SÉPTIMO DIA

4.3.1

V

and its Constituents

An ID-VDS trace of a transistor can be defined to be composed of three regimes: turn-on, resistive, and saturation. Turn-on regime is defined for a VDS in range of {0 V, VDS ON}, wherein VDS ON is the minimum VDS that should be applied to launch ID >

Figure 4.3: A partial cross section of a BAVET is shown to highlight the design methodology for a gate-barrier in InAlAs layer. InAlAs layer is designed to contain a p-doped region over a thickness of tp and an unintentionally doped region, which

acts as a spacer layer of thickness ti. InGaAs layer is sandwiched between the InAlAs

layer and WBI region.

0 mA.mm−1 (see Fig. 4.4). Sandwiched between the turn-on and saturation regimes is a resistive regime with lower and higher limits set at VDS ON and VDS SAT, respectively. Saturation in IDis observed for VDS= VDS SAT, a condition representative of the saturation regime. X-intercept of a line fitted to the resistive regime defines VDS ON. VDS SAT is the X-axis component at the intersection point of two lines fitted linearly to resistive and saturation regimes. If we assume that ID ≈ 0 mA.mm−1 for VDS < VDS ON, a relation:

VDS SAT= VDS ON+ (ID MAX× RON) (4.1)

can be used to represent VDS SAT in terms of its constituents: VDS ON, RON, and ID MAX. One could determine on resistance, RON, and maximum current, ID MAX, from the resis- tive and saturation regimes, respectively in the manner shown in Fig. 4.4.

Values for VDS SAT, VDS ON, VSAT are medians derived from respective box plots. Box statistics is performed on ID-VDS traces measured at VGS = 0 V.

4.3.2

Necessity of using Statistics

When measuring devices across a die or a wafer, a spread in their response can exist. It can arise from non-uniformities pertaining to their growth or fabrication processes.

Such a spread in response can be made worse in wafer-bonded devices, which owe their operation to electrical conduction through WBI. Applying statistics to a data set is therefore deemed necessary to separate unreal trends from authentic phenomena and accurately examine the behavior of such wafer-bonded devices. Thus, in this work, experimental data is first processed using box-plot statistic, analyzed and understood by the use of medians.

Figure 4.4: ID-VDS characteristics of a BAVET measured for a VGS. The experimen-

tally measured trace is shown by a solid line, which is linearly fitted. The fitted traces are plotted in dashed-line form. VDS ONis the x-intercept of the intersection point of

VDS axis and the line fitted in linear regime. The intersection point of lines, fitted to

linear and saturation regimes, denotes VDS SATin the x-intercept while the y-intercept

represents ID MAX. RON is expressed by inverse of the slope in linear regime.

4.4

Approach to Analysis

The analysis procedure is described in the following steps.

(i) BAVETs are operated under DC bias and room temperature conditions. Fig. 4.5 presents the measured ID-VDS responses of i, p-i, and p-BAVETs.

manner shown in Fig. 4.4. For an example case shown herein, a VGS of 0 V is chosen.

(iii) Additional BAVETs, belonging to each structure, are characterized for their VDS SAT in above mentioned conditions. Specifically, 13 devices in each structure are exam- ined for their ID-VDS response.

(iv) The analysis is taken further by representing the extracted values of VDS SATin form of a box plot (see Fig. 4.6). VDS SAT can then be expressed by the median of the box as long as the standard deviations remain much less than the median. Standard deviation is the extent by which the upper or lower limit of the box is separated from the median line (see Fig. 4.6).

(v) Box plots of VDS SAT, when derived for different device designs, can be compared for underlying trends (see Fig. 4.6).

