The fully self-consistent Hartree-Fock (HF) plus random phase approximation (RPA) based on Skyrme-type interaction is used to study the existence problem of proton semi-bubble structure in the $2_1^+$ state of $^{34}$Si. The experimental excitation energy and the B(E2) strength of the $2_1^+$ state in $^{34}$Si can be reproduced quite well. The tensor effect is also studied. It is shown that the tensor interaction has a notable impact on the excitation energy of the $2_1^+$ state and a small effect on the B(E2) value. Besides, its effect on the density distributions in the ground and $2_1^+$ state of $^{34}$Si is negligible. Our present results with T36 and T44 show that the $2_1^+$ state of $^{34}$Si is mainly caused by proton transiton from $pi 1d_{5/2}$ orbit to $pi 2s_{1/2}$ orbit, and the existence of a proton semi-bubble structure in this state is very unlikely.
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