在两篇关于通过二极管PN结测量Boltzmann常熟的博文中 PN结中存在的Boltzmann常数 以及 利用二极管的P-N结的I-V特性测量Boltzmann常数给出了 使用NPN三极管来获得PN结的电压与电流之间的关系。而不是直接通过测量二极管的PN结的电压与电流的关系测量Boltzmann常数。其中具体的半导体内部的原因还需要后面进一步的文献调研。但是在上面的测量关系中，存在一个平时没有注意到的问题，那么是三极管的发射极对集电极电压的影响。
■ 测量电路
将NPN晶体管的基极接地，通过电阻R1连接可调电压源。通过数控可调电压源来改变NPN晶体管的发射极的电流，进而改变了晶体管的发射极的电压。 使用万用表测量三极管集电极对地之间的电压VC。
下面测量VALL，VR， VC之间的关系。
01实验测量结果
1. NPN:3904
▲ 发射极电压与集电极电压之间的关系
▲ 发射极电压与集电极电压之间的关系
vr=[-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.00,-0.01,-0.01,-0.01,-0.01,-0.02,-0.02,-0.02,-0.03,-0.03,-0.04,-0.04,-0.05,-0.05,-0.06,-0.06,-0.07,-0.07,-0.08,-0.08,-0.09,-0.10,-0.11,-0.11,-0.12,-0.13,-0.14,-0.14,-0.15,-0.16,-0.17,-0.17,-0.18,-0.19,-0.20,-0.20,-0.21,-0.22,-0.23,-0.24,-0.25,-0.25,-0.26,-0.27,-0.28]
vall=[-0.00,-0.01,-0.02,-0.03,-0.04,-0.05,-0.06,-0.07,-0.08,-0.09,-0.10,-0.11,-0.12,-0.13,-0.14,-0.15,-0.16,-0.17,-0.18,-0.19,-0.20,-0.21,-0.22,-0.23,-0.24,-0.26,-0.27,-0.28,-0.29,-0.29,-0.31,-0.32,-0.33,-0.34,-0.34,-0.36,-0.37,-0.38,-0.39,-0.40,-0.41,-0.42,-0.43,-0.44,-0.45,-0.46,-0.47,-0.48,-0.49,-0.50,-0.51,-0.52,-0.53,-0.54,-0.55,-0.56,-0.57,-0.58,-0.59,-0.60,-0.61,-0.62,-0.63,-0.64,-0.65,-0.66,-0.67,-0.68,-0.69,-0.70,-0.71,-0.72,-0.73,-0.73,-0.74,-0.75,-0.76,-0.77,-0.78,-0.79,-0.80,-0.81,-0.83,-0.84,-0.84,-0.85,-0.86,-0.87,-0.88,-0.89,-0.90,-0.91,-0.92,-0.93,-0.94,-0.95,-0.96,-0.97,-0.98,-0.99]
vc=[0.86,0.86,0.85,0.85,0.85,0.85,0.85,0.85,0.85,0.85,0.85,0.85,0.85,0.85,0.85,0.85,0.84,0.84,0.84,0.84,0.84,0.84,0.84,0.84,0.83,0.83,0.83,0.83,0.82,0.82,0.82,0.81,0.80,0.78,0.77,0.74,0.70,0.65,0.58,0.47,0.33,0.12,-0.07,-0.28,-0.37,-0.39,-0.40,-0.42,-0.43,-0.45,-0.46,-0.47,-0.49,-0.50,-0.51,-0.52,-0.53,-0.54,-0.55,-0.56,-0.57,-0.58,-0.58,-0.59,-0.60,-0.60,-0.61,-0.62,-0.62,-0.63,-0.63,-0.63,-0.64,-0.64,-0.64,-0.65,-0.65,-0.65,-0.66,-0.66,-0.66,-0.67,-0.67,-0.67,-0.68,-0.68,-0.68,-0.68,-0.68,-0.69,-0.69,-0.69,-0.69,-0.69,-0.70,-0.70,-0.70,-0.70,-0.70,-0.70]
#!/usr/local/bin/python
# -*- coding: gbk -*-
#============================================================
# TEST1.PY -- by Dr. ZhuoQing 2020-08-05
#
# Note:
#============================================================
from headm import *
from tsmodule.tsvisa import *
from tsmodule.tsstm32 import *
dp1308open()
printf('Begin :\r\n\a')
dp1308n25v(0)
time.sleep(2)
setv = linspace(0, 1, 100)
vrdim = []
valldim = []
vcdim = []
for v in setv:
dp1308n25v(v)
time.sleep(1.5)
meter = meterval()
vcdim.append(meter[2])
valldim.append(meter[0])
vrdim.append(meter[3])
dp1308n25v(0)
tspsave('data', vr=vrdim, vall=valldim, vc=vcdim)
plt.plot(setv, valldim, label='VALL')