The scope of this manuscript analyzes box VDS SAT for three structures differing in their doping of InAlAs. Extraction of median VDS SAT in i-BAVETs is made difficult, as only a hint of saturation behavior is evident in their ID-VDS characteristics at VGS = 0 V (see Fig. 4.5(a)). Applying VDS greater than 20 V is required for an accurate extraction of VDS SAT. The parameter analyzer limits operating at such high voltages, leading to a scarcity of data for i-BAVETs. As a result box plot VDS SAT for i-BAVETs is absent from Fig. 4.6 and we are led to assume the median to be greater than 15 V.

(a) (b) (c)

Figure 4.5: ID-VDS characteristics measured for (a) i, (b) p-i- and (c) p-BAVETs.

4.5

V

in Bavets and Doping in InAlAs

4.5.1

Is V

affected by a variation performed to device struc-

ture, especially doping in InAlAs?

On arranging box plots of VDS SAT against the doping in InAlAs, a strong dependence of VDS SAT on the latter is implied (see Fig. 4.5). The median of VDS SAT follows a trend by which it increases in the order of p-, p-i, i-structure. It can conversely be stated: VDS SAT reduces when traced in the reverse order. A methodology is thus revealed by which VDS SAT can be controlled in BAVETs. The basis of this methodology lies in the design of the layer structure. Understanding the mechanism by which the method works is thus worth investigating.

4.5.2

V

vs. Doping in InAlAs

An earlier section described two factors: VDS ON, and RON times ID MAX that add up to determine VDS SAT. Investigating the influence of doping on VDS ON becomes the starting point in seeking the mechanism behind the relationship of doping and VDS SAT.

Figure 4.6: Box VDS SATis shown as a function of doping in InAlAs. For each box, the

red line denotes the median while the upper and lower limits of standard deviation are denoted by the top and bottom edges of the box. Box data for i-BAVETs is unavailable but approximately estimated to be greater than 15 V. Median increases monotonically in the order of p-, p-i-, and i-BAVETs.

Table 4.2: VDS SAT, VDS ON and VSAT for Different Bavet Structures BAVET Structure VDS SAT (V) VDS ON (V) VKNEE (V)

p 4.6 1.08 3.608

p − i 10 4 6.51

i > 15 2.8 > 12 V

When the analysis approach, described in Section 4.4, is applied to derive box plot VDS ON vs. doping in InAlAs, a bell shaped trend is witnessed, the maxima of which occurs for p-i-BAVET (see Fig. 4.7).

4.5.3

Contributions of V

to V

Table 4.2 lists VDS SAT and VDS ON for each type of BAVET. It is observed that for each BAVET VDS ON has a minor contribution to VDS SAT. In performing subtraction of VDS SAT and VDS ON, the primary contributor, referred to as VKNEE, is obtained (see Table 4.2). From the fact that VKNEE is equivalent to the product term in (4.1), it can

Figure 4.7: VDS ON expressed in its box-plot form for p, p-i and i-BAVETs. A bell

shaped trend is depicted in VDS ON vs. InAlAs doping.

then be suggested that VDS SAT is majorly on account of VKNEE and its constituents: ID MAX and RON.

The dependence of VDS ON on doping in InAlAs implies another important aspect about VDS SAT. The bell shaped dependence between VDS ON and doping is relatively weaker than the latter’s incremental effect on VDS SAT (see Fig 4.7). Therefore, VDS ON, with its dependence on doping, does not solely furnish the changes brought in VDS SAT. For the change must then be primarily absorbed through variations caused in VKNEE. The trend in VKNEE is evident from its box vs. doping plot shown in Fig. 4.8. We proceed, in this study of the origin of anomalous VDS SAT, by investigating on why VKNEE monotonously increases in the order of p, p-i, i-BAVETs (see Fig. 4.8).

Values for VKNEE, RON and ID MAX are medians derived from respective box plots. Box statistics is performed on ID-VDS traces measured at VGS = 0 V.

Figure 4.8: Box VKNEE vs. doping in InAlAs, wherein the difference of VDS SAT and

VDS ON is assigned to VKNEE. Varying p- to i-doping, through p-i-doping, in BAVETs

enhances VKNEE.