45
Fig. 2 Optical path for top-illuminated light.
Our work is to develop a method to estimate the coupling efficiency of V-groove structure and try to find the associated affecting factors. The processing steps to fabricate a QWIP with V-grooves are also proposed in this work for practical test. The responsivities of the QWIP with V-grooves are measured and compared with experimental results based on traditional edge coupling scheme. The IR absorpton spectrum and spectral response are also measured for comparison.
B. 研究方法
1. Coupling Efficiency Estimation
In this section, the responsivity of a QWIP with V-grooves is estimated and used as an index to evaluate the V-groove coupling scheme. The responsivity R of a detector, is defined as the ratio of the photocurrent Ip over the optical power Pi transmitted into the detector, i.e. efficiency of the detector [9]. Among them,
η
d is defined as average number of optical transitions per photon incident into the sample, and is given by)] where A is the area of the detector, Ac is the effective coupling area, M is the material removal factor, R is the reflection coefficient of the detector surface, s is the times that a photon passes the detector, N is the number of periods in a MQW structure, fQ is the oscillator strength, Nd is the doping density in the well,
θ
is the angle of incidence, W is the width of the well, nw and m* are the refractive index and the effective mass ofthe well respectively, and Γ is the absorption linewidth [1]. The term (1/2) is used to count in the fact that only the component with the TM polarization can be absorbed for the unpolarized light. During fabricating a QWIP with V-grooves, some part of the MQW is removed by wet etching. The removal of material will affect the responsivity of the detector. Therefore, a parameter M is used to count in this effect.
In order to evaluate the coupling efficiency of V-groove coupling scheme, the edge coupling scheme that couples the incident light through a 45∘facet on the edge of the substrate is introduced first. The infrared light is back-illuminated onto the detector through the facet as illustrated in Fig. 3. Although the edge coupling is not useful for practical applications, it is still a standard to evaluate a QWIP’s intrinsic performance by virtue of the simple processing steps and the readily known light intensity inside the sample. It can also be a standard to evaluate another coupling scheme by comparing its responsivity with that of the edge coupling [1]. For convenience, a quantity named responsivity ratio (abbreviated as R ratio) is defined as
scheme
The R ratio is the figure of merit of a particular coupling scheme and is independent on the quantum well parameters [1].
45o
Fig. 3 The light incident geometry under edge coupling. The light passes the QWIP two times.
45o
With the definition of R ratio, the coupling efficiency of V-groove structure can be easily evaluated. All we need to do is plotting the optical path and substituting all related parameters into Eqs. (2) and (3) to calculate the R ratio. Since the light can be illuminated from backside or topside of the sample, we will discuss both conditions respectively.
When the light is back-illuminated onto a QWIP with V-grooves, the light is
coupled by the total internal reflection on the slant sidewall as shown in Fig. 4. The slope of the sidewall generated by wet etching is about 54∘instead of 45∘[10]. The light passes the detector by two times just the same as the edge coupling scheme. It is noted that the effective area Ac to couple the normal incident light is restricted by the area of sidewalls and varies with the geometry of the detector. The angle of incidence for TIR coupling scheme is 72∘ which is larger than 45∘for the edge coupling scheme.
°
° 18 36
° 54 72o
θ= A
effective coupling area Ac
Fig. 4 The optical path for the TIR coupling scheme in the V-groove structure.
One may wish to reduce the width of QWIP wires in order to increase the number wires and hence the effective coupling area in a single detector pixel. When the sidewall separation is sufficiently narrowed, the optical path of the incident light will be different as shown in Fig. 5. This should be considered when designing the detector.
° 36
° 54
° 36
18°
Fig.5 The optical path of TIR coupling scheme when the width of the QWIP wires re sufficiently narrowed.
a
The top-illuminated situation is considered now. Referring to Fig. 6, 90% of the incident photon (TM mode) will pass through the air-GaAs interface and turns into a new direction by the refraction effect. The remaining 10% of photons are reflected and have 75% opportunity to enter the QWIP through another interface. We can calculate the R ratio easily as for the backside-illumination case. The R ratio for this condition is expected to be smaller than that in the backside-illumination case
°
° 54 60
° 39
Fig. 6 The optical path when the light is incident from the topside of the QWIP with -grooves.
d, the R ratio on this condition is less than that on the back-illuminated condition.
Number of V-grooves
ratio versus the number of V-grooves in a QWIP for V
To evaluate the efficiency and feasibility of the V-groove coupling scheme, we calculate the R ratio for a series of QWIPs with different number of V-grooves. The parameters of the MQW structure are assumed as Nd=1.2x1018cm-3, well width W=50 angstroms, oscillator strength fQ=1, number of wells N=30, and absorption linewidth Γ=20 meV. For a given QWIP, we calculated R ratio vs. the number of V-grooves within the QWIP. The result is shown in Fig. 7. For sufficiently large number of V-grooves, the R ratio is greater than one. The R ratio on top-illuminated condition is given in Fig. 8. As expecte
1
the back-illuminated condition.
Number of -grooves
R ratio versus the number of V-grooves in a QWIP for e top-illuminated condition.
Anisotropic Wet Etching
For anisotropic wet etching process, the slowest etching planes dictate the final shape of the etched profile. The [111] Ga planes therefore dominate the profile since the etching rate on [111] Ga is the slowest for most reaction-limited etchants. The etched profile generated by anisotropic etching is shown in Fig. 9. Typical reaction-rate-limited etchants yield outward sloping edges along [011] direction and inward sloping edges, i.e. trenching effect, along [011] dir . As the microscopic photographs shown in Fig. 10, the Q wires parallel
ection
WIP [011]direction yield a perfect V-groove, while the wires parallel [011] direction almost disap
due to the severe trenching effect. Thus, the wires on our mask should parallel
peared ] 1 01 [ direction to ensure the correct profile when fabricating the QWIP. On the other hand, the selection of the etchants is also important because the etching rate and angle of sidewall vary with etchants. After many tests on various etchants, the NH4OH-H2O2-H2O (3:1:50) etchant is selected to fabricate the QWIPs with V-grooves because it has proper etching rate and yields a proper slope of sidewall, about 50∘.
R ratio
X (100) surface. The etchants that etch the [111] Ga type planes as the slowest rates would yield anisotropic etch profile as shown.
ig. 10 The profile produced by the anisotropic etching process. The wires in the F
left photograph are parellel to the [011] direction and those in the right photograph are parallel to [011] direction.