AlGaN/GaN Transport Studies of Two-Dimensional Electron Gas in AlGaN/GaN Quantum Well at Low Temperature and High Magnetic Field
1
2
ω * c = eb/ m θ Bcosθ 3
4
5
τ ω c hω c k B T δρ = T, B xx 2π E i A i( ) cos( + φi) hω i ρ ( ω τ ) i i i i i A T, B) = exp( ) i i ( 2 2 [1 + ( ωiτ i) ] 2 π ω τ i i ξ sinh( ξ i ξ 2π 2 * = k T / hω ω = eb m i B τ i ρ i φ i i i' th i i ) i / i 6
k B h = h/ 2π h m i i i k, = 0 x k y E δρ i xx = E F E i πh n = m 2 i * i nih 1 = A i ( T, B) cos(2π + φi ) 2e B i ω i hn i f = i 2e m i = 0, 1 ni i E10 = E1 E 0 ( k x = 0, k y = 0) 7
(B) R xy R xy 2 = h / ν n e = νeb / h eb / h ( B) e ν ν R R xx xx 8
9
10
1 e H + 2m c 2 = ( p A) E 2 2 1 h k z ( n + ) h c + 2 2m = ω ω = c * m eb 11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
????????? 30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57 V I 6 10 1.0 =
58
59
60
6 I = 1.0 10 V 61
62
6 I = 1.0 10 V 63
6 6 II= = 1.0 10 10 V 64
600 DCSdH 550 500 Rxx(Ohm) 450 400 350 300 250 0 2 4 6 8 10 12 B(T) (a) 600 AACSdH 550 500 Rxx(Ohm) 450 400 350 300 0 2 4 6 8 10 12 (b) B(T) 65
66
67
68
69
70
71
72
n H µ H 73
nh µ H 20 nm Si-doped Al x Ga 1-x N 10 nm Al x Ga 1-x N spacer 1~2 µm GaN Al 2 O 3 substrate 74
75 θ cosθ B H R er H n 1 = n e
Bcosθ f 1 f 2 m * = 0.215m0 76
E1 E 2 f f2 = f 1 f f beat 2 n1 n 2 1 77
f hn / e = f = hn / e n n 2 E E = 2πh ( n n ) / m * E E 78
Themt1G1 degree=0 LED=10440 s 210 200 190 Rxx (arb.unit) 180 170 160 150 140 130 0 2 4 6 8 10 12 B (T) Themt1H1 degree=15 LED=10440 s 210 200 190 Rxx (arb.unit) 180 170 160 150 140 130 0 2 4 6 8 10 12 B (T) Themt1H3 degree=30 LED=10440 s 210 200 190 Rxx (arb.unit) 180 170 160 150 140 130 0 2 4 6 8 10 12 B (T) 79
Themt1H4 degree=45 LED=10440 s 210 200 190 Rxx (arb.unit) 180 170 160 150 140 130 0 2 4 6 8 10 12 B (T) Themt1H7 degree=60 LED=10440 s 210 200 190 Rxx (arb.unit) 180 170 160 150 140 130 0 2 4 6 8 10 12 B (T) 210 Themt1H8 degree=75 LED=10440 s 200 190 Rxx (arb.unit) 180 170 160 150 140 130 0 2 4 6 8 10 12 B (T) 80
1.0 TuHemt1C1 BK-X 2 degree=0 Led=0s 0.8 f 1 =274.9565 T A 1 =0.8837 SdH amplitude (arb. unit) 0.6 0.4 0.2 0.0 f 2 =33.9130 T A 2 =0.1114 0 100 200 300 400 500 600 SdH frequency (T) 1.0 TuHemt1D1 BK-X 2 degree=0 Led=240s SdH amplitude (arb. unit) 0.8 0.6 0.4 0.2 0.0 f 2 =33.9130 T A 2 =0.1353 f 1 =274.9565 T A 1 =0.9002 0 100 200 300 400 500 600 SdH frequency (T) 5 TuHemt1E2 BK-X 2 degree=0 Led=1440s SdH amplitude (arb. unit) 4 3 2 1 0 f 2 =33.9130 T A 2 =0.9816 f 1 =274.4348 T A 1 =4.5245 0 100 200 300 400 500 600 SdH frequency (T) 81
