PL spectra at room temperature can

be used to obtain complementary information of the PM-

HEMT wafers. First, peak separation is especially sensitive

to thicknesses in the range of loo-150 A that, fortunately,

are the ones normally used in PM-HEMTs. Deviations in the

well width can, therefore, be detected by observing the modi-

fications in the energy distance of the main peaks. On the

other hand, the peak relative intensity is determined by both

the QW width and the sheet charge density. Samples with

similar 2DEG densities and In content present very different

relative peaks intensity at RT as a result of the variation in

the well width. In the same way, for a given well width, the

relative peak intensity is modified by changing the carrier

density as has been observed in gated samples also at RT.

Thus, differences in the n, parameter from samples with the

same QW thickness can be simply related to variations in the

peak relative intensities. In this case, a higher I,,/I,, ratio

will indicate a higher confined charge density. At 4 K,

I,,/I,, coincides quite accurately with the overlap ratio

&,/0,, in most of the samples analyzed having the Fermi

energy above the n=2 band edge (see Table II). Unfortu-

nately, at RT there is not such a quantitative agreement, al-

though the peak intensities follow the expected tendency

with the 2DEG density. Thus, it is not possible to assess at

RT the IZ, parameter with a high accuracy only by the I,,/I,,

ratio, but it can be qualitatively compared in samples with

similar channel thickness.

From the above results it can be deduced that the accu-

racy of our technique depends on the values of the param-

eters that we consider in each sample, and on the temperature

5942

J.

Appl.

Phys., Vol. 76, No. 10, 15 November 1994

Gilp6rez et a/.

structure and the actual HEMT parameters were confirmed

by these measurements.

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TABLE III. 4 K an d RT determination of the parameters n, , L (A), and x (96).

Sample

No.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

ns (10 cm-)

L 6) x @4

4K

RT 4K RT

4K RT

2.08

1.96

150

150

18.5

19

2.07

1.92

120

120

14.2

15

2.09

2.00

140

140 15.5

15

1.92

1.87

175

170 12.2

13

1.79

1.83

120

120 20.0

19

1.62

1.58

130

130 19.2

19

1.22 1.13 150 150 13.5 13

1.11

1.01

130

130

12.0

12

1.03

0.97

145

150 15.0 15

1.03

0.92

145

150

12.0

12

1.04

0.99

140

140

11.5

11

1.03

1.06

165

160

7.5 7

0.96

1.02

145

150

9.0 9

0.91

0.84

150

150 15.0

15

0.70

0.75

140

140

16.0

16

0.92

0.85

200

200 12.0

11

at which the assessment s being performed. For instance, the

determination of the well thickness is more precise for nar-

row QWs, where the accuracy of the technique can be of the

order of an atomic monolayer for low-temperature assess-

ments. The uncertainty of the method increases with the tem-

perature due to the,~difficulties in the determination of the

k=O transitions energies. We estimate error bars lower than

10 meV in the determination of these energies at RT, that are

equivalent to uncertainties of about a l%, 10 A, and 2X10i1

cmm2 m the assessment of the parameters x, L, and n,, re-

spectively. These uncertainties are of the order of those usu-

ally accepted in the MBE growth process.

VI. CONCLUSIONS

ment method is its applicability at both cryogenic and room

temperatures. It is concluded that 77 K and RT photolumi-

nescence spectra provide enough information to determine

the deviations of the grown PM-HEMT structures from their

nominal design values. The uncertainty of the method is al-

ways higher at RT since the difficulties in the determination

of the k=O transitions are more important. In any case, we

estimate error bars at RT lower than 1% In content, 10 w in

QW thickness, and 2X 1O1lcme2 in 2DEG density, and lower

for decreasing temperatures. These uncertainties are in the

range of those usually accepted in the MBE growth process.

PL can be, therefore, considered as a very adequate contact-

less, nondestructive technique for the assessment of PM-

HEMT wafers.

In conclusion, we have presented a study of the use of

PL spectroscopy, even at room temperature, for the determi-

nation of relevant parameters in n-type PM AlGaAs/InGaAs/

GaAs HEMT structures such as the In& mole fraction, the

QW thickness, and the 2DEG density. We have first pre-

sented in detail the optical properties of these structures, es-

pecially the dependence of the PL and PLE spectra on the

Fermi level energy and on the temperature. It has been

shown that at moderate low and at room temperatures two

transitions, E,, and E21, are present in the PL spectra. The

assessment procedure is based on the comparison between

these k=O energy transitions and the recombination energies

derived from calculations of the subband structure. With this

aim, a one-dimensional , self-consistent calculation of the

Poisson and Schrodinger equations has been developed. The

method uses the approximation of a linear dependence of the

El, and E,, energies on the parameters x, L, and

It,. The

QW width L is first determined from the El, and Ezl energy

distance and, then, a two-equation system is solved for x and

n, . Such a procedure has been applied to a significant num-

ber of wafers, and the assessments have been validated by

independent measurements using PLE, SdH, gated samples,

and destructive physical techniques. As compared with other

techniques, probably the main advantage of present assess-

ACKNOWLEDGMENTS

Part of this work reflects some of the efforts made in the

ESPRIT 2035 Project in relation to the assessment of

InGaAs PM-HEMTs. It has been supported by the EEC and

CICYT (Spain). We thank I. Eddison (GEC-Marcony), J.

Castagnd (Picogiga), and J. Favre (Thomson-CSF) for their

cooperation. The use of the SERC Central Facility at Shef-

field is acknowledged.

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