plt.plot(setv, vcdim, label='VC')
plt.plot(setv, vrdim, label='VR')
plt.xlabel("Set Voltage(V)")
plt.ylabel("Measure(V)")
plt.grid(True)
plt.tight_layout()
plt.legend(loc='upper right')
plt.show()
#------------------------------------------------------------
# END OF FILE : TEST1.PY
#============================================================
1. NPN:1906
▲ 1906的发射极与集电极之间的关系
vr=[-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0002,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0002,-0.0001,-0.0001,-0.0002,-0.0002,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0002,-0.0001,-0.0001,-0.0002,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0002,-0.0002,-0.0002,-0.0002,-0.0002,-0.0003,-0.0004,-0.0005,-0.0007,-0.0009,-0.0012,-0.0017,-0.0024,-0.0031,-0.0043,-0.0057,-0.0075,-0.0098,-0.0123,-0.0154,-0.0189,-0.0223,-0.0265,-0.0308,-0.0358,-0.0403,-0.0465,-0.0523,-0.0575,-0.0636,-0.0698,-0.0762,-0.0829,-0.0887,-0.0957,-0.1025,-0.1100,-0.1173,-0.1242,-0.1318,-0.1394,-0.1460,-0.1539,-0.1613,-0.1692,-0.1772,-0.1851,-0.1932,-0.2002,-0.2084,-0.2166]
vall=[-0.0029,-0.0132,-0.0222,-0.0326,-0.0427,-0.0532,-0.0636,-0.0736,-0.0838,-0.0929,-0.1032,-0.1137,-0.1236,-0.1339,-0.1429,-0.1547,-0.1651,-0.1740,-0.1845,-0.1945,-0.2049,-0.2150,-0.2242,-0.2345,-0.2446,-0.2553,-0.2656,-0.2757,-0.2860,-0.2949,-0.3053,-0.3156,-0.3257,-0.3361,-0.3450,-0.3566,-0.3671,-0.3760,-0.3864,-0.3968,-0.4068,-0.4172,-0.4261,-0.4365,-0.4465,-0.4571,-0.4675,-0.4776,-0.4880,-0.4983,-0.5072,-0.5176,-0.5276,-0.5379,-0.5470,-0.5586,-0.5691,-0.5781,-0.5884,-0.5988,-0.6087,-0.6190,-0.6279,-0.6382,-0.6481,-0.6587,-0.6689,-0.6787,-0.6889,-0.6991,-0.7079,-0.7180,-0.7276,-0.7377,-0.7465,-0.7578,-0.7679,-0.7766,-0.7866,-0.7964,-0.8061,-0.8161,-0.8246,-0.8347,-0.8442,-0.8546,-0.8646,-0.8740,-0.8839,-0.8938,-0.9024,-0.9124,-0.9220,-0.9318,-0.9419,-0.9516,-0.9615,-0.9701,-0.9800,-0.9899]
vc=[1.1074,1.1068,1.1070,1.1093,1.1085,1.1086,1.1087,1.1078,1.1084,1.1090,1.1074,1.1066,1.1072,1.1061,1.1069,1.1059,1.1051,1.1050,1.1058,1.1051,1.1033,1.1032,1.1027,1.1017,1.1019,1.1013,1.1008,1.1006,1.1003,1.0999,1.0998,1.0980,1.0979,1.0961,1.0944,1.0912,1.0885,1.0864,1.0807,1.0744,1.0671,1.0548,1.0390,1.0128,0.9774,0.9237,0.8504,0.7517,0.6048,0.4006,0.1686,-0.1239,-0.3786,-0.4589,-0.4730,-0.4885,-0.5019,-0.5132,-0.5247,-0.5362,-0.5465,-0.5568,-0.5654,-0.5749,-0.5840,-0.5930,-0.6015,-0.6091,-0.6164,-0.6233,-0.6290,-0.6349,-0.6401,-0.6452,-0.6494,-0.6544,-0.6586,-0.6620,-0.6656,-0.6690,-0.6721,-0.6752,-0.6776,-0.6804,-0.6829,-0.6855,-0.6878,-0.6899,-0.6921,-0.6941,-0.6958,-0.6977,-0.6994,-0.7012,-0.7029,-0.7045,-0.7060,-0.7073,-0.7088,-0.7102]