1.0 TuHemt1F1 BK-X 2 degree=0 Led=3240s 0.8 f 1 =274.4348 T A 1 =0.8972 SdH amplitude (arb. unit) 0.6 0.4 0.2 0.0 f 2 =33.9130 T A 2 =0.1983 0 100 200 300 400 500 600 SdH frequency (T) 1.0 TuHemt1G1 BK-X 2 degree=0 Led=10440s SdH amplitude (arb. unit) 0.8 0.6 0.4 0.2 0.0 f 2 =33.9130 T A 2 =0.1845 f 1 =274.4348 T A 1 =0.9039 0 100 200 300 400 500 600 SdH frequency (T) 82
2.040 2.035 2.030 n (10 13 cm -2 ) 2.025 2.020 2.015 2.010 2.005 0 2000 4000 6000 8000 10000 12000 LED (sec) 83
HEMT1A1 BK-X 2 angle=0 Led=0 s SdH amplitude (arb. unit) 3.0 2.5 2.0 1.5 1.0 0.5 f 1 =214.4348 T A 1 =2.4807 0.0 0 100 200 300 400 500 600 SdH frequency (T) HEMT1B1 BK-X 2 angle=0 Led=180 s SdH amplitude (arb. unit) 3.0 2.5 2.0 1.5 1.0 0.5 f 2 =12.0000 T A 2 =0.6158 f 1 =212.8696 T A 1 =2.6378 0.0 0 100 200 300 400 500 600 SdH frequency (T) 84
HEMT1C1 BK-X 2 angle=0 Led=780 s 3.0 SdH amplitude (arb. unit) 2.5 2.0 1.5 1.0 0.5 f 2 =12.0000 T A 2 =0.8378 f 1 =212.8696 T A 1 =2.6708 0.0 0 100 200 300 400 500 600 SdH frequency (T) HEMT1D1 BK-X 2 angle=0 Led=1380 s 3.0 SdH amplitude (arb. unit) 2.5 2.0 1.5 1.0 0.5 0.0 f 2 =12.5217 T A 2 =0.8718 f 1 =212.8696 T A 1 =2.6809-0.5 0 100 200 300 400 500 600 SdH frequency (T) 85
1.32 1.31 1.30 n (10 13 cm -2 ) 1.29 1.28 1.27-200 0 200 400 600 800 1000 1200 1400 LED (sec) 86
HEMT64G1 angle=0 LED=7980s/10mA + 6000s/50mA 500 Rxx (arb.unit) 400 0 2 4 6 8 10 12 B (T) HEMT64H1 angle=15 LED=7980s/10mA + 6000s/50mA 500 Rxx (arb.unit) 400 0 2 4 6 8 10 12 B (T) HEMT64H2 angle=30 LED=7980s/10mA + 6000s/50mA 500 Rxx (arb.unit) 400 0 2 4 6 8 10 12 B (T) 87
HEMT64H3 angle=45 LED=7980s/10mA + 6000s/50mA 540 520 500 Rxx (arb.unit) 480 460 440 420 400 380 360 0 2 4 6 8 10 12 B (T) 550 HEMT64H4 angle=60 LED=7980s/10mA + 6000s/50mA 500 Rxx (arb.unit) 450 400 350 0 2 4 6 8 10 12 B (T) 550 HEMT64H6 angle=75 LED=7980s/10mA + 6000s/50mA 500 Rxx (arb.unit) 450 400 350 0 2 4 6 8 10 12 B (T) 88
