InGaAs/InAlAs SAGCM 눈사태 광다이오드에 대한 이론 연구

결과 및 토론

본 절에서는 시뮬레이션을 통해 이론적 분석과 결론을 구체적으로 연구하였다. 먼저, "전하층 두께의 영향" 섹션에서 전하층의 도핑 레벨 허용오차에 대한 전하층 두께의 영향을 연구했습니다. 그런 다음 "전기장 분포에 대한 터널링 효과" 섹션에서 터널링 효과와 증배 눈사태 필드 간의 관계를 분석하고 확인했습니다.

전하층 두께의 영향

[14]에서 InGaAs/InAlAs APD의 적절한 필드 분포는 이러한 규칙을 준수해야 합니다. 보증 V _pt <V _br 및 V _br − V _pt 온도 변동 및 작동 범위의 변화를 처리하기 위한 안전 여유가 있어야 합니다. 흡수층에서 전기장은 광유도 캐리어에 충분한 속도를 보장하기 위해 50~100kV/cm보다 커야 합니다. 동시에 전기장은 흡수층에서 터널링 효과를 피하기 위해 180kV/cm 미만이어야 합니다. 전기장 분포는 장치 성능에 큰 영향을 미칩니다. 흡수층에서 전기장의 선택은 실제 요구 사항에 대한 작은 통과 시간, 암전류 및 높은 응답성 간의 균형을 유지합니다.

In the simulation, we used the structure of APD-1 (multiplication is 800 nm thick) and adjusted the charge layer thickness from 50 to 210 nm to study the influence of charge layer thickness on doping level range and verify the theoretical conclusions in analytical model. In the simulation, we selected different doping level ranges in the charge layer so that the electric field distribution complies with the rules. The simulation results on the relationship between thickness and doping level range in the charge layer are presented in Fig. 9a. As the charge layer thickness increases, the suitable doping level range in charge layer decreases. A relatively large doping level range exists in the thin charge layer, and under this doping level range, the device will have a suitable electric field distribution. Apparently, the doping level range is determined by charge layer thickness. The simulation result of APD-2 (with a thickness of multiplication of 200 nm) is presented in Fig. 9b, which has a similar result. Moreover, it can be found that the calculated results of Fig. 2 and simulation results of Fig. 9b match well as shown in Fig. 9c. The small difference between the calculated results and simulation results is caused by the different values of avalanche field in the simulation and calculation. The avalanche field in simulation engine is used 6.4 × 10 ⁵  V/cm, while in the calculation, we use the value of 6.7 × 10 ⁵  V/cm from [27].

아 Relationship between suitable doping level and thickness of charge layer (APD-1). The thickness of charge layer is 50 nm (black square), 90 nm (black circle), 130 nm (black triangle), 170 nm (black down-pointing triangle), 210 nm (black diamond). 아 presents the suitable doping level region for different thickness of charge layer. As the charge layer thickness increases, the suitable doping level range in the charge layer decreases. A relatively large doping level range exists in the thin charge layer, and under this doping level range, the device will have a suitable electric field distribution. Apparently, the doping level range is determined by charge layer thickness. ㄴ Relationship between suitable doping level and thickness of charge layer (APD-2). The thickness of charge layer is 50 nm (black square), 70 nm (black circle), 90 nm (black triangle), 110 nm (black down-pointing triangle), 130 nm (black diamond), and 150 nm (black pentagon). The figure description of b is similar to a . ㄷ Comparison of calculated results in Fig. 2 and simulated results in Fig. 9b. Dashed line:calculated results. Closed symbols:simulated results (black square). ㄷ presents the comparison of calculated results in Fig. 2 and simulated results in Fig. 9b. The calculated results and simulated results correspond well

The charge layer thicknesses of 210 and 50 nm (APD-1) were selected to show the simulation details and the influence of doping level on the electric field distribution. Figure 10a, c shows the current simulation results of different doping levels in thicknesses of 210 and 50 nm, respectively. Figure 10b, d shows the electric field distribution simulation results using the same structure. The simulation results show that thicknesses of 210 and 50 nm have doping level ranges of 1.0 × 10 ¹⁷ –1.3 × 10 ¹⁷ cm ⁻³ and 3.9 × 10 ¹⁷ –5.7 × 10 ¹⁷ cm ⁻³ , 각각.

아 Photocurrent and dark current with different doping level (thickness of charge layer is 210 nm). Solid line:doping level in the charge layer is 1.3 × 10 ¹⁷ cm ⁻³ . Dashed line:doping level in charge layer is 1.15 × 10 ¹⁷ cm ⁻³ . Dashed dot line:doping level in charge layer is 1.0 × 10 ¹⁷ cm ⁻³ . 아 Presents the simulation results of currents with different doping level. The device with a charge layer thickness of 210 nm only has a relatively narrow and suitable doping level. A minimal change in the doping level has greatly influence the punch-through voltage, breakdown voltage, and current-voltage characteristic. ㄴ Avalanche field with different doping level (thickness of charge layer is 210 nm). Solid line:doping level in charge layer is 1.3 × 10 ¹⁷ cm ⁻³ . Dashed line:doping level in charge layer is 1.15 × 10 ¹⁷ cm ⁻³ . Dashed dot line:doping level in charge layer is 1.0 × 10 ¹⁷ cm ⁻³ . ㄴ Presents the simulation results of fields with different doping level. The device with a charge layer thickness of 210 nm only has a relatively narrow and suitable doping level. A minimal change in the doping level has greatly influenced the electric field distribution. ㄷ Photocurrent and dark current with different doping level (thickness of charge layer is 50 nm). Solid line:doping level in charge layer is 5.7 × 10 ¹⁷ cm ⁻³ . Dashed line:doping level in charge layer is 4.8 × 10 ¹⁷ cm ⁻³ . Dashed dot line:doping level in charge layer is 3.9 × 10 ¹⁷ cm ⁻³ . ㄷ Presents the simulation results of currents with different doping level. The device with a charge layer thickness of 50 nm has a relatively wide and suitable doping level. A minimal change in the doping level has a small influence on the current-voltage characteristic. d Avalanche field with different doping level (thickness of charge layer is 50 nm). Solid line:doping level in charge layer is 5.7 × 10 ¹⁷ cm ⁻³ . Dashed line:doping level in charge layer is 4.8 × 10 ¹⁷ cm ⁻³ . Dashed dot line:doping level in charge layer is 3.9 × 10 ¹⁷ cm ⁻³ . d Presents the simulation results of fields with different doping level. The device with a charge layer thickness of 50 nm only has a relatively wide and suitable doping level. A minimal change in the doping level has a small influence on the electric field distribution

Clearly, the device with a charge layer thickness of 210 nm only has a relatively narrow and suitable doping level. A minimal change in the doping level has greatly influence the current-voltage characteristic and electric field distribution. As a result, the performance of APD varies significantly via several percent deviations of doping concentrations in the thicker charge layer. This conclusion is the same as the theoretical analysis. Concurrently, when designing APD structures, choosing a thin charge layer will give a high level of doping tolerance, as well as confer APD with good controllability.

Finally, the relationship between charge layer and multiplication thickness was simulated. Figure 11a presents the avalanche field with multiplication region thicknesses of 100, 200, and 300 nm in the APD-2 structure (with a charge layer thickness of 70 nm). Figure 11b presents the charge layer doping range with different multiplication thicknesses at the suitable electric field distribution condition. The charge layer thicknesses are 50, 70, and 90 nm. Clearly, a high avalanche field exists in the thin multiplication layer. As the multiplication region thickness decreases, the electric field difference between multiplication and absorption layers increases. As a result, a thin multiplication layer needs a high product of the charge layer doping level and thickness to reduce the high avalanche field.

아 Avalanche breakdown electric field with different multiplication thicknesses. Solid line:w _m  = 100 nm. Dashed line:w _m  = 200 nm. Dashed dot line:w _m = 300 nm. 아 Presents the simulation results of electric field distribution with different w _m . As the w _m decreases, the avalanche field in the multiplication increase. ㄴ Relationship between multiplication thickness and charge layer. The thickness of multiplication is 300 nm (black square), 200 nm (black circle), 100 nm (black triangle). ㄴ Presents the relationship between multiplication thickness and charge layer. A thin multiplication layer needs a high product of the charge layer doping level and thickness to reduce the high avalanche field

Tunneling Effect on the Electric Field Distribution

The simulation in this part will study the tunneling effect on the electric field in the device. From the theoretical analysis, the tunneling effect has an influence on the avalanche field in multiplication. Thus, the simulation will design to study the influence of electric field in the absorption layer that exceeds the tunneling threshold value. First, group A, with the structure of APD-1, charge layer thickness of 90 nm, and different charge layer doping levels of 1.4 × 10 ¹⁷ –2.4 × 10 ¹⁷ cm ⁻³ , was simulated for electric field distribution when the device avalanche breaks down. The result is shown in Fig. 12a. When the charge layer doping level exceeds 2.0 × 10 ¹⁷ cm ⁻³ , the field in the absorption layer becomes lower than the tunneling threshold field and the avalanche field in the multiplication layer reaches the same value. However, when the doping level is less than 2.0 × 10 ¹⁷ cm ⁻³ , the field in the absorption layer exceeds the tunneling threshold field and the avalanche field in the multiplication layer decreases with the decrease of the doping level in charge layer. Similar results were observed in the APD-2 structure (with a charge layer thickness of 90 nm and doping level of 2.2 × 10 ¹⁷ –3.6*10 ¹⁷ cm ⁻³ ) (Fig. 12b). That is, if the electric field in the absorption layer exceeds the tunneling threshold value at or over the breakdown voltage, then the breakdown electric field in the multiplication will decrease.

아 Avalanche breakdown electric field with different doping levels (APD-1). Thickness of charge layer is 90 nm. Red dashed lines:the field of absorption is larger than the tunneling threshold field. Black solid lines:the field of absorption is less than the tunneling threshold field. 아 Presents the simulation results of electric field distribution with different doping level while avalanche breakdown. When doping level of charge layer exceeds 2.0 × 10 ¹⁷ cm ⁻³ , the field in the absorption layer becomes lower than the tunneling threshold field, and the avalanche field in the multiplication layer reaches the same value with different doping level. However, when the doping level is less than 2.0 × 10 ¹⁷ cm ⁻³ , the field in the absorption layer exceeds the tunneling threshold field, and the avalanche field in the multiplication layer decreases with the decrease of the doping level. Thus, if the electric field in the absorption layer exceeds the tunneling threshold value at or over the breakdown voltage, then the breakdown electric field in the multiplication will decrease. Thus, the electric field in the absorption should be less than the tunneling threshold value to maintain the high field in the multiplication layer when the device avalanche breaks down. ㄴ Avalanche breakdown electric field with different doping levels (APD-2). Thickness of charge layer is 90 nm. Red dashed lines:the field of absorption is larger than the tunneling threshold field. Black solid lines:the field of absorption is less than the tunneling threshold field. The figure description of b is similar to a . ㄷ Relationship between field and bias voltage in multiplication and absorption (APD-1). Thickness of charge layer is 90 nm. Electric field of multiplication (black square). Electric field of absorption (red triangle). ㄷ Presents the relationship between the electric field and bias voltage in multiplication and absorption layers. When the electric field in the absorption layer reaches the tunneling threshold value, the avalanche breakdown electric field in the multiplication gradually decreases. Moreover, the absorption field slope increases when the electric field in the absorption layer exceeds the tunneling threshold. d Relationship between field and bias voltage in multiplication and absorption (APD-2). Thickness of charge layer is 90 nm. Electric field of multiplication (black square). Electric field of absorption (red triangle). The figure legend of d is similar to a

Groups B (APD-1 thickness of 90 nm, doping level of 2.4 × 10 ¹⁷ cm ⁻³ in charge layer and APD-2 thickness of 90 nm, doping level of 3.6 × 10 ¹⁷ cm ⁻³ ) were designed to demonstrate the relationship between the threshold electric field in the absorption layer and avalanche field in the multiplication layer. The multiplication and absorption electric fields vary with the bias voltage on the device. As shown in Fig. 12c, d, when the electric field in the absorption layer reaches the tunneling threshold value, the avalanche breakdown electric field in the multiplication gradually decreases. Moreover, when the absorption field exceeds the tunneling threshold, the avalanche breakdown electric field in the multiplication layer plummets. Furthermore, the absorption field slope increases when the electric field in the absorption layer exceeds the tunneling threshold.

The phenomenon in Fig. 12 can be explained by the theoretical analysis that tunneling has an influence on the charge density in the “Methods” section. When the electric field reaches the tunneling threshold value in the absorption layer, the charge density ρ becomes unequal to the dopant ion. The multiplication field will decrease as the negative ion increases, and the absorption field will increase as the positive ion increases. Concurrently, the absorption field slope will increase due to the tunneling effect. As a result, the electric field in the absorption should be less than the tunneling threshold value to maintain the high field in the multiplication layer and the low dark current when the device avalanche breaks down.