3. NPN:8050
▲ 8050三级的发射极电压与集电极电压之间的关系
vr=[-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0002,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0002,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0002,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0001,-0.0002,-0.0001,-0.0002,-0.0002,-0.0001,-0.0002,-0.0002,-0.0002,-0.0003,-0.0003,-0.0004,-0.0006,-0.0007,-0.0009,-0.0012,-0.0017,-0.0022,-0.0031,-0.0042,-0.0054,-0.0070,-0.0090,-0.0113,-0.0141,-0.0169,-0.0204,-0.0242,-0.0286,-0.0332,-0.0379,-0.0430,-0.0485,-0.0534,-0.0593,-0.0651,-0.0713,-0.0769,-0.0844,-0.0911,-0.0970,-0.1040,-0.1108,-0.1179,-0.1251,-0.1314,-0.1389,-0.1462,-0.1540,-0.1616,-0.1690,-0.1766,-0.1845,-0.1913,-0.1992,-0.2069,-0.2148,-0.2229,-0.2309,-0.2390,-0.2459,-0.2541,-0.2623]
vall=[-0.0028,-0.0132,-0.0222,-0.0325,-0.0427,-0.0532,-0.0635,-0.0735,-0.0838,-0.0929,-0.1032,-0.1136,-0.1235,-0.1338,-0.1429,-0.1546,-0.1651,-0.1741,-0.1844,-0.1944,-0.2048,-0.2150,-0.2241,-0.2345,-0.2445,-0.2553,-0.2656,-0.2756,-0.2860,-0.2949,-0.3052,-0.3157,-0.3256,-0.3361,-0.3450,-0.3566,-0.3670,-0.3760,-0.3864,-0.3968,-0.4068,-0.4172,-0.4261,-0.4365,-0.4465,-0.4571,-0.4674,-0.4775,-0.4879,-0.4981,-0.5073,-0.5175,-0.5274,-0.5377,-0.5467,-0.5582,-0.5684,-0.5774,-0.5874,-0.5976,-0.6072,-0.6173,-0.6260,-0.6358,-0.6453,-0.6554,-0.6651,-0.6745,-0.6840,-0.6938,-0.7022,-0.7117,-0.7208,-0.7303,-0.7387,-0.7496,-0.7590,-0.7672,-0.7767,-0.7859,-0.7951,-0.8046,-0.8127,-0.8222,-0.8313,-0.8411,-0.8505,-0.8594,-0.8688,-0.8782,-0.8864,-0.8958,-0.9048,-0.9141,-0.9236,-0.9329,-0.9423,-0.9503,-0.9597,-0.9691]
vc=[0.7587,0.7577,0.7565,0.7564,0.7565,0.7574,0.7572,0.7562,0.7545,0.7538,0.7533,0.7527,0.7516,0.7523,0.7513,0.7502,0.7500,0.7497,0.7479,0.7466,0.7440,0.7423,0.7396,0.7372,0.7357,0.7333,0.7290,0.7234,0.7169,0.7099,0.6989,0.6824,0.6613,0.6289,0.5900,0.5164,0.4210,0.3066,0.1305,-0.0908,-0.3017,-0.3925,-0.4078,-0.4216,-0.4344,-0.4478,-0.4602,-0.4718,-0.4830,-0.4935,-0.5027,-0.5127,-0.5224,-0.5323,-0.5409,-0.5515,-0.5606,-0.5684,-0.5770,-0.5851,-0.5925,-0.5999,-0.6058,-0.6123,-0.6180,-0.6238,-0.6289,-0.6336,-0.6382,-0.6424,-0.6459,-0.6496,-0.6530,-0.6564,-0.6591,-0.6624,-0.6652,-0.6675,-0.6700,-0.6724,-0.6746,-0.6767,-0.6785,-0.6806,-0.6824,-0.6843,-0.6861,-0.6878,-0.6893,-0.6910,-0.6922,-0.6938,-0.6951,-0.6965,-0.6978,-0.6991,-0.7003,-0.7014,-0.7026,-0.7037]
※ 结论
通过实验研究可以看到三极管，在基极直接接地的情况下，发射极的电压与集电极之间具有很强的耦合关系。这一点本质上来自于三极管内部的特殊结构，也由此产生了独特的电流放大功能。
在实验中也揭露了：
- 在发射极与基极都接地的情况下，空载的集电极电压表现出了一个高电压电位。那么这个点位是否能够对外输出电能呢？
- 不同的三极管上述控制关系也有所变化？那么这与三级的管特性（电流放大倍数、耐压等）有什么关系呢？