SdH amplitude (arb. unit) 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0-0.1 HEMT62A1 BK-X 2 angle=0 Led=0 s f 2 =159.6522 T A 2 =0.8343 f 1 =177.9130 T A 1 =1.1205 0 100 200 300 400 500 600 SdH frequency (T) 2.5 HEMT62B1 BK-X 2 angle=0 Led=180 s SdH amplitude (arb. unit) 2.0 1.5 1.0 0.5 f 2 =163.8261 T A 2 =1.610 f 1 =179.4783 T A 1 =2.2137 0.0 0 100 200 300 400 500 600 SdH frequency (T) 2.5 HEMT62C1 BK-X 2 angle=0 Led=780 s SdH amplitude (arb. unit) 2.0 1.5 1.0 0.5 f 2 =163.3043 T A 2 =1.5925 f 1 =180.0000 T A 1 =2.1888 0.0 0 100 200 300 400 500 600 SdH frequency (T) 89
HEMT62D1 BK-X 2 angle=0 Led=2580 s SdH amplitude (arb. unit) 2.0 1.5 1.0 0.5 f 2 =163.8261 T A 2 =1.5646 f 1 =180.5217 T A 1 =2.0565 0.0 0 100 200 300 400 500 600 SdH frequency (T) HEMT62E1 BK-X 2 angle=0 Led=7980 s SdH amplitude (arb. unit) 2.0 1.5 1.0 0.5 f 2 =164.3478 T A 2 =1.5660 f 1 =180.5217 T A 1 =1.9361 0.0 0 100 200 300 400 500 600 SdH frequency (T) HEMT62F1 BK-X 2 angle=0 Led=13380 s SdH amplitude (arb. unit) 2.0 1.5 1.0 0.5 f 2 =164.8696 T A 2 =1.5784 f 1 =181.0435 T A 1 =1.9308 0.0 0 100 200 300 400 500 600 SdH frequency (T) 90
1.94 1.93 1.92 1.91 n (10 13 cm -2 ) 1.90 1.89 1.88 1.87 1.86-2000 0 2000 4000 6000 8000 10000 12000 14000 LED (sec) 91
200 TuHEM1C1 angle=0 LED=720 s Rxx (Ohm) 100 0 2 4 6 8 10 12 B (T) TuHEM1C1 BK-X 2 angle=0 Led=720 s SdH amplitude (arb. unit) 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0-0.1 f 2 =33.9130 T A 2 =0.1765 f 1 =270.2609 T A 1 =0.9856 0 100 200 300 400 500 600 SdH frequency (T) 92
1300 HEMT1C1 angle=0 LED=780 s 1200 1100 Rxx (Ohm) 1000 900 800 700 600 0 2 4 6 8 10 12 B (T) HEMT1C1 BK-X 2 angle=0 Led=780 s 3.0 SdH amplitude (arb. unit) 2.5 2.0 1.5 1.0 0.5 f 2 =12.0000 T A 2 =0.8378 f 1 =212.8696 T A 1 =2.6708 0.0 0 100 200 300 400 500 600 SdH frequency (T) 93
HEMT62C1 angle=0 LED=780 s 700 Rxx (Ohm) 600 0 2 4 6 8 10 12 B (T) 2.5 HEMT62C1 BK-X 2 angle=0 Led=780 s SdH amplitude (arb. unit) 2.0 1.5 1.0 0.5 f 2 =163.3043 T A 2 =1.5925 f 1 =180.0000 T A 1 =2.1888 0.0 0 100 200 300 400 500 600 SdH frequency (T) 94
1300 Sample H3 Al 0.25 Ga 0.75 N/GaN 1200 13380 s R XX (arb. units) 1100 1000 900 800 7980 s 2580 s 780 s 700 180 s 600 0 s 500 0 2 4 6 8 10 12 Magnetic field (T) 95
185 180 f 1 SdH frequency (T) 175 170 165 Sample H3 Al 0.25 Ga 0.75 N/GaN f 2 160 155-2000 0 2000 4000 6000 8000 10000 12000 14000 Illumination time (s) 96
97
